Rigorous coupled-wave approach and transformation optics

In order to predict the performance parameters of a thin-film photovoltaic solar cell, the first step is to solve the Maxwell equations throughout the device so as to predict the electron-hole generation rate in the semiconductor layers. While many numerical methods are applicable, the rigorous coupled-wave approach (RCWA) is attractive due to the speed of solution. In addition, during the design process, it is easy to model different cells without remeshing that is inherent in finite-element techniques. In recent work, we have undertaken a mathematical analysis of RCWA for two-dimensional problems with incident p-polarized light and shown that the method is convergent, even if the worst-case rate of convergence is quite slow. To overcome this shortcoming when the periodic bimedium interfaces are graphs of single-valued functions, we have devised a modified C-method where we use transformation optics to flatten the interfaces, at the cost of making constitutive parameters anisotropic in the governing equations. After transformation, discontinuities in the solution can be handled exactly. The use of RCWA for the transformed problem results in the C-RCWA method, with greatly improved convergence rates compared to using RCWA directly. C-RCWA can also be used for full three-dimensional problems, so ameliorating the loss of convergence due to field discontinuities at bimedium interfaces inherent in the standard RCWA.