Analysis of transient radiative transfer in semitransparent graded index medium

The formulation of transient radiative transfer in semitransparent graded index medium is outlined. The discontinuous finite element method is extended to solve the transient radiative transfer equation within semitransparent graded index medium both in the time- and the frequency-domain. Four numerical examples, including one- and two-dimensional geometries exposed to collimated pulse irradiation, are studied. The results show that the discontinuous finite element method is efficient, accurate and stable, and can be used for solving the transient radiative transfer problems in semitransparent graded index medium. Due to ray-trajectory bend resulting from the gradient of refractive index, the transient radiative transfer in semitransparent graded index medium exhibits distinctive behavior from that in uniform index medium. Therefore, the effect of graded index in the medium, when exists, has to be taken into consideration when the time-resolved radiation signals are used to infer the medium's optical and radiative property distributions.