Klein tunneling of Dirac solitons in binary waveguide arrays

Abstract

We systematically investigate the optical analog of the relativistic quantum Klein tunneling effect in binary waveguide arrays (BWAs) in the presence of Kerr nonlinearity where the Dirac solitons are used to construct the initial beams. The transmission coefficient of Dirac solitons obtained by direct beam propagation simulations in the low-power regime as a function of the potential step height and incidence angle is numerically shown for the first time, to the best of our knowledge, to be in excellent agreement with earlier predicted theoretical results in all ranges of parameters. The conditions for observing Klein tunneling are analytically derived and are also in excellent agreement with simulation-based results. We show that the nonlinearity in BWAs can severely influence the Klein tunneling effect. Our simulations show that initial beams based on Dirac solitons are much better candidates than Gaussian beams to quantitatively study the Klein tunneling effect in detail, especially in the regime where the incidence angle is very close to the Bragg angle.