Electrodynamic modeling of threshold-free lasing in photonic time crystals

An electrodynamic model is presented in this Letter to describe thresholdless lasers, utilizing the application of photonic time crystals (PTCs). By integrating the distinctive physical properties of PTCs and employing a comprehensive model based on a four-level system, the feasibility of achieving thresholdless laser operation is demonstrated. The proposed electrodynamic model comprehensively captures the intricate interplay between the electromagnetic field and the PTC medium. The model takes into account the ultrafast periodic variations in the refractive index of the PTCs, which arise from their time crystal-like behavior. Additionally, the dynamic response of the four-level system is considered, factoring in the processes of population inversion and relaxation. This Letter seeks to elucidate the underlying mechanisms that facilitate thresholdless laser operation in PTC-based systems. Through our electrodynamic modeling approach, we demonstrate that the ultrafast variations in the refractive index of PTCs give rise to a self-sustaining laser action, obviating the need for a lasing threshold. Moreover, we investigate the impact of various parameters, including pump power and modulation period, on the laser's performance and output characteristics. The developed electrodynamic model provides a comprehensive framework for comprehending and designing thresholdless lasers based on photonic time crystals. This research contributes to the advancement of thresholdless laser technology and opens up possibilities for applications in optical communications, sensing, and quantum photonics.