ℏω versus ℏk: dispersion and energy constraints on time-varying photonic materials and time crystals [Invited]

Abstract

Photonic time-varying systems have attracted significant attention owing to their rich physics and potential opportunities for new and enhanced functionalities. In this context, the duality of space and time in wave physics has been particularly fruitful to uncover interesting physical effects in the temporal domain, such as reflection/refraction at temporal interfaces and momentum-bandgaps in time crystals. However, the characteristics of the temporal/frequency dimension, particularly its relation to causality and energy conservation ( ℏ ω is energy, whereas ℏ k is momentum), create challenges and constraints that are unique to time-varying systems and are not present in their spatially varying counterparts. Here, we overview two key physical aspects of time-varying photonics that have only received marginal attention so far, namely temporal dispersion and external power requirements, and explore their implications. We discuss how temporal dispersion, an inherent property of any physical causal material, makes the fields evolve continuously at sharp temporal interfaces and may limit the strength of fast temporal modulations and of various resulting effects. Furthermore, we show that changing the refractive index in time always involves large amounts of energy. We derive power requirements to observe a time-crystal response in one of the most popular material platforms in time-varying photonics, i.e., transparent conducting oxides, and we argue that these effects are almost always obscured by less exotic nonlinear phenomena. These observations and findings shed light on the physics and constraints of time-varying photonics, and may guide the design and implementation of future time-modulated photonic systems.

Photonic time crystals: A materials perspective

“…The realization of Photonic-Time-Crystals (PTCs) holds great potential to unlock new physics and phenomena applicable to non-resonant light amplification, tunable lasing, and a plethora of yet unexplored quantum light-matter interactions [1][2][3][4][5][6][7][8][9][10]. In order to realize photonic time-crystals operating in the optical frequency range, several challenges need to be addressed [11]. Most importantly, to achieve a detectable time-reflected signal and/or wide momentum bandgaps, the refractive index of the optical medium must be modulated by an appreciable amount (in the range 0.1-1) all while occurring in a time scale of a single optical cycle of the wave propagating in the medium.…”

Tunable virtual gain in resonantly absorbing media

“…In the temporal analogs of photonic crystals, one can observe the momentum bandgaps inside which one can observe amplification of waves [25][26][27][28]. However, practical possibilities of time-varying photonics are strongly limited by the difficulties with fast and spatially uniform modulations of materials and by interference with common nonlinear effects [29].…”

Spin-controlled photonics via temporal anisotropy

“…[31,32]. While there are inherent constraints and technological challenges in the temporal modulation of constitutive parameters [33], experimental studies are continuing to progress, and recent results have demonstrated feasibility in this area [34][35][36].…”