Single-nanoantenna driven nanoscale control of the VO2 insulator to metal transition

Research article Luca Bergamini*, Bigeng Chen, Daniel Traviss, Yudong Wang, Cornelis H. de Groot, Jeffrey M. Gaskell, David W. Sheel, Nerea Zabala, Javier Aizpurua and Otto L. Muskens Single-nanoantenna driven nanoscale control of the VO 2 insulator to metal transition https://doi.org/10.1515/nanoph-2021-0250 Received May 19, 2021; accepted July 20, 2021; published online August 9, 2021 Abstract: The ultrafast concentration of electromagnetic energy in nanoscale volumes is one of the key features of optical nanoantennas illuminated at their surface plasmon resonances. Here, we drive the insulator to metal phase transition in vanadium dioxide (VO 2 ) using a laser-induced pumping effect obtained by positioning a single gold nanoantenna in proximity to a VO 2 thermochromic material. We explore how the geometry of the single nanoantenna affects the size and permittivity of the nanometer-scale VO 2 regions featuring phase transition under different pumping conditions. The results reveal that a higher VO 2 phase transition effect is obtained for pumping of the longitudinal or transversal localized surface plasmon depending on the antenna length. This characterization is of paramount importance since the single nanoantennas are the building blocks of many plasmonic nanosystems. Finally, we demonstrate the picosecond dynamics of the VO 2 phase transition characterizing this system, useful for the realization of fast nano-switches. Our work shows that it is possible to miniaturize the hybrid plasmonic-VO 2 system down to the single-antenna level, still maintaining a controllable behavior, fast picosecond dynamics, and the features characterizing its optical and thermal response. Keywords: active metasurface; insulator-metal phase transition; photonic nanoswitch; picosecond dynamics; single plasmonic nanoantenna; VO 2 . 1 Introduction Plasmonic single nanoantennas have intrigued vast interest due to their various exceptional properties [1–5]. Excited by an electromagnetic wave that falls within the antenna’s plasmonic resonance band, the electrons around the surface of this nanostructure are driven collectively to form localized charge density oscillations, so-called surface plasmons, with the same frequency of the electromagnetic wave [6, 7]. During this process, the energy of the excitation wave is efficiently transferred into these localized surface plasmons (LSP), thus leading to a strong field enhancement at the surface of the nanoantenna, which is usually subwavelength sized [8–10]. Therefore, plasmonic nanoantennas allow light–matter interaction strengthening [3, 11, 12] and efficient photon manipulation at the nano-scale [1, 13–15], as well as boosting nonlinear response [2, 16–18]. The remarkable properties of nanoantennas have stimulated research combining local electromagnetic enhancement with phase change materials. Materials undergoing structural and/or electronic phase transitions as a response to an external stimulus [19–23], such as, for instance, a magnetic field, a light pulse, or direct heating, show a considerable change in their dielectric properties. This feature has been very successfully exploited to achieve large optical modulation contrast in nanophotonic switching devices [24–26]. Among those materials, vanadium dioxide (VO 2 ) is characterized by a reversible insulator-to-metal transition (IMT), taking place around a critical temperature of 68 °C [27] and making it a promising *Corresponding author: Luca Bergamini, Department of Electricity and Electronics, FCT-ZTF, UPV-EHU, 48080 Bilbao, Spain; and Materials Physics Center, CSIC-UPV/EHU and DIPC, 20018 San Sebastian Spain, E-mail: [email protected]. https://orcid. org/0000-0001-7786-1499 Bigeng Chen, Physics and Astronomy, Faculty of Physical Sciences and Engineering, University of Southampton, Highfield, SO17 1BJ Southampton UK; and Research Center for Optical Fiber Sensing, Zhejiang Lab, Hangzhou 311100, China Daniel Traviss, Yudong Wang, Cornelis H. de Groot and Otto L. Muskens, Physics and Astronomy, Faculty of Physical Sciences and Engineering, University of Southampton, Highfield, SO17 1BJ Southampton UK Jeffrey M. Gaskell and David W. Sheel, Materials and Physics Research Centre, University of Salford, Manchester, M5 4WT, UK Nerea Zabala, Department of Electricity and Electronics, FCT-ZTF, UPV-EHU, Bilbao, 48080, Spain; and Materials Physics Center, CSIC-UPV/EHU and DIPC, San Sebastian 20018, Spain Javier Aizpurua, Materials Physics Center, CSIC-UPV/EHU and DIPC, San Sebastian 20018, Spain Nanophotonics 2021; 10(14): 3745–3758 Open Access. © 2021 Luca Bergamini et al., published by De Gruyter. This work is licensed under the Creative Commons Attribution 4.0 International License. building block for high-performance optical devices [28–31], potentially with fast recovery times in the picosecond range [32, 33]. In a previous study, we showed that the combination of arrays of gold antennas on top of a VO 2 substrate can lead to a significant optical switching effect on the VO 2 permittivity, with the advantage of much lower switching energy requirement and faster recovery time as compared to a bare VO 2 film without antennas [34]. Here, we demonstrate all-optical modulation on picosecond timescales of individual gold antennas fabricated onto a VO 2 substrate. The gold nanoantenna-VO 2 (AuNA-VO 2 ) system is considered as a single entity with a hybrid response, where the nanoantenna drives the surrounding VO 2 phase transition through nanoscale electromagnetic confinement and the resulting changes in the VO 2 are amplified by the antenna's high sensitivity to changes in its local dielectric environment. Compared to more complex nanostructured antenna geometries loaded with small VO 2 patches [35], the antenna-on-film geometry is simple in design and operates on the selection of a nanoscale active volume through the resonant pumping arrangement. Through a combined numerical and experimental approach, we explore how different parameters, such as the antenna geometry and illumination conditions within a pump-probe scheme, modify the antenna-induced VO 2 phase change. We first characterize the effect on the VO 2 phase change produced by a single gold nanoantenna when both the longitudinal and transversal LSP are selectively excited. Then, we show how this effect changes if the size of the nanoantenna changes, namely if the LSP resonances are tuned. We also study the radiation pattern of the antenna and the effect of using a detector with a finite numerical aperture (N.A.) to explain the features of the obtained optical spectra. Finally, we demonstrate the picosecond dynamics of the AuNA-VO 2 phase change, which makes this system wellsuited for the realization of optical switching technology at up to MHz speed. In this respect, the configuration of an isolated single antenna is of interest as it represents the smallest possible switching unit for applications. Hence, the determination of the key parameters underlying the antenna capability of inducing the phase change and producing a hybrid nonlinear optical response is desirable for designing optimized nanostructures, such as nanoscale nonlinear optical devices and switches. 2 Experimental setup In our study, we consider individual gold nanoantennas fabricated on top of a VO 2 film. As shown in Figure 1(A), the first step of the fabrication process was the deposition of 50-nm-thick VO 2 films on boroaluminosilicate glasses coated with a 30 nm thin layer of fluorine-doped tin oxide (FTO), which allowed for the production of VO 2 films with low surface roughness and a suitable thermochromic transition temperature. The procedure followed for the realization of these high-quality films is detailed in reference [36]. In short, VO 2 was deposited using atmospheric pressure chemical vapor deposition at a temperature of 375 °C using vanadium (IV) chloride and water as the precursors for growth. High-quality films of <10 nm roughness were obtained using this method, with a thickness of around 50 nm achieved for a growth time of 90 s. Gold nanoantennas of 45 nm thickness, were fabricated on top of the VO 2 film by using e-beam lithography and liftoff. A Ti layer of 5 nm thickness was used to improve the adhesion of the gold to the VO 2 . Single-antenna spectroscopy was performed using a spatial modulation microscopy (SMM) technique [14, 15, 37–39]. A schematic of the SMM setup is displayed in Figure 1(B). A picosecond probe light filtered from a broadband supercontinuum light source (Fianium, 450– 2500 nm) was focused on the nanoantennas via a reflective Cassegrain objective (Edmund Optics, 0.5 N.A.). Individual spectral components from 1.1 to 1.9 μm wavelength, with a bandwidth of 2% of the center wavelength, were selected from the supercontinuum source using a subtractive mode double prism monochromator. The polarization was fixed along the length direction of the nanoantennas. A piezoactuated flexure mirror driven at 200 Hz produced onedimensional periodic displacement of the focused light spot with respect to the nanoantennas, i.e., spatial modulation (SM) of the spot. Another objective (Mitutoyo 100×, 0.5 N.A.) was placed after the transparent sample to collect transmitted light for subsequent lock-in amplification detection. We also applied an optical chopper to modulate the probe beam for better signal recovery using the dualchannel demodulation option of the lock-in amplifier (Ametek Model 7270). The SMM technique allows single antenna spectroscopy by means of a position-modulated probe beam and provides the normalized SM transmission of the single antenna (ΔT/T) SMM ,defined as the difference in transmission between the surface with antenna and without antenna, normalized to the average transmission [37–39]. For an antenna that is absorbing or scattering light away from the forward beam, the transmission with the antenna is reduced and hence (ΔT/T) SMM is negative. In general, the inverse quantity (−ΔT/T) SMM is considered to be connected to the particle extinction cross-section minus the fraction of forward scattering captured by the detection system [39]. 3746 L. Bergamini et al.: Single-nanoantenna driven nanoscale control This relationship becomes considerably more complicated for the geometry under study where the particle is positioned on a partially reflecting and absorbing substrate which itself varies under different optical pumping conditions. It is therefore difficult to separate the antenna cross-section from the VO 2 background and in this study, we, therefore, compare the value (−ΔT/T) SMM itself to the theoretical response. In order to optically induce the IMT of the VO 2 films, we used optical pump pulses of 11 ps time duration which were focused onto the sample using the same optical system as the supercontinuum probe, as sketched in Figure 1(B). The pump was generated from the fiber oscillator operating at 1060 nm (Fianium) through a second amplifier stage parallel to the supercontinuum source. The polarization of this beam was selectively taken along either the length (|| polarization) or the width (⊥polarization) of the nanoantenna, as illustrated schematically in Figure 1(C). The initial temperature of the sample was kept at 45 °C and the repetition rate was set to 1 MHz in all studies apart from those explicitly investigating the temperature or repetition rate dependence of the effects. The supercontinuum output was used as a probe to record the SM signal of the sample at a variable time delay from the pump pulse. Both pump and probe beams are reflected by the piezo flexure mirror placed directly behind the objective, and therefore the position of the pump focus is also modulated in the same way as the probe. As a result, the SM signal compares the pumped AuNA-VO 2 hybrid to the pumped bare VO 2 substrate and produces the change of probe transmission (−ΔT/T) SMM at the same optical pump power. By comparing the antenna-VO 2 hybrid (−ΔT/T) SMM obtained under pumping conditions with the one obtained with pump off, we can monitor the antenna-mediated pump effect on the VO 2 IMT. 3 Modeling method The strong pump-dependent optical response of the AuNA-VO 2 hybrid includes a combination of direct heating and antenna-mediated heating of the VO 2 by the pump laser. At the same time, the presence of the antenna with its LSP excitation, occurring in the concerned wavelength range, enhances the detection of changes in the VO 2 .We performed detailed numerical simulations of the thermoplasmonic response in order to interpret the experimental results and realize a qualitative comparison of the antennamediated effects on the VO 2 IMT. To mimic the pump-probe experiments performed on the single AuNA-VO 2 samples, three-step simulations were carried out using the commercial COMSOL Multiphysics software [40]. The system was modeled according to the geometry and conditions of the experiments described in the previous section. The first and second simulation steps reproduce the pumping process, through the combination of an electrodynamical calculation followed by a heat-dynamical calculation. This combination allows determining how the complex VO 2 permittivity spatially changes around the Figure 1: (A) Sketch of the single Au antennaVO 2 system. (B) Schematic of the combined SMM and pump-probe experimental setup. (C) Sketch of the laser pump-probe illumination conditions. The black, blue, and red arrows represent the incident electric field of the probe, of the || polarized pump, and of the ⊥polarized pump, respectively. The green arrow indicates the incident wavevector in the three cases. L. Bergamini et al.: Single-nanoantenna driven nanoscale control 3747 AuNAs (see Section 2.2 of Supplementary Information). In the first step of our multiphysics simulation, we calculated the overall direct and antenna-mediated absorption of the pump light by the VO 2 , considered here as an insulator layer. In the second step, the outcome of the optical modeling was used to obtain, through the thermal diffusion simulation, a temperature spatial map of the system at a time of 40 ps after the pump was switched off. In our simulations, we considered an initial sample base temperature of 45 °C. Results obtained after optical absorption and thermal diffusion simulations (steps 1 and 2 of the model) are shown in Figure 2(A) and (B) for a 312 nm long gold nanorod (matching the actual nanorod in the experiment), for polarizations respectively parallel and perpendicular to the antenna, as sketched in Figure 1(C). The temperature profile is then mapped onto a permittivity, following a temperature and wavelength-dependent model, as shown in Figure 2(C) and (D). In order to more accurately model the observed behavior, we have included in our mapping procedure a gradual temperaturedependent behavior of the permittivity. Here, the complex VO 2 permittivity changes according to a smoothed Heaviside temperature step function centered around 68 °C and varying between the values characterizing the insulator (below 58 °C) and metal (above 78 °C) behavior (see also Section 2.1 of Supplementary Material for more details). Therefore, the VO 2 permittivity becomes a function of two variables, i.e., the incident probe light wavelength and the VO 2 temperature. This behavior is in line with detailed experimental studies of the temperature-dependent permittivity [5], but it constitutes a new approach going beyond the approximation made in previous studies [34] where the IMT was modeled as a discrete step in the optical response at the threshold temperature. Finally, the temperature profile is converted into a profile of the dielectric function by mapping the IMT transition onto this temperature profile, as displayed in Figure 2(E) and (F). As a side note, latent heat at the critical temperature [41] was also included in the model by increasing the heat capacity in a 2°C temperature window around the critical temperature (see Section 2.2 of Supplementary Information). The third step involves calculating the transmission of the system by incorporating the new spatial distribution of the VO 2 permittivity value. The three steps are done for the AuNA-VO 2 hybrid, as well as for a bare VO 2 substrate without antenna under identical pumping conditions. From the calculated transmissions with and without the nanoantenna under the same pump conditions, the theoretical normalized differential transmission (−ΔT/T) th values are obtained similar to the experimental case. Note Figure 2: Colormaps of the antenna-mediated pump induced temperature (θ) for (A) || pump and (B) ⊥pump. These colormaps refer to an antenna with dimensions 312 ×103 ×50 nm (L×W×H) and a pump wavelength of 1060 nm. The 3D plot of the (C) real and (D) imaginary part of the VO 2 permittivity used in the simulations of the system, as a function of both wavelength and temperature. The green line indicates the VO 2 permittivity values for the 1450 nm cut wavelength used for the plots in (E) and (F). Colormaps of the antenna-mediated pump-induced real part of the VO 2 permittivity (ε R ) for (E) || pump and (F) ⊥pump. These colormaps refer to a probe wavelength of 1450 nm. Cuts along half either (A, E) the width or (B, F) the length of the antenna are performed to better display the hot spots due to || pump and ⊥pump, respectively. All simulations are characterized by an initial sample temperature of about 45 °C. 3748 L. Bergamini et al.: Single-nanoantenna driven nanoscale control that the resulting (−ΔT/T) th depends on the size of the simulated area and thus the quantitative matching with the experiment requires matching the area under consideration to the diffraction-limited spot size, which scales effectively with the square of the wavelength (see Section 2.3 of Supplementary Material for a detailed discussion). In our simulations, the areas are smaller, and instead of artificially scaling the transmission, we have chosen to directly plot the theoretical values from the modeling and perform a qualitative comparison. In addition to the above model analysis, it was found that the phenomenology of the observed effects depends critically on the selected numerical aperture of the detection system. The reason for this is the effect of forward scattering, which adds an important contribution in the differential transmission toward longer wavelength, effectively reducing the (−ΔT/T) SMM values and even completely flipping its sign. These effects follow previous single-particle studies in the regime where extinction and forward scattering are of comparable magnitude [4] and will be discussed further below. 4 Results 4.1 VO 2 phase transition produced by single-antenna-mediated optical pump In our experiment, we first considered a single gold nanoantenna with a size of 312 ×103 ×50 nm (L×W×H), for which the scanning electron microscopy (SEM) image is shown in the inset of Figure 3(A). The normalized SM transmission signal (−ΔT/T) SMM of the antenna without a pump is presented in Figure 3(A) (black line) and shows a peak at around a wavelength of 1550 nm due to the LSP excitation in the antenna. The value of (−ΔT/T) SMM of around 10−2signifies that the presence of the antenna results in a reduction of the transmission of 1% compared to the bare VO 2 film. For an isolated antenna and assuming negligible forward scattering, given the diffraction-limited spot size of around 7 μm2, the value of (−ΔT/T) SMM translates to an extinction cross-section of 1.3 ×10−13 m2. The blue and red lines in Figure 3(A) show the (−ΔT/T) SMM response for the same antenna under picosecond optical pumping of the AuNA-VO 2 hybrid at a pulse energy of 0.6 nJ, for parallel and perpendicular orientation of the pump electric field, respectively. Optical pumping results in a blue shift and a reduction of the peak height of the plasmon mode for both polarizations. Additionally, the (−ΔT/T) SMM spectrum develops a negative overshoot, in the presence of pumping, at longer probe wavelengths beyond the LSP position. The negative overshoot becomes more pronounced upon further increasing the pump power, as illustrated in Figure S9 of the Supplementary Material. The sign reversal in the (−ΔT/T) SMM signal indicates that rather than scattering light away from the transmission, the antenna increases forward transmission compared to the bare substrate under similar pumping conditions. In our numerical modeling, we found that this effect depends critically on the numerical aperture of the detection optics, as is explained in more detail in Section 4.3 further below. To shed light on the precise pumping conditions in this nJ range of optical powers for both the VO 2 substrate and the AuNA-VO 2 hybrid, we performed a sweep of the optical pump power from 0.25 to 1 nJ, covering the range over which the IMT switching condition takes place. Figure 3(B) and (C) respectively show results for the overall transmission T, normalized to the transmission with pump off (T 0 ), and for the SM signal (−ΔT/T) SMM corresponding to the AuNA-VO 2 hybrid, both at a fixed wavelength of 1450 nm. This wavelength is chosen as it most clearly shows the strongest pump-polarization-dependent effect for intermediate pump energy. A full set of (−ΔT/T) SMM data for three different wavelengths around the antenna resonance peak is presented in Supplementary Material Section 2.8, Figure S12. Given the small effect of the antennas of around 1%, the T/T 0 response is governed by the bare VO 2 film without the AuNA. Over the full range of pump powers, we find that the illumination induces a reduction of around 10% of the global transmission T, of which 5% is reached at an energy of 0.6 nJ (indicated by the magenta vertical line). In comparison, Figure 3(C) shows that the (−ΔT/T) SMM signal for the AuNA-VO 2 hybrid at an energy of 0.6 nJ has a reduction of around 50% for the perpendicular pump polarization (red curve). Therefore, the main contribution to the (−ΔT/T) SMM spectra results from a change in ΔT (i.e., antenna effect), rather than changes in Titself (i.e., pumping of the VO 2 substrate). The antenna-mediated response in Figure 3(C) is articulated by the large difference between pumping parallel and perpendicular to the antenna length, as given by the blue and red curves in Figure 3(C), respectively. In fact, for the bare VO 2 substrate in Figure 3(B), changing the polarization of the pump laser does not have any effect and the two curves are overlapping. This polarization-dependent response for the pump is only seen for pump energies in the range 0.4–1 nJ. Indeed, the results for the AuNA-VO 2 hybrid of Figure 3(C) show that the pump energy range can be roughly divided into three parts, depending on the effect that the two pump polarizations produce on the optical L. Bergamini et al.: Single-nanoantenna driven nanoscale control 3749 response of the system. For low pump energies (<0.4 nJ), the two pump polarizations originate a similar variation of the system optical response, which is close to the value without the pump. This is due to the almost negligible antenna effect produced by the relatively low pump energies. At intermediate pump energies between 0.4 and 1 nJ, different behavior of the (−ΔT/T) SMM response is found due to the different antenna-mediated effects for the two polarizations. Finally, the two polarizations produce again similar (−ΔT/T) SMM for energies as high as 1 nJ. For the higher energy regime, the pump energy is sufficient to induce direct heating of the VO 2 film while the resonant antenna-mediated effects are no longer uniquely driving the local IMT, therefore the response becomes again independent of pump polarization. The results of the modeling of the L= 312 nm antenna under the same experimental pump and probe conditions are shown in Figure 3(D)–(F), obtained using the detailed calculations presented in Figure 2 for the same system. The calculated normalized differential transmission spectra under laser pumping at different polarizations are indicated by the blue and red curves in Figure 3(D). The Figure 3: (A–C) Measured and (D–E) simulated response of AuNA-VO 2 system, for the single antenna with dimensions of 312 ×103 ×50 nm (L×W×H). The inset of (A) shows the SEM image of this antenna. (A) Normalized spatial modulation transmission (−ΔT/T) SMM and (D) normalized differential transmission (−ΔT/T) th as a function of the probing wavelength for the 312 nm long antenna for conditions of no pump (black curve), parallel pump (||, blue curve) and perpendicular pump (⊥, red curve). The pump laser is characterized by a wavelength of 1060 nm and an energy of 0.6 nJ. The green line indicates the 1450 nm probing light wavelength considered in plots (B, C, E, and F). (B) Measured and (E) simulated T/T 0 as a function of the pump energy at 1450 nm probe wavelength and for || pump (blue curve) and ⊥pump (red curve). Blue and red curves perfectly overlap in (E), as the simulated response of a flat infinite stack does not depend on the polarization of the normally impinging light. (C) Measured (−ΔT/T) SMM and (F) simulated (−ΔT/T) th as a function of the pump energy at 1450 nm probe wavelength and for || pump (blue curve) and ⊥pump (red curve). Magenta lines in (B, C, E, and F) indicate the pump energy of 0.6 nJ considered in (A, D). All measurements and simulations are performed at a repetition rate of 1 MHz and sample base temperature of 45 °C. 3750 L. Bergamini et al.: Single-nanoantenna driven nanoscale control simulations are qualitatively in agreement with the experiments, where the difference in vertical scale corresponds to a difference in the illumination area used for the calculations compared to the experiment. Under pumping conditions corresponding to 0.6 nJ pulse energy, we see a similar trend where the mode blue shifts and the peak amplitude decreases. The difference in LSP amplitude and profile between the two pump polarizations can be traced back to the formation of VO 2 hot spots as seen in Figure 2(E) and (F), which are regions around the antenna where the VO 2 permittivity transitions from the dielectric to the metallic state, depending on the final temperature. The presence of these hot spots is inferred by both the temperature maps (Figure 2(A) and (B)), due to pump at a wavelength of 1060 nm, and the after-pump VO 2 permittivity maps, obtained at a wavelength of 1450 nm (Figure 2(E) and (F)). As revealed by the temperature maps, none of the two pump polarizations produces a temperature equal to or greater than 78 °C, which is the requirement for achieving a complete IMT transition, with a 0.6 nJ pump energy and an initial sample temperature of 45 °C. Indeed, the main effect is to decrease the real part of the permittivity: as a consequence, the pumped antenna feels a surrounding medium with a smaller permittivity with respect to the unperturbed antenna in absence of pumping, resulting in a blue shift of the plasmon peak. The greater peak blue shift and decrease for the polarization perpendicular to the antenna (⊥, red curve) with respect to the parallel polarization (||, blue curve) can be explained in terms of the interplay between two effects: the value of the VO 2 permittivity assumed in the VO 2 hot spots and the size of these hot spots. The former depends on the VO 2 absorption, through either the longitudinal or transversal AuNA plasmon mode, i.e., the electronic excitation along the long or short axis of the antenna, respectively, at the pump wavelength of 1060 nm. This electronic excitation, in turn, depends on both the relative position of the plasmon peaks with respect to this pump wavelength and their absolute intensity and width. As revealed by the simulations, the longitudinal mode peak is located at a wavelength of around 1550 nm, while the transversal mode peak occurs around 1000 nm (see Section 2.4 of Supplementary Material). The transversal mode is therefore located closer to the 1060 nm pump than the longitudinal mode. Even if the longitudinal plasmon peak is more intense and broader, the transversal plasmon is more efficiently excited. The overall effect is a similar intensity of the antenna excitation for the two polarizations at the pump wavelength of 1060 nm, which in turn leads to similar maximum temperature values (see Figure 2(A) and (B)) and minimum values of the VO 2 permittivity inside the VO 2 hot spots (see Figure 2(E) and (F)). However, the shape of the antenna and the more efficient excitation of the antenna transversal mode produce a total volume of the VO 2 hot spots larger in the case of perpendicular pump polarization than under parallel pump polarization. These two effects, namely a similar minimum value of the VO 2 real permittivity and larger overall volume of the VO 2 hot spots, lead to a greater blue shift and resonance damping for the perpendicular pump. Simulations were also performed to retrieve the T/T 0 and (−ΔT/T) th theoretical curves as a function of the pump energy, as displayed in Figure 3(E) and (F), respectively. A qualitative agreement of the simulations with the experiments of Figure 3(B) and (C) is found. The theoretical results confirm that the main contribution to the phase transition of the VO 2 in the hot spots is due to the presence of the pumped antenna and not to the direct effect of the pump on the VO 2 film. Moreover, the increase of temperature in specific sites of the VO 2 close to the nanoantenna can be attributed to significant absorption of the electromagnetic field in these sites and not to a conductive flux of heat from the pumped antenna itself. In fact, the conductive heat flux contribution is negligible, consistent with previous studies on antenna arrays [34] and confirmed by the obtained temperature maps (see Figure 2(A) and (B)), which do not reveal a uniform distribution of the temperature in the VO 2 around the antenna as expected under a conductive heat flux. Finally, for a comprehensive description of the analyzed spectra, we note the flattening tail of both the (−ΔT/T) SMM and (−ΔT/T) th curves in the red part of the optical range, namely for wavelengths greater than 1800 nm. Further investigations reveal that these flattening tails are due to the onset of the intraband transitions in the FTO layer, which slightly affects also the plasmon peak position and intensity (see Section 2.5 of Supplementary Material for a detailed discussion). 4.2 Effect of antenna size/resonance tuning on the VO 2 hot spots The strong redshift of the longitudinal plasmon resonance of the L= 312 nm antenna positioned on the high-index VO 2 substrate means that the optical wavelength distance between the LSP and the pump wavelength at 1060 nm is significant. A situation where the antenna resonance is located closer to the pump wavelength is obtained for a shorter antenna. The realized antenna, shown in the SEM image in the inset of Figure 4(A), is characterized by a size of 222 ×110 ×50 nm (L×W×H). This example allows L. Bergamini et al.: Single-nanoantenna driven nanoscale control 3751 studying the influence of the antenna geometry on the creation of VO 2 hot spots. The obtained experimental and simulated curves, showing the plasmon peak evolution under conditions of laser pumping at 0.6 nJ for both polarizations, are displayed in Figure 4(A) and (C), respectively. The curves exhibit qualitatively good agreement, especially in the red part of the spectrum. In the blue part of the spectrum the simulations reveal a crossing between the curves, with the (−ΔT/T) th referred to the perpendicular pump higher than the one of the parallel pump, while the experimental curves approach each other but do not cross. These small differences may be attributed to variations in the modeled and experimental configurations, possibly related to local variations in the granular VO 2 film itself and in the antenna morphology, which are challenging to address precisely using modeling. We note that these shorter antenna dimensions are very close to the limits of our experimental capabilities both in nanofabrication and single-antenna spectroscopy. Nevertheless, the overall qualitative agreement between experiments and simulations confirms the validity of the temperatureand wavelength-dependent VO 2 permittivity used in our modeling. The simulations reveal that, for this shorter antenna, the pumping with polarization parallel to the antenna produces a greater suppression with respect to the perpendicular pump. In this antenna, the longitudinal mode is located at around 1350 nm wavelength, while the transversal mode is at around 1000 nm (see Section 2.4 of Supplementary Material), so that the optical distance to the pump wavelength of 1060 nm is still larger for the longitudinal mode than for the transversal mode. However, the longitudinal mode is more intense and broader than the transversal one, and this leads to a slightly higher excitation at the pump wavelength of 1060 nm for parallel pumping. At the same time, the maximum temperature value, and in turn the maximum VO 2 permittivity change, is almost the same for the two pump polarizations, as revealed by the temperature maps of Figure 4(E) and (F). What makes the peak decrease larger for the parallel pump polarization as compared to the perpendicular pump polarization is the overall volume of the created hot spots, which is bigger for the former than for the latter. The T/T 0 curves as a function of the pump laser energy are also reported in Figure 4(B) and (D). A T/T 0 reduction of around 2.5% is found at the wavelength of 1350 nm for Figure 4: (A) Measured normalized spatial modulation transmission (−ΔT/T) SMM and (C) simulated normalized differential transmission (−ΔT/T) th as a function of probe wavelength for a 222 nm long antenna (antenna size L×W×H= 222 ×110 ×50 nm). The behavior under (black curve) no pump is compared to the ones under (blue curve) || pump and (red curve) ⊥pump. The pump laser is characterized by a wavelength of 1060 nm and an energy of 0.6 nJ. The green lines indicate the 1350 nm cut probing light wavelength used for plots (B, D). The inset of (A) shows the SEM image of the realized 222 nm long single antenna. (B) Measured and (D) simulated T/T 0 as a function of the pump energy. The curves refer to a probe wavelength of 1350 nm and to both (blue curve) || pump and (red curve) ⊥pump. The magenta lines indicate the cut pump energy of 0.6 nJ considered in plots (A, C). Blue and red curves perfectly overlap in (D) as the simulated response of a flat infinite stack does not depend on the polarization of the normally impinging light. Colormaps of the antenna-mediated pump induced temperature for (E) || pump and (F) ⊥pump. These colormaps refer to a pump wavelength of 1060 nm. Cut along half either (E) the width or (F) the length of the antenna is performed to better display the hot spots due to || pump and ⊥pump, respectively. All the presented measurements and simulations are performed with a repetition rate of 1 MHz and an initial sample temperature of about 45 °C. 3752 L. Bergamini et al.: Single-nanoantenna driven nanoscale control pump energy of 0.6 nJ, which is again much smaller than the approximately 50% reduction observed for the (−ΔT/T) SMM and (−ΔT/T) th curves under the same conditions. This result corroborates that the direct effect of the pump laser on the phase change of the VO 2 layer is not predominant with respect to the antenna-mediated one produced by the pumping of the LSP resonance. The results reported in Figures 3 and 4 are part of a larger series of spectra taken at pump energies between 0 and 1 nJ. These results are summarized in Supplementary Material Section 2.6. Additionally, similar results for a number of single nanoantennas and dimer antennas are presented in Supplementary Material Section 2.10, showing that the observed responses are general for all AuNAs investigated. 4.3 Effect of the finite numerical aperture of the detector on the single-antenna response In the attempt of improving the qualitative agreement between the experimental and calculated curves, we performed a further theoretical investigation of the effects of the finite detection aperture on the optical response. We found that the finite numerical aperture of the detector strongly affects the recorded response of the single nanoantenna, especially at longer wavelengths far from the plasmon resonance. If we collect the light in the farfield inside a cone determined by the numerical aperture of the detector (0.5 N.A., which corresponds to a total angle of the cone of 60°in air and 40°in the SiO 2 ), under conditions of no pumping we obtain the results shown by the black solid curves in Figure 5(A) and (B) for the 222 nm long and 312 nm long antenna, respectively. When compared to the results by a detector with a large aperture (black dashed curves in Figure 5(A) and (B)), it is clear that the finite numerical aperture of the detector results in an overall reduction of the apparent extinction as well as a change in the overall shape of the resonance profile. Reducing the N.A. affects mainly the shape in the red part of the spectra, leading to a decrease of the optical response (−ΔT/T) th . For the 222 nm long antenna, the (−ΔT/T) th curve becomes negative, similar to the trend observed in experiments (Figure 4(A)). The change from positive values to negative values of (−ΔT/T) can be explained by the wavelength-dependent radiation pattern of the antenna which is projected onto the Figure 5: (A, B) Simulated normalized differential transmission (−ΔT/T) th as a function of probe wavelength for a (A) 222nm long antennaand a (B) 312 nm long antenna (width and height equal to the antennas studied before). The response obtained with a detector characterized by a large N.A. (black dashed curve) and a 0.5 N.A. (black solid curve) is compared. In the latter case, the detector is placed 4 um away from the antenna, as shown by the green line of panels C and D. The behavior under a 0.6 nJ parallel pump is also reported for a detector with collecting 0.5 N.A. (blue curve). (C, D) The calculated difference between the z-component of the Poynting vector of the system with (P z ) and without the antenna (P z,sub ) at a wavelength of (C) 1300 nm and (D) 2000 nm, which correspond to the point 1 and 2 marked in panel A. The difference is normalized to the intensity of the probing laser (I 0 ). The XZ plane refers to a plane parallel to the antenna length and passing through the middle of the antenna width. The maps are obtained under no pump, namely when the VO 2 film is completely dielectric. The green line and the white rectangle mark off the edge of the 0.5 N.A. detector and of the antenna, respectively. The displayed colorscale holds for both maps. L. Bergamini et al.: Single-nanoantenna driven nanoscale control 3753