Temporal glide symmetry enforces a parity sideband selection rule in scalar bulk media

Abstract

Symmetry is a powerful way to control coupling between photonic mode families. In spatially periodic structures, glide symmetry can protect band contacts and suppress stop bands. Here we show a different role for temporal glide, a spatiotemporal counterpart combining reflection with a half-period time translation. In a scalar time-modulated trilayer waveguide, temporal glide imposes an exact selection rule linking frequency conversion to transverse-mode symmetry: the parity content of every Floquet eigenstate alternates with sideband index, up to a state-dependent sign. In scattering, this means that a mode of definite parity can emit only into the opposite transverse parity at odd sidebands and into the same parity at even sidebands. We verify the rule directly in bulk Floquet eigenstates and in finite-section time-domain simulations. An incident odd waveguide mode is converted into an even frequency sideband, while all symmetry-forbidden output channels at the analysed sidebands are suppressed to numerically negligible values. Rather than acting as a temporal copy of spatial-glide band sticking, temporal glide provides a distinct symmetry principle for converting electromagnetic energy between selected modes and frequencies.