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Pseudo-Hermitian operators can be used in modeling electromagnetic wavepropagation in stationary lossless media. We extend this method to a class ofnon-dispersive anisotropic media that may display loss or gain. We explorethree concrete models to demonstrate the utility of our general results andreveal the physical meaning of pseudo-Hermiticity and quasi-Hermiticity of therelevant wave operator. In particular, we consider a uniaxial model where thisoperator is not diagonalizable. This implies left-handedness of the medium inthe sense that only clockwise circularly polarized plane-wave solutions arebounded functions of time.

Pseudo-Hermiticity and Electromagnetic Wave Propagation: The case of anisotropic and lossy media