Monte Carlo simulation of transient radiative transfer in a medium with a variable refractive index

In this work, a Monte Carlo method is developed to simulate transient radiative transfer in a refractive planar medium exposed to a collimated pulse irradiation. The time of flight in closed form is derived for a medium with a linearly varying refractive index. The time-resolved reflectance and transmittance of the slab are obtained by tracing photon bundles and calculating the time of flight. There is a very satisfying correspondence between the present results and the discrete ordinates solutions. The magnitude of numerical uncertainty decreases with the increase of bundles. To simulate transient radiative transfer in an optically thick medium, we need a large number of bundles. The reflectance decreases with the increase of the positive gradient of the refractive index considered. The appearance instant of the transmittance peak postpones as the refractive index increases. Influence of the optical thickness, the scattering albedo and the anisotropically scattering coefficient on the time-resolved reflectance and transmittance is also investigated.