Jerry A. Krill

Vector stochastic variational principles for electromagnetic wave scattering

Vector stochastic variational principles are derived for the statistics of the scattering of a plane electromagnetic wave from inhomogeneous and anisotropic conducting dielectric objects or surfaces with arbitrary random electrical and geometrical characteristics. These stochastic variational formulations are based on deterministic variational principles of the general form T = (4\pi)^{-1}N_{1}N_{2}/D , where T is a component of the far-field scattering amplitude and N_{1}, N_{2} , and D are integrals involving the fields or currents at the scatterers. The nonstochastic nature of the incident field allows the statistical moments of T and of the differential scattering cross section |T|^{2} to be expressed as the vector stochastic variational principles \langleT^{n}\rangle = (4\pi)^{-n}\langleN_{1}^{n}\rangle \langleN_{2}^{n}\rangle/\langleD^{n}\rangle and \langle|T|^{2n}\rangle = (4\pi)^{-2n}\langle|N_{1}|^{2n}\rangle \langle|N_{2}|^{2n}\rangle/\langle|D|^{2n}\rangle for arbitrary scatterer statistics. They are readily observed to be inherently simpler than direct averages such as \langleT^{n} \rangle = (4\pi)^{-n} \langleN_{1}^{n}N_{2}^{n}/D^{n}\rangle , and should should allow practical application of variational techniques to random scattering problems.

A flat laser array aperture

We describe a design concept for a flat (or conformal) thin-plate laser phased-array aperture. The aperture consists of a substrate supporting a grid of single-mode optical waveguides fabricated from a linear electro-optic material. The waveguides are coupled to a single laser source or detector. An arrangement of electrodes provides for two-dimensional beam steering by controlling the phase of the light entering the grid. The electrodes can also be modulated to simultaneously provide atmospheric turbulence modulation for long-range free-space optical communication. An approach for fabrication is also outlined.

A computational alternative for variational expressions that involve dyadic Green functions

The dyadic Green function is convenient in formulating integral expressions for eletromagnetic wave scattering. The nature of this functions singularity, however, can lead to computational difficulties. The fact that this singular behavior can be avoided by recasting the integral expressions in terms of the scalar Helmholtz Green function is demonstrated. The use of the scalar Green function can lead to simplification of scattering calculations. Applications to variational formulations are discussed.

VARIATIONAL CALCULATIONS OF ELECTROMAGNETIC SCATTERING FROM TWO RANDOMLY SEPARATED RAYLEIGH DIELECTRIC CYLINDERS.

The exact solution, Born approximation, and its variational improvement are obtained for the scattering of electromagnetic waves from two randomly separated Rayleigh dielectric cylinders. This special model is used to test a recently developed vector stochastic variational principle. The variational results are shown to account accurately for the geometric polarizability of the cylinders as well as for multiple scattering and interference.