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The Time‐Dependent Green's Function for Electromagnetic Waves in Moving Simple Media

### Abstract

This paper treats the problem of radiation from sources of arbitrary time dependence in a moving medium. The medium is assumed to be lossless, with permittivity ε and permeability μ, and to move with constant velocity *v̄* with respect to a given inertial reference frame *xyz*. It is shown how the Maxwell‐Minkowskiequations for the electromagnetic fields in the moving medium can be integrated by means of a pair of vector and scalar potential functions analogous to those commonly used with stationary media. The wave equation associated with these potential functions is derived, and a scalar Green's function is defined to satisfy the same type of equation, with a delta‐function source term δ(r − r′) δ(*t − t*′), and the casuality condition. The solution for the Green's function is derived in closed form, by means of a Fourier integral method. The resulting Green's function is useful not only for calculating the fields from arbitrary sources in moving media, but also for its pedagogical value. It is simpler to understand the phenomenon of Cerenkov radiation using this method than it is from the conventional approach to the Cerenkov problem.

© 1966 The American Institute of Physics

Received 28 March 1966
Published online 22 December 2004