Laser emission induced by time-modulated impedance surfaces

In the past decade, there has been renewed interest in studying materials with time-dependent constitutive parameters. These structures offer solutions to the major limitations of their spatial counterparts, of which metamaterials are a subclass; however, physically realizing such structures is extremely challenging, as controlling the bulk properties of a material periodically and in a controlled manner is a nontrivial task. In contrast, the temporal modulation of a thin impedance layer is more realistic and achievable. In this work, we demonstrate that one of the most significant effects of active materials---the amplified emission of radiation---can be achieved by enclosing a static material within a time-modulated impedance layer. This effect is shown for both one- and two-dimensional cavities. For the latter, we demonstrate that different multipolar modes can be radiated. Additionally, we incorporate angular dependence into the time-modulated impedance, creating the circular analogue of a spatiotemporally modulated material. This enables the radiation of chiral eigenmodes from a circular cavity due to the coupling of time and cylindrical harmonics of the wave field. Our findings indicate that engineered active surfaces can be utilized to develop a new type of lasing system for various classical waves.