Radiative intensity solution and thermal emission analysis of a semitransparent medium layer with a sinusoidal refractive index

The radiative intensity in a sinusoidal refractive index semitransparent medium layer is solved by the curved ray-tracing method in combination with the pseudo-source adding method. One boundary of the medium layer is an opaque diffuse substrate wall. The other boundary is a semitransparent specular or diffuse surface, from which the medium thermal emission emerges. With considering a linear temperature distribution, the radiative intensity formulae are, respectively, deduced under the two boundary conditions. On the basis of the radiative intensity solutions, the directional and hemispherical emission of the medium layer with a specular surface as well as the hemispherical emission of that with a diffuse surface are calculated. The influences of the optical thickness, sinusoidal refractive index distribution and linear temperature distribution on the thermal emission are investigated. The results show that the effects of refractive index and temperature distribution are significant and are different under the two reflecting modes of the surface.