Short-pulsed laser propagation in a participating slab with Fresnel surfaces by lattice Boltzmann method

Abstract

Abstract The lattice Boltzmann method (LBM) is extended to solve transient radiative transfer in one-dimensional slab containing participating medium with Fresnel surfaces subjected to collimated short pulse irradiation. The contribution of the collimated pulse to transient radiative transfer is considered as a source term in the radiative transfer equation. In the medium having Fresnel surfaces, the intensity includes two parts, the collimated intensity and scattered or diffuse intensity. With considering multiple specular reflections, the analytical expression of collimated intensity is derived. By using a fully implicit backward differencing scheme to discretize the transient term in the radiative transfer equation, a lattice Boltzmann structure is devised for the transient radiative transfer problem. Firstly, LBM solutions for time-resolved signals are validated by comparison with results obtained by Monte Carlo method, and the difference between the case with Fresnel surfaces and the case with diffusely reflecting surfaces is discussed. Afterward, the transient radiative transfer with Fresnel surface is investigated. The angular distributions of the intensities are given. Several interesting trends on the time-resolved signals are observed and analyzed. Finally, effects of the refractive index, the optical thickness, scattering phase function and Gaussian pulse on transmittance and reflectance signals are investigated.