Approximate thermal emission models of a two-dimensional graded index semitransparent medium

This study develops numerical models for thermal emission in a two-dimensional semitransparent graded-index medium. Two piecewise continuous refractive index models, the bar model and the slab model, are presented. The formal is a combination of rectangular bars each having its own unique refractive index. The latter is a combination of slabs, each of which has a linear refractive index distribution. Two interface hypotheses are discussed: the reflection/refraction hypothesis and the refraction/total reflection hypothesis. The backward ray tracing method and the backward Monte Carlo method are employed for calculation. The apparent directional emissivity of a semitransparent medium with linear and nonlinear refractive index distributions is calculated. The results show that piecewise continuous refractive index can be used for modeling semitransparent media with continuously variable refractive index. Emission from the medium is complex and quite different from a medium with a constant refractive index, when the absorption coefficient is small and/or the refractive index varies greatly in the medium. The refractive/totally reflective inner interface in the bar model gives a more precise emission distribution and can be extended to simulate emission from a medium with a complex three-dimensional refractive index distribution.