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