Analysis of the Ishimaru parabolic equation: the Languerre invariance of the output time impulses shape

We show that the approach utilized in Ishimaru's (1977) model to describe a time EM impulse shape behavior in homogeneous nondissipative scattering medium can be extended to inhomogeneous dissipative media. The model extension is based on Omstein-Uhlenbeck dissipative stochastic process application. We have also found the explicit expression for the problem of determining the Green function. The time-dependent term of the Green function is of a Laguerre type for all the considered conditions.