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. It is shown that uncertainty considerations play an important role in relating the path-integral solutions to the approximate asymptotic solutions. The solutions for the high-frequency propagators derived in this work preserve the random information accumulated along the propagation path and therefore can be applied to the analysis of double-passage effects where the correlation between the forward-backward propagating fields has to be accounted for. This results in double-passage algorithms, which have been applied to analyze the resolution of two point scatterers. Under strong scattering conditions, the backscattering effects cannot be neglected and the ray trajectories cannot be treated separately. The final part is devoted to the generalized parabolic extension method applied to the scalar Helmholtz's equation, and possible approximations for obtaining numerically manageable solutions in the presence of random media.
ASJC Scopus subject areas
- Arts and Humanities (miscellaneous)
- Acoustics and Ultrasonics