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.