Experimental observation of second-harmonic generation and diffusion inside random media

TL;DR

This study experimentally investigates the distribution of second-harmonic light inside a highly-scattering porous gallium phosphide slab, revealing that the scattering parameter at the fundamental frequency is key to understanding the second-harmonic yield.

Contribution

The paper introduces a combined experimental and diffusion model approach to analyze second-harmonic generation distribution inside random media, challenging previous assumptions about the role of the coherence length.

Findings

The ratio of mean free path at second-harmonic frequency to coherence length does not explain the second-harmonic yield.

The scattering parameter at the fundamental frequency is the most relevant factor for the total second-harmonic yield.

Experimental measurements align with a diffusion model incorporating boundary conditions.

Abstract

We have experimentally measured the distribution of the second-harmonic intensity that is generated inside a highly-scattering slab of porous gallium phosphide. Two complementary techniques for determining the distribution are used. First, the spatial distribution of second-harmonic light intensity at the side of a cleaved slab has been recorded. Second, the total second-harmonic radiation at each side of the slab has been measured for several samples at various wavelengths. By combining these measurements with a diffusion model for second-harmonic generation that incorporates extrapolated boundary conditions, we present a consistent picture of the distribution of the second-harmonic intensity inside the slab. We find that the ratio $\ell_{2\omega}/L_c$ of the mean free path at the second-harmonic frequency to the coherence length, which was suggested by some earlier calculations, cannot describe the second-harmonic yield in our samples. For describing the total second-harmonic yield, our experiments show that the scattering parameter at the fundamental frequency $\k_{1\omega}\ell_{1\omega}$ is the most relevant parameter in our type of samples.