Klein tunneling through a rectangular potential barrier in a binary waveguide array

We analytically and numerically investigate the optical analog of the quantum relativistic Klein tunneling of a particle through a large repulsive rectangular potential barrier. This quantum relativistic model can be mimicked and analyzed by studying the propagation of a Dirac soliton in a binary waveguide array (BWA). The rectangular potential step in this platform is created by introducing a certain offset for waveguides’ refractive indices. We analytically derive the transmission coefficients of plane waves through the rectangular potential step in BWAs and also in the continuous model in free space. We demonstrate that the analytical transmission coefficient in the discrete model with BWAs is in strikingly perfect agreement with the simulations-based results. © 2023 Elsevier Inc.