Reference-wave solutions for high-frequency fields propagating in random media.

Ray theory plays an important role in determining the propagation properties of high-frequency fields and their statistical measures in complicated random environments. According to the ray approach, the field at the observer can be synthesized from a variety of field species arriving along multiple ray trajectories resulting from refraction and scattering from boundaries and from scattering centers embedded in the random medium. For computations of the statistical measures, it is desirable therefore to possess a solution for the high-frequency field propagating along an isolated ray trajectory.

Phase-space beam summation analysis of rough surface waveguide.

A Gaussian beam summation (GBS) formulation is introduced for a doubly rough boundary waveguide, wherein the coherent and incoherent scattered fields are decomposed into a discrete phase-space summation of Gaussian beams (GB) that emanate from the rough surfaces in all directions. The scheme involves deterministic GB propagators and stochastic GB-to-GB (GB2GB) scattering matrices for the coherent and incoherent fields, where each scattered beam is propagated inside the waveguide and is scattered again from the rough boundaries. The GB2GB matrices are calculated from the statistical moments of the scattering amplitude, which are given either analytically or empirically.

A phase-space Gaussian beam summation representation of rough surface scattering.

A Gaussian beam (GB) summation representation for rough surface scattering is introduced. In this scheme, the coherent and incoherent scattered fields are described by a phase-space summation of GBs that emanate from the rough surface at discrete set of points and directions. It thus involves stochastic GB2GB scattering matrices for the coherent and incoherent fields, and deterministic GB propagators.

Reference-wave solution for the two-frequency propagator in a statistically homogeneous random medium.

Spatial and temporal structures of ultrawide-band high-frequency fields can be appreciably affected by random changes of the medium parameters characteristic of almost all geophysical environments. The dispersive properties of random media cause distortions in the propagating signal, particularly in pulse broadening and time delay. Theoretical analysis of pulsed signal propagation is usually based on spectral decomposition of the time-dependent signal and the analysis of the two-frequency mutual coherence function.

Reference-wave solutions for the high-frequency fields in inhomogeneous-background random media.

Ray theory plays an important role in determining the propagation properties of high-frequency fields and their statistical measures in complicated random environments. For computations of the statistical measures it is therefore desirable to have a solution for the high-frequency field propagating along an isolated ray trajectory. A new reference wave is applied to obtain an analytic solution of the parabolic wave equation that describes propagation along the ray trajectory of the deterministic-background medium.

Reference-wave solutions for the high-frequency field in random media.

Ray trajectories, as has been shown in the recently formulated stochastic geometrical theory of diffraction, play an important role in determining the propagation properties of high-frequency wave fields and their statistical measures in complicated random environments. The field at the observer can be presented as the superposition of a variety of field species arriving at the observer along multiple ray trajectories resulting from boundaries and scattering centers embedded into the random medium. In such situations the intensity products from which the average intensity measures can be constructed and which, in general, are presented as even products of the total field, will contain sums of products of mixed field species arriving along different ray trajectories.

Modeling of high-frequency propagation in inhomogeneous background random media.

When a high-frequency electromagnetic wave propagates in a complicated scattering environment, the contribution at the observer is usually composed of a number of field species arriving along different ray trajectories. In order to describe each contribution separately the parabolic extension along an isolated ray trajectory in an inhomogeneous background medium was performed. This leads to the parabolic wave equation along a deterministic ray trajectory in a randomly perturbed medium with the possibility of presenting the solution of the high-frequency field and the higher-order coherence functions in the functional path-integral form.