Four methods are applied to calculate the acousto-optic (AO) coupling in one-dimensional (1D) phoxonic crystal (PXC) cavity: transfer matrix method (TMM), finite element method (FEM), perturbation theory, and Born approximation. Two types of mechanisms, the photoelastic effect (PE) and the moving interface effect (MI), are investigated. Whether the AO coupling belongs to linear or quadratic, the results obtained by the perturbation theory are in good agreement with the numerical results. We show that the combination method of FEM and perturbation theory has some advantages over Born approximation. The dependence of linear and quadratic couplings on the symmetry of acoustic and optical modes has been discussed in detail. The linear coupling will vanish if the defect acoustic mode is even symmetry, but the quadratic effect may be enhanced. Based on second-order perturbation theory, the contribution of each optical eigenfrequency to quadratic coupling is clarified. Finally, the quadratic coupling is greatly enhanced by tuning the thickness of the defect layer, which is an order of magnitude larger than that of normal defect thickness. The enhancement mechanism of quadratic coupling is illustrated. The symmetry of the acoustic defect mode is transformed from odd to even, and two optical defect modes are modulated to be quasi-degenerated modes. This study opens up a possibility to achieve tunable phoxonic crystals on the basis of nonlinear AO effects. Graphical abstract

中文翻译：

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一维多层光子晶体腔中的强二次声光耦合

应用四种方法来计算一维 (1D) 光子晶体 (PXC) 腔中的声光 (AO) 耦合：传递矩阵法 (TMM)、有限元法 (FEM)、微扰理论和 Born 近似。研究了两种类型的机制，光弹性效应 (PE) 和移动界面效应 (MI)。无论AO耦合是线性的还是二次的，微扰理论得到的结果与数值结果吻合较好。我们表明，FEM 和微扰理论的结合方法比 Born 近似具有一些优势。已经详细讨论了线性和二次耦合对声学和光学模式对称性的依赖性。如果缺陷声模均匀对称，线性耦合将消失，但二次效应可能会增强。基于二阶微扰理论，阐明了每个光学特征频率对二次耦合的贡献。最后，通过调整缺陷层的厚度大大增强了二次耦合，该厚度比正常缺陷厚度大一个数量级。说明了二次耦合的增强机制。声学缺陷模式的对称性由奇数变为偶数，两个光学缺陷模式被调制为准简并模式。这项研究为基于非线性 AO 效应实现可调光子晶体开辟了可能性。图形概要 这比正常缺陷厚度大一个数量级。说明了二次耦合的增强机制。声学缺陷模式的对称性由奇数变为偶数，两个光学缺陷模式被调制为准简并模式。这项研究为基于非线性 AO 效应实现可调光子晶体开辟了可能性。图形概要 这比正常缺陷厚度大一个数量级。说明了二次耦合的增强机制。声学缺陷模式的对称性由奇数变为偶数，两个光学缺陷模式被调制为准简并模式。这项研究为基于非线性 AO 效应实现可调光子晶体开辟了可能性。图形概要