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Spatial and/or temporal propagation of light waves in periodic opticalstructures offers a rather unique possibility to realize in a purely classicalsetting the optical analogues of a wide variety of quantum phenomena rooted inrelativistic wave equations. In this work a brief overview of a few opticalanalogues of relativistic quantum phenomena, based on either spatial lighttransport in engineered photonic lattices or on temporal pulse propagation inBragg grating structures, is presented. Examples include spatial and temporalphotonic analogues of the Zitterbewegung of a relativistic electron, Kleintunneling, vacuum decay and pair-production, the Dirac oscillator, therelativistic Kronig-Penney model, and optical realizations of non-Hermitianextensions of relativistic wave equations.

Classical Simulation of Relativistic Quantum Mechanics in Periodic Optical Structures