Abstract
Particles moving in spatially periodic potentials can model condensed matter systems where electrons interact with ions that form crystalline structures in space. Condensed matter-like behavior can be observed not only for massive particles but also for photons. Photonic crystals are systems where the refractive index of a material changes periodically in space. The corresponding dispersion relation reveals a band structure where certain frequencies of electromagnetic waves are forbidden and the waves cannot propagate in a material. When the refractive index changes periodically not in space but in time, photonic time crystals can be observed. Then, gaps of the dispersion relation are present in the wave number domain instead of the frequency domain. Here we describe photonic time crystals and show that they can reveal topological behavior whose signatures are visible in the time dimension. Introduction to photonic crystals in space is also given.
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