SIMULATION OF PLANE ELECTROMAGNETIC WAVE PROPAGATION IN AN INHOMOGENEOUS NONABSORBING MEDIUM

Abstract

The paper presents analytical solutions of the parabolic Ishimaru equation for the electromagnetic field coherence function, which describe the temporal properties of a pulse at the output of an inhomogeneous non-dissipative scattering medium. An explicit expression for the Green’s function of the problem is found. It is shown that the time part of the Green’s function has an invariant Laguerre form. The results of numerical calculations of the shape of the studied time pulses at the exit of the span of the medium are also presented. The paper shows that the approach used in the Ishimaru model to describe the temporal evolution of the envelope of a monochromatic electromagnetic pulse in homogeneous non-dissipative scattering media can be developed for use in inhomogeneous non-dissipative media. An attempt was made to take into account the influence of the inhomogeneity of the medium on the shape of the resulting pulse. To solve the stated problem, it was necessary to overcome the difficulties associated with the calculation of the resulting path integral in the space of diffusion trajectories. This made it possible to obtain an explicit expression for the Green’s function of the problem and construct a computational algorithm, on the basis of which a number of numerical experiments were carried out. The analysis of the results of the work was carried out on the basis of the apparatus of quadratic integral functionals based on the solutions of stochastic differential equations. From the theory of similar functionals, it is obtained that all poles of the Green’s function G(t) are simple, the function G(t) is identically equal to zero at t = 0 (fluctuation region), the function G(t) has one maximum and two inflection points (main region), the function G(t) has exponential asymptotics at t → ∞ (peripheral region). The paper studies the invariant temporal properties of the envelope of monochromatic electromagnetic pulses recorded after passing through a flat layer of a scattering inhomogeneous medium, i. e. properties that remain unchanged when the parameters of the medium vary, in particular, the distribution of the concentration of scattering centers.