Lattice Resonances in Periodic Arrays of Time-Modulated Scatterers

Abstract

Lattice resonances are collective optical modes supported by periodic arrays of scatterers, arising from their coherent interaction enabled by the underlying periodicity. Owing to their collective nature, these resonances produce optical responses that are both stronger and spectrally narrower than those of individual scatterers. While such phenomena have been extensively studied in conventional time-invariant systems, recent advances in time-varying photonics present new opportunities to exploit and enhance the extraordinary characteristics of these collective modes. Here, we investigate lattice resonances in periodic arrays of time-modulated scatterers using a simple framework based on the dipolar approximation and time-Floquet theory, where each scatterer is modeled as a harmonic oscillator with periodically varying optical properties. We begin by analyzing the response of an individual scatterer, leveraging our model to identify the complex eigenfrequencies that define its dynamics. We show that, for the appropriate modulation amplitude and frequency, the imaginary part of one of these eigenfrequencies vanishes, leading to amplification. Building on this, we extend our analysis to a periodic array to investigate the effect of the interplay between temporal modulation and lattice resonances. In contrast to isolated scatterers, the collective nature of lattice resonances introduces a markedly more intricate spectral dependence of the amplification regime. Notably, this amplification emerges at substantially lower modulation strengths, facilitated by the enhanced light-matter interaction and increased lifetime provided by these collective resonances. Our work establishes a simple theoretical framework for understanding collective lattice resonances in time-modulated arrays, enabling dynamic control and amplification of these modes.