The Maxwell field, its adjoint field and the ‘conjugate’field in anisotropic absorbing media

Abstract

In absorbing media, where Maxwell's equations are not seif-adjoint, the adjoint field is introduced via the differential operator adjoint to the Maxwell operator. The concomitant vector can be made equal to the time averaged Poynting vector at a boundary with a non-absorbing medium. In general, the adjoint field represents an electromagnetic field in a medium other than the absorbing medium under consideration. To draw conclusions about the latter, a [conjugate field] in this medium is defined, using a conjugating transformation of the Maxwell operator and field. Relations between the conjugate and adjoint fields are established, allowing one to gather physical information about the first absorbing medium from the adjoint field.