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