Exact ray theory for the calculation of the optical generation rate in optically thin solar cells
M.A. Brandsrud, E. Seima, R. Lukacs, A. Kohler, E. S. Marstein, E. Olsen, R.Blümel
There is a profound duality between rays and waves. In fact, 70 years ago, in the context of quantum mechanics, Feynman showed that rays, properly equipped with phases and correctly summed, provide exact solutions of the quantum mechanical wave equation. In this paper, constructing explicit, exact ray solutions of the one-dimensional Helmholtz equation as a model for optically thin solar cells, we show that the ray-wave duality is also exact in the context of the electromagnetic wave equations. We introduce a complex index of refraction in order to include absorption. This have so far not been treated in the quantum ray-splitting literature. We show that inclusion of exact phases is mandatory and that a ray theory without phases may result in amplitude errors of up to 60%. We also show that in the case of multi-layered solar cells the correct summation order of rays is important. Providing support for the notion that rays provide the “skeleton” of electromagnetic waves, we perform a Fourier transform of the (experimentally measurable) solar cell reflection amplitude, which reveals the rays as peaks in the optical path length spectrum. An application of our exact ray theory to a silicon solar cell is also provided. Treating the one-dimensional case exactly, our paper lays the foundation for constructing exact ray theories for application to solar cell absorption cross section in two and three dimensions.