The Maxwell and adjoint systems for complex media: Physical significance and applications

Abstract

Useful information on the solutions to the Maxwell system of first order linear differential equations may be obtained with the aid of two distinct, but not independent, sets of adjoint equations, the formally adjoint system which reduces to the complex conjugate equations in loss free media, and the Lorentz adjoint system which reduces to the time reversed equations in loss free media. The formally adjoint system is used to define a generalized energy flux vector, to decompose wavefields into constituent modes and to define their amplitudes. The Lorentz adjoint system is used to construct time reversed, “complementary” media, and time reversed wavefields and sources that are Lorentz reciprocal to the given wavefields and sources. In some problems, such as the determination of reciprocal scattering matrices or reciprocal modal Green’s functions, it is necessary to employ both adjoint systems.