Second-harmonic generation tuning by stretching arrays of GaAs nanowires

We present a wearable device with III–V nanowires in a flexible polymer, which is used for active mechanical tuning of the second-harmonic generation intensity. An array of vertical GaAs nanowires was grown with metalorganic vapour-phase epitaxy, then embedded in polydimethylsiloxane and detached from the rigid substrate with mechanical peel off. Experimental results show a tunability of the second-harmonic generation intensity by a factor of two for 30% stretching which matches the simulations including the distribution of sizes. We studied the impact of different parameters on the band dispersion and tunability of the second-harmonic generation, such as the pitch, the length, and the diameter. We predict at least three orders of magnitude active mechanical tuning of the nonlinear signal intensity for nanowire arrays. The flexibility of the array together with the resonant wavelength engineering make such structures perspective platforms for future bendable or stretchable nanophotonic devices as light sources or sensors.

We also study the optical resonance supported in an array of NWs with length L = 900 nm, diameter D = 300 nm for which the second-harmonic generation (SHG) tunability under stretching is strongest. The linear transmission spectrum and the SHG conversion efficiency spectrum for this NWs array are given in Figure S2a-b. The resonance at λres = 1270 nm wavelength indicated by the arrow is visible in the transmission and SHG spectrum. In Figure S2c-d we plotted the electric and magnetic field intensity distributions |E(2ω)| 2 and |H(2ω)| 2 (normalized to the incoming electric field) at a resonant wavelength of λres = 1270 nm and a non-resonant wavelength of λnr = 1240 nm. The second-harmonic (SH) electric field is the strongest at the edges of the NW while the SH magnetic field is the strongest inside the NW. Inside the NW at resonant wavelength, we can observe five nodes in the SH electric field distribution and six nodes in the SH magnetic field distribution, which may indicate a multipole or Fabry-Perot resonance. In Figure S3, we compare the linear electric field distributions (normalized to the incoming electric field) at rest configuration, when the pitch p = 600 nm, (see Figure S3a,b) with the fields at high resonance when the pitch p = 690 nm for x-polarization (see Figure S3c,d) and p = 780 nm for y-polarization (see Figure S3e,f). The field distributions are shown at the xy-plane with the NW in the centre. We observe in the stretched case the same linear electric field distributions ( Figure S3b,d,f) as shown in Figure 2a with mode 1 (y-polarization) and mode 2 (x-polarization).

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The electric field corresponding to mode 2 at resonance (see Figure S3d) is also distributed in ydirection to the neighbour NW, indicating a strong coupling between NWs. Figure S3. (a) SHG conversion efficiency spectrum for an array of NWs with length L = 900 nm, diameter D = 300 nm and pitch p = 600 nm. (b) At the resonant position λ = 1270nm, we plot the electric field distribution normalized to the incoming field. It is shown in xy-plane with the NW contour delimited by the red circle. (c-d) Similar plots for maximum resonance with xpolarization, which is for a pitch p = 690 nm and (e-f) for y-polarization which is for a pitch p = 780 nm. Field distribution as similar as in Figure 2a in the main text.
We computed the SHG conversion efficiency of an array of NWs with length L = 900 nm, diameter D = 300 nm and pitch p = 600 nm for which we changed only one parameter in order to observe the impact on the resonance. The length L is varied from 600 nm to 1100 nm, the diameter 5 D from 260 nm to 300 nm and the whole structure is rescaled from 85% to 115% (the length, diameter and pitch are simultaneously changed by this factor) (see Figure S4). An increase in length or diameter will red-shift the resonant wavelength position and tune the intensity of the resonance (see Figure S4a,b), while rescaling the system will shift the resonance but preserve the maximum resonance intensity (see Figure S4c). It is possible to choose these three parameters to tune the resonant intensity and wavelength position. Figure S4. Resonance shift and intensity variation in an array of NWs for which we tuned (a) the length from 600 nm to 1100 nm, (b) the diameter from 260 nm to 300 nm and (c) rescaled the system from 85% to 115% (the length, diameter and pitch simultaneously by the same factor). An increase in length or diameter changes the resonance intensity and red-shifts its position, while rescaling the system only shifts the resonant position without affecting the intensity of the resonance.

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The previous simulations, as well as all simulations for an infinite array in this manuscript, are performed for a rectangular unit cell geometry with specific boundary conditions (Floquet periodicity)(see Figure S5a). In this section we are interested in a single building block element of the array. The numerical simulation to compute the spectrum and multipole decomposition of a single NW is performed with a spherical geometry (see Figure S5b). Yet, the steps to compute the linear scattering and the SHG spectrum (with multipole decomposition) are always the same in all our simulation codes, see Figure S5c. (c) Steps to compute the linear scattering and the SHG spectrum.
We compute with the finite element method simulations the scattering intensities and the multipole decomposition for a single nanowire (NW) with two different geometries of length L = 500 nm and diameter D = 260 nm ( Figure S6) and of length L=900 nm and diameter 300 nm ( Figure S7). 7 We observe that for the smaller NW around a wavelength of 1100 nm the electric dipole (ED) and the magnetic dipole (MD) are dominant, while for the second NW, the ED and the MD dominate around 1400 nm. The spatial field distribution intensities of the electric |E| 2    To study the impact on the resonance of single NWs length, we calculate the linear scattering intensity for a nanowire with diameter D=260 nm and different lengths, see Figure S8a. The resonance shifts to longer wavelengths as the length of the NW increases. The multipole decomposition, shown in Figure S7b as a percentage of electric and magnetic dipole, reveals that these types of multipoles are dominating for NWs with length above 700 nm. The resonance shifts to higher wavelengths for longer NWs. (b) Percentage at resonance of electric and magnetic dipole obtained from the multipole decomposition. Higher orders are not negligible anymore for a nanowire with length above 800 nm.

S3 Detail on sample with NWs distribution of size
The fabrication procedure is described in the manuscript (see also Figure 4a). We show here the sample after metalorganic vapour-phase epitaxy (MOVPE) (see Figure S9a), after the Polydimethylsiloxane (PDMS) deposition (see Figure S9b) and after mechanical extraction with a Razor blade (see Figure S9c). We also capture two images to show the extracted NWs. The first Image, shown in Figure S9d, is obtained with a 5x objective (under light illumination), the second image, shown in Figure S9e, is obtained with a 100x objective (the contrast was expressed with a yellow/purple colormap). We can clearly observe with the 100x objective the periodicity of the structure given by the NWs. More details about the fabrication procedure are given in Methods. The NWs composing the flexible photonic structure have varying sizes that we can describe with a distribution. For that we analysed several SEM images taken after MOVPE growth of the NWs and measured the lengths, diameters of the NWs and the pitch as the distance between NW centres.
We observe that all NWs have the same diameter distribution but that NWs close to the edge are longer than in the middle of the sample. We can use this to characterize two regions where NWs 11 have different lengths but similar diameters. The distributions are shown in Figure S10a-b for the two areas, with respectively a SEM image in the inset. The counts are described with a Weibull function as it fits best the asymmetric Gaussian-like distributions. The mean length for the shorter NWs is 560 ± 100 nm, while for the longer NWs it is 930 ± 125 nm. We can also observe that around 10% of NWs are not fully grown. The results for the radius are shown in Figure S10c and do not show a significant difference for different spots, the mean radius is 133 ± 18 nm. Figure S10. Distribution of length for the region with a) short NWs (around 500 nm length) and b) long NWs (around 900 nm length). Insets show the corresponding scanning electron microscopy images used to calculate the distribution of sizes. A Weibull function was taken to fit the distribution. c) Distribution of NWs radius shown for three different spots. The distribution is fitted with an inverted Weibull function. The distribution of diameter is constant over the whole sample.

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The model used to compute into a single spectrum the SHG efficiency of an array with NWs of different sizes is explained in the Method section and illustrated here. Due to the not completely optimized bottom up growth method for the NWs, their heights and diameters varied locally as shown in Figure S10. A direct comparison between experimental results and simulations was not adequate as the latter was done for an ideal sample with NWs of unique height and diameter. As a first approximation, we calculated the discrete probability of having a NW with a certain size from corresponding SEM images, and added together the simulated spectrums of the ideal cases with their respective discrete weights. However, for the nonlinear SHG conversion efficiency spectrums, the IR resonance was too narrow and it would have needed a lot of simulations to avoid an unrealistic saw-like spectrum. Therefore we developed another method to come up with a single spectrum. Each SHG efficiency spectrum possesses a main peak that is fitted with a Gaussian function. We extracted for arrays with NWs of different lengths and diameters the amplitude

S4. Transmission measurement
We measured the linear transmission spectrum for the two different regions with short (around 500 nm length) and long NWs (around 900 nm length). The setup used here is the same one as used for this other linear measurement. 3

S5. Characterization of SHG signal
We provide an extensive characterization of the signal measured experimentally. We can observe a speckle pattern with the camera for every spot and both excitation polarization, see Figure S13a for x-and y-polarization. The Count rate recorded by the camera is above 10 3 1/s per pixel. The power dependence of the signal is also quadratic as expected for SHG signals (see Figure S13b). Figure S13c shows the spectrum of the excitation laser (in red), this excitation spectrum artificially frequency doubled (dotted) and the collected SHG signal (in blue). We clearly do not observe fluorescence from the sample. dependence of the signal compared to a quadratic curve and (c) intensity spectrum of the excitation laser compared to the filtered signal. We clearly identify the signal as SHG.