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

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 ℓ 2ω /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 1ω ℓ 1ω is the most relevant parameter in our type of samples.

Albedo and gain threshold of a diffusive Raman random laser

“…As such, they allow stimulated Raman studies to be extended to mesoscopic random media, as is the case for second and higher harmonic generation [2,3].…”

“…Numerical solution of eqn (A4) with these boundary conditions gives generally good agreement with the two-stream analysis, except for minor differences in the calculated flux distributions near the boundaries. Diffusion theory has had some success in modelling powder lasers [12] and second harmonic generation in microporous GaP [2] reflector at rear boundary (c) 100% reflectors at both boundaries. showing the increasing penetration depth as ϖ⇒1.…”

“…A number of non-linear optical effects have been observed in random laser media via the enhanced interaction arising from multiple scattering and gain, namely second and higher harmonic generation [1][2][3], anti-Stokes random lasing [4], up-conversion lasing [5] and surface plasmon enhanced Raman scattering [6] and random lasing [7].…”

“…A linear analysis of the propagation of light in powdered laser media has previously been made using the Kubelka-Munk two-flux equations with constant coefficients [11] and the dynamics of a 1D random laser modelled using the time-dependent diffusion equation [12]. Diffusion analysis has also been applied to model two-photon absorption in a random medium [13] and the distribution of second harmonic light in porous GaP [2]. Here we describe a semi-analytic two-stream model of diffusive Raman gain in a random medium, which calculates the diffuse reflected and transmitted radiation 'streams' directly, and gives good qualitative agreement with experimental data for the diffuse Raman reflectance and Raman transmission gain of barium nitrate powder [10].…”

Cavity-enhanced second-harmonic generation in strongly scattering nonlinear media

“…According to traditional second-order nonlinear optics, the relation between SH and FW should be perfect quadratic; that means P = 2. However, we arrived at P = 1.81, which was not a perfect quadratic relation because of the complex absorption and strong scattering inside the particles [28]. Then, we got P = 2.04 and P = 1.93 at positions 1 and 2 , respectively, based on the same power fitting [ Figs.…”