One-dimensional photonic crystals with different termination layer thicknesses and very narrow Bloch surface wave and guided wave based resonances for sensing applications

  Citation: Fort, T.; Kanok, R.; Hlubina, P.; Pokorny, P.; Sobota, J. One-Dimensional Photonic Crystals with Different Termination Layer Thicknesses and Very Narrow Bloch Surface Wave and Guided Wave Based Resonances for Sensing Applications. Photonics 2022,9, 561. https://doi.org/10.3390/ photonics9080561 Received: 4 July 2022 Accepted: 8 August 2022 Published: 10 August 2022 Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. Copyright: © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). photonics hv Article One-Dimensional Photonic Crystals with Different Termination Layer Thicknesses and Very Narrow Bloch Surface Wave and Guided Wave Based Resonances for Sensing Applications Tomas Fort 1,* , Roman Kanok 2,* , Petr Hlubina 2, Pavel Pokorny 1and Jaroslav Sobota 1 1Institute of Scientific Instruments of the Czech Academy of Sciences, Kralovopolska 147, 612 64 Brno, Czech Republic 2Department of Physics, Technical University Ostrava, 17. Listopadu 2172/15, 708 00 Ostrava-Poruba, Czech Republic *Correspondence: [email protected] (T.F.); r[email protected] (R.K.) Abstract: We demonstrate an efficient sensing of both gaseous and aqueous analytes utilizing Bloch surface waves (BSWs) and guided waves (GWs) excited on a truncated one-dimensional photonic crystal (1DPhC) composed of six TiO 2 /SiO 2 bilayers with a termination layer of TiO 2 . For the gaseous analytes, we show that 1DPhC can support the GW excited by an s -polarized wave and the theoretical shift of the resonance wavelength is linear for small changes in the analyte refractive index (RI), giving a constant RI sensitivity of 87 nm per RI unit (RIU). In addition, for the aqueous analytes, the GW excited by s -polarized and BSW by p -polarized waves can be resolved and exploited for sensing applications. We compare two designed and realized 1DPhCs with termination layer thicknesses of 60 nm and 50 nm, respectively, and show experimentally the differences in their very narrow reflectance and phase responses. An RI sensitivity and figure of merit as high as 544.3 nm/RIU and 303 RIU −1 , respectively, are obtained for the smaller thickness when both s - and p -polarized BSWs are excited. This is the first demonstration of both very deep BSW-based resonances in two orthogonal polarizations and a very narrow resonance in one of them. Keywords: photonic crystal; Bloch surface wave; termination layer; reflectance; phase shift; Kretschmann configuration 1. Introduction One-dimensional photonic crystals (1DPhCs) are structures with a periodic modulation of refractive index (RI) in one spatial dimension. There is an analogy between the propagation of photons in a 1DPhC and the propagation of electrons in a periodic potential of a crystal lattice, and so the concept of band gaps can be adopted [ 1 ]. The photonic band gap determines the range of wavelengths of light that cannot propagate through the infinite 1DPhC. In practice, only the truncated 1DPhC can be prepared, which can be represented by a multilayer dielectric structure (MDS), referred to as a Bragg reflector. Within the range of wavelengths corresponding to the photonic band gap, the Bragg reflectors are highly reflective, but they can also guide waves on their surface—the Bloch surface waves (BSWs). For the excitation of the BSWs, a coupling device has to be used to fulfill the phasematching condition since the tangential component of the wave vector of the BSWs lies beyond a free space light line. A common way is to use the total internal reflection in a glass prism in the Kretschmann configuration that is widely used to excite the surface plasmon resonance (SPR) [ 2 ]. The BSWs show up as a dip in the reflectance spectrum, similar to the SPR, and they also can be exploited in sensing applications. However, contrary to the SPR, narrower resonance dips are related to the BSW since the MDS is composed of low-loss dielectrics, and both s - and p -polarized waves can be used for the BSW excitation. Moreover, the photonic band gap position and width depend on the MDS geometry and materials, and thus can be varied by the fabrication of the MDS so that ultra-large omnidirectional Photonics 2022,9, 561. https://doi.org/10.3390/photonics9080561 https://www.mdpi.com/journal/photonics Photonics 2022,9, 561 2 of 13 photonic band gaps are possible [ 3 ]. The sensors based on the BSWs often use not only a wavelength [ 4 – 11 ], but also angular [ 5 , 11 – 14 ] interrogations. Importantly, sensors utilizing a phase detection have also been demonstrated [15–18]. In this paper, we demonstrate an efficient sensing of both gaseous and aqueous analytes utilizing a MDS composed of 6 TiO 2 /SiO 2 bilayers with a termination layer of TiO 2 . For the gaseous analyte, we show that the proposed structure can support a guided wave (GW) excited by an s -polarized wave. The GW is accompanied by a reflectance minimum (a dip), which theoretically shifts linearly with small changes in the analyte RI. For the designed and realized 1DPhC and aqueous analytes, the BSWs excited by both s and p -polarized waves can be resolved and utilized for sensing applications. We study the effect of the termination layer thickness on the sensor response by a direct comparison of two MDSs differing only by the termination layer thicknesses. The sensor performance is evaluated in terms of the RI sensitivity and also figure of merit (FOM). We show that the MDS with a termination layer thickness of 50 nm shows both higher sensitivity and FOM than the MDS with a termination layer thickness of 60 nm. In addition, one of the MDSs demonstrates for the first time not only very deep BSW-based resonances in two orthogonal polarizations, but also a very narrow resonance in a single polarization. 2. Materials and Methods 2.1. Structures under Study A truncated 1DPhC can be represented by a stack of alternating dielectric layers. For the purpose of this study, two MDSs were prepared, each composed of six TiO 2 /SiO 2 bilayers with a termination layer of TiO 2 . The 1DPhC was inspected by a scanning electron microscope (DualBeam FIB-SEM Helios G4, Thermo Fisher Scientific, Waltham, MA, USA) with images shown in Figure 1. The MDSs differ only in the thickness of the termination layer, which is 60 nm in the first case (MDS 60 ) and 50 nm in the second case (MDS 50 ). The thicknesses of all other TiO 2 and SiO 2 layers are tTiO2= 100 nm and tSiO2= 85 nm, respectively, giving the spatial period Λ=tTiO2+tSiO2= 185 nm. Both MDSs were prepared on a glass substrate by a method of electron beam evaporation; the process is described in detail elsewhere [19]. (a) (b) Figure 1. SEM images of the 1DPhC with overall (a) and detail (b) views. 2.2. Experiment 2.2.1. Experimental Setup We performed two kinds of experiments with the prepared MDSs. First, we measured interference reflectance R45(λ) in the experimental setup shown in Figure 2. During the measurements, one of the MDSs on the glass substrate was attached to a BK7 glass prism (Ealing, Inc., Scotts Valley, CA, USA) using index matching oil (Cargille, nD = 1.516). Using a white light source (halogen lamp HL-2000, Ocean Optics, Orlando, FL, USA), a light Photonics 2022,9, 561 3 of 13 beam was generated and then coupled into an optical fiber and transmitted to a collimating lens. The collimated beam then passed through a linear polarizer (LPVIS050, Thorlabs, Newton, NJ, USA) oriented by the angle γP= 45 ◦ with respect to the plane of incidence and reached the air/prism interface at outer angle of incidence α . The inner angle of incidence θ is given by relation θ(λ) = 60 ◦−sin−1[sin α/nBK7(λ)] , where nBK7(λ) is the wavelength-dependent RI of the glass prism. After reflection from the MDS, the beam passed through a linear analyzer (LPVIS050, Thorlabs, Newton, NJ, USA) oriented by the angle γA=± 45 ◦ with respect to the plane of incidence and it was coupled to a read optical fiber (M15L02, Thorlabs, Newton, NJ, USA) by a microscope objective. As a detector, a compact spectrometer (USB4000, Ocean Optics, Orlando, FL, USA) was used. WLS CL P BC A MO S PC TiO2 TiO2/SiO2 glass substrate 6× α θ detail of the MDS droplet of analyte prism bilayers Figure 2. Experimental setup: a MDS in the Kretschmann configuration; white light source (WLS), collimating lens (CL), polarizer (P), birefringence crystal (BC), analyzer (A), microscope objective (MO), spectrometer (S), personal computer (PC), optical fibers (shown as blue lines). A recorded interference spectrum then followed the equation [9] R±45(λ) = 1 4{Rs(λ) + Rp(λ) + 2qRs(λ)Rp(λ)cos [∆(λ) + δ±]}, (1) where Rs(λ) and Rp(λ) are the spectral reflectances of s - and p -polarized light waves, respectively, ∆(λ) is a phase change between them due to the BSW or GW excitation, and δ± is a phase term related to the orientation of the analyzer ( δ+= 0 for γA= 45 ◦ and δ−=π for γA=− 45 ◦ ). This technique exploits the phase properties of BSWs and GWs to pronounce the related reflectance dips. All measured spectra were normalized with respect to the reflectance Rp(λ)measured for air. Second, we measured an optical phase shift φ(λ) using a spectral interferometric technique. In the measurement, a birefringence quartz prism of thickness 6 mm was included in the experimental setup, which caused an additional phase difference ∆BC(λ) between s - and p -polarized waves. As a result, a spectral interferogram (a channeled spectrum) consisting of fringes could be resolved. Two such interferograms were recorded to determine the phase shift φ(λ) . One for the case when the BSW or GW was generated, given by the overall phase Φ(λ) = ∆BC(λ) + ∆(λ) , including the phase contributions of both the birefringence crystal and BSW or GW, and second for the case when the waves were not generated, given by ΦR(λ) = ∆BC(λ) + ∆R(λ) , where ∆R(λ) is a reference phase term. The reference interferogram was obtained in the setup, not including the MDS. Both interferograms were processed by a windowed Fourier transform [ 18 ] to obtain the overall phases Φ(λ)and ΦR(λ), and then the phase shift φ(λ) = Φ(λ)−ΦR(λ)was calculated. 2.2.2. Analytes We performed measurement for room air (temperature t= 22 ◦ C, relative humidity RH = 30%) to show a possibility of the sensing of low RI analytes. The effect of temperature changes is not considered, even if it is interesting from the point of view of the thermal Photonics 2022,9, 561 4 of 13 stability of the sensor [ 20 , 21 ]. Next, we prepared six aqueous solutions of NaCl with various RIs nD in a range of 1.3331–1.3599, corresponding to NaCl concentration ranging from 0 weight percents (wt%) to approximately 10 wt%. The RI was measured with refractometer AR200 (Reichert, New York, NY, USA) at sodium D line ( λD= 589 nm) at the room temperature. 2.3. Theoretical Analysis Measurements are accompanied by the theoretical analysis. The reflectance was calculated by a transfer matrix method (TMM) [ 22 ], and we included the following dispersion relation for TiO2and SiO2layers [19] n2(λ) = A+Bλ2 λ2−C2, (2) where A , B and C are constants with values A= 2.7655, B= 2.2, C= 0.26524 µ m and A= 1.34836, B= 0.756, C= 0.10683 µ m for TiO 2 and SiO 2 , respectively, and λ is wavelength in µ m. Approximate extinction coefficients of TiO 2 and SiO 2 , kTiO2= 0.0016 and kSiO2=0.00034 were included in the calculations. Dispersion of the water is expressed by the Sellmeier formula [23] n2 w(λ) = 1+ 4 ∑ n=1 Diλ2 λ2−Ei , (3) where Di and λi are constants with values D1= 5.684027565 × 10 −1 , D2=1.726177391 ×10−1, D3= 2.086189578 × 10 −2 , D4= 1.130748688 × 10 −1 , E1= 5.101829712 × 10 −3µ m 2 , E2=1.821153936 ×10−2µm2,E3= 2.620722293 × 10 −2µ m 2 and E4=1.069792721 ×10−2µm2(valid for temperature of 20◦). Both the substrate and the prism are made of BK7 glass, and its dispersion is described by the Sellmeier formula [24] n2 BK7(λ) = 1+ 3 ∑ n=1 Fiλ2 λ2−Gi , (4) where Ei and λi are constants with values F1= 1.03961212, F2= 0.231792344, F3= 1.01046945, G1= 6.00069867 × 10 −3µ m 2 , G2= 2.00179144 × 10 −2µ m 2 , G3= 1.03560653 × 10 2µ m 2 . Finally, we used the RI of air nair =1. 3. Results 3.1. Reflectances for Air and Water First, we measured the reflectance ratio R−45(λ)/Rp(λ) for the MDS 60 , as shown in Figure 3a by the dashed line. In the same figure, we also show the theoretical reflectance ratio for different analyte RIs in a range of 1–1.01 and for the angle of incidence θ= 45.5 ◦ , when the reflectances Rs(λ) and Rp(λ) and the phase difference ∆(λ) are calculated using the transfer matrix method [18]. Photonics 2022,9, 561 5 of 13 640 660 680 700 720 740 0 50 100 150 200 250 300 GWs GWp Wavelength (nm) R−45/Rp(%) n=1.000 n=1.002 n=1.004 n=1.006 n=1.008 n=1.010 724 725 726 5 10 15 20 0.2 0.3 0.4 0.5 0.6 0.24 0.26 0.28 0.3 ¯ β ¯ω (a) (b) Figure 3. ( a ) Theoretical reflectance ratio R−45(λ)/Rp(λ) as a function of wavelength for different RIs of the analyte and the angle of incidence θ= 45.5 ◦(α≈ 22 ◦ ). Experimental result for air is shown by the dashed line. ( b ) Band structure of the 1DPhC for s -polarized wave with dots corresponding to the GWs for air (black) and water (blue), and the surface waves for water (red). Analyzing the theoretical results, both reflectance minima correspond to the guided waves. The narrow one at a wavelength of around 725 nm shifts linearly with the RI and is excited by an s -polarized wave. We support this by a band structure of an infinite 1DPhC composed of TiO 2 /SiO 2 bilayers shown in Figure 3b. The band structure determination is based on solving an eigenvalue problem [ 1 ], giving the dependence of the angular frequency ω on the propagation constant β . We use the reduced quantities ¯ ω=ω c Λ 2π and ¯ β=βΛ 2π and included the dispersion relations and thicknesses of the thin layers specified in the previous section. The yellow regions represent the allowed bands of frequencies, while the white regions represent the photonic band gaps. The black dots located out of the photonic band gap denote the position of the reflectance dips determined for an angle of incidence θ ranging from 43 to 48 ◦ , thus confirming that the appropriate wave is the GW. The dip positions are obtained for a structure containing 100 bilayers of TiO 2 /SiO 2 and including no termination layer. Moreover, we compute an optical field distribution [ 22 ] within the MDS 60 , and it is shown in Figure 4a. The field intensity grows with distance from the substrate and it has its maximum value near the MDS/analyte interface. The shape of the field envelope in the crystal, which differs from the exponential one, is due to the GW [25]. By tracing the dip positions (the resonance wavelengths), we obtain a linear dependence on the RI, as shown in Figure 4b. The sensor response can be characterized in terms of the RI sensitivity defined as Sn=δλR δn, (5) where δλR is change in the resonance wavelength and δn is change in the RI of the analyte. In this case, a constant value of 87 nm per RI unit (RIU) is reached. Next, we introduce figure of merit ( FOM ), which is a parameter that takes into account also a width of the resonance dip and is defined as FOM =DSn FWHM, (6) where FWHM is full width at half maximum of the resonance dip and D is its depth. In this case, for FWHM =5.3 nm and D=0.96, FOM has a value of 15.7 RIU−1. Photonics 2022,9, 561 6 of 13 0 200 400 600 800 1,000 1,200 1,400 1,600 0 20 40 60 80 Distance from substrate interface (nm) Normalized Optical Field Intensity λ= 724.5nm (s-pol.) 1.000 1.002 1.004 1.006 1.008 1.010 724.5 724.7 724.9 725.1 725.3 725.5 Refractive Index (RIU) Wavelength (nm) (a) (b) Figure 4. ( a ) Normalized optical field distribution of s -polarized wave in the MDS 60 for air with the RI n= 1 and the angle of incidence θ= 45.5 ◦ ( α≈ 22 ◦ ). ( b ) Resonance wavelength as a function of analyte RI. 3.2. Water and Aqueous Analytes It is very well known that an entrance slit width of a spectrometer affects the spectral resolution. Since the resonance dip related to the GW can be very narrow, it can be sometimes problematic to resolve it if the entrance slit is not sufficiently narrow. The resolution of the fiber-optic spectrometers is given by the effective width of the light beam from a core of the read optical fiber [ 26 ]. As an example, we used two read optical fibers with core diameters of 25 µ m and 50 µ m, respectively, to show the difference in the recorded reflectance ratio R+45(λ)/Rp(λ) for water. As can be seen from Figure 5a, the narrowest dip at a wavelength of approximately 660 nm is almost twice deeper when the fiber with the 25 µm core diameter is used. 500 530 560 590 620 650 680 0 100 200 300 BSWpGWp GWs Wavelength (nm) R+45/Rp(%) d=50 µm d=25 µm 0.3 0.4 0.5 0.6 0.7 0.3 0.32 0.34 0.36 0.38 0.4 ¯ β ¯ω (a) (b) Figure 5. ( a ) Comparison of spectra recorded by the spectrometer employing a read optical fiber of two different core diameters d . ( b ) Band structure of the 1DPhC for p -polarized wave. Black dots correspond to a multilayer consisting of 450 bilayers, blue and red dots to the MDS including the termination layer with thickness of 60 nm and 50 nm, respectively. Photonics 2022,9, 561 7 of 13 Analyzing the obtained reflectance ratio, one of three resolved dips can be associated with the BSW (labeled as BSW p ), and it is excited by a p -polarized wave at a wavelength of approximately 518 nm (for a given angle of incidence), and the remaining two resolved dips can be associated with s -polarized waves. In the band structure for the s -polarized wave shown in Figure 3b, blue dots out of the photonic band gap represent the guided states for water as the analyte. We can extend our considerations following an approach presented in [ 27 ], including also the effect of the termination layer. In the case of the termination layer thickness of 50 nm, the red dots located inside the photonic band gap are obtained. Similarly, for a p -polarized wave, we computed the band structure shown in Figure 5b and the reflectance dip positions are depicted by black dots for a multilayer consisting of 450 bilayers. In the case when the termination layer is included in the calculations, blue dots and red dots are obtained for thicknesses of 60 nm and 50 nm in the MDSs, respectively. All the obtained states are located within the photonic band gap. 3.3. Termination Layers with Thicknesses of 60 nm and 50 nm In this section, we compare the two prepared MDSs in their sensing abilities related to aqueous analytes. In Figure 6a,b, the measured reflectance ratios R+45(λ)/Rp(λ) are shown for MDS 60 and MDS 50 , respectively, for different RIs of the analyte. It can be seen that the reflectance dips related to both s - and p -polarized waves (BSW or GW) are deeper for the MDS60, but their shift with RI change is smaller than in the case of MDS50. 500 530 560 590 620 650 680 0 100 200 300 BSWpGWpGWs Wavelength (nm) R+45/Rp(%) 1.3331 1.3358 1.3427 1.3492 1.3587 1.3599 500 530 560 590 620 650 680 0 100 200 300 BSWpGWp BSWs Wavelength (nm) R+45/Rp(%) 1.3331 1.3358 1.3427 1.3492 1.3587 1.3599 (a) (b) Figure 6. Experimental reflectance ratio R−45(λ)/Rp(λ) as a function of wavelength for different RIs of the analyte: MDS60 (a) and MDS50 (b). The dashed lines are the theoretical results for water. The theoretical results obtained for pure water with the RI n= 1.333 are shown by the dashed lines. For the reflectance dip wavelengths, we calculated the optical intensity distributions within the MDSs, as shown in Figure 7a,b. They clearly illustrate the substantially enhanced optical field with an exponential tail for the MDS 50 than for the MDS 60 , and thus increased penetration depth of the field in the analyte. The discrepancy between the theoretical and experimental reflectances can be attributed to the variable thicknesses of all TiO 2 and SiO 2 layers in the real MDS as illustrated for a different MDS in a previous paper [10]. Photonics 2022,9, 561 8 of 13 0 200 400 600 800 1,000 1,200 1,400 1,600 0 20 40 60 80 Distance from substrate interface (nm) Normalized Optical Field Intensity λ= 522 nm (p-pol.) λ= 663 nm (s-pol.) 0 200 400 600 800 1,000 1,200 1,400 1,600 0 70 140 210 280 350 Distance from substrate interface (nm) Normalized Optical Field Intensity λ= 509 nm (p-pol.) λ= 648 nm (s-pol.) (a) (b) Figure 7. Normalized optical field distribution in MDS at different wavelengths for water and angle of incidence θ=64◦(α≈ −6◦): MDS60 (a) and MDS50 (b). In Figure 8a, we show the resonance wavelength of both waves as a function of the RI for both structures. In the case of BSW p , the wavelength shift is about 7.9 nm for MDS 60 nm and about 11.1 nm for MDS 50 . In the case of the GWs in s polarization, the wavelength shift is about 3.3 nm for MDS 60 nm and about 7.3 nm for MDS 50 when the GW is transformed into the BSW. 1.333 1.338 1.344 1.349 1.355 1.360 513 517 521 525 529 533 Refractive Index (RIU) Wavelength (nm) BSWp(MDS60) BSWp(MDS50) 654 658 662 666 670 674 GWs(MDS60) BSWs(MDS50) 1.333 1.338 1.344 1.349 1.355 1.360 0 200 400 600 Refractive index (RIU) Sensitivity (nm/RIU) BSWp(MDS60) BSWp(MDS50) GWs(MDS60) BSWs(MDS50) (a) (b) Figure 8. Dependencies of resonance wavelength (a) and RI sensitivity (b) on RI. A direct comparison of sensitivities to the RI is shown in Figure 8b. The sensitivities change linearly with the RI, and they are higher for MDS 50 than for MDS 60 in the whole RI range. The sensitivity can be further enhanced by decreasing the termination layer thickness, but this is accompanied by the dip depth decrease [ 19 ] and thus a smaller FOM increase. A summary of the sensor performance parameters is presented in Table 1. Photonics 2022,9, 561 9 of 13 Table 1. Sensor performance parameters resulting from the reflectance measurements. Sensor Parameters for Aqueous Analytes Structure MDS60 MDS50 Wave BSWpGWsBSWpBSWs S(nm/RIU) 203.8–370.2 70.3–161.7 295.5–544.3 180.7–371.4 FWHM (nm) 13.3 2.7 10 2 D0.96 0.78 0.96 0.44 FOM (RIU−1) 9.2–26.7 20.3–52.1 28.4–52.3 39.8–81.7 Comparing the results with the available ones [ 4 , 16 , 19 , 28 – 30 ], the resonance depths obtained are the greatest; however, the sensitivities are smaller than those for a single polarization [ 4 , 16 , 28 ], or for both polarizations [ 19 ], including also sensors employing fibers [ 29 ] and operated in a near infrared spectral region. The sensitivities are close to those for sensors employing a D-shaped optical fiber [30]. 3.4. Phase Responses In this section, we analyze the experimental phase responses of both MDSs. As for the other resonance phenomena, such as a SPR [ 31 , 32 ], an abrupt phase change is related to the BSWs [ 16 ], and it can be exploited for sensing applications. In Figure 9a,b, the phase shifts measured for both MDS 60 and MDS 50 are shown. While the phase shifts due to the BSW p are similar in both cases, the phase shifts due to the s -polarized waves are substantially different, both in magnitude and sign of its change. Moreover, while a slope of the phase shift due to the s -polarized GW is similar for every RI in the case of the MDS 60 , it varies in the case of MDS 50 , when the GW is transformed into the BSW. It is interesting to note that a similar behavior is revealed for a SPR phase response of a simple structure when the thickness of a gold layer is changed [ 31 , 32 ]. In the same figures, we show by dashed lines the theoretical phase ∆(λ)obtained using TMM. 500 550 600 650 700 −15 −10 −5 0 650 655 660 665 670 −14 −12 −10 −8 BSWp GWs Wavelength (nm) Phase Shift (rad) 1.3331 1.3358 1.3427 1.3492 1.3587 1.3599 500 550 600 650 700 −15 −10 −5 0 5 BSWp BSWs Wavelength (nm) Phase Shift (rad) 1.3331 1.3358 1.3427 1.3492 1.3587 1.3599 650 655 660 665 670 −13 −12 −11 −10 (a) (b) Figure 9. Phase shift as a function of wavelength for different RIs of the analyte: MDS 60 ( a ) and MDS50 (b). The dashed lines are the theoretical functions. In Figure 10a,b, derivatives of the phase shifts are shown for MDS 60 and MDS 50 , respectively. The derivative peak position can be traced as the RI changes, similar to tracing the reflectance dip.