Various representations are considered for 2- and 3-dimensional electromagnetic wavefunctions in uniformly moving media. Rather than solving the relevant wave equation for the fields, the present formalism exploits the transformation formulas for plane waves in moving media, and as a starting point a spectral (plane-wave) representation is constructed. The procedure applies to arbitrary orders of β, but for simplicity only first-order velocity effects are considered in detail. Then, similarly to the velocity-independent problem, waves in uniformly moving media are represented in terms of complex integrals, special function series, inverse-distance differential-operator series, and surface integrals. Since familiar forms and functions are used, the present representations are extensions of the corresponding velocity-independent expressions. The latter are available at any given stage by letting the velocity vanish or by replacing the moving medium by free space. Scattering by circular cylinders and spheres is considered, and results are specialized to the case of thin cylinders; the new velocity effects introduce additional multipole terms. The original wavefunctions are transformed into the frame of reference of the medium at rest. Scattering by arbitrary objects moving in free space follows as a special case.
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics