Resonant states of structured photonic time crystals

TL;DR

This paper develops a comprehensive resonant state theory for structured photonic time crystals, revealing fundamental phenomena like eigenfrequency shifts, mode ladders, and parametric amplification, crucial for advancing space-time optics applications.

Contribution

It introduces a novel theoretical framework for resonant states in finite-sized structured PTCs, addressing a key gap in understanding their dynamics and enabling tailored photonic device design.

Findings

Eigenfrequencies depend quadratically on modulation amplitude for weak modulations.

Each static resonant state generates an infinite ladder of modes spaced by the modulation frequency.

Parametric amplification arises from a resonant process, not just bulk bandgap effects.

Abstract

Photonic time crystals (PTCs) are spatially uniform media with periodic modulation in time, enabling momentum bandgaps and the parametric amplification of light. While their potential in optical systems is very promising, practical implementations require temporally modulating nanostructures of finite size, for which the physics is no longer governed by bulk properties but by resonant states, or quasinormal modes. Despite their importance, a quantitative theory describing the dynamics of these modes has been missing -- a gap we address here by developing a comprehensive resonant state theory for PTCs with arbitrary geometry. Our framework provides a detailed understanding of the resonant behavior of "structured" PTCs and uncovers several fundamental phenomena. For weak modulations, we find a universal quadratic dependence of the eigenfrequencies on the modulation amplitude. Moreover, each static resonant state gives rise to an infinite ladder of new eigenmodes, spaced by integer multiples of the modulation frequency. Crucially, we show that parametric amplification in these systems arises from a fundamentally resonant process, not captured by the momentum bandgap picture of "bulk" PTCs. We apply our theory to a realistic Bragg microcavity, demonstrating the design of tailored parametric resonances. Due to its generality and predictive power, our approach lays the foundation for the systematic study and engineering of structured PTCs, advancing the emerging field of space-time optics.