Propagation of optical pulses in a spatiotemporal dispersive medium

This review focuses on novel phenomena that emerge when optical pulses propagate through a spatiotemporal dispersive medium whose refractive index is modulated, both in space and time, in a traveling-wave fashion. Using optical fibers as an example of a dispersive medium, we first derive an equation governing the evolution of short pulses in such a medium. This equation is used to discuss the phenomena such as temporal reflection and refraction, total internal reflection, and waveguiding from a moving boundary with different refractive indices on its two sides. The use of solitons, forming through the Kerr effect, shows how such effects can be observed with silica fibers by employing a pump-probe configuration. A pair of solitons provide the temporal analog of a waveguide or a Fabry-Perot resonator. A new kind of grating, called a spatiotemporal Bragg grating, is formed when a train of pump pulses creates periodic high-index regions inside an optical fiber moving at the speed of pump pulses. The interaction of probe pulses with such a Bragg grating is studied both within and outside of momentum gaps. It is also shown that a photonic analog of Anderson localization is possible when disorder is introduced into a spatiotemporal Bragg grating.