Inverse Klein tunneling effect in binary waveguide arrays

Abstract

We have systematically investigated the optical analog of the inverse Klein tunneling effect---a quantum relativistic effect emerging from the Dirac equation and that is inverse to the well-known Klein tunneling effect. Inverse Klein tunneling can be observed if an electron moves through an inverse potential step from one region with high potential into the adjacent region with low potential. We propose to mimic this effect by launching a Dirac soliton around Dirac points in binary waveguide arrays where the inverse potential step can be easily created by introducing an offset for refractive indices of the waveguides. We obtain the analytical formulas for the transmission coefficient of a plane wave through the inverse potential step in the discrete model with binary waveguide arrays and in the continuous model. As expected, around the Dirac points these two theoretical results are in good agreement. We also show that the theoretical transmission coefficient in binary waveguide arrays is in excellent agreement with the numerical results obtained directly via the beam propagation simulation method. This verification confirms the validity of our model and theoretical results on inverse Klein tunneling in binary waveguide arrays. Some important relations for the transmission coefficient while comparing the inverse Klein tunneling effect and the Klein tunneling effect are also provided.