New methods for measuring and monitoring chromatic dispersion in optical communication systems
Abstract
This PFC main goal is to introduce new approaches on the chromatic dispersion measurement field, based on the big range of possibilities the setup of a general standard RF-tone modulation chromatic modulation method provides, and to show its good performance pointing towards a real-time on-line monitoring system for optical communication networks. The project’s objectives are defined considering two well-delimited stages. First, we will study some standard RF-tone-addition techniques for measuring chromatic dispersion, specifically the Modulation Phase Shift Method (MPSM) [2] and the Peucheret`s Method [3]. We will analyze their operating principles, recognize all the variables involved in their basic configurations and evaluate their performances under different measurement conditions. We will also study the implications of real-time on-line monitoring of chromatic dispersion in optical networks. We have to consider that the test signal has to travel together with the data; therefore, it is a priority to keep the optical carrier unaltered in the transmission and reception procedures. This background will help us to identify the main drawbacks of both methods which motivate the proposal of a new improved technique based on a similar mathematical basis but with better performance in terms of accuracy and cost trade-off. The general features of this new approach will be exposed on a basic setup designed for a laboratory environment, so that we can contrast it with the conventional techniques. This method dubbed Asymmetric Modulation Bias-Controlled Method (ABCM) will focus on RF modulated signal amplitude and will take advantage of its direct relation with chromatic dispersion. One of the basic building blocks of these standard methods is the device that imposes the RF pure-tone modulation to the optical signal, namely the Mach-Zehnder interferometric modulator usually in the conventional push-pull configuration and biased at the quadrature point. In the context of the new improved CD measurement methods, we will observe how the Mach-Zehnder modulator Bias Voltage concept gains relevance; becoming the main variable to be handled by the use of a dual drive Mach-Zehnder modulator in asymmetric configuration. Finally, we will analyze this ABCM method performance while some fixed parameters (RF Frequency, Nominal Dispersion, resolution) take different values in order to find out the optimum operating conditions. The problem when trying to apply the ABCM to the real-time on-line monitoring of optical networks is that it relies in the eventual cancellation of the optical carrier which in a network monitoring application is shared with the data and it is essential for a proper data recovery. We must find an alternative where this optical carrier cancellation is not essential for the monitoring function and that would be the ABCM-SC (SC for suppressed carrier) Therefore, on a second stage, we will focus on giving this new perspective about dispersion measurement a direct application in optical communications field. We will restructure the ABCM into a practical dispersion monitoring system for optical communication networks. This improved monitoring technique will be based on a proof-of-concept study (no real data transmission considered) to evaluate the method’s performance in terms of accuracy, robustness and adaptability, building the basis for data transmission experiments in future projects. An important aspect to take into account will be the way we carry out the RF tone addition procedure without altering the optical carrier (transmitted data). To accomplish this requirement we will use a Bessel function analysis to achieve a carrier-suppressed modulation of the RF tone, which introduces another important handling parameter: the RF Tone Amplitude. We will also be concerned about isolating the emitter part (where data is transmitted) from the monitoring point (where dispersion is measured), but at the same time complementing each other to operate in a real-time situation. Finally, we will study the requirement of including the second RF harmonic detection together with the first harmonic as it adjusts better to a real-time monitoring system and increases the accuracy level in chromatic dispersion measurement.
Full text
1 PROJECTE FI DE CARRERA NEW METHODS FOR MEASURING AND MONITORING CHROMATIC DISPERSION IN OPTICAL COMMUNICATION SYSTEMS Autor: Cristhian A. Obando Velazco Directora: María C. Santos Blanco Data: 15 de Febrer de 2010
New methods for measuring and monitoring chromatic dispersion in optical communication systems 2
Table of contents 3 Table of contents 1. INTRODUCTION ............................................................................................................... 6 1.1. Objectives ..................................................................................................................... 6 1.2. Project Organization ..................................................................................................... 8 2. BASIC CONCEPTS .............................................................................................................. 9 2.1 Dispersion Theory .......................................................................................................... 9 2.1.1 Intermodal dispersion ................................................................................................. 9 2.1.2 Chromatic Dispersion .................................................................................................. 9 2.2 RF tone-based chromatic dispersion measurement techniques ..................................... 12 2.2.1 Mach-Zehnder Modulator ......................................................................................... 12 2.2.1.1 Configurations ........................................................................................................ 13 2.2.1.2 Transfer Function ................................................................................................... 14 2.2.2 Mach-Zehnder (push pull) + DUT + Detector Mathematical Analysis without considering amplitude distortions ........................................................................................................ 16 2.2.3 Mach-Zehnder (asymmetric) + DUT + Detector Mathematical Analysis without considering amplitude distortions ...................................................................................... 17 2.2.4 Mach-Zehnder (push pull) + DUT + Detector Mathematical Analysis considering amplitude distortions ........................................................................................................ 18 2.2.5 Mach-Zehnder (asymmetric) + DUT + Detector Mathematical Analysis considering amplitude distortions ........................................................................................................ 19 2.2.6 Modulation Phase Shift Method (MPSM) ................................................................... 21 2.2.7 Peucheret`s Method .................................................................................................. 23 2.3 Dispersion Compensating Elements .............................................................................. 24 2.3. 1 Dispersion Compensating Fiber ................................................................................. 24 2.3.2 Chirped Fiber Bragg Grating ....................................................................................... 25 2.4 VPI Simulation Tool ...................................................................................................... 26 2.4.1 Signal Representation ............................................................................................... 26 2.4.3 Restrictions on Global Parameters ............................................................................. 27 2.4.4 Module Parameters................................................................................................... 27 2.4.5 Sweep Configuration ................................................................................................. 28 2.4.6 Simulation example................................................................................................... 28 3. ASYMMETRIC-MODULATION BIAS CONTROLLED METHOD (ABCM) ................................. 33 3.1 Description and Mathematical Analysis ........................................................................ 33
New methods for measuring and monitoring chromatic dispersion in optical communication systems 4 3.2 VPI simulations ............................................................................................................ 35 3.2.1 Analysis of the dispersion inserted by the DUT ........................................................... 36 3.2.2.1 RF Frequency Sweep ............................................................................................... 42 3.2.2.2 RF Amplitude sweep ............................................................................................... 44 3.2.2.3 Nominal Dispersion Sweep ..................................................................................... 46 3.3 Experiments ................................................................................................................. 48 3.3.1 Laboratory Equipment ............................................................................................... 48 3.3.1.1 Optical and Electrical Sources ................................................................................. 48 3.3.1.1.1 Laser New Focus 6427 .......................................................................................... 48 3.3.1.1.2 Programmable DC Source PROMAX FA-851 .......................................................... 49 3.3.1.2 Optical devices ....................................................................................................... 50 3.3.1.2.1 Modulator FUJITSU FTM7921ER/052 H74M-5208-062 .......................................... 50 3.3.1.2.2 Polarization Controller ......................................................................................... 51 3.3.1.3 Passive Devices ...................................................................................................... 52 3.3.1.3.1 Bias-tee ............................................................................................................... 52 3.3.1.3.2 Optical detector Agère ......................................................................................... 52 3.3.1.4 Devices under test (DUTs) ....................................................................................... 53 3.3.1.4.1 Fiber Brag Grating PIRELLI CDC-04074 .................................................................. 53 3.3.1.4.2 Chromatic Dispersion Compensating Fiber ........................................................... 54 3.3.1.5 Measurement Devices ............................................................................................ 55 3.3.1.5.1 Network Analyzer HP 8753D ................................................................................ 55 3.3.1.5.2 Optical Multimeter HP 8153A .............................................................................. 57 3.3.2 Experimental Transfer Function ................................................................................. 58 3.3.2.1 Setup ..................................................................................................................... 58 3.3.2.2 Transfer Function for FUJITSU Modulator ................................................................ 59 3.3.3 ABCM Experiment ..................................................................................................... 60 3.3.3.1 General description ................................................................................................ 60 3.3.3.2 Setup characterization ............................................................................................ 62 3.3.3.3 Results ................................................................................................................... 65 3.3.3.3.1 Results obtained with the FBG ............................................................................. 65 3.3.3.3.2 Results obtained with the DCF ............................................................................. 66 4. ASYMMETRIC MODULATION BIAS-CONTROLLED METHOD - SUPPRESSED CARRIER (PROOF OF CONCEPT) ..................................................................................................................... 67 4.1 Description and Mathematical Analysis ........................................................................ 67
Table of contents 5 4.2 VPI simulations ............................................................................................................ 71 4.2.1 Analysis of the dispersion inserted by the DUT ........................................................... 75 4.2.2 Analysis of the effect caused by the setup’s parameters ............................................. 77 4.2.2.1 RF Frequency Sweep ............................................................................................... 78 4.2.2.2 RF Amplitude Sweep .............................................................................................. 80 4.2.2.3 Nominal Dispersion Sweep ..................................................................................... 84 4.2.2.4 Coupling factor Sweep ............................................................................................ 86 4.3 Experiments ................................................................................................................. 87 4.3.1 Laboratory Equipment ............................................................................................... 87 4.3.1.1 Optical Coupler ...................................................................................................... 87 4.3.1.2 Laser HP 83424A ..................................................................................................... 88 4.3.1.3 Agilent Spectrum Analyzer ...................................................................................... 89 4.3.2 General description of the experiment ....................................................................... 90 4.3.3 Setup characterization............................................................................................... 90 4.3.4 Carrier Suppression Experiment ................................................................................. 91 4.3.5 Dispersion Measurement Experiment ........................................................................ 93 5. CONCLUSIONS AND FUTURE LINES ................................................................................. 97 6. ANNEX ......................................................................................................................... 100 7. INDEX OF TABLES ......................................................................................................... 121 8. INDEX OF FIGURES ....................................................................................................... 122 9. BIBLIOGRAPHIC REFERENCES ........................................................................................ 125
New methods for measuring and monitoring chromatic dispersion in optical communication systems 6 1. INTRODUCTION With the progressive increase of data flow to travel through communication networks all around the world, high-capacity low-loss physical media are an urgent and important need. In this purpose, optical fiber appears as an outstanding choice due to its large bandwidth and low attenuation features. In the path towards next-generation optical networks with increased bit rates and complexity, compensation of fiber optic transmission impairments turns into a critical issue. Small variations due to temperature, stress, aging or dynamic path reconfiguration, may have a tremendous impact in performance and therefore adaptive compensation based on highprecision real-time on-line monitoring is essential [1]. Chromatic dispersion (CD) stands out as one of the most limiting impairments. Great research efforts have been devoted to find cost-effective and accurate techniques for its real-time online monitoring. In this regard, the use of radiofrequency (RF) pilot tones added at the emitter is advantageous because it offers good sensitivity, high dynamic range and reconfigurability, it also simplifies the receiver and allows monitoring at any given point in the network without the need to recover the data, and finally because the tones are useful for other network management issues such as channel identification. [1]. 1.1. Objectives This PFC main goal is to introduce new approaches on the chromatic dispersion measurement field, based on the big range of possibilities the setup of a general standard RF-tone modulation chromatic modulation method provides, and to show its good performance pointing towards a real-time on-line monitoring system for optical communication networks. The project’s objectives are defined considering two well-delimited stages. First, we will study some standard RF-tone-addition techniques for measuring chromatic dispersion, specifically the Modulation Phase Shift Method (MPSM) [2] and the Peucheret`s Method [3]. We will analyze their operating principles, recognize all the variables involved in their basic configurations and evaluate their performances under different measurement conditions. We will also study the implications of real-time on-line monitoring of chromatic dispersion in optical networks. We have to consider that the test signal has to travel together with the data; therefore, it is a priority to keep the optical carrier unaltered in the transmission and reception procedures. This background will help us to identify the main drawbacks of both methods which motivate the proposal of a new improved technique based on a similar mathematical basis but with better performance in terms of accuracy and cost trade-off. The general features of this new approach will be exposed on a basic setup designed for a laboratory environment, so that we can contrast it with the conventional techniques. This method dubbed Asymmetric Modulation Bias-Controlled Method (ABCM) will focus on RF
Introduction 7 modulated signal amplitude and will take advantage of its direct relation with chromatic dispersion. One of the basic building blocks of these standard methods is the device that imposes the RF pure-tone modulation to the optical signal, namely the Mach-Zehnder interferometric modulator usually in the conventional push-pull configuration and biased at the quadrature point. In the context of the new improved CD measurement methods, we will observe how the Mach-Zehnder modulator Bias Voltage concept gains relevance; becoming the main variable to be handled by the use of a dual drive Mach-Zehnder modulator in asymmetric configuration. Finally, we will analyze this ABCM method performance while some fixed parameters (RF Frequency, Nominal Dispersion, resolution) take different values in order to find out the optimum operating conditions. The problem when trying to apply the ABCM to the real-time on-line monitoring of optical networks is that it relies in the eventual cancellation of the optical carrier which in a network monitoring application is shared with the data and it is essential for a proper data recovery. We must find an alternative where this optical carrier cancellation is not essential for the monitoring function and that would be the ABCM-SC (SC for suppressed carrier) Therefore, on a second stage, we will focus on giving this new perspective about dispersion measurement a direct application in optical communications field. We will restructure the ABCM into a practical dispersion monitoring system for optical communication networks. This improved monitoring technique will be based on a proof-of-concept study (no real data transmission considered) to evaluate the method’s performance in terms of accuracy, robustness and adaptability, building the basis for data transmission experiments in future projects. An important aspect to take into account will be the way we carry out the RF tone addition procedure without altering the optical carrier (transmitted data). To accomplish this requirement we will use a Bessel function analysis to achieve a carrier-suppressed modulation of the RF tone, which introduces another important handling parameter: the RF Tone Amplitude. We will also be concerned about isolating the emitter part (where data is transmitted) from the monitoring point (where dispersion is measured), but at the same time complementing each other to operate in a real-time situation. Finally, we will study the requirement of including the second RF harmonic detection together with the first harmonic as it adjusts better to a real-time monitoring system and increases the accuracy level in chromatic dispersion measurement.
New methods for measuring and monitoring chromatic dispersion in optical communication systems 8 1.2. Project Organization This PFC is divided in five chapters which follow a general-to-particular subject matter where each chapter makes reference to the previous one. Chapter 2 Basic Concepts: provides a complete explanation of the theoretical knowledge that supports this PFC’s proposals and makes a general description of the main devices and tools used. Chapter 3 ABC Technique: presents the structured study of this new method for measuring chromatic dispersion including mathematical analysis, VPI simulations, and experimental verification; and it also proposes different operating situations. Chapter 4 ABC – SC Technique: aims at redefine the technique exposed in the previous chapter to develop a new system capable to satisfy real –time dispersion monitoring requirements. It follows the same method of study used in the previous chapter. Chapter 5 Conclusions: evaluates the performance of the two techniques proposed in this PFC by making use of the results obtained in charts and graphics, and verifies the achievement of the objectives.
Basic concepts 9 2. BASIC CONCEPTS 2.1 Dispersion Theory Dispersion is a typical phenomenon in optical media which yields the time spread of a transmitted pulse. It is caused by the different delays suffered by each of the optical signal’s components, so that at the detector, these components are recovered at different arrival times, generating a distorted signal with respect to the transmitted one. There are two well-defined types of dispersion: 2.1.1 Intermodal dispersion Intermodal dispersion is characteristic of multimode fibers where the optical signal propagates in many “modes”, each one following a different trajectory inside the fiber’s core in the rays theory analogy. Therefore, all the modes from a determined pulse experience different delays, generating the pulse spread explained above. 2.1.2 Chromatic Dispersion Chromatic dispersion is present in all types of fibers but in the multimode fiber the more relevant effect comes from intermodal dispersion. In this work, we will be mainly concerned with single-mode fiber where no intermodal dispersion occurs, and therefore we will only study chromatic dispersion. The physical phenomenon behind chromatic dispersion is explained below: Figure 2.1 Chromatic dispersion basic schema A generic optical pulse with carrier frequency transmitted through a single-mode fiber under ideal conditions (non-lossy transmission line with no deformation of the fundamental mode), can be represented like this: , (1) where the At is a slowly varying function of time as compared to the second term , and the last term -. reflects phase constant dependence with frequency (minus sign indicates the signal propagates on the ‘z’ axis positive direction).
New methods for measuring and monitoring chromatic dispersion in optical communication systems 16 m w; (15) It is also important to mention that, experimentally, we verified how the operating point can take a different value from one measurement to other. This phenomenon is known as bias drift [5] and is caused by the Mach-Zehnder dependence with temperature, and also due to environmental conditions, vibrations, etc. 2.2.2 Mach-Zehnder (push pull) + DUT + Detector Mathematical Analysis without considering amplitude distortions Within a basic setup of a dispersion measurement technique based on RF tone modulation, the study of the block composed by the Mach-Zehnder, the DUT and the detector becomes an essential issue, as it establishes all the possible expressions for the detected signal, including amplitude and phase terms from which the different techniques calculate the dispersion coefficient g. As it is shown in Figure 2.2, the optical source’s output is amplitude modulated by the Mach Zehnder Modulator. In the usual configuration it is a single-drive push pull modulator biased at the quadrature point. After that the modulated signal passes through the DUT. Finally, the optical detector recovers the envelope following a square-law characteristic. We will analyze both the push-pull and the asymmetrical MZ configurations as they set the basis of the chromatic dispersion measurement methods described in section 2.2. The mathematical analysis will be developed under some particular conditions which are characteristic of RF tone based dispersion monitoring techniques: • We will work under a small signal condition, that is, <<< 1. Thus, we can use the approximation: = 1; • The development will be done using “low-pass equivalent” expressions to simplify operations, which means working with a carrier frequency equal to 0. First, at the modulator’s output, in a push-pull configuration typical of standard method MPSM we get: Passing through the DUT, the optical signal suffers different phase shifts at the carrier and the sidebands, as it is shown below: • Phase shift at the carrier: • Phase shifts at the sidebands: b and
Basic concepts 17 The optical detector takes charge of recovering RF envelope. It consists on a square-law detector and a low-pass filter. So the detected power results: If we consider , the detected power results: (16) In the expression obtained, the first term represents the DC component which has no relevance on the dispersion calculation. The second term is RF fundamental harmonic. We can notice how the sidebands’ phase shifts, which are directly related to the chromatic dispersion value, appear in both amplitude and phase expressions, as the semi sum and semi difference respectively. Also we observe the bias voltage presence in the amplitude term but contained in two independent sinusoidal factors. 2.2.3 Mach-Zehnder (asymmetric) + DUT + Detector Mathematical Analysis without considering amplitude distortions This setup can also be implemented using a Mach-Zehnder in an asymmetric configuration, developing the mathematical analysis in a similar way. Therefore, if we use again the low-pass equivalent expressions we will have: Passing through the DUT:
New methods for measuring and monitoring chromatic dispersion in optical communication systems 18 Finally, following the same conditions at the optical detector, the detected power results: (17) If we compare the detected power obtained in this case with that of the push-pull configuration some different features emerge, i.e. the appearance of the bias voltage together with the semi sum of the sidebands’ phase shifts inside the sine function argument. The new dispersion measurement approach exposed in this PFC takes advantage of this fact to establish the operating principle. 2.2.4 Mach-Zehnder (push pull) + DUT + Detector Mathematical Analysis considering amplitude distortions In all previous analysis, we considered a DUT which only alters the optical signal phase with respect to frequency; however, some other devices used in optical communication systems, yield also a certain magnitude attenuation at each frequency component. Thus, in this context, the mathematical analysis requires the use of additional trigonometric identities to obtain a compact expression for detected power. First, for a push-pull configuration, the procedure is as follows: At DUT’s input, we receive the same optical signal from the modulator as in previous case: But now after it passes through the DUT we have:
Basic concepts 19 At the optical detector’s output, after applying the square-law and the low-pass filtering, we obtain: Finally, if we use the following trigonometric identity: The detected power results: (18) 2.2.5 Mach-Zehnder (asymmetric) + DUT + Detector Mathematical Analysis considering amplitude distortions Once again, if we repeat this analysis for a Mach Zehnder modulator in asymmetric configuration instead, the procedure is as shown below:
New methods for measuring and monitoring chromatic dispersion in optical communication systems 20 Therefore, at the Optical Detector's output the detected power results: Finally, by applying an analogous trigonometric identity: The detected power here results: (19) From the expression above, it is observed how the RF modulating signal phase recovered is not equal to the semi difference between the two major sidebands phase shifts but a much more complex term, unlike the previous case. This fact represents a huge inconvenience for phasebased measuring techniques like MPSM, because, even though the phase shifts at both sidebands are still contained in the phase term, we cannot consider this term as a good approximation of the optical phase shift inserted by the DUT, and therefore there is no guarantee to obtain a correct chromatic dispersion characterization from it.
Unfortunately, this situation expression (19), the bias voltage and the sum of phases in the am within the same sinusoidal (basis of ABCM) join both parameters in a well Now, we will describe two of the most popular techniques for dispersion measurement: Modulation PhaseShift Method (MPSM) and Peucheret`s Method, whose operating principles served as inspiration and conceptual basis for the new methods featured in this PFC. 2.2.6 Modulation Phase Shift Method MPSM obtains the group delay response of a device under test (DUT) by measuring the change in phase of a sinusoidal radio frequency (RF) modulation envelope as the wavelength is changed. Figure 2.5 shows the basic setup for Modulation is impressed using an external modulator, usually a Mach push – pull configuration, and recovered by an optical receiver. Phase data are recovered by ratio detection with respect to a reference RF path. As MPSM is included within the modulation on the optical signal to generate two major sidebands on the carrier (considering small signal condition), where each of them is affected by a phase shift while passing through the DUT , so that, in reception, the network analyzer takes charge of recovering the signal at . The mathematical expression for this signal is obtained from −= cos( 2 2 θ AA P B mo d is also a pending task for ABCM, because as we observe from expression (19), the bias voltage and the sum of phases in the am plitude recovered are not (basis of ABCM) and it would be a very complex procedure trying to join both parameters in a well -known expression. Now, we will describe two of the most popular techniques for dispersion measurement: Shift Method (MPSM) and Peucheret`s Method, whose operating principles served as inspiration and conceptual basis for the new methods featured in this PFC. Modulation Phase Shift Method (MPSM) obtains the group delay response of a device under test (DUT) by measuring the change in phase of a sinusoidal radio frequency (RF) modulation envelope as the wavelength is shows the basic setup for MPSM [7] . The optical source is a tun Modulation is impressed using an external modulator, usually a Mach – Zehnder Modulator in pull configuration, and recovered by an optical receiver. Phase data are recovered by respect to a reference RF path. Figure 2.5 MPSM basic setup the techniques which use RF modulation, it applies an amplitude modulation on the optical signal to generate two major sidebands on the carrier (considering small signal condition), where each of them is affected by a phase shift while passing through , so that, in reception, the network analyzer takes charge of recovering the signal at . The mathematical expression for this signal is obtained from the RF component in − + − + +−+ 2 cos 2 cos)sin() ϕϕ ωϕ ϕϕ θ t moB B Basic concepts 21 is also a pending task for ABCM, because as we observe from plitude recovered are not would be a very complex procedure trying to Now, we will describe two of the most popular techniques for dispersion measurement: Shift Method (MPSM) and Peucheret`s Method, whose operating principles served as inspiration and conceptual basis for the new methods featured in this PFC. obtains the group delay response of a device under test (DUT) by measuring the change in phase of a sinusoidal radio frequency (RF) modulation envelope as the wavelength is . The optical source is a tun eable laser. Zehnder Modulator in pull configuration, and recovered by an optical receiver. Phase data are recovered by techniques which use RF modulation, it applies an amplitude modulation on the optical signal to generate two major sidebands on the carrier (considering small signal condition), where each of them is affected by a phase shift while passing through , so that, in reception, the network analyzer takes charge of recovering the signal at the RF component in (16) − (20)
New methods for measuring and monitoring chromatic dispersion in optical communication systems Figure 2. From the signal above, the difference between the optical phase shifts acquired by the two major sidebands. After that , we approximate the group delay at the operating wavelength from this electrical phase, as it is explained below: where the first factor is defined as the fractional cycle of RF phase shift (expressed in degrees) and the second f actor represents the period of the RF sine wave. Now, by sweeping the optical wavelength with the complete delay curve for the required bandwidth, and then, chromatic dispersion at the nominal wavelength is calculated by dividing the change of group delay by the wavelength change which stimulates it: In order to achieve accurate measures it is important to have a stable wavelength step size, which completely depends on the tuneable laser stability. In expression (22) we can notice how the group delay and the measured electrical phase present opposite slopes. The phase of a sinusoidal signal can be interpreted as the argument of this signal when the time variable is equal to cero. For example, if we θ + . The time delay presented in a sinusoidal signal can be defined as the time value which cancels the argument. For example, the time delay of these concepts, it is of extreme importance to highlight that when the group delay is estimated New methods for measuring and monitoring chromatic dispersion in optical communication systems 2. 6. Optical phase shifts inserted by the DUT network analyzer will recover the electrical phase as the semi difference between the optical phase shifts acquired by the two major sidebands. 2 −+ − =∆ φφ φ , we approximate the group delay at the operating wavelength from this electrical phase, as it is explained below: m g fd d1 360 ° ∆ −≈−= φ ω φ τ where the first factor is defined as the fractional cycle of RF phase shift (expressed in degrees) actor represents the period of the RF sine wave. Now, by sweeping the optical wavelength with the aid of a tuneable laser, we obtain the complete delay curve for the required bandwidth, and then, chromatic dispersion at the nominal wavelength is calculated by dividing the change of group delay by the wavelength λ τ λ τ ∆ ∆ ≈= gg d d D In order to achieve accurate measures it is important to have a stable wavelength step size, which completely depends on the tuneable laser stability. In expression (22) we can notice how the group delay and the measured electrical phase The phase of a sinusoidal signal can be interpreted as the argument of this signal when the time variable is equal to cero. For example, if we have ( ) θω +tcos , the phase of this signal is The time delay presented in a sinusoidal signal can be defined as the time value which cancels the argument. For example, the time delay of ( ) θω +tcos is w / θ − these concepts, it is of extreme importance to highlight that when the group delay is estimated New methods for measuring and monitoring chromatic dispersion in optical communication systems 22 network analyzer will recover the electrical phase as the semi difference between the optical phase shifts acquired by the two major sidebands. (21) , we approximate the group delay at the operating wavelength from this electrical (22) where the first factor is defined as the fractional cycle of RF phase shift (expressed in degrees) tuneable laser, we obtain the complete delay curve for the required bandwidth, and then, chromatic dispersion at the nominal wavelength is calculated by dividing the change of group delay by the wavelength (23) In order to achieve accurate measures it is important to have a stable wavelength step size, In expression (22) we can notice how the group delay and the measured electrical phase The phase of a sinusoidal signal can be interpreted as the argument of this signal when the , the phase of this signal is The time delay presented in a sinusoidal signal can be defined as the time value which w . Having in mind these concepts, it is of extreme importance to highlight that when the group delay is estimated
Basic concepts 23 based in phase measurements, is necessary to invert the sign of the phase before computing it. 2.2.7 Peucheret`s Method Peucheret`s method uses the same setup as MPSM, so, the detected power at RF frequency is also the one of expression (20); however, instead of measuring the signal’s phase, it focuses on the amplitude term. As it was explained before, chromatic dispersion is strongly related with the phase shifts at the sidebands, and in this case, we will attempt to calculate it from the semi sum of these phase shifts which is contained into the RF amplitude term. Nevertheless, due to the channel noise, insertion loss and other signal attenuation factors, it would be necessary to have extremely accurate equipment and a very reliable calibration procedure if we want to measure the exact amplitude value. This is why Peucheret’s method operates on the envelope’s dips. In order to obtain these dips, Peucheret proposes to carry out a RF Frequency sweep on the setup. The mathematical analysis will be first conducted for the case where no amplitude distortion coming from the DUT is relevant, and then it will be extended to consider a relevant amplitude distortion coming from the DUT. Once again we start the analysis from expression (20): − + − + −= −+−+ 2 cos 2 cos)sin()cos( 2 2 ϕϕ ωϕ ϕϕ θθ t AA P moBB mo d (24) To obtain a “zero” in the amplitude term, we have: (25) As we know from, dispersion theory: (26) Therefore, replacing expression (25) in (26) results: (27) Now, we consider characterizing a DUT that inserts different amplitude attenuation levels at each frequency component. The mathematical analysis for this situation was also made in section 2.2.2. Here, we get the RF modulating signal from expression (19):
New methods for measuring and monitoring chromatic dispersion in optical communication systems 24 (28) It is inferred that we reach an amplitude dip when the cosine function takes its minimum value (-1), so we have: We notice we are under the same condition than for the non-amplitude degradation DUT and therefore, expression (27) is still valid to calculate chromatic dispersion coefficient. Thus, this analysis confirms Peucheret’s method robustness for characterizing this kind of devices, in contrast to MPSM. Nevertheless, there is an important problem in Peucheret’s method, which is the fact that depending on the amount of dispersion introduced by a determined DUT, the RF frequency needed to reach a dip could be too high; therefore, a very large sweep will be required to find it. Moreover, the use of high frequencies on the setup presents two main inconveniences: it may occur that equipment available cannot operate at those frequencies; and also, it is known that increasing the RF Frequency level implies moving the sidebands even further from the carrier losing resolution and accuracy in calculations. Peucheret tries to solve this problem by including a constant dispersion offset before the DUT in the setup, so the amount of total dispersion to measure increases so that the dip can be reached by using a lower RF frequency, and the level of dispersion desired is now the change in the total dispersion (DUT and offset). However, this procedure relies too much on dispersion offset’s stability during the entire process, which is hard to reach in highly dispersive channels. 2.3 Dispersion Compensating Elements 2.3. 1 Dispersion Compensating Fiber The Dispersion Compensating Fiber or DCF is simply a spool of a special type of fiber that has a very large negative dispersion, that is, a group delay spectrum with a negative slope. This amount of dispersion is several times the one of a conventional fiber. Thus, if we place a determined length of DCF after an optical fiber link, we can compensate the dispersion accumulated along the link. DCF presents some inconveniences. First, 1 Km of DCF with a typical nominal dispersion of -200 ps/nm·km just compensates 10-12 Km of standard SMF (G.652). Also, the attenuation caused by this compensating element at 1550 nm is as large as: three times that in standard fiber. Third, because of its reduced modal diameter, the optical intensity inside the fiber is so high that there is an accentuation of nonlinear effects.
Basic concepts 25 Additionally, although DCFs seem to have a wide wavelength band suitable for WDM applications, their nearly constant dispersion – slope across a large operational optical wavelength band pass does not exactly balance the group delay spectrum of SMFs. Thus, while DCFs neutralize the effect of chromatic dispersion at a single wavelength, a group of wavelengths away from that wavelength will be either underor overcompensated for dispersion. This effect is known as the “Dispersion-slope mismatch”. Nowadays, there is work in improving the performance of DCFs. There are new DFCs based in structure of bimodal fiber, reaching a nominal dispersion of approximately -770 tu/Ywx w with the same loss as a standard SMF. 2.3.2 Chirped Fiber Bragg Grating Chirped Fiber Bragg Gratings (CFBG) are considered the best option to cope with chromatic dispersion effects, due to their low-insertion loss and simplicity to be integrated and fabricated. A FBG consists on a short fiber section which reflects certain wavelengths and transmits the others. This is achieved by changing periodically the media’s refraction index, because, according to Fresnel equations (from which Bragg wavelength O is deduced), the light traveling through a determined media with different refraction indexes could be reflected or refracted. So, the grating period behavior must be such that the wavelength reflected fulfills the relation: O =2YΔ. It is important to mention that FBGs also experience the Dispersion-slope mismatch explained for DCFs. Figure 2.7 Fiber Bragg Grating operating principle In CFBG (Chirped FBG), unlike UFBG (Unchirped FBG), the induced refraction index does not have a sinusoidal variation with constant period, but the period becomes progressively shorter along the grating length. Due to the fact that the fiber`s dispersion coefficient in the third window is positive, when the wavelength increases the delay suffered increases too. To compensate this effect, it is necessary to make the larger wavelength travel shorter distances and the opposite way. This procedure makes possible to recover the original wave form at the system’s output. 1 λ 2 λ 3 λ 1 λ 2 λ 3 λ 1 λ 2 λ 3 λ Incident and dispersedpulse Reflected and reshaped pulse Decreasing grating period ( chirp ) t t 1 λ 2 λ 3 λ 1 λ 2 λ 3 λ 1 λ 2 λ 3 λ 1 λ 2 λ 3 λ 1 λ 2 λ 3 λ Incident and dispersedpulse Reflected and reshaped pulse Decreasing grating period ( chirp ) t t
New methods for measuring and monitoring chromatic dispersion in optical communication systems 32 Figure 2.15 Bias sweep configuration • Results Figure 2.16. Transfer Function of an Asymmetric MZ Modulator Figure 2.16 shows the MZ modulator transfer shows the MZ modulator transfer shows the MZ modulator transfer function in an asymmetric configuration. It corresponds with the DC component of (47), where the half – wave voltage is equal to the sensitivity of the electrodes (3.5 volts), as it has been demonstrated in section 2.2.1.2.
Asymmetric-modulation bias controlled method (ABCM) 33 3. ASYMMETRIC-MODULATION BIAS CONTROLLED METHOD (ABCM) 3.1 Description and Mathematical Analysis This first technique is devoted to verify that we can accomplish a high degree of accuracy when we calculate chromatic dispersion using a RF modulated signal’s amplitude term instead of the phase term. In the same way as in Peucheret’s method, the idea consists on finding the envelope dips (where the sinusoidal argument takes a well-known value); and then, through a direct mathematical development, the total amount of dispersion can be calculated. However, in this case no RF Frequency sweep is required. We will choose a fixed frequency appropriately and we will make a bias voltage sweep instead. Figure 3.1 ABCM basic setup The setup used in this method consists on a laser source operating at a fixed wave length (third window) whose output gets into a Dual drive Mach-Zenhder Modulator in asymmetric configuration. The optical signal is not altered at the modulator’s upper branch, while at the lower branch, it is phase modulated by a RF tone inserted together with a bias voltage. The sum of both branches’ signals results in an amplitude-modulated signal. The modulator’s output passes through the DUT, where it acquires the phase shifts, and then through the detector, obtaining expression (17) as we already verified in section 2.2.2: = I Z¡u I ~ 2 4; I ¢ cos ~ 2sin £ b C£ 2;£ C~ 2cos ¢ C£ b ;£ 2 4 The first term is the DC component and the second one is the RF first harmonic. Analyzing this second term we notice that in the amplitude factor the cosine function depends exclusively on the bias voltage value; so that it yields “zeros” in fixed locations: ¤ = 2nC1 ¥ ; however, the
New methods for measuring and monitoring chromatic dispersion in optical communication systems 34 sine function depends on the semi sum of the phase shifts at both sidebands as well. Dispersion information is contained in this last term, so we need to determine the location of the zeros yielded by the sine function, defined as “moving zeros”, to calculate g value. In absence of dispersion (no phase shifts in the sine’s argument), the moving zeros will be located at ¤ = 2Y m , therefore, under dispersion effects, these zeros will be shifted a certain distance from these reference locations positively or negatively, according to the dispersion’s magnitude and sign. To explain the complete procedure to calculate the chromatic dispersion, we start looking for an expression that relates the sum of phase shifts term with g value. The phase shifts inserted at both sidebands can be expressed using the Taylor Expansion defined in £ b £ ;U T ΔC MI k ]_ ` ] lΔ I (34) £ £ ;U T ;ΔC MI k ]_ ` ] l;Δ I (35) ]_ ` ] ; Im\ h g; j h Im\ g (36) Note that in contrast to section X where all quantities were given as distributed quantities along the fiber length, here we consider the total dispersion (after multiplying by total length). Applying expression (7) we have: Then, replacing (36) in expressions (34) and (35) and forming the sum of phase shifts term, we obtain: £ b C£ ;2£ ∑£ Imj h R ¨h \ (37) where O is the operating wave length, P ¢ is the RF tone frequency and c the velocity of light in vacuum. Now, in order to get an amplitude dip (zero), the sine’s argument must be equal to nN, so we have: £ b C£ 2;£ C~ 2nN £ b C£ ;2£ C~ 2nN (38) where ~ m < . Thus, if we replace expression (37) in expression (38), we obtain the exact locations of moving zeros and the final expression to calculate g: 2NgO I P ¢I ZCN m 2nN 2Y; Ij h R ¨h \ g m (39)
Asymmetric-modulation bias controlled method (ABCM) 35 g = k2Y; < < l \ Ij h R ¨h (40) where is the voltage neccessary to get the Y ª moving zero, P ¢ is the RF frequency, and Z and O are the velocity of light and the operating wavelength respectively. In this analysis, according to the setup, we considered that the RF modulating signal and the Bias voltage are inserted into the same electrode, however if we decide to use a different electrode for each one, the final expression obtained will be the same as in (40), but with a plus sign instead of the minus one. We notice how the level of accuracy in g calculation depends on the Bias voltage step width ( sweep resolution) and the RF frequency chosen. In numerical terms, a 0.01 V error in measurement represents approximately a 180/P ¢I ps/nm error in g calculation (with P ¢ in GHz, Z 3¬10 w/u and O = 1559 nm). Therefore, once we have fixed a proper Bias voltage resolution (conditioned by equipment available), we can minimize the error yielded in measurements by choosing a high enough RF frequency, but then the taylor approximation for the dispersion may fail because we would get too much far from the optical carrier (See expression (34) and (35)). The explanation above tries to establish the lower edges for both bias voltage resolution and RF frequency; however, there are also some restrictions which do not allow increasing these parameters too much. In the case of the bias voltage resolution, after a determined level, if we keep reducing the step width, there will be almost no improvement in g resolution, but there will be an unnecessary extra processing charge. In terms of RF frequency, if we look back to expression (40), we observe that for big dispersion values, the frequency must be low enough to avoid the bias voltage corresponding to the Y ª dip gets too much close to ®Y m (depending on dispersion sign), because if so, it will be difficult to distinguish the “moving zeros” from the “fixed zeros”. 3.2 VPI simulations This section is devoted to illustrate and verify the mathematical analysis’ results obtained for the ABCM, working in an ideal simulation schematic (noise-free transmission channel, no equipment limitations, etc), and it also gives us the chance to analyze the method’s behavior while we change its different parameters, so that we can identify the operation edges for each case. In this purpose, we will expose the complete process to carry out ABCM using this powerful simulation tool. On a first stage, after making a Bias sweep, VPI will return Amplitude-vs-Bias graphics where we can easily locate the amplitude dips, obtain the respective bias voltages; and finally by applying expression (40), calculate D value.
New methods for measuring and monitoring chromatic dispersion in optical communication systems On a second stage, in order to observe parameter, VPI provides us multidimensional sweeping options modules, which allow the processing and storage of large amounts of data samples. It is also important to highlight that modulator in asymmetric configuration 2.2.1 and whose transfer function was already obtained 3.2.1 Analysis of the dispersion Figure 3.2 VPI setup for ABCM section 5DC source 6Photodetector 7 In this fir st part, we will use t bias graphic for three specific situations: positive and negative dispersion, By this analysis, we want to distance from each other , and W e will make a bias sweep from We fill the setup’s parameters changes: • RF amplitude is set to 0.03 V and • The fiber section , when value equal to 17 • The Phase Detector’ s New methods for measuring and monitoring chromatic dispersion in optical communication systems On a second stage, in order to observe the method’s behavior when we vary us multidimensional sweeping options and Text Visualization modules, which allow the processing and storage of large amounts of data samples. is also important to highlight that along this section all setups will use a Mach modulator in asymmetric configuration , whose operation method was described in section transfer function was already obtained using VPI. the dispersion inserted by the DUT ABCM : 1Optical source 2Sine function generator 3 Photodetector 7 - Phase and Magnitude detector 8 st part, we will use t he setup featured in Figure 3.2 . We will display an three specific situations: when the setup includes a DUT ( fiber positive and negative dispersion, and without the DUT. to identify the “moving zeros”, verify they are separated a , and observe the shift caused by the dispersion effect. e will make a bias sweep from -1 to 8 V with a step width of 0.01 V and a fixed RF fr setup’s parameters with the same values as in section 2.2.6.6 , except amplitude is set to 0.03 V and RF frequency will be 2GHz. , when required, will have 80Km of length and a dispersion , which makes a total dispersion of s frequency must be set to the RF frequency (2GHz New methods for measuring and monitoring chromatic dispersion in optical communication systems 36 the method’s behavior when we vary a determined and Text Visualization modules, which allow the processing and storage of large amounts of data samples. will use a Mach – Zehnder , whose operation method was described in section generator 3 - MZM 4Fiber Phase and Magnitude detector 8 - 2D Analyzer . We will display an amplitude-vsfiber section) with identify the “moving zeros”, verify they are separated a effect. a fixed RF fr equency. , except for a few and a dispersion -per-meter frequency must be set to the RF frequency (2GHz ).
Asymmetric-modulation bias controlled method (ABCM) 37 Results After running these three simulations (DUT with null, positive and negative dispersion, and 2GHz RF frequency), the graphics obtained are shown in figure Y. On the top, we have the result for a non-dispersive DUT simulation. The graphic is a rectified sine function ( ) B θ sin , where the amplitude dips (both fixed and moving zeros) are located at = 0,® m, ® 2 m, ®3 m, ... This behavior is verified in section 3.1, where we concluded that in absence of dispersion (no phase shifts at the sidebands nor at the carrier), the amplitude term will be only composed by the product of two bias-dependent sinusoidal functions: cos:~ 2@sin:~ 2@¯ 2sin~ Otherwise, the graphic on the center, which corresponds to the DUT with positive dispersion, lets us distinguish the fixed and moving zeros. The first ones, as in the previous simulation, are located at ® m, ® 3 m, ® 5 m … (odd positions). However, the moving zeros have suffered a certain shift to the left from their reference positions 0,®2 m, ® 4 m, ... (even positions). This shift is due the phases sum term within the sine function argument, as explained in section 3.1. Therefore, the amplitude term results: Acos ~ 2sin £ b C£ 2;£ C~ 2
New methods for measuring and monitoring chromatic dispersion in optical communication systems 38 Figure 3.3 Amplitude-vs-Bias graphics for: a. null dispersion (top) b. Positive dispersion (center) c. Negative dispersion (bottom). Fixed zeros in blue, moving zeros in red
Asymmetric-modulation bias controlled method (ABCM) 39 Finally, the graphic on the bottom was obtained using a DUT with negative dispersion. Its behavior is similar to the previous case except for the fact that the moving zeros have displaced to the right this time. Therefore, it verifies that expression (40), used for g calculation, contemplates the sign of dispersion. In general, the moving zeros play an essential part in ABCM, as we only need to identify their locations in the Bias voltage axis and directly replace these values in expression (40) to obtain g. If we look at the zoomed-in image in Figure 3.3.b, we notice that the shift suffered by the moving zeros is equal to -310 mV. Thus, if we replace this value in expression (40) for Y 0, we have: g:0.31 3.5@3¬10 2¬1559.25 I 4 I g1366 ps/nm We observe that the dispersion calculated has an error equal to 6 ps/nm (0,44%) with respect to the nominal value, which can be included within the acceptable error range. We also observe from setup in Figure 3.2 that in all these simulations both the bias voltage and the RF tone are input through the same electrode. Nevertheless, in the mathematical development we verified that it is also possible to apply both signals through different branches, and we will then use expression (40) with the opposite sign. Figure 3.4 features the Amplitude-vs-Bias graphic obtained for a DUT with positive dispersion using only one electrode. We notice how the moving zeros have suffered a shift of the same magnitude as in the previous case but to the opposite direction. This fact explains the sign change in expression (40).
New methods for measuring and monitoring chromatic dispersion in optical communication systems 40 Figure 3.4 Amplitude-vs-Bias graphic for Positive Dispersion inputting Bias and RF tone through different branches. Fixed zeros in blue, moving zeros in red We ran the same schematic but considering a 6 GHz RF Frequency this time. Figure 3.5 provides the resulting amplitude-vs-bias graphic (we kept the DUT’s nominal dispersion equal to 1360 ps/nm). Figure 3.5 Amplitude-vs-Bias graphic for a 1360 ps/nm nominal dispersion with a 6GHz RF frequency. Fixed zeros in blue, moving zeros in red
As it is shown in Figure 3.5 , t replace this value in expression D ispersion value obtained in this case a (1360 ps/nm) as compared to section 3.1 , where we stated that closer to the no minal value as we increase 3.2.2 Analy sis of the effect caused by Figure 3.6 VPI setup for ABCM In this section, we will run the 3.6, to evaluate its performance in conditions. For this purpose, we will make use of VPI’s Sweep Control. The innermost loop will always be the width, to obtain the “n = 0” Asymmetricmodulation bias controlled , t he moving zeros’ shift in this case is equal to - 2.78 expression (40) considering the new RF frequency , it results: 1361 ps/nm ispersion value obtained in this case a pproximates better to the nominal dispersion (1360 ps/nm) as compared to the 2 GHz simulation. This behavior matche s with the analysis in , where we stated that if we keep the same Bias voltage resolution, minal value as we increase RF frequency. sis of the effect caused by the setup’s main parameters ABCM (Second stage). Highlighted with discontinuous line: module In this section, we will run the ABCM while varying some key paramet ers of the setup in F to evaluate its performance in different contexts and identify the best operating conditions. For this purpose, we will make use of the bidimensional sweep option innermost loop will always be the bias voltage sweep from - 3.5 to 0 V with a 0.01 V step dip on each run; while the outermost loop will be the studying modulation bias controlled method (ABCM) 41 2.78 V. Thus, if we , it results: nominal dispersion value s with the analysis in if we keep the same Bias voltage resolution, value gets Highlighted with discontinuous line: Text ers of the setup in F igure and identify the best operating the bidimensional sweep option provided in 3.5 to 0 V with a 0.01 V step outermost loop will be the studying
New methods for measuring and monitoring chromatic dispersion in optical communication systems 48 To give an explanation to the special features highlighted above, we must focus on the bias voltage resolution and evaluate its effect on the dispersion calculation replacing it in expression (40). If we consider that the bias samples are separated 0.01V, we know that the maximum error contemplated in the bias measurement will be of 0.005 V, which means a 0.022 ps/nm error. This value is exactly the highest difference observed in the graphic between the dispersion calculated and its nominal value, that is, the dispersion value calculated is rounded up until it overpasses this limit (at the drop points) where it is rounded down and so on. Therefore, this analysis verifies the fact that there is no other issue with the nominal dispersion additional to the error related with the bias resolution. Moreover, this error itself is not a big inconvenience for calculations, as it is kept within a tolerable range (+- 0.022 ps/nm ). 3.3 Experiments 3.3.1 Laboratory Equipment Next we will describe the devices used in ABCM’s setup 3.3.1.1 Optical and Electrical Sources 3.3.1.1.1 Laser New Focus 6427 This device (Figure 3.13) will be the light source to carry out chromatic dispersion measurement in ABCM. It is a tunable laser and it also features control of the output power up to 7 dBm. It can be connected to a PC through a GPIB port, so that its parameters can be controlled remotely, which will not be necessary in this experiment as we work on a fixed optical frequency. Figure 3.13 Laser New Focus 6427
Asymmetric-modulation bias controlled method (ABCM) 49 The most relevant technical features of New Focus 6427 are shown in Table 3.1. Laser NEW FOCUS 6427 Optical BW 1520 - 1570 nm Optical Power - 3 - 7 dBm Connetor Type FC/APC Table 3.1. NEW FOCUS 6427 Features. 3.3.1.1.2 Programmable DC Source PROMAX FA-851 This instrument (Figure 3.14) will provide the DC voltage to be inserted in the modulator as the bias voltage. It will be connected to the PC through its RS-232 port, so that a Matlab program will automatically set the bias voltage to be inserted into the modulator along the whole bias sweep. This procedure will be required for both the Transfer function and ABCM. In addition, since it has 3 power supply outputs available, it will also feed up the O/E detector. Figure 3.14 FA-851
New methods for measuring and monitoring chromatic dispersion in optical communication systems 50 3.3.1.2 Optical devices 3.3.1.2.1 Modulator FUJITSU FTM7921ER/052 H74M-5208-062 Fujitsu FTM7921ER/052 H74M-5208-062 (Figure 3.15) is a dual drive modulator which has an input for each of its two interferometric branches. In this experiment we will work on the modulator’s asymmetric configuration, that is, we will apply the bias voltage and the RF signal through the same input while the other one stays in open circuit. This modulator disposes of two arms with SMA adapters which are bind to the electrodes through a GPO connector. We will only use one of them, so the bias voltage and the RF signal will be inserted together through a bias-tee. Since the electro-optical effect by which the light gets modulated in the MZ modulator is polarization dependent, the input fiber to the Fujitsu modulator is polarization maintaining (PM), meaning it only allows the propagation of one specific light polarization, so that we will require a polarization controller in order to minimize the insertion loss. Since standard fiber presents a cylindrical symmetry, the light beam can be polarized on any direction perpendicular to its axis. Thus, some devices include a polarization preserver fiber with cylindrical section at the input, so that light’s polarization follows a determined fixed direction. In fact, this preserver fiber will reduce or suppress the light component with polarization in the perpendicular direction. This fact implies a power loss if the input polarization doesn’t match with preserver fiber polarization. Figure 3.15 FUJITSU FTM7921ER/052 H74M-5208-062
Asymmetric-modulation bias controlled method (ABCM) 51 The most relevant technical features of this modulator can be observed in table 3.2. FUJITSU FTM7921 ER/052 H74M - 5208 - 062 Modulator Optical BW 1530 - 1608 nm Electrical BW 8.5 GHz Electrode Impedance 50 Ω Insertion Loss (IL) 6 - 7 dB (según banda) V Π (V max - V mín ) 4 V Optical connectors type FC/UPC Table 3.2. FUJITSU FTM7921ER/052 H74M-5208-062 features. 3.3.1.2.2 Polarization Controller In Fujitsu Modulator description we explained why a polarization controller is required to make the light at the input acquire a polarization very similar to the one of the PM fiber. In this setup our polarization control will be based on applying mechanic deformations to the standard fiber, as it is shown on Figure 3.16. As seen, the optical fiber coils up around each of three mobile parts with 180º rotation capability. As obtained in …, we will have to twirl the fiber twice at the mobile parts on the extremes and four times at the one on the center. Figure 3.16. Polarization Controller
New methods for measuring and monitoring chromatic dispersion in optical communication systems 52 3.3.1.3 Passive Devices 3.3.1.3.1 Bias-tee This device (Figure 3.17) is required to insert both RF signal and bias voltage through the same modulator’s arm. It is just a kind of multiplexor which has 3 ports organized in a T distribution, so that the RF signal (which can go from 45 MHz to 26.5 GHz) an the bias voltage are entered through two different SMA connectors and get out together through an only one output connected to the modulator. In conclusion, the bias tee lets us multiplex two electrical signals in the same cable, one in Radiofrequency and the other in DC. Figure 3.17. Bias tee 3.3.1.3.2 Optical detector Agère This device (Figure 3.18) takes charge of transforming optical power received into an electrical current. In this process the carrier wave of the signal at the output of MZ modulator will be cancelled out and we will just keep the modulating wave. The detector’s output is connected to the Network Analyzer to measure the amplitude required for ABCM.
Asymmetric-modulation bias controlled method (ABCM) 53 Figure 3.18. AGERE Systems 2860E The most relevant features of AGERE Systems 2860E are shown in table 3.3. Optical Detector OC - 192/STM - 64 Optical BW 1280 - 1580 nm Optical BW 30 KHz - 9 GHz Vcc (Power supply ) 8 V Table 3.3. AGERE Systems 2860E features 3.3.1.4 Devices under test (DUTs) 3.3.1.4.1 Fiber Brag Grating PIRELLI CDC-04074 Fiber Brag Grating Pirelli (Figure 3.19) is designed to compensate for the amount of dispersion that 80 km of fiber would yield. These 80 Km are verified considering the device presents a 1252.35 ps/nm total dispersion and under third window we estimate a 16ps/nm·km dispersion slope. Kml FIBER 8027,78 ps/(nm·km) 16 ps/nm 1252.35 ≈== Since this is a dispersion compensating device, the sign of dispersion will be opposite to that in the fiber. This is a narrow band device as we can observe in the specifications (table 3.9). Nevertheless, since the laser New Focus 6427 has a tunable frequency set containing the FBG’s operating band, we will just have to adjust the laser output wavelength to the FBG band.
New methods for measuring and monitoring chromatic dispersion in optical communication systems 54 Figure 3.19. PIRELLI CDC-04074 The most relevant features of the device are shown in table 3.4. Pirelli CDC - 04074 Optical BW 1557.27 - 1561.19 nm Nominal Dispersion 1252.35 ps/nm Insertion Loss 6.18 dB Connector Type FC/UPC Table 3.4. CDC-04074 features 3.3.1.4.2 Chromatic Dispersion Compensating Fiber This is a very special type of fiber with much more dispersion than standard fiber and with the opposite sign. Unlike Pirelli FBG, the own fiber acts as the source of dispersion, thus, it has no restriction about optical bandwidth. It has FC/APC connector at both extremes; this is why we will need adapter fiber sections in between to connect it to the modulator in one extreme and to the optical detector in the other, since they both have UPC connectors.
Asymmetric-modulation bias controlled method (ABCM) 55 Figure 3.20 Chromatic Dispersion Compensating Fiber The most relevant features of this device are shown in table 3.5. Dispersion Compensating Fiber Nominal Dispersio n 671 ps/nm Insertion Loss (1575 nm) 5.15 dB Connector Type FC/APC Table 3.5. Dispersion Compensating Fiber features 3.3.1.5 Measurement Devices 3.3.1.5.1 Network Analyzer HP 8753D For the setup in this experiment we need a Network Analyzer. We will use a HP 8753D model (Figure 3.21). This device will let us carry out dispersion measurements required for ABCM. Besides taking charge of measurements, HP 8753D will be useful as a RF signal supplier through its port 2, and will be able to adjust its power and frequency. Therefore, binding in mind that the RF signal is obtained from port 1 and the output signal of the setup is inserted through port 2, we will work with parameter S21 in amplitude mode.
New methods for measuring and monitoring chromatic dispersion in optical communication systems 56 Figure 3.21 HP 8753D The most relevant features of the Network Analyzer as both measurer and signal generator are shown in tables 3.6 and 3.7 respectively. Network Analyzer HP 8753D ( measurer ) BW 30 KHz - 6 GHz M aximum input power 10 dBm Connectors type N Table 3.6. HP 8753D measurer features Network Analyzer HP 8753D (Signal Generator) BW 30 KHz - 6 GHz M aximum output power 10 dBm Mínimum output power - 15dBm Connectors type N Table 3.7. HP 8753D signal generator features
Asymmetric-modulation bias controlled method (ABCM) 57 3.3.1.5.2 Optical Multimeter HP 8153A This device (Figure 3.22) is used specifically to make power measurements. This procedure is very important for instance to obtain Transfer Functions and to detect bad connections or dirty or damaged fibers in our setups. It has a GPIB port, so it can be connected to a PC and be controlled automatically through a Matlab program. This device, if configured in RMT (remote) mode, can be used together with another instrument to carry out Transfer Functions in an automatic way, all controlled by a very simple Matlab code. Figure 3.22 HP 8153A This device has an analog output through a BNC connector. This output is used by the multimeter to provide an output signal between 0 and 2 volts in relation to the received optical signal. The most relevant technical features of HP 8153A for our own application are shown in table 3.8. Multimeter HP 8153A Optical BW 450 - 1700 nm Supported Error ±2.2% Power margin - 110 - 27 dBm Connector type SC/UPC Table 3.8. HP 8153A features.
New methods for measuring and monitoring chromatic dispersion in optical communication systems 64 we expect to measure, in this case it is 671ps/nm corresponding to the Fiber section; and also it depends on RF frequency set (3GHz). Thus, the maximum step width allowed for the bias sweep is obtained as follows: ( ) 22 0 12 2 m bb fV VVc D λ π − ⋅ −= ; ( ) 12 22 0 2 bb m VV c fVD −= ⋅ − λ π ( ) ( ) ( ) 8 2 9 2 9 12 10 3 10310155937,32671 × ××⋅⋅⋅ −=− − bb VV ; ( ) mVVV bb 75,329 12 =− Once we found the maximum bias step width we can use, we proceed to choose a proper value for this parameter considering a certain security margin; therefore we choose a step width of 200mV.This value is five times bigger than the step width set for the simulations, however, it still provides good accuracy in measurements. One final consideration about the equipment is related to the Dual drive Mach-Zehnder Modulator available. This Modulator has one positive input and also a negative one, so that if we insert both the RF signal and the bias voltage through the positive input, we will obtain a positive phase shift, otherwise, if we use the negative input we will have a negative phase shift. In this particular method, this above feature implies that in Figure 42 the moving zeros will suffer a displacement to the x axis positive or negative direction if we use the positive or negative input respectively.
Asymmetric-modulation bias controlled method (ABCM) 65 3.3.3.3 Results 3.3.3.3.1 Results obtained with the FBG Figure 3.27 ABCM measures obtained for FBG As we can see in Figure 3.27, there is a significant displacement of the moving zeros but also a small displacement of the fixed zeros about 0.01 from its natural location. This can be attributed to some bias drift of the modulator, so we will consider this value as a calibration reference to calculate the moving zero exact displacement. ( ) ( ) VVV bb 62,01,046,618,7 12 =−−=− Once we have the real displacement of the moving zeros we just need to apply expression (40) to calculate chromatic dispersion. Thus, considering m value obtained in FUJITSU modulator Transfer function of section 3.3.2.2, we have: ( ) ( ) ( ) nmpsnmns fV VVc D m bb /59,1261/26159,1 10310155937,32 62,0103 2 2 9 2 9 8 22 0 12 −=−= ××⋅ × = −⋅ −= − λ π Measured Dispersion vs Nominal Dispersion Measured value - 1261,59 ps/nm Nominal value - 1252,35 ps/nm Table 3.11 Measured Dispersion vs Nominal Dispersion for FBG
New methods for measuring and monitoring chromatic dispersion in optical communication systems 66 3.3.3.3.2 Results obtained with the DCF Figure 3.28 ABCM measures obtained for DCF In this case, as we notice in Figure 3.28, there is no displacement for the fixed zeros, that is, no calibration is required this time. Therefore, the calculation corresponding to chromatic dispersion final expression is as follows: ( ) ( ) ( ) ( ) nmpsnmns fV VVc D m bb /84,691/69184,0 10310155937,32 46,68,6103 2 2 9 2 9 8 22 0 12 −=−= ××⋅ −× = −⋅ −= − λ π Measured Dispersion vs Nominal Dispersion Measured value - 691,84 ps/nm Nominal value - 671ps/nm Table 3.12 Measured Dispersion vs Nominal Dispersion for DCF As we can observe in tables 3.11 and 3.12, the dispersion values obtained are very close to their nominal values; that is, both measurements were carried out with the expected accuracy.
Asymmetric modulation bias-controlled method - suppressed carrier 67 4. ASYMMETRIC MODULATION BIAS-CONTROLLED METHOD - SUPPRESSED CARRIER (PROOF OF CONCEPT) 4.1 Description and Mathematical Analysis Even though the ABCM exposes the general concept of this PFC, its usage is devoted to laboratory tests, due to the unavoidable carrier alteration (altering data detection) yielded when we carry out the bias voltage sweep. Thus, if we want to implement a high-accuracy dispersion monitoring system and apply it in an optical communication network without altering the data recovery, the setup must be redesigned. Therefore, in this chapter we present a new approach for on-line chromatic dispersion monitoring but still based on RF tone addition. The tone’s amplitude must be such that in the resulting modulated signal the carrier gets cancelled (carrier suppression), so that it does not interfere with the intensity modulated optical carrier (data stream) when both signals are combined. Once again the bias voltage sweep applied together with the RF tone takes charge of changing the optical phase shift between the RF bands and the carrier, so that at the monitoring point the voltage difference between the zero-amplitude bias corresponding to the RF frequency and to its second harmonic can be used to calculate dispersion coefficient. Operating principle The basic scheme of ABCM - SC is shown in Figure 4.1. At the emitter side the output from a laser source is split into two branches. At the upper branch the optical carrier is intensity modulated by the data, while at the other branch the optical signal passes through a phase modulator controlled by the RF tone and the DC voltage signal ( ) tV B going at a constant slow time rate from ; m to m (at least), where m is the modulator’s half wave voltage. Figure 4.1 General schematic for Dispersion Monitoring System LASER IM PM DATA ( ) tfA RFRF π 2cos ( ) tV B EMITTER 2f RF f RF MONITORING POINT 1 τ T π V− π V t T 2 τ
New methods for measuring and monitoring chromatic dispersion in optical communication systems 68 We mentioned that in this PFC we will strictly focus on verifying the method’s mathematical basis and evaluating its performance in terms of accuracy and stability. Therefore, to simplify the study, no intensity-modulated data will be considered at the upper branch (optical signal passes unaltered). The phase modulated optical signal at the lower branch is expressed as follows: z{ = S ²³ (41) where ~ = m< < and ~ = m< ²³ < . Since we want to cancel out the carrier component at the lower branch, in this case we will not work under a small signal condition, but we will use the Bessel functions expansion to find out the proper RF tone amplitude. Using again low-pass equivalent expressions we have: z{ | I ´ ²³ (42) z{ | I ´ ¢µ9¶ ¨ (43) where w is the modulation index. So if we make use of the Jacobi-Anger identity: \z·¸ ∑ S¹ Sº¹ » S V S¸ (44) and we express the RF-dependent exponential term considering it up to 2º order, we obtain: z{ 2´ » wC» M w ¨ C» M w ¨ ;» I w I ¨ ;» I w I ¨ (45)
Asymmetric modulation bias-controlled method - suppressed carrier 69 Figure 4.2 Bessel Functions: order 0 (red), order 1 (green) and order 2 (blue) Now, looking at Figure 4.2, we realize that » w acquires a null value for w = 2.405. Then, the three Bessel terms’ values will be: » 2.405¼0 » M 2.405¼0.52 » I 2.405¼0.43 Replacing these values in expression (45), it results: z{ | I ´ 0.52 ¨ C ¨ ;0.43 I ¨ C I ¨ (46) Expression (46) represents the output of the phase modulator, where as we can see, the carrier’s component has been suppressed. Thus, the data at the upper branch will be kept unaltered when combining the two signals. We must emphasize the fact that as we are not considering a small signal condition for the RF tone, we need to ensure a proper splitting ratio between the branches to keep the effective optical modulation index within moderate values. Here is where the role of the couplers within the setup acquires importance. If we define a coupling factor “", the signal at the DUT’s input will be: ¾¿_S | I ´}1;C ~ Á 0.52 w C ; w ;0.43 2 w C ;2 w (47)
New methods for measuring and monitoring chromatic dispersion in optical communication systems 70 Then, passing it through the DUT, we have: ¾¿ ?Âà = 2´1; 0 C ~ Á 0.52 w 1C C ; w 1; ;0.43 2 w 2C C ;2 w 2; 2´Ä1; 0 C ~ Á o 0.52 1C C 1; 2 w 1C ; 1; 2 C ; w ; 1C ; 1; 2 ;0.43 2C C 2; 2 2 w 2C ; 2; 2 C ;2 w ; 2C ; 2; 2 lÅ | I 1;cos C 0 ; 0.52sin C 1C C 1; 2 C~ Á cosk ¢ C 1C ; 1; 2 l; 0.43cos C 2C C 2; 2 C~ Á cosk2 ¢ C 2C ; 2; 2 l (49) Expression (49) illustrates how the carrier and the first and second harmonics’ sidebands have acquired a certain phase shift coming from the dispersive system (DUT), so that, like in the previous method, an accurate detection and measurement of the phase shift are essential for chromatic dispersion calculation. Therefore, at the monitoring point, after applying a square-law detection, neglecting terms affected by I , the detected power will be: Æ ¾¿ ?ÂÃ Æ I 2 M h | h MÇ ; .ÈI| h sin 1C C 1; 2 ; 0 C~ Á cosk ¢ C 1C ; 1; 2 l; .ÈÉ| h cos 2C C 2; 2 ; 0 C~ Á cosk2 ¢ C 2C ; 2; 2 l (50) From the expression obtained above, we must highlight that the really important terms are the sine and the cosine functions, which represent the detected envelopes for the first and the second harmonic respectively. Then, expressing these envelopes in terms of Bias voltage and chromatic dispersion coefficient, we obtain: ( ) ( ) 2 2 sin D RF B o RF i f V t D f V c π π π λ = + (51) ( ) ( ) ( ) 2 2 2 cos 2 D RF B o RF i f V t D f V c π π π λ = + (52)
Asymmetric modulation bias-controlled method - suppressed carrier 71 where c is the velocity of light in vacuum and o λ is the carrier’s wavelength. Both envelopes present a relative electrical phase shift which depends on the D value. Now, we have to carry out the mathematical development for the case when we get an amplitude zero at both harmonics, as it is explained below: 1 st harmonic: m < M C mj h R ¨h \ =nN (53) 2 nd harmonic: m < I C mj h IR ¨ h \ 2nC1 m I (54) From expressions (53) and (54) we finally obtain a direct expression to calculate g: g = M I ; < h < i < \ Éj h R ¨h (55) In absence of dispersion both envelopes are 2/ π out of phase and then 5.0/ =∆ π VV , so, in the same way we infer that 5.0/ <∆ π VV for 0 > D and 5.0/ >∆ π VV for 0 < D . Therefore, both magnitude and sign of the dispersion coefficient can be obtained with this technique, subject to the periodic nature of the two detected envelopes which limits, on a first look, the maximum dispersion magnitude that can be unambiguously determined (in section 4.2.2.1 we will discuss how this is actually not a limitation). Dispersion monitoring window and dispersion resolution are in fact key parameters of any chromatic dispersion monitoring system based on pilot tones which set a trade-off in the RF frequency choice. 4.2 VPI simulations As it was done for the ABCM, now we are going to demonstrate the validity of ABCM – SC through a theoretical and numerical analysis, using the VPI simulation tool. The procedure will be the same except for the fact that we first need to determine the appropriate RF Tone amplitude to accomplish the “w = 2.405” condition (necessary to cancel the carrier). It must be emphasized that for the RF modulation we consider phase instead of intensity modulation, and therefore we must find a proper way of simulating it with VPI. We found that the better way to do it is by using a generic MZ modulator block in which the sign of the phase shift acquired by each of the two interferometric branches is the same (set “LowerArmPhaseSense” to positive) and then we enter the same RF tone in both electrodes. See Figure 4.3. We will set the modulator’s m at 3.5 V, so that, we can now obtain the value required from the expression below:
New methods for measuring and monitoring chromatic dispersion in optical communication systems 72 w = N m Thus, we have: =N2.405 3.5 Therefore, 2.68 As we are working in a simulation environment (ideal conditions) this value can be directly set as the RF tone amplitude. Figure 4.3 features a basic Phase modulation schema, representing the lower branch on ABCM - SC setup. Through this simulation we will make sure that the carrier cancellation is done correctly. To carry out the simulation, in addition to the 2.68V RF amplitude, the optical source, MZM and RF Frequency must be configured with the same parameters we will use in the main simulation. The bias voltage into the phase modulator in the final setup (Figure 4.3) will be the parameter that sets the phase difference between sidebands and carrier to yield detected RF amplitude nulls, but for now, in order to get the RF amplitude value required for carrier cancellation into the PM branch of Figure 4.3 it does not have any relevant effect but adding a constant phase shift that does not affect the optical spectrum, and therefore we just set it to zero. Figure 4.3 VPI schematic for phase modulation with carrier suppression The graphic displayed by the Spectrum Analyzer in figure 32 is indeed the one we expected. It presents several pairs of sidebands, whose amplitudes decrease as they get further from
Asymmetric modulation bias-controlled method - suppressed carrier 73 harmonic 0 (carrier frequency), and the most important aspect is that the optical carrier has been reduced to an almost imperceptible power level. Figure 4.4 Spectrum of the phase modulated optical signal Figure 4.5 shows a zoomed-in image of the optical spectrum which only exposes the most important features of ABCM - SC: the two main pairs of sidebands (for the first and the second harmonics) with similar power levels and the suppressed carrier (- 63 ÌÍw). Figure 4.5 Zoom on Figure 4.4 highlighting main sidebands and suppressed carrier
New methods for measuring and monitoring chromatic dispersion in optical communication systems 80 Figure 4.10 Chromatic Dispersion-vs-RF frequency Curve We observe, just as in ABCM simulation, how the Null-amplitude bias delta decreases as frequency increases; however, it doesn’t keep the same behaviour till the end, yielding a level hop around 4.8 GHz. This feature reflects that we have arrived to the upper edge for the RF frequency, which indicates that at this frequency value the zero amplitude bias from one of the two harmonics has over passed the allowed range, so the rest of the graphic should be dismissed. However, unlike ABCM, if we look at expression (55), it does not depend on “Y”; thus, it is not necessary to know the dips’ order as long as we make sure both dips correspond to the same order. Nevertheless, for this particular analysis we decided to restrict the possible dips location to finite ranges to simplify the dips obtaining algorithm. This level hop at 4.8 GHz is also featured in figure 38, which shows dispersion-vs-RF Frequency relation. Here we can see how the dispersion level approximates to the nominal value (1.36 ps/nm) and gets even closer to it for 1 GHz. If we want to make a comparison with ABCM, we can state that in this case the graphic reaches a good stability sooner, however, the maximum frequency allowed is around 4.8GHz. 4.2.2.2 RF Amplitude Sweep In ABCM - SC, the RF Amplitude acquires an even more important role than in ABCM. It is the main parameter to handle during the carrier suppression process, which is a particular consequence of the phase modulation of the optical carrier. 01234567 x 10 9 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 Dispersion vs RF Frequency
Asymmetric modulation bias-controlled method - suppressed carrier 81 We know from the introduction section that the main purpose of cancelling the optical carrier in the RF tone phase modulated signal is to avoid altering the recovery of data when both signals are combined. This is in fact the reason why this technique can be applied to a real-time optical network monitoring system, unlike ABCM. However, the accuracy of the dispersion measurement is not related with the data alteration along transmission, but with keeping the signals’ amplitude level within the acceptable range to support the approximations of the mathematical analysis. Thus, we need to yield a considerable difference level between the carrier and the two first harmonics’ sidebands, and between these ones and the rest of the harmonics. The considerations exposed above establish an important restriction to the RF amplitude value in terms of data preservation and accuracy in measurements. First, we will focus on the carrier cancellation issue. We will carry out a certain number of simulations with the schematic featured in Figure 4.3, while we sweep manually the RF amplitude around values close to the ideal one obtained in the math analysis (2.68 V). The exact values will be: 2.60, 2.65, 2.70, 2.75, 2.80 and 2.85 V. After running these simulations, the Optical Spectrum Analyzer Module yielded a different spectral representation for each run as it is shown in Figure 4.11. We observe that the first harmonic has an amplitude level around -20 dBm along all simulations; however, the carrier suffers a considerable level variation on each RF amplitude step. The carrier level increases as we get further from 2.68, so that we have almost 20 dB of difference from the extreme values to the center. This behavior demonstrates how susceptible the carrier level is to RF amplitude variations. Therefore, we must keep this parameter as close as possible to the reference value if we want to achieve a good carrier cancellation.
New methods for measuring and monitoring chromatic dispersion in optical communication systems Figure 4.11 Spectrums of the phase modulated optical signal obtained with RF amplitude equal to: a) 2.60 V b) 2.65 V c) 2.70 V d) 2.75 V e) 2.80 V f) 2.85 V New methods for measuring and monitoring chromatic dispersion in optical communication systems the phase modulated optical signal obtained with RF amplitude equal to: a) 2.60 V b) 2.65 V c) 2.70 V d) 2.75 V e) 2.80 V f) 2.85 V New methods for measuring and monitoring chromatic dispersion in optical communication systems 82 the phase modulated optical signal obtained with RF amplitude equal to: a) 2.60 V b) 2.65 V c) 2.70 V d) 2.75 V e) 2.80 V f) 2.85 V
Asymmetric modulation bias-controlled method - suppressed carrier 83 On the other hand, we need to evaluate the technique’s behavior in terms of accuracy, just as we have been doing in the previous analysis. We will make a large RF amplitude sweep so that we can easily identify the lower and upper edges of the acceptable range. The RF amplitude (outermost loop) will go from 0.12 V to 4.12 V as these values are far enough from the reference level to perceive measurement errors. The step width will be of 0.16 V, which makes a total of 26 samples. Results The results corresponding to this simulation are featured in the Harmonics Null-Amplitude Bias Difference-vs-RF amplitude curve and in the Dispersion-vs-RF amplitude curve in Figure 4.12 and 4.13 respectively. We observe in figure 41 how the curve starts with 2 ps/nm dispersion at 0.12 V and then it approximates very quickly to the nominal dispersion (1.36 ps/nm), reaching the closest value (1.351 ps/nm) at 0.8 V and keeping this until 2.9 V. The range we have just delimited is where the RF amplitude must be allocated in order to preserve ABCM -SC accuracy. Figure 4.12 Zero-amplitude Bias Delta-vs-RF amplitude curve 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 1.05 1.1 1.15 1.2 1.25 1.3 Delta Null Bias vs RF Amplitude
New methods for measuring and monitoring chromatic dispersion in optical communication systems 84 Figure 4.13 Chromatic Dispersion-vs-RF amplitude curve Going deeper into the analysis, we realize that the upper and lower edges of the range obtained are not equidistant from 2.68 V; this means, the carrier suppression is not the main property involved while evaluating results. Thus, it is more important to keep the RF amplitude small enough with respect to the signal traveling in upper branch. In conclusion, we can state that the most important issue within ABCM - SC is related with the accuracy in the dispersion measurement. We have to determine a range of RF amplitude possible values; however, since this method is supposed to be applied on a real time optical network, we must set this value as close as possible to the reference value obtained in carrier suppression analysis. It is also important to conduct BER measures for the modulation format to avoid affecting transmitted data. 4.2.2.3 Nominal Dispersion Sweep The analysis of Nominal Dispersion parameter has nothing new with respect to the one carried out for ABCM. We observe from expression (55) that the relation between the dispersion and the RF frequency is very similar to the one we had for ABCM in expression (40). Thus, we assume that if we work within the range obtained in the RF frequency sweep section, we will not have any problems while measuring very high or very low dispersion values. Therefore, this analysis will once again focus on describing how the variation of nominal dispersion (set in the fiber section) affects the method’s accuracy, and we will also study its relation with the bias resolution. 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2Dispersion vs RF Amplitude
Asymmetric modulation bias-controlled method - suppressed carrier 85 As we are using the same fiber module as DUT, the outermost loop for the bidimensional sweep will be the fiber’s length, which will go from 0 to 160 km with a step width of 5 km. Results Figure 4.14 represents Null amplitude Bias Delta voltage-vs-Nominal Dispersion Curve, which has a linear behavior from the beginning to the end. This linearity is also observed in figure 4.15, containing the relation between the measured dispersion and the nominal dispersion. Figure 4.14 Zero-amplitude Bias Delta-vs-Nominal Dispersion Curve Figure 4.15 Chromatic Dispersion-vs-Nominal Dispersion Curve 0 0.5 1 1.5 2 2.5 3 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 Delta Null Bias vs Nominal D 0 0.5 1 1.5 2 2.5 3 0 0.5 1 1.5 2 2.5 3Dispersion vs Nominal D
New methods for measuring and monitoring chromatic dispersion in optical communication systems 86 The most salient point in Figure 4.15 is that once again the nominal dispersion value has an almost imperceptible effect on the dispersion calculated, so that the ABCM - SC is able to keep a good performance no matter the level of dispersion the optical system has, subject to the limit of maximum measureable dispersion which depends on the RF frequency. 4.2.2.4 Coupling factor Sweep The presence of couplers within the setup is one of the new features introduced by ABCM - SC. We will carry out a bidimensional sweep with the coupling factor () as the outermost loop parameter, going from 0.51 to 0.99 (the number indicates the factor applied to the upper branch). Results We obtained the Null amplitude Bias Delta-vs-Alpha and Dispersion-vs-Alpha curves featured in Figure 4.16 and Figure 4.17 respectively. Figure 4.16 Zero-amplitude Bias Delta-vs-Alpha Curve 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 1.25 1.3 1.35 1.4 Delta Null Bias vs Alpha
Asymmetric modulation bias-controlled method - suppressed carrier 87 Figure 4.17 Chromatic Dispersion-vs-Alpha Curve We notice the graphics obtained have a quite similar behavior to the ones obtained in the RF amplitude analysis. This fact shows how both parameters are, in different levels, involved on yielding the magnitude difference between the optical carrier and the first and second harmonics. Now, observing Dispersion-vs-Alpha curve on itself, we realize it starts with a dispersion value around 1 ps/nm at 0.51 alpha sample, and then dispersion increases following a “steps” shape, and getting the closest to nominal dispersion, with a 1.351 ps/nm value at around 0.75 . Therefore, this last alpha value represents the minimum point or lower edge to maximum accuracy in chromatic dispersion calculation. We can see how the dispersion calculated keeps unaltered almost until the end of ’s range; however from 0.97 the curve starts growing again. Anyway, it is totally inefficient to use couplers with those alpha values in real environments. 4.3 Experiments 4.3.1 Laboratory Equipment Next we will describe the devices need to carry out ABCM – SC which were not used in ABCM. 4.3.1.1 Optical Coupler This is a passive device used in optical systems for multiplexing (branching or joining) the optical signal from one or more light sources to one or more light receiving devices. The power distribution into the outputs depends on the wavelength and the polarization. The couplers 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 1.05 1.1 1.15 1.2 1.25 1.3 1.35 1.4 1.45 1.5 Dispersion vs Alpha
New methods for measuring and monitoring chromatic dispersion in optical communication systems available in the laboratory were fabricated by thermally fusing into intimate contact. The coupling factor ( connect inputs and outputs. In this experiment we will use two couplers within the setup: a 50/50 coupler immediately after the laser source to split the optical signal into the two branches (the upper branches simulating the data flow and the lower one to be phase modulated by the RF tone); 80/20 coupler between the emitter side and the monitoring point in order to achieve the amplitude level difference between signals of both branches. 4.3.1.2 Laser HP 83424A This instrument (Figure 4.19 require wavelength tuning and where its frequencies margin is contained within the laser’s supportable bandwidth. This is why it can of the modulator. This laser does not have a power regulator at the output, so that the power provided h as a constant value (see table 4.1 In this experiment, the HP 83424 suppression setup in order to heter carrier and the sidebands are displaced to a frequency range supportable by the spectrum analyzer. The most relevant technical features of New methods for measuring and monitoring chromatic dispersion in optical communication systems available in the laboratory were fabricated by thermally fusing the fibers so that their cores get into intimate contact. The coupling factor ( ) is reached by using different fiber lengths to experiment we will use two couplers within the setup: a 50/50 coupler immediately after the laser source to split the optical signal into the two branches (the upper branches simulating the data flow and the lower one to be phase modulated by the RF tone); between the emitter side and the monitoring point in order to achieve the amplitude level difference between signals of both branches. Figure 4.18 Optical Coupler 4.19 ) can be used as a light source in measurements which do not and where its frequencies margin is contained within the laser’s This is why it can be used for instance to obtain the Transfer Functions This laser does not have a power regulator at the output, so that the power as a constant value (see table 4.1 ). In this experiment, the HP 83424 A will be used as a secondary light source in suppression setup in order to heter odyne the RF tone phase modulated signal, so that the carrier and the sidebands are displaced to a frequency range supportable by the Figure 4.19 HP 83424A The most relevant technical features of HP 83424A are shown in table 4.1. New methods for measuring and monitoring chromatic dispersion in optical communication systems 88 fibers so that their cores get ) is reached by using different fiber lengths to experiment we will use two couplers within the setup: a 50/50 coupler immediately after the laser source to split the optical signal into the two branches (the upper branches simulating the data flow and the lower one to be phase modulated by the RF tone); and a between the emitter side and the monitoring point in order to achieve the can be used as a light source in measurements which do not and where its frequencies margin is contained within the laser’s Transfer Functions This laser does not have a power regulator at the output, so that the power will be used as a secondary light source in the carrier odyne the RF tone phase modulated signal, so that the carrier and the sidebands are displaced to a frequency range supportable by the electrical
Asymmetric modulation bias-controlled method - suppressed carrier 89 Table 4.1 HP 83424A Laser features 4.3.1.3 Agilent Spectrum Analyzer In this experiment all measurements will be obtained by using an Agilent super heterodyne Spectrum Analyzer. This device will display the spectrum components of the modulated signal (sidebands and carrier), so that we can manually cancel out any of these components by just adjusting the bias voltage (in the dispersion measurement experiment) or RF signal (in the carrier suppression experiment). Since this device is an electrical Spectrum Analyzer, we will have to optically heterodyne the phase modulated optical signal with the carrier from an additional laser such that the spectral difference between both lasers is contained within the SA frequency range. Thus, we will be recover the downconverted signal with a detector and display it on the SA to carry out measurements. It also provides an electrical output with enough power to be used as a RF source in the phase modulation process. Figure 4.20 HP Agilent Spectrum Analyzer HP 83424 A Laser Optical BW 1553 nm Optical Power 3 dBm Type of connector FC/UPC
New methods for measuring and monitoring chromatic dispersion in optical communication systems 96 We can see from the dispersion value obtained that even when we have approximated fairly well to the nominal value (which is the best reference we have about FBG real dispersion value),it is not as good as in the ABCM experiment. This fact may be because we are not working under a small signal condition, that is, there is not enough difference level between the sidebands and the carrier with data. Thus, to solve this issue we should use a phase modulator with the output connected to a 80/20 coupler to yield a significant amplitude difference between the phase modulated signal and the upper optical carrier. Therefore, the optimum setup for this experiment should be the one shown in Figure 4.26. Figure 4.26 Optimun ABCM –SC Setup (not implemented) Electrical signal Optical signal
Asymmetric modulation bias-controlled method - suppressed carrier 97 5. CONCLUSIONS AND FUTURE LINES We can state that all the objectives specified in chapter 1 have been accomplished along the chapters of this PFC, and, as happens with all new and innovative proposals, some new studying topics and possible applications emerged from this study. The main purpose of the project was to introduce two new methods for measuring chromatic dispersion: ABCM and ABCM – SC, therefore, the conclusions will be organized according to the chapters which contemplate each method. Chapter 3. Asymmetric Modulation Bias Controlled Method (ABCM) ABCM was introduced as a solid alternative for conventional RF tone based dispersion measurement techniques. We specifically analyzed the method’s close relation with Peucheret’s (calculates dispersion from the amplitude term), highlighting the improved features of ABCM, specially the fact of replacing the RF sweep by a bias voltage sweep, allowing free choice of the RF frequency which is a fundamental parameter in the dispersion measurement. Bias voltage was identified as a key handling parameter in dispersion measurement, taking advantage of the fundamental role acquired in RF tone modulation by using a Mach-Zehnder in asymmetric configuration. We were able to obtain a direct expression to calculate chromatic dispersion, (40). We verified that through this expression both the magnitude and sign of dispersion can be determined. Within the zero-amplitude Bias obtaining process, we realized how the combined performance of “moving zeros” (contain dispersion information) together with “fixed zeros” (serve as reference) yield a self-referenced measurement system. In terms of accuracy in the measurements, the VPI simulator helped us to determine the best operation conditions for the most relevant parameters involved. The following table summarizes the study of all these parameters: Parameter Features RF Frequency • Establishes an interdependence with Bias resolution. • As it increases, the system is able to measure smaller dispersion values (better resolution) but smaller maximum dispersion value • The acceptable range starts from 1.5 GHz (ideal conditions) • From a practical viewpoint, if too high a poorer approximation of the local D is obtained RF Amplitude • Must be kept under a small signal condition • The acceptable range ends at 0.8 V (ideal conditions). • From a practical viewpoint, If too low we do not get a enough dip’s definition Nominal Dispersion • There is no restriction for the total amount of dispersion to be measured. • Accuracy just depends on Bias Resolution
New methods for measuring and monitoring chromatic dispersion in optical communication systems 98 In the experimental section we verified that the accuracy reached by ABCM under real laboratory conditions is acceptable; however, we notice that the calibration of the system is extremely important, since small variations of the m or the zero-amplitude bias represent important variations in the D value obtained. Chapter 4. Asymmetric Modulation Bias Controlled Method with Suppressed Carrier (ABCM - SC) We redefined successfully the setup of ABCM to adapt it to a real time dispersion monitoring environment, and in this purpose we had to challenge some of RF tone based measuring methods conventional properties: • The RF tone amplitude was out of the small signal condition range, as we needed to reach a value near the 20 dBm to cancel out the optical carrier according to Bessel Functions theory. • The tone addition modulation was a phase modulation instead of an intensity modulation. • The system required the determination of the bias required to cancel the detected first and second harmonics to calculate chromatic dispersion. The difference in the bias required to cancel each one of the harmonics gives the ABCM –SC the selfreference feature. The small signal requirement to yield significant a level difference between the carrier with modulated data and the phase modulated signal was achieved by including optical couplers within the setup. One of the advantages of ABCM – SC is the fact of isolating the carrier suppression and the dispersion measurement procedures in the emitter side and the monitoring point respectively, simplifying the support and failures detection tasks. The main features of the parameters studied in the simulation section for ABCM - SC are exposed in the following table: Parameter Features RF Frequency • Establishes interdependence with Bias resolution. • As it increases, the system is able to measure smaller dispersion values(better resolution) but smaller maximum dispersion value • The acceptable range starts from 0.8 GHz (ideal conditions) • From a practical viewpoint, if too high a poorer approximation of D is obtained RF Amplitude • Must be set according to the Modulator’s m value • Establishes a trade-off between alteration of data (carrier suppression) and accuracy. Nominal Dispersion • There is no restriction for the total amount of dispersion to be measured. • Accuracy just depends on Bias Resolution Coupling factor • Lower edge located around 0.8 (for the data signal) • Upper values (bigger than 0.9) are dismissed due to inefficiency issues.
Conclusions and future lines 99 Finally, the experimental section has verified the feasibility of the ABCM-SC. Future Lines The ABCM has been proposed as a low-cost chromatic dispersion measurement system. Here we have experimentally proven its validity in a setup which has included a costly vectorial network analyzer. As a future line it is proposed to setup a simplified low-cost system using mixers and low-cost detectors and to explore the possibility of building an integrated low-cost ABCM measurement system. To study ABCM – SC considering the transmission of real intensity modulated data and to analyze some key parameters related like BER, SNR, etc. To automate both methods exposed by a software application with a graphical interface, to make it more suitable to final users.
New methods for measuring and monitoring chromatic dispersion in optical communication systems 100 6. ANNEX • Matlab Program used in section 3.3.2.1 to obtain the Transfer Function of a Modulator function varargout = fun_trasf(varargin) 2 % FUN_TRASF M-file for fun_trasf.fig 3 % FUN_TRASF, by itself, creates a new FUN_TRASF or raises the existing 4 % singleton*. 5 % 6 % H = FUN_TRASF returns the handle to a new FUN_TRASF or the handle to 7 % the existing singleton*. 8 % 9 % FUN_TRASF('CALLBACK',hObject,eventData,handles,...) calls the local 10 % function named CALLBACK in FUN_TRASF.M with the given input arguments. 11 % 12 % FUN_TRASF('Property','Value',...) creates a new FUN_TRASF or raises the 13 % existing singleton*. Starting from the left, property value pairs are 14 % applied to the GUI before fun_trasf_OpeningFcn gets called. An 15 % unrecognized property name or invalid value makes property application 16 % stop. All inputs are passed to fun_trasf_OpeningFcn via varargin. 17 % 18 % *See GUI Options on GUIDE's Tools menu. Choose "GUI allows only one 19 % instance to run (singleton)". 20 % 21 % See also: GUIDE, GUIDATA, GUIHANDLES 22 23 % Edit the above text to modify the response to help fun_trasf 24 25 % Last Modified by GUIDE v2.5 12-Jan-2010 17:06:47 26 27 % Begin initialization code - DO NOT EDIT 28 gui_Singleton = 1; 29 gui_State = struct('gui_Name', mfilename, ... 30 'gui_Singleton', gui_Singleton, ... 31 'gui_OpeningFcn', @fun_trasf_OpeningFcn, ... 32 'gui_OutputFcn', @fun_trasf_OutputFcn, ... 33 'gui_LayoutFcn', [] , ... 34 'gui_Callback', []); 35 if nargin && ischar(varargin{1}) 36 gui_State.gui_Callback = str2func(varargin{1}); 37 end 38 39 if nargout 40 [varargout{1:nargout}] = gui_mainfcn(gui_State, varargin{:}); 41 else 42 gui_mainfcn(gui_State, varargin{:}); 43 end 44 % End initialization code - DO NOT EDIT 45 46 47 % --- Executes just before fun_trasf is made visible. 48 function fun_trasf_OpeningFcn(hObject, eventdata, handles, varargin) 49 % This function has no output args, see OutputFcn. 50 % hObject handle to figure 51 % eventdata reserved - to be defined in a future version of MATLAB 52 % handles structure with handles and user data (see GUIDATA) 53 % varargin command line arguments to fun_trasf (see VARARGIN) 54 55 % Choose default command line output for fun_trasf 56 handles.output = hObject;
Annex 101 12/02/10 18:35 C:\Users\cristhian86\Downloads\Fiber-Test\fun_trasf.m 2 of 8 57 58 % Update handles structure 59 guidata(hObject, handles); 60 61 imagen = imread( 'optic_fiber.jpg' ); 62 axes( handles.axes3 ); 63 image( imagen ); 64 axis off; 65 66 % UIWAIT makes fun_trasf wait for user response (see UIRESUME) 67 % uiwait(handles.figure1); 68 69 70 % --- Outputs from this function are returned to the command line. 71 function varargout = fun_trasf_OutputFcn(hObject, eventdata, handles) 72 % varargout cell array for returning output args (see VARARGOUT); 73 % hObject handle to figure 74 % eventdata reserved - to be defined in a future version of MATLAB 75 % handles structure with handles and user data (see GUIDATA) 76 77 % Get default command line output from handles structure 78 varargout{1} = handles.output; 79 80 81 % --- Executes on button press in unidaddBm. 82 function unidaddBm_Callback(hObject, eventdata, handles) 83 % hObject handle to unidaddBm (see GCBO) 84 % eventdata reserved - to be defined in a future version of MATLAB 85 % handles structure with handles and user data (see GUIDATA) 86 87 % Hint: get(hObject,'Value') returns toggle state of unidaddBm 88 89 90 % --- Executes on button press in unidaduW. 91 function unidaduW_Callback(hObject, eventdata, handles) 92 % hObject handle to unidaduW (see GCBO) 93 % eventdata reserved - to be defined in a future version of MATLAB 94 % handles structure with handles and user data (see GUIDATA) 95 96 % Hint: get(hObject,'Value') returns toggle state of unidaduW 97 98 99 % --- Executes on button press in Ayuda. 100 function Ayuda_Callback(hObject, eventdata, handles) 101 % hObject handle to Ayuda (see GCBO) 102 % eventdata reserved - to be defined in a future version of MATLAB 103 % handles structure with handles and user data (see GUIDATA) 104 105 %Cargamos la imagen desde LA CARPETA WORK DEL MATLAB!! 106 %uiopen('C:\Documents and Settings\Administrador\Escritorio\TFC ARNAU_PATRI\GUI_Arnau_Patri\ayuda_fun_transf.fig') 107 h=figure(ayuda_fun_transf); 108 109 110 %imagen = imread( 'ayuda_fun_transf.jpg' ); 111 %axes( handles.axes2 ); 12/02/10 18:35 C:\Users\cristhian86\Downloads\Fiber-Test\fun_trasf.m 3 of 8 112 %image( imagen ); 113 %axis off; 114 115 %open ayuda_fun_transf.fig
New methods for measuring and monitoring chromatic dispersion in optical communication systems 102 116 117 function VbiasIn_Callback(hObject, eventdata, handles) 118 % hObject handle to VbiasIn (see GCBO) 119 % eventdata reserved - to be defined in a future version of MATLAB 120 % handles structure with handles and user data (see GUIDATA) 121 122 % Hints: get(hObject,'String') returns contents of VbiasIn as text 123 % str2double(get(hObject,'String')) returns contents of VbiasIn as a double 124 % global VSTART; 125 % global vstart; 126 %VSTART = str2double(get(handles.VbiasIn,'String')); 127 %vstart = str2double(VSTART); 128 %handles.VbiasIn = vstart; 129 %guidata(hObject,handles); 130 131 132 % --- Executes during object creation, after setting all properties. 133 function VbiasIn_CreateFcn(hObject, eventdata, handles) 134 % hObject handle to VbiasIn (see GCBO) 135 % eventdata reserved - to be defined in a future version of MATLAB 136 % handles empty - handles not created until after all CreateFcns called 137 138 % Hint: edit controls usually have a white background on Windows. 139 % See ISPC and COMPUTER. 140 if ispc && isequal(get(hObject,'BackgroundColor'), get (0,'defaultUicontrolBackgroundColor')) 141 set(hObject,'BackgroundColor','white'); 142 end 143 144 145 146 function VbiasFi_Callback(hObject, eventdata, handles) 147 % hObject handle to VbiasFi (see GCBO) 148 % eventdata reserved - to be defined in a future version of MATLAB 149 % handles structure with handles and user data (see GUIDATA) 150 151 % Hints: get(hObject,'String') returns contents of VbiasFi as text 152 % str2double(get(hObject,'String')) returns contents of VbiasFi as a double 153 % global VSTOP; 154 % global vstop; 155 % VSTOP = get(hObject,'String'); 156 % vstop = str2double(VSTOP); 157 % handles.VbiasFi = vstop; 158 % guidata(hObject,handles); 159 160 161 % --- Executes during object creation, after setting all properties. 162 function VbiasFi_CreateFcn(hObject, eventdata, handles) 163 % hObject handle to VbiasFi (see GCBO) 164 % eventdata reserved - to be defined in a future version of MATLAB 165 % handles empty - handles not created until after all CreateFcns called 166 12/02/10 18:35 C:\Users\cristhian86\Downloads\Fiber-Test\fun_trasf.m 4 of 8 167 % Hint: edit controls usually have a white background on Windows. 168 % See ISPC and COMPUTER. 169 if ispc && isequal(get(hObject,'BackgroundColor'), get (0,'defaultUicontrolBackgroundColor')) 170 set(hObject,'BackgroundColor','white'); 171 end 172 173 174
Annex 103 175 function Resolucion_Callback(hObject, eventdata, handles) 176 % hObject handle to Resolucion (see GCBO) 177 % eventdata reserved - to be defined in a future version of MATLAB 178 % handles structure with handles and user data (see GUIDATA) 179 180 % Hints: get(hObject,'String') returns contents of Resolucion as text 181 % str2double(get(hObject,'String')) returns contents of Resolucion as a double 182 % global VPASO; 183 % global vpaso; 184 % VPASO = get(hObject,'String'); 185 % vpaso = str2double(VPASO); 186 % handles.Resolucion = vpaso; 187 % guidata(hObject,handles); 188 189 190 % --- Executes during object creation, after setting all properties. 191 function Resolucion_CreateFcn(hObject, eventdata, handles) 192 % hObject handle to Resolucion (see GCBO) 193 % eventdata reserved - to be defined in a future version of MATLAB 194 % handles empty - handles not created until after all CreateFcns called 195 196 % Hint: edit controls usually have a white background on Windows. 197 % See ISPC and COMPUTER. 198 if ispc && isequal(get(hObject,'BackgroundColor'), get (0,'defaultUicontrolBackgroundColor')) 199 set(hObject,'BackgroundColor','white'); 200 end 201 202 203 function[Potencia]=HP8153A_pow1() 204 205 %global HP8153A_pow1; 206 207 % Esta funcion entrega la potencia del multimetro HP8153A en Watts 208 209 % Se crea un objeto gpib 210 multimeter=gpib('ni' , 0, 22); 211 212 % Se abre el objeto 213 fopen(multimeter); 214 215 % Se pide la identicacion del instrumento 216 fprintf(multimeter, '*idn?'); 217 instrument=fscanf(multimeter); 218 219 % Se configura el instrumento para que realize las mediciones en Watts 12/02/10 18:35 C:\Users\cristhian86\Downloads\Fiber-Test\fun_trasf.m 5 of 8 220 %fprintf(multimeter,'SENS2:POW:UNIT W') 221 222 %Se toman tres mediciones de potencia y se promedian 223 fprintf(multimeter, 'READ:pow?') 224 Potencia1=fscanf(multimeter,'%g'); 225 %Pasamos la medida de dBm a mW: 226 PmW1=10^(Potencia1/10); 227 228 fprintf(multimeter, 'READ:pow?') 229 Potencia2=fscanf(multimeter,'%g'); 230 %Pasamos la medida de dBm a mW: 231 PmW2=10^(Potencia2/10); 232 233 fprintf(multimeter, 'READ:pow?')
New methods for measuring and monitoring chromatic dispersion in optical communication systems 104 234 Potencia3=fscanf(multimeter,'%g'); 235 %Pasamos la medida de dBm a mW: 236 PmW3=10^(Potencia3/10); 237 238 %************************************************************************** 239 %************************************************************************** 240 241 %AMB EL RADIOBUTTON HEM DACONSEGUIR COMENTAR O DESCOMENTAR AQUESTES LÍNIES, 242 %NECESITEM AJUDA DE LA CONCHI/OLGA YA! 243 244 Potencia=(PmW1+PmW2+PmW3)/3; %Aqui tenemos la potencia en uW. 245 246 %Pasamos la Potencia de mW a dBm: 247 %Potencia=10*log10(Potencia); 248 249 250 fclose(multimeter) 251 delete(multimeter) 252 clear multimeter 253 254 % --- Executes on button press in Ejecutar. 255 function Ejecutar_Callback(hObject, eventdata, handles) 256 % hObject handle to Ejecutar (see GCBO) 257 % eventdata reserved - to be defined in a future version of MATLAB 258 % handles structure with handles and user data (see GUIDATA) 259 260 %function[]=ftrans_mod_lineal() 261 % Esta funcion grafica la funcion de transferencia de un modulador óptico. 262 % Se sirve del HP8153A como medidor de potencia y del AG34970A como fuente 263 % de tensión de bias. 264 265 clc 266 clear all 267 268 data=guidata(gcbo); 269 vstart = str2double(get(data.VbiasIn, 'String')); 270 vstop=str2double(get(data.VbiasFi, 'String')); 271 vpaso=str2double(get(data.Resolucion, 'String')); 272 273 274 %Creamos un fichero para guardar los datos 275 [fitxer,path]=uiputfile('*.dat','Guardar'); 12/02/10 18:35 C:\Users\cristhian86\Downloads\Fiber-Test\fun_trasf.m 6 of 8 276 fitxer=sprintf('%s%s',path,fitxer); 277 fi=fopen(fitxer,'wt' ); 278 279 %Se piden los datos del rango de tensiones y el paso para el voltaje de bias 280 %VSTART = get(hObject,'String'); 281 282 %vstart=str2num(VSTART); 283 %vstart=VSTART; 284 fprintf(fi, 'Vbias inicial (V):\t'); 285 fprintf(fi, '%g\n',vstart); 286 287 288 %vstop=str2num(VSTOP); 289 %vstop=VSTOP; 290 fprintf(fi, 'Vbias final (V):\t'); 291 fprintf(fi, '%g\n',vstop); 292 293 294 %vpaso=str2num(VPASO);
Annex 105 295 %vpaso=VPASO; 296 vpaso=vpaso*1e-3; 297 fprintf(fi, 'resolucion (V):\t'); 298 fprintf(fi, '%g\n\n',vpaso); 299 300 %Creamos un contador para el vector de datos adquiridos 301 j=1; 302 fprintf(fi, 'Vbias (V)\tPout (μW)\n'); 303 304 %Bucle de adquisición de datos 305 for i=vstart:vpaso:vstop 306 307 %********************************************* 308 %DC(i); 309 s1=serial('COM1' ); 310 311 fopen(s1); 312 313 % fprintf(s1, '*IDN?'); 314 % nombre = fscanf(s1) 315 v=i; 316 317 fprintf(s1, 'CHAN1:VOLT %g ;CURR 1.0',v); 318 pause(2) 319 fprintf(s1, '*VOLT?'); 320 voltage = fscanf(s1) 321 322 fclose(s1); 323 delete(s1); 324 clear s1; 325 326 %********************************************AJUDA OLGA!!!!! 327 %Aqui pasem de mW a uW, amb els dBm també multipliquem igual????? 328 329 pause(5) 330 potencia = HP8153A_pow1; % Medicion de potencia en Watts (W) 331 %potencia = potencia*1e6; % Medicion de potencia en Micro Watts (μW) 12/02/10 18:35 C:\Users\cristhian86\Downloads\Fiber-Test\fun_trasf.m 7 of 8 332 potencia = potencia*1e3; % Medicion de potencia en Micro Watts (μW) 333 pot(j) = potencia; 334 j=j+1; 335 fprintf(fi,'%g\t',i); 336 fprintf(fi,'%g\n',potencia); 337 end 338 339 st=fclose(fi); 340 341 %En el vector "pot" tenemos las medidas 342 %Se grafica las funcion de transferencia del Modulador 343 vbias=[vstart:vpaso:vstop]; 344 %close all 345 figure 346 plot(vbias,pot) 347 title('Función de transferencia del modulador'); 348 zoom on 349 ylabel('Pout (μW)'); 350 xlabel('Vbias (V)'); 351 352 353 % --- Executes on button press in Limpiar_Variables. 354 function Limpiar_Variables_Callback(hObject, eventdata, handles) 355 % hObject handle to Limpiar_Variables (see GCBO)
New methods for measuring and monitoring chromatic dispersion in optical communication systems 112 54 end 55 56 dispersion 57 58 figure(1) 59 60 plot(Dnom,null_bias) 61 title('Null Bias (n=0) vs Nominal Dispersion' ); 62 figure(2) 63 64 plot(Dnom,dispersion) 65 title('Dispersion vs Nominal Dispersion');
Annex 113 • Matlab Program to obtain the Null Amplitude Bias Difference vs RF frequency and Dispersion vs RF frequency graphics in section 4.2.2.1 clc 2 clear all 3 close all 4 5 %--------------------------------------- The files are loaded ------------------------------------- 6 load monRFsweepv1.txt 7 load monRFsweepv2.txt 8 9 %------------------------------------------ Simulation data --------------------------------------- 10 Freq_Laser=192.4e12; 11 Bias_Resolution=0.01; 12 Volth1_I=-3.5; 13 Volth1_F=0; 14 Volth2_I=-1.75; 15 Volth2_F=1.75; 16 Vpi=3.5; 17 18 19 %--------------------------------------- Frequency Resolution ---------------------------------- 20 Freq=(200e6:200e6:6.2e9); 21 Delta_Freq=200e6; 22 23 24 %----------------------------------------- Amplitude minimums -------------------------------- 25 AMP1=monRFsweepv1(:,2); 26 a1=4; 27 aux1=(Volth1_F-Volth1_I)/Bias_Resolution; 28 total1 = (Volth2_F-Volth1_I)/Bias_Resolution; 29 b1=aux1+1; % Number of steps of the bias sweep 30 31 bias1=monRFsweepv1(1:b1,1); 32 bias1 33 null_bias1=zeros([(Freq(length(Freq))-Freq(1))/(Delta_Freq),1]); 34 35 for i=1:(((Freq(length(Freq))-Freq(1))/(Delta_Freq))+1) 36 [minimum,index]= min(AMP1(a1:b1)); 37 null_bias1(i)=bias1(index+3); 38 a1=b1+total1-aux1+4; 39 b1=a1+aux1-3; 40 end 41 42 null_bias1 43 44 %----------------------------------------- Amplitude minimums -------------------------------- 45 AMP2=monRFsweepv2(:,2); 46 47 aux2=(Volth2_F-Volth2_I)/Bias_Resolution; 48 total2 = (Volth2_F-Volth1_I)/Bias_Resolution; 49 a2=total2-aux2+4; 50 b2=total2+1; % Number of steps of the bias sweep 51 14/02/10 11:24 C:\MATLAB7\work\mon_RFsweep.m 2 of 2 52 bias2=monRFsweepv2(total2-aux2+1:b2,1); 53 bias2
New methods for measuring and monitoring chromatic dispersion in optical communication systems 114 54 null_bias2=zeros([(Freq(length(Freq))-Freq(1))/(Delta_Freq),1]); 55 56 for i=1:(((Freq(length(Freq))-Freq(1))/(Delta_Freq))+1) 57 [minimum,index]= min(AMP2(a2:b2)); 58 null_bias2(i)=bias2(index+3); 59 a2=b2+total2-aux2+4; 60 b2=a2+aux2-3; 61 end 62 63 null_bias2 64 65 66 67 %-------------------------------------- Dispersion in ps/nm -------------------------------------- 68 69 c=3e8; 70 Wlength = c/Freq_Laser; 71 72 dispersion=zeros([(Freq(length(Freq))-Freq(1))/(Delta_Freq),1]); 73 74 for i=1:(((Freq(length(Freq))-Freq(1))/(Delta_Freq))+1) 75 dispersion(i)=(1/2-(null_bias2(i)-null_bias1(i))/Vpi)*(c/(3*Wlength*Wlength*Freq (i)*Freq(i))); 76 77 end 78 79 dispersion 80 81 figure 82 83 plot(Freq,null_bias2-null_bias1) 84 title('Delta Null Bias vs RF Frequency'); 85 figure 86 87 plot(Freq,dispersion) 88 title('Dispersion vs RF Frequency');
Annex 115 • Matlab Program to obtain the Null Amplitude Bias Difference vs RF amplitude and Dispersion vs RF amplitude graphics in section 4.2.2.2 1 clc 2 clear all 3 close all 4 5 %--------------------------------------- The files are loaded ------------------------------------- 6 load ampv1.txt 7 load ampv2.txt 8 9 %------------------------------------------ Simulation data --------------------------------------- 10 Freq_Laser=192.4e12; 11 Bias_Resolution=0.01; 12 Volth1_I=-3.5; 13 Volth1_F=0; 14 Volth2_I=-1.75; 15 Volth2_F=1.75; 16 Vpi=3.5; 17 18 19 %--------------------------------------- Frequency Resolution ---------------------------------- 20 Amp=(0.12:0.16:4.12); 21 Delta_Amp=0.16; 22 23 24 %----------------------------------------- Amplitude minimums -------------------------------- 25 AMP1=ampv1(:,1); 26 a1=4; 27 aux1=(Volth1_F-Volth1_I)/Bias_Resolution; 28 total1 = (Volth2_F-Volth1_I)/Bias_Resolution; 29 b1=aux1+1; % Number of steps of the bias sweep 30 31 bias1=ampv1(1:b1,2); 32 bias1 33 null_bias1=zeros([(Amp(length(Amp))-Amp(1))/(Delta_Amp),1]); 34 35 for i=1:(((Amp(length(Amp))-Amp(1))/(Delta_Amp))+1) 36 [minimum,index]= min(AMP1(a1:b1)); 37 null_bias1(i)=bias1(index+3); 38 a1=b1+total1-aux1+4; 39 b1=a1+aux1-3; 40 end 41 42 null_bias1 43 44 %----------------------------------------- Amplitude minimums -------------------------------- 45 AMP2=ampv2(:,1); 46 47 aux2=(Volth2_F-Volth2_I)/Bias_Resolution; 48 total2 = (Volth2_F-Volth1_I)/Bias_Resolution; 49 a2=total2-aux2+4; 50 b2=total2+1; % Number of steps of the bias sweep 51 14/02/10 11:22 C:\MATLAB7\work\mon_Ampsweep.m 2 of 2 52 bias2=ampv2(total2-aux2+1:b2,2); 53 bias2
New methods for measuring and monitoring chromatic dispersion in optical communication systems 116 54 null_bias2=zeros([(Amp(length(Amp))-Amp(1))/(Delta_Amp),1]); 55 56 for i=1:(((Amp(length(Amp))-Amp(1))/(Delta_Amp))+1) 57 [minimum,index]= min(AMP2(a2:b2)); 58 null_bias2(i)=bias2(index+3); 59 a2=b2+total2-aux2+4; 60 b2=a2+aux2-3; 61 end 62 63 null_bias2 64 65 66 67 %-------------------------------------- Dispersion in ps/nm -------------------------------------- 68 69 c=3e8; 70 Wlength = c/Freq_Laser; 71 RFfreq = 2e9; 72 73 dispersion=zeros([(Amp(length(Amp))-Amp(1))/(Delta_Amp),1]); 74 75 for i=1:(((Amp(length(Amp))-Amp(1))/(Delta_Amp))+1) 76 dispersion(i)=(1/2-(null_bias2(i)-null_bias1(i))/Vpi)*(c/ (3*Wlength*Wlength*RFfreq*RFfreq)); 77 78 end 79 80 dispersion 81 82 figure 83 84 plot(Amp,null_bias2-null_bias1) 85 title('Delta Null Bias vs RF Amplitude'); 86 figure 87 88 plot(Amp,dispersion) 89 title('Dispersion vs RF Amplitude');
Annex 117 • Matlab Program to obtain the Null Amplitude Bias Difference vs Nominal dispersion and Dispersion vs Nominal Dispersion graphics in section 4.2.2.3 1 clc 2 clear all 3 close all 4 5 %--------------------------------------- The files are loaded ------------------------------------- 6 load monDsweepv1.txt 7 load monDsweepv2.txt 8 9 %------------------------------------------ Simulation data --------------------------------------- 10 Freq_Laser=192.4e12; 11 Bias_Resolution=0.01; 12 Volth1_I=-3.5; 13 Volth1_F=0; 14 Volth2_I=-1.75; 15 Volth2_F=1.75; 16 Vpi=3.5; 17 18 19 %--------------------------------------- Frequency Resolution ---------------------------------- 20 L=(0:5000:160000); 21 Delta_L=5000; 22 Dnom=L*17e-6; 23 Delta_D=Delta_L*17e-6; 24 25 26 %----------------------------------------- Amplitude minimums -------------------------------- 27 AMP1=monDsweepv1(:,2); 28 a1=4; 29 aux1=(Volth1_F-Volth1_I)/Bias_Resolution; 30 total1 = (Volth2_F-Volth1_I)/Bias_Resolution; 31 b1=aux1+1; % Number of steps of the bias sweep 32 33 bias1=monDsweepv1(1:b1,1); 34 bias1 35 null_bias1=zeros([(Dnom(length(Dnom))-Dnom(1))/(Delta_D),1]); 36 37 for i=1:(((Dnom(length(Dnom))-Dnom(1))/(Delta_D))+1) 38 [minimum,index]= min(AMP1(a1:b1)); 39 null_bias1(i)=bias1(index+3); 40 a1=b1+total1-aux1+4; 41 b1=a1+aux1-3; 42 end 43 44 null_bias1 45 46 %----------------------------------------- Amplitude minimums -------------------------------- 47 AMP2=monDsweepv2(:,2); 48 49 aux2=(Volth2_F-Volth2_I)/Bias_Resolution; 50 total2 = (Volth2_F-Volth1_I)/Bias_Resolution; 51 a2=total2-aux2+4; 14/02/10 11:23 C:\MATLAB7\work\mon_Dsweep.m 2 of 2 52 b2=total2+1; % Number of steps of the bias sweep 53
New methods for measuring and monitoring chromatic dispersion in optical communication systems 118 54 bias2=monDsweepv2(total2-aux2+1:b2,1); 55 bias2 56 null_bias2=zeros([(Dnom(length(Dnom))-Dnom(1))/(Delta_D),1]); 57 58 for i=1:(((Dnom(length(Dnom))-Dnom(1))/(Delta_D))+1) 59 [minimum,index]= min(AMP2(a2:b2)); 60 null_bias2(i)=bias2(index+3); 61 a2=b2+total2-aux2+4; 62 b2=a2+aux2-3; 63 end 64 65 null_bias2 66 67 68 69 %-------------------------------------- Dispersion in ps/nm -------------------------------------- 70 71 c=3e8; 72 Wlength = c/Freq_Laser; 73 RFfreq = 2e9; 74 75 dispersion=zeros([(Dnom(length(Dnom))-Dnom(1))/(Delta_D),1]); 76 77 for i=1:(((Dnom(length(Dnom))-Dnom(1))/(Delta_D))+1) 78 dispersion(i)=(1/2-(null_bias2(i)-null_bias1(i))/Vpi)*(c/ (3*Wlength*Wlength*RFfreq*RFfreq)); 79 80 end 81 82 dispersion 83 84 figure 85 86 plot(Dnom,null_bias2-null_bias1) 87 title('Delta Null Bias vs Nominal D' ); 88 figure 89 90 plot(Dnom,dispersion) 91 title('Dispersion vs Nominal D');
Annex 119 • Matlab Program to obtain the Null Amplitude Bias Difference vs Coupling factor and Dispersion vs Coupling Factor graphics in section 4.2.2.4 1 clc 2 clear all 3 close all 4 5 %--------------------------------------- The files are loaded ------------------------------------- 6 load monAlphasweepv1.txt 7 load monAlphasweepv2.txt 8 9 %------------------------------------------ Simulation data --------------------------------------- 10 Freq_Laser=192.4e12; 11 Bias_Resolution=0.01; 12 Volth1_I=-3.5; 13 Volth1_F=0; 14 Volth2_I=-1.75; 15 Volth2_F=1.75; 16 Vpi=3.5; 17 18 19 %--------------------------------------- Frequency Resolution ---------------------------------- 20 Alpha=(0.51:0.02:0.99); 21 Delta_Alpha=0.02; 22 23 24 %----------------------------------------- Amplitude minimums -------------------------------- 25 AMP1=monAlphasweepv1(:,2); 26 a1=4; 27 aux1=(Volth1_F-Volth1_I)/Bias_Resolution; 28 total1 = (Volth2_F-Volth1_I)/Bias_Resolution; 29 b1=aux1+1; % Number of steps of the bias sweep 30 31 bias1=monAlphasweepv1(1:b1,1); 32 bias1 33 null_bias1=zeros([(Alpha(length(Alpha))-Alpha(1))/(Delta_Alpha),1]); 34 35 for i=1:(((Alpha(length(Alpha))-Alpha(1))/(Delta_Alpha))+1) 36 [minimum,index]= min(AMP1(a1:b1)); 37 null_bias1(i)=bias1(index+3); 38 a1=b1+total1-aux1+4; 39 b1=a1+aux1-3; 40 end 41 42 null_bias1 43 44 %----------------------------------------- Amplitude minimums -------------------------------- 45 AMP2=monAlphasweepv2(:,2); 46 47 aux2=(Volth2_F-Volth2_I)/Bias_Resolution; 48 total2 = (Volth2_F-Volth1_I)/Bias_Resolution; 49 a2=total2-aux2+4; 50 b2=total2+1; % Number of steps of the bias sweep 51 14/02/10 11:22 C:\MATLAB7\work\mon_Alphasweep.m 2 of 2
New methods for measuring and monitoring chromatic dispersion in optical communication systems 120 52 bias2=monAlphasweepv2(total2-aux2+1:b2,1); 53 bias2 54 null_bias2=zeros([(Alpha(length(Alpha))-Alpha(1))/(Delta_Alpha),1]); 55 56 for i=1:(((Alpha(length(Alpha))-Alpha(1))/(Delta_Alpha))+1) 57 [minimum,index]= min(AMP2(a2:b2)); 58 null_bias2(i)=bias2(index+3); 59 a2=b2+total2-aux2+4; 60 b2=a2+aux2-3; 61 end 62 63 null_bias2 64 65 66 67 %-------------------------------------- Dispersion in ps/nm -------------------------------------- 68 69 c=3e8; 70 Wlength = c/Freq_Laser; 71 RFfreq = 2e9; 72 73 dispersion=zeros([(Alpha(length(Alpha))-Alpha(1))/(Delta_Alpha),1]); 74 75 for i=1:(((Alpha(length(Alpha))-Alpha(1))/(Delta_Alpha))+1) 76 dispersion(i)=(1/2-(null_bias2(i)-null_bias1(i))/Vpi)*(c/ (3*Wlength*Wlength*RFfreq*RFfreq)); 77 78 end 79 80 dispersion 81 82 figure 83 84 plot(Alpha,null_bias2-null_bias1) 85 title('Delta Null Bias vs Alpha'); 86 figure 87 88 plot(Alpha,dispersion) 89 title('Dispersion vs Alpha' ); Matlab Program to obtain the Transfer Function of a Modulator:
Index of tables 121 7. INDEX OF TABLES Table 3.1. NEW FOCUS 6427 Features. ....................................................................................... 49 Table 3.2. FUJITSU FTM7921ER/052 H74M-5208-062 features. ................................................ 51 Table 3.3. AGERE Systems 2860E features ................................................................................. 53 Table 3.4. CDC-04074 features .................................................................................................... 54 Table 3.5. Dispersion Compensating Fiber features .................................................................... 55 Table 3.6. HP 8753D measurer features ..................................................................................... 56 Table 3.7. HP 8753D signal generator features .......................................................................... 56 Table 3.8. HP 8153A features. ..................................................................................................... 57 Table 3.9 FUJITSU Experimental features.................................................................................... 60 Table 3.10 Optical Power values ................................................................................................. 63 Table 3.11 Measured Dispersion vs Nominal Dispersion for FBG................................................ 65 Table 3.12 Measured Dispersion vs Nominal Dispersion for DCF ................................................ 66 Table 4.1 HP 83424A Laser features ........................................................................................... 89 Table 4.2 Measured Dispersion vs Nominal Dispersion for FBG.................................................. 95