Application of the anisotropic bond model to second-harmonic generation from amorphous media

TL;DR

This paper develops an anisotropic bond model to analyze second-harmonic generation in amorphous media, incorporating comprehensive physical effects and providing analytic expressions that align with experimental data.

Contribution

It introduces a detailed anisotropic bond model for SHG that includes retardation, spatial dispersion, and magnetic effects, advancing understanding of SHG at the atomic scale in amorphous materials.

Findings

Analytic expressions for SHG in amorphous materials derived.

Estimated SHG signals for fused silica agree with experimental data.

Predictions enable further experimental validation of the model.

Abstract

As a step toward analyzing second-harmonic generation (SHG) from crystalline Si nanospheres in glass, we develop an anisotropic bond model (ABM) that expresses SHG in terms of physically meaningful parameters and provides a detailed understanding of the basic physics of SHG on the atomic scale. Nonlinear-optical (NLO) responses are calculated classically via the four fundamental steps of optics: evaluate the local field at a given bond site, solve the force equation for the acceleration of the charge, calculate the resulting radiation, then superpose the radiation from all charges. The ABM goes beyond previous bond models by including the complete set of underlying contributions: retardation (RD), spatial-dispersion (SD), and magnetic (MG) effects, in addition to the anharmonic restoring force acting on the bond charge. We apply the ABM to obtain analytic expressions for SHG from amorphous materials under Gaussian-beam excitation. These materials represent an interesting test case not only because they are ubiquitous but also because the anharmonic-force contribution that dominates the SHG response of crystalline materials and ordered interfaces vanishes by symmetry. Using the paraxial-ray approximation, we reduce the results to the isotropic case in two limits, that where the linear restoring force dominates (glasses), and that where it is absent (metals). Both forward- and backscattering geometries are discussed. Estimated signal strengths and conversion efficiencies for fused silica appear to be in general agreement with data, where available. Predictions are made that allow additional critical tests of these results.