Rigorous Coupled-Wave Analysis (RCWA) is a semi-analytical method, used to determine the optical response of nanostructures, such as meta-materials. Recently, the ability to combine RCWA with automatic differentiation for optical response optimization has been demonstrated. We seek to build upon this use by attempting to address RCWA’s poor performance on parallel computer architecture, stemming from the presence of an eigendecomposition. We do this by outlining an alteration of RCWA, which replaces the eigendecomposition with a matrix square root and matrix exponential evaluation. Furthermore, we demonstrate that these matrix functions can be evaluated using algorithms which are both differentiable and readily evaluated in parallel. Finally, we show that replacing the eigendecomposition with these matrix functions resolves the bottleneck and paves the way for higher-accuracy parameter retrieval using RCWA approaching real-time performance, without compromising stability.