Analytical solution of electromagnetic heating in a stratified absorbing medium

We consider the temperature evolution in a skin tissue when it is exposed to an electromagnetic wave. The heating is caused by the absorbed power as the electromagnetic wave attenuates inside the skin. In many applications, the characteristic depth of attenuation is small in comparison with the lateral size of the electromagnetic beam. Because of this separation of length scales, the lateral heat conduction is negligible at leading order. Previously, we studied electromagnetic heating in a skin of a single homogeneous layer. We derived the leading-term analytical solution and the asymptotic corrections up to the second order for lateral heat conduction and for oblique incidence. In this study, we derive the analytical solution in the case of perpendicular incidence on a stratified skin tissue with a layer-specific profile for electromagnetic attenuation. It should be emphasized that in the current study, the heat capacity and conductivity are still uniform over the entire skin tissue; only the electromagnetic attenuation is stratified resulting in a layer-specific heating profile.