(Invited) Linear and Nonlinear Optical Properties of Individual Silicon Nanowires
Authors: Wiecha Peter , Arbouet Arnaud , Girard Christian , Baron Thierry , Lecestre Aurélie , Larrieu Guilhem , Paillard Vincent 
Published: February 2020

High-refractive index semiconductor nanostructures provide original optical properties thanks to the occurrence of size- and shape-dependent optical resonances, which can be used to enhance and engineer light-matter interaction. In particular scattering and absorption efficiencies or local electromagnetic field intensity can be amplified and spectrally tuned, opening a multitude of possible applications in photovoltaics or field-enhanced spectroscopies. High-refractive index semiconductor nanostructures have thus attracted increasing interest as low-loss alternatives to plasmonic particles.

In photonics, nonlinear optical effects also play an important role, providing several functionalities such as coherent up-conversion of light, generation of short pulses, or all-optical signal processing. A hindrance is that nonlinear effects are intrinsically weak. Plasmonic nanostructures, acting as nanoantennas able to strongly localize far-field radiations, are very promising candidates to improve nonlinear optical effects, which is one of the reasons of the increasing interest for nonlinear plasmonics.

However, as mentioned above, plasmonic nanoparticles usually suffer from high losses. As an alternative, enhanced nonlinear properties can be obtained in semiconductor nanostructures by properly using resonant optical modes. For example, intense second harmonic generation (SHG) was achieved in nanowires of III-V compounds, or enhanced third harmonic generation (THG) could be produced in silicon nanostructures. SHG (THG) corresponds to the coherent conversion of two (three) low-energy photons into a single photon at double (triple) energy.

SHG from bulk centrosymmetric materials including silicon is impossible in the dipole approximation, since they have vanishing second order susceptibility (the inversion symmetry forbidding even order terms in the electric polarization expansion). Second order processes can therefore occur only when symmetry is broken, for instance in the presence of interfaces or field gradients. For very small systems, the high surface to volume ratio allows that rather strong second order effects may arise, possibly further supported by local field enhancement due to resonant modes. This can be interesting for silicon-based photonics compatible with CMOS technology.

We present here linear and nonlinear properties of individual strain-free silicon nanowires (Si-NWs).

First, we show experimentally and theoretically the optical resonance modes (Mie resonances) supported by the NW as function of diameter and polarization of the excitation, and how these modes may be used to modify the photoluminescence of Si nanocrystals placed in the NW near-field.

Second, we investigate the nonlinear emission composed of a broad nonlinear PL band and the SH peak. We show that SHG from the Si-NWs is strongly increased if a Mie optical mode corresponding to the fundamental (laser) wavelength is supported by the nanowire. According to nonlinear scattering theory and the so-called Miller's rule, the highest SHG is predicted for an optimum overlap of resonant modes and linear susceptibilities, at both the fundamental and harmonic wavelengths, respectively. Contrary, no SHG can be detected in absence of any resonance. This behavior as well as experimental SHG mappings of individual Si-NWs, are well reproduced by numerical simulations (Green Dyadic Method - GDM).

In first approximation, second order effects in centrosymmetric nanostructures are modeled assuming that the c2
^^^
surface contribution from field components normal to the surface are the most significant. Other possible sources of SHG are neglected in a first step as commonly done.

However, this approach fails explaining the polarization behavior of the SHG from Si-NWs with diameters up to about 150 nm. Using the c2
^^^
surface contribution leads to SHG polarization perpendicular to the Si-NW axis, independently of the polarization of the incident light parallel of perpendicular to the nanowire axis. This is in contradiction with the experimental findings where, for small diameters below 150 nm, the polarization of both fundamental and harmonic radiations are always observed parallel. Thus, the SH polarization is found parallel to the Si-NW axis for TM excitation (incident electric field along the axis). Using GDM, we explain this behavior with SHG contributions arising from tangential fields at the surface as well as from strong field gradients in the bulk, proving that there is a changeover of the main SHG contribution as function of NW diameter.

In summary, Si-NWs provide useful research tools for the investigation of SHG from centrosymmetric materials, with the possibility to address different nonlinear susceptibility contributions. They could also be interesting for nonlinear silicon-based photonic applications if enhanced SHG and polarization control could be achieved. We finally show a few examples of Si nanostructures obtained by e-beam lithography in Silicon On Insulator substrates in order to explicitly tailor the SH response.