Inverse Sauter effect through a smooth potential step in binary waveguide arrays

We have systematically investigated the quantum relativistic inverse Sauter effect which is the prohibition of the inverse Klein tunneling effect of electrons through a smooth inverse potential step if its declining transition width is large enough. We can simulate this inverse Sauter effect by launching a Dirac soliton in binary waveguide arrays where the smooth transition region of the inverse potential step can be easily realized if we modify the effective refractive indices of the waveguides so that the smooth declining transition region of the inverse potential step can be described by a linear, exponential, or sinusoidal function. As expected, if the transition obeys the linear and sinusoidal laws, then the inverse Klein tunneling is practically suppressed if the transition width is comparable to or larger than the Compton length. Meanwhile, in the case of the exponential transition law analyzed in this work, the inverse Klein tunneling still can take place even if the transition width is significantly larger than the Compton length. © 2024 Elsevier Inc.