Hybridization of the rigorous coupled-wave approach with transformation optics for electromagnetic scattering by a surface-relief grating
Hybridization of the rigorous coupled-wave approach with transformation optics for electromagnetic scattering by a surface-relief grating
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DOI：
10.1016/j.cam.2022.114338
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发表时间：
2022-04
期刊：
影响因子：
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通讯作者：
B. Civiletti;A. Lakhtakia;P. Monk
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作者：
B. Civiletti;A. Lakhtakia;P. Monk
我们将严格耦合波法(RCWA)与变换光学相结合，发展了一种混合坐标变换方法，用于求解含有表面浮雕光栅的二维域中的时间调和Maxwell方程。为了证明这种方法对于p偏振态是收敛的，我们研究了几个不同但相关的散射问题。通过施加广义非陷阱条件，我们可以证明这些问题的先验估计。为此，我们证明了一个Rellich恒等式，并使用密度论点将估计推广到更一般的问题。这些先验估计然后被用来分析混合方法。我们得到了关于两个不同参数的收敛速度，第一个是表示深度维空间离散化的切片厚度，第二个是电场和磁场相量相对于另一维的Rayleigh-Bloch展开式中保留的项数。用数值例子进行的测试表明，收敛速度比我们的分析预测的要快。该混合方法不会受到标准RCWA中的吉布斯现象的影响。
We hybridized the rigorous coupled-wave approach (RCWA) with transformation optics to develop a hybrid coordinate-transform method for solving the time-harmonic Maxwell equations in a 2D domain containing a surface-relief grating. In order to prove that this method converges for the p-polarization state, we studied several different but related scattering problems. The imposition of generalized non-trapping conditions allowed us to prove a-priori estimates for these problems. To do this, we proved a Rellich identity and used density arguments to extend the estimates to more general problems. These a-priori estimates were then used to analyze the hybrid method. We obtained convergence rates with respect to two different parameters, the first being a slice thickness indicative of spatial discretization in the depth dimension, the second being the number of terms retained in the Rayleigh–Bloch expansions of the electric and magnetic field phasors with respect to the other dimension. Testing with a numerical example revealed faster convergence than our analysis predicted. The hybrid method does not suffer from the Gibbs phenomenon seen with the standard RCWA.