Abstract We investigate the existence and stability of gap solitons supported by an optical lattice in biased photorefractive (PR) crystals having both the linear and quadratic electro-optic effect. Such PR crystals have an interesting interplay between the linear and quadratic nonlinearities. Gap solitons are predicted for the first time in such novel PR media. Taking a relevant example (PMN-0.33PT), we find that the gap solitons in the first finite bandgap are single humped, positive and symmetric solitons while those in the second finite band gap are antisymmetric and double humped. The power of the gap soliton depends upon the value of the axial propagation constant. We delineate three power regimes and study the gap soliton profiles in each region. The gap solitons in the first finite band gap are not linearly stable while those in the second finite band gap are found to be stable against small perturbations. We study their stability properties in detail throughout the finite band gaps. The interplay between the linear and quadratic electro-optic effect is studied by investigating the spatial profiles and stability of the gap solitons for different ratios of the linear and quadratic nonlinear coefficients.

中文翻译：

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由具有线性和二次电光效应的偏置光折变晶体中的光学晶格支持的间隙孤子

摘要 我们研究了具有线性和二次电光效应的偏置光折变 (PR) 晶体中由光学晶格支持的间隙孤子的存在和稳定性。这种 PR 晶体在线性和二次非线性之间具有有趣的相互作用。在这种新颖的公关媒体中首次预测了间隙孤子。举一个相关的例子（PMN-0.33PT），我们发现第一个有限带隙中的间隙孤子是单峰的、正对称的孤子，而第二个有限带隙中的孤子是反对称的、双峰的。间隙孤子的功率取决于轴向传播常数的值。我们描绘了三种功率机制并研究了每个区域的间隙孤子分布。第一个有限带隙中的间隙孤子不是线性稳定的，而第二个有限带隙中的孤子对小扰动是稳定的。我们在整个有限带隙中详细研究了它们的稳定性特性。通过研究不同线性和二次非线性系数比率下间隙孤子的空间分布和稳定性，研究了线性和二次电光效应之间的相互作用。