Dirac Dynamics in Waveguide Arrays: From Zitterbewegung to Photonic Topological Insulators

Simulating the evolution of a nonrelativistic quantum-mechanical particle in a periodic potential by propagating an optical wave packet in an array of evanescently coupled waveguides has received continuous and increasing attention in recent years. However, one can also simulate the evolution of a relativistic quantum particle in free space, as described by the spinor-type Dirac equation, by carefully designing the periodic optical potential. In this chapter, the optical simulation of various phenomena based on the Dirac equation will be discussed, such as Klein tunneling, Zitterbewegung, relativistic gauge fields, and photonic topological insulators, which all can be realized in the framework of paraxial optics in periodic media, without requiring specially synthesized materials with subwavelength controlled properties.