Stationary Charge Radiation in Anisotropic Photonic Time Crystals

Time metamaterials offer a great potential for wave manipulation, drawing increasing attention in recent years. Here, we explore the exotic wave dynamics of an anisotropic photonic time crystal (APTC) formed by an anisotropic medium whose optical properties are uniformly and periodically changed in time. Based on a temporal transfer matrix formalism, we show that a stationary charge embedded in an APTC emits radiation, in contrast to the case of isotropic photonic time crystals, and its distribution in momentum space is controlled by the APTC band structure. Our approach extends the functionalities of time metamaterials, offering new opportunities for radiation generation and control, with implications for both classical and quantum applications.