Symmetry-Protected Lossless Modes in Dispersive Time-Varying Media

We give an exact application of a recently developed, operator-based theory of wave propagation in dispersive, time-varying media. Using this theory we find that the usual symmetry of complex conjugation plus changing the sign of the frequency, required for real valued fields, implies that the allowed propagation constants in the medium are either real valued or come in conjugate pairs. The real valued wave numbers are only present in time-varying media, implying that time variation leads to modes that are free from dissipation, even in a lossy medium. Moreover, these symmetry-unbroken waves lack a defined propagation direction. This can lead to a divergent transmission coefficient when waves are incident onto a finite, time-varying slab. The techniques used in this work present a route towards further analytic applications of this operator formalism.