Optical analogs of pair production and annihilation in binary waveguide arrays with a curved section

Abstract

We study theoretically and numerically the optical analogs of the relativistic quantum electron-positron dynamic pair production (PP) and annihilation processes in a single binary waveguide array (BWA) consisting of a curved section located between two straight sections at the input and output. Both of these processes can be mimicked by the breakup of beams in the curved section, which plays the role of the external oscillating field. Thanks to our scheme, we are able to observe not only the PP, but also annihilation in a single BWA with a single input beam. Moreover, this scheme allows us to obtain the numerical results for PP and annihilation probabilities by directly simulating beam propagation in binary waveguide arrays, and then compare them to the theoretical results for the same discrete model. This kind of verification demonstrates the striking excellent agreement between them in wide ranges of all relevant parameters. We also show that under certain conditions the probabilities of these two processes based on the discrete model with binary waveguide arrays agree quite well with those based on the truly continuous Dirac equation in quantum field theory.