Non-Hermitian photonic time quasicrystal

Abstract

Photonic time crystals amplify waves through temporal modulation. We study a temporal analogue of the non-Hermitian Aubry-André-Harper model. By continuing an incommensurate temporal modulation into the complex phase plane, we find that the bulk amplification rate as a function of the complexification coordinate is organized into distinct integer phases, with its slope locked to an integer within each phase. This integer is Avila's acceleration, connecting a global structure of quasiperiodic operator theory with a directly observable optical propagation response. The quantized response persists in the presence of defects in the time-dependent permittivity modulation that preserve the underlying analytic phase structure. As a wave-level consequence, two input frequencies belonging to different integer phases acquire exponentially separated amplification, producing spectral selection and reshaping the temporal beat pattern. Our results establish that a global integer of quasiperiodic operator theory can govern a tunable, quantized growth response in a non-Hermitian photonic time quasicrystal.