The numerical analysis of RCWA and its use in simulating thin-film solar cells
Date
2020
Authors
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Publisher
University of Delaware
Abstract
The ability to rapidly compute the electromagnetic field inside a thin-film solar cell given a set of constitutive parameters of the cell is an important tool in the field of solar cell optimization. Many numerical methods exist to model diffraction of electromagnetic waves by periodic gratings. Among these, spectral methods are popular for their computational speed and easy application to many different grating geometries. The main theme of this thesis is to study the convergence properties of a quasi-spectral method called the Rigorous Coupled-Wave Approach (RCWA). To do this, we investigate the relevant scattering problems: scattering of an s- or p-polarized incident plane-wave by an inhomogenous, periodic medium. In each of these two cases, we establish convergence of the RCWA under appropriate assumptions on the consti- tutive parameters of the cell. In many cases we consider, the variational formulation is not coercive so we employ Rellich identities to establish convergence. We present numerical examples to test our prediction of the convergence rate, which suggests that our analytical results could be pessimistic. We also study a new spectral method that combines the RCWA with transformation optics, whereby the domain is first mapped to a simpler one using a coordinate transform. Our preliminary numerical tests demonstrate that this hybrid method could be more stable than the standard RCWA, and might extend to 3D to rapidly solve the full 3D Maxwell system in crossed gratings.
Description
Keywords
Grating, Numerical analysis, RCWA