Time-dependent optical materials: photonic time crystals as an illustrative case

Optical materials with properties varying over time are introduced in this article, with a special focus on temporal photonic crystals. Initially, spatial variations of optical characteristics, such as electric permittivity and magnetic permeability, are explored, highlighting phenomena like refraction and the formation of band gaps in spatial photonic crystals. Simultaneously, temporal variations of these characteristics are examined, presenting an introduction to the theory and associated phenomena, such as temporal refraction and reflection induced by abrupt temporal variations. The concept of temporal photonic crystals is then introduced, explaining how temporal periodicity can create propagation gaps for specific frequencies. It becomes evident the importance and potential applications of time-dependent materials in optics.

Keywords:
Electric and magnetic fields; dielectric constant; optics; electric permittivity