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Tensor of the second-order nonlinear susceptibility in asymmetrically strained silicon waveguides: analysis and experimental validation

机译：不对称应变硅波导中二阶非线性磁化率张量：分析与实验验证

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摘要

We theoretically consider the existence of multiple nonzero components of the second-order nonlinear susceptibility tensor, χ~(2), generated via strain-induced symmetry breaking in crystalline silicon. We determine that, in addition to the previously reported χ_(xxy)~(2) component, the χ_(yyy)~(2) component also becomes nonzero based on the remaining symmetry present in the strained material. In order to characterize these two nonlinearities, we fabricate Fabry-Perot waveguide resonators on 250 nm thick silicon-on-insulator wafers clad with 180 nm of compressively stressed (-1.275 GPa) silicon nitride. We measure the shifts in these devices' modal effective indices in response to several bias electric fields and calculate the χ_(eff,xxy)~(2) and χ_(eff,yyy)~(2) nonlinear susceptibility tensor elements induced by the breaking of the guiding material's inversion symmetry. Through the incorporation of finite element simulations encompassing the theoretical distribution of strain, the applied bias field, and the optical modes supported by the waveguide geometry, we extract two phenomenological scaling coefficients which relate the induced optical nonlinearities to the local strain gradient.
机译：我们从理论上考虑了二阶非线性磁化率张量χ〜（2）的多个非零分量的存在，这些分量是通过应变诱导对称性破坏晶体硅而产生的。我们确定，除了先前报告的χ_（xxy）〜（2）分量外，基于应变材料中剩余的对称性，χ_（yyy）〜（2）分量也变为非零。为了表征这两个非线性，我们在250 nm厚的绝缘体上覆有180 nm压缩应力（-1.275 GPa）氮化硅的硅上制造Fabry-Perot波导谐振器。我们测量这些设备响应几个偏置电场的模态有效指标的变化，并计算由断裂引起的χ_（eff，xxy）〜（2）和χ_（eff，yyy）〜（2）非线性磁化张量元素引导材料的反演对称性。通过合并有限元模拟，其中包括应变的理论分布，施加的偏置场以及波导几何支持的光学模式，我们提取了两个现象学的比例系数，这些系数将感应的光学非线性与局部应变梯度相关联。

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