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.

中文翻译：

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Dirac孤子在二元波导阵列中的克莱因隧道效应

我们系统地研究了存在Kerr非线性的二元波导阵列（BWA）中相对论量子Klein隧穿效应的光学类似物，其中Dirac孤子用于构造初始光束。据我们所知，首次在数字上显示了在低功率状态下通过直接光束传播模拟获得的狄拉克孤子的透射系数与潜在台阶高度和入射角的关系，与较早地在所有参数范围内预测的理论结果。观察克莱因隧道效应的条件是通过分析得出的，并且与基于仿真的结果也非常吻合。我们表明，BWA中的非线性会严重影响Klein隧穿效应。