Time Reflection and Refraction in Temporal Periodic Structures

In electromagnetism, dualities exist between time and space since they both contribute to the propagation of electromagnetic waves to some extent. Such dualities provide us with an alternative tool to manipulate the electromagnetic waves via temporal discontinuities in addition to spatially symmetry - breaking structures. In this work, we investigate the reflection and refraction of time-periodic structures, which can be regarded as a temporal analogy to the distributed Bragg reflector. The Fresnel-like coefficients are derived by imposing appropriate boundary conditions. It is suggested that such temporal modulated structures may pave the way for complementary manipulation of electromagnetic waves.