Lattice Boltzmann method for short-pulsed laser transport in a multi-layered medium

Abstract

We construct a lattice Boltzmann method (LBM) for transient radiative transfer in one-dimensional multi-layered medium with distinct refractive index in each layer. The left boundary is irradiated normally by a short-pulsed laser. The Fresnel interfaces conditions, which incorporate reflection and refraction, are used at the boundaries and the interfaces. Based on the Fresnel׳s law and Snell׳s law, the interfacial intensity formulas are introduced. The collimated and diffuse intensities are treated individually. At a transient time step, the collimated component is first solved by LBM and then embedded into the transient radiative transfer equation as a source term. To keep the consistency of the directions in all the layers, angular interpolation of the intensities at the interfaces is adopted. The transient radiative transfer in a two-layer medium is first investigated, and the time-resolved results are validated by comparing with those by the Monte Carlo method (MCM). Of particular interest, the angular intensities along the slab at different times are presented to illustrate a variety of interesting phenomena, and the discontinuous nature of the intensity at the interfaces is discussed. The effects of various parameters on the time-resolved signals are examined.