**3. Results**

In Figure 3a, we show the measured p-polarized SHG signal from the blank reference sample of the bare p-Si(111) as a function of azimuthal rotation of the sample for two orthogonal circular polarization states of the laser pump (RCP and LCP), while in Figure 3b we show the measured p-polarized SHG signal of the flat GaAs sonicated substrate under the same experimental conditions.

**Figure 3.** (**a**) p-polarized SHG signal from the bare p-Si(111) sample for RCP and LCP light with a maximum signal of 400 counts; (**b**) p-polarized SHG signal from the flat GaAs sonicated sample for RCP and LCP light with a maximum signal of 5500 counts; (**c**) SEM image of the sonicated GaAs sample. Horizontal residual GaAs crystallites are evident. In the measurements the azimuthal rotation angle is relative.

The Si substrate response showed a clear, but low, SHG signal with three-fold symmetry, as expected from the 111 crystallographic orientation. Si is a third order nonlinear material, and thus the SHG signal is due to surface contribution. There was a small CD due to a normal incidence on the asymmetric 111 surface.

Meanwhile, the flat GaAs sample showed a larger SHG signal (×14 times the one of Si) due to its bulk nonlinear coefficient [25]. In Figure 3c, the SEM image of the reference flat GaAs sample is shown, which was obtained by Sample C after sonication in order to remove the NWs. In the figure, the largest objects are the parasitic crystallites. The orientation of these crystallites correlated with the silicon substrate, and their microstructures showed a three-fold geometrical symmetry with two possible orientations for the crystallites, one being rotated by 180 degrees with respect to the other, leading to a six-fold microstructure symmetry (also evidenced by the hexagonal shaper of the SHG measurements). The roughness on the Si surface of the substrate in Figure 3c is parasitic polycrystalline AlGaAs/GaAs, which formed during the shell growth. Since this layer grew on the oxide-covered areas of the Si substrate, the orientation of these small crystallites was random and gave rise to the main isotropic SHG signal in Figure 3b.

In Figure 4, we show the measured SHG-CD in p-pol light for both Si(111) and the sonicated GaAs samples, defined as

$$\text{SHG-CD} = \frac{I\_{LCP}^{(2\omega)} - I\_{RCP}^{(2\omega)}}{I\_{LCP}^{(2\omega)} + I\_{RCP}^{(2\omega)}} \tag{1}$$

where *I* (2ω) *LCP* is the intensity of SHG signal when the fundamental pumping light is circularly left polarized, and *I* (2ω) *RCP* is the intensity of SHG signal when the fundamental pumping light is circularly right polarized.

In the case of Si(111), the SHG-CD was regular even when it was lower than 0.2, while in the case of GaAs it was randomly distributed at values lower than 0.1.

On the left side of each panel of Figure 5, the measured p-polarized SHG signal from Samples A,B,C,D are shown without gold as a function of the azimuthal rotation of each sample for two orthogonal circular polarization states of the laser pump (RCP and LCP), while on the right side of each panel of Figure 5, the measured p-polarized SHG signal of Samples A,B,C,D are shown with asymmetric gold coating. It is evident that the asymmetry in the structures of Samples A,B,C (with Au) led to a strong difference in the SHG signal as a function of the handedness of the circular polarized light, while the SHG response of Sample D with Au was very similar to its uncoated counterpart.

**Figure 4.** SHG-CD signal of the p-Si(111) reference and of the flat GaAs substrate. In the measurements the azimuthal rotation angle is relative.

**Figure 5.** p-polarized SHG signal from: (**a**) Sample A; (**b**) Sample B; (**c**) Sample C; (**d**) Sample D. On the left side of each panel the samples without Au coating for RCP and LCP light are shown, while on the right side of each panel, the samples with Au coating are shown. Adapted from [26]. In the measurements the azimuthal rotation angle is relative.

By concerning the magnitude of the SHG signal, the maximum signal was 50,000 counts for Sample A without Au, while the Au coating decreased the SHG signal to 16,000 counts. The magnitude of SHG for sample A (no Au) was nine times larger than the magnitude of the flat GaAs sample, while the magnitude of Sample A (Au) was three times larger. This indicates that the SHG was enhanced by the geometrical resonances of the GaAs NWs, and that the Au layer did not increase the SHG signal but hindered it by selective absorption of one handedness of circular polarized light respect to the other, leading to a lower signal, but with a higher CD.

Samples B,C,D without Au showed maximum signals of 60,000, 40,000, and 40,000 counts, respectively, which decreased to 10,000, 10,000, and 14,000, counts, respectively, when coated with Au [26].

In Figure 6, we show the SHG-CD of the Samples calculated by Equation (1).

**Figure 6.** SHG-CD signal of the Samples without Au and with Au. SHC-CD for: (**a**) Sample A; (**b**) Sample B; (**c**) Sample C; (**d**) Sample D. In the measurements the azimuthal rotation angle is relative.

For all the four samples, the symmetric samples provided negligible SHG-CD, despite the large magnitude of SHG signals. Sample A with Au, showed a SHG-CD as high as 0.5. Similarly, the asymmetric Sample B with Au led to a SHG-CD of 0.5.

By considering Sample C, despite a SHG magnitude comparable with previous cases, the SHG-CD was dramatically decreased at a level of about 0.3-0.25 due to the resonant behavior of Sample C around 800 nm (see Figure 2a). This is because the diameter of the wires achieved larger values and thus red-shifted the spectral position of the resonance [3,10].

In the case of Sample D, the SHG-CD was negligible for both symmetric and asymmetric samples due to the complete lack of resonance at 800 nm (see Figure 2a) [3]. Here, the diameter of the wires was so large that the modes fell in the transparent region of the GaAs spectrum at larger wavelengths with respect to the band gap.

#### **4. Discussion**

Even though the lithography-free and self-assembled growth methods used for wire growth suffered from an intrinsic degree of disorder, we nevertheless saw a good agreement in the general trend of the SHG-CD signal as a function of the wires' diameters, and we were able to quantitatively compare different samples with a reasonable degree of approximation. In these experiments, we demonstrated two main issues. The first one is the possibility for strong circular dichroic responses from asymmetric samples formed by GaAs NWs partially covered in a thin Au film. This could have applications in different fields, including the ability to generate photons in a SH field, while selective pumping with circular polarized light could be viewed as a possibility for boosting the processes of circular polarized photon generation or absorption. Secondly, we observed that geometric resonance is an essential feature in this extrinsic chiral behavior. Only when resonant leaky modes were present was the geometric-induced CD enhanced in the second harmonic field. The resonance can be finely tuned by changing the diameter of the NWs. We passed from 138-nm diameter wires that showed a strong resonance around 750 nm, to 151-nm diameter wires with a strong resonance at 810 nm. As the diameter increased to 165 nm, the resonance shifted to longer a wavelength (850 nm), decreasing its magnitude as the wavelength approached the transparent region of GaAs. In these cases, we passed from a large CD of 50% (0.5) to a CD of 25%. Finally, for larger-diameter wires (197 nm), the resonance completely disappeared in the GaAs bandgap region, and negligible CD was present, despite the strong SHG signal, destroying any information about the geometrically induced asymmetry of the sample.

**Author Contributions:** Conceptualization, methodology and validation A.B. and C.S.; measurements A.B., G.L.; linear investigation, G.L., E.P.; fabrication, T.H., E.K., M.R.P., S.T., supervision, C.S., M.G., T.H. All authors have read and agreed to the published version of the manuscript.

**Funding:** Funding from the Academy of Finland Projects NESP (decision number 294630), QuantSi (323989) and NanoLight (decision number 310985) are acknowledged. EU COST MP1403 NQO is also acknowledged.

**Acknowledgments:** The Authors acknowledge J. T. Collins, D. C. Hooper and V. K. Valev, for fruitful discussions and help in the measurement realizations. A.B. acknowledges LASAFEM Sapienza Università di Roma Infrastructure Project prot. n. MA31715C8215A268.

**Conflicts of Interest:** The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.
