Approximate expressions of the Ishimaru parabolic equation analysis within the problem of EM impulse propagation through diffusing dissipative media

We show that the approach utilized in Ishimarus'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 Ornstein-Uhlenbeck dissipative stochastic process application. We also derive the explicit expression for the problem Green function. The time-dependent term of the Green function is of a Laguerre type for all the considered conditions. In the case of Laguerre-like input pulses it allowed us to show the Laguerre properties of the output pulses.