Space–Time Duality in Optics: Its Origin and Applications

The concept of space–time duality in optics was originally based on the mathematical connection between the diffraction of beams in space and the dispersion of pulses in time. This concept has been extended in recent years from the temporal analog of reflection for optical pulses to photonic time crystals in a medium where refractive index varies with time in a periodic fashion. In this review, I discuss how the concept of space–time duality and the use of nonlinear optics has led to many advances in recent years. Starting from the historical origin of space–time duality, time lenses and their applications are reviewed first. Later sections cover phenomena such as soliton-induced temporal reflection, time-domain waveguiding, and the formation of spatiotemporal Bragg gratings.