Influence of gradient index to the temperature field of semitransparent medium

The temperature field of a semitransparent medium with gradient index was calculated. Two types of the refractive index distribution with black boundaries or specular semitransparent boundaries were discussed. One is linear refractive index distribution, and the other is sinusoidal refractive index distribution. We focused on their influence on the temperature field. When the medium has black boundaries, the inner total reflection happens; while the radiative energy transfers from optically denser medium to optically thinner medium, one boundary's influence to the heat transfer will be enhanced. When the medium has specular semitransparent boundaries, other than the above effect, the heat transfer happened on the boundaries also affects the inner temperature field of the medium.