Abstract
During recent years, ray tracing has frequently been used to study the absorption characteristics of structured solar cells. However, wave properties such as absorption enhancement due to resonances in optically thin solar films, cannot be explained by pure classical ray models. Here we present an exact three-dimensional ray model for oblique incidence of a plane electromagnetic wave on a thin film and show that the resonant structure of the absorption cross section calculated from our ray model is identical to exact calculations by electromagnetic wave theory. Both parallel and perpendicular polarized light are described exactly by the ray model presented. We validate the resonant structure of the absorption cross section of our ray model by an experimentally realized layered film, where we obtain perfect agreement between experiment and theory. We demonstrate further that for a beam with a finite beam waist, in accordance with Beer-Lambert's law, absorption occurs along the path of the beam, while, in the case of a plane wave incident on an optically thin film, and contrary to Beer-Lambert's law, absorption occurs along the axis perpendicular to the surface of the film. • Presents a three-dimensional ray model that describes exactly the absorption properties of layered materials. • The ray model reveals the resonant structure of the absorption cross section exactly, confirmed by exact wave calculations and experiments. • The paper highlights pitfalls for explaining interference in films by rays, which modern textbooks often are not aware of. • In the case of absorption, the absorption is normal to the surface of the film and not along the path of the classical ray.
Highlights
In optical systems where the wavelength is smaller than the struc tures applied to the surfaces, geometrical optics approaches have been successfully applied for evaluating and understanding the absorption efficiency of materials
We demonstrate further that for a beam with a finite beam waist, in accordance with Beer-Lambert’s law, absorption occurs along the path of the beam, while, in the case of a plane wave incident on an optically thin film, and contrary to Beer-Lambert’s law, absorption occurs along the axis perpendicular to the surface of the film
Correcting the ray model discussed in the previous section, we demonstrate that we need to consider the phase difference of rays with respect to the wave front of the incoming and outgoing plane waves in order to obtain an exact ray model, i.e., a ray model that reproduces the exact electromagnetic results for oblique incidence
Summary
In optical systems where the wavelength is smaller than the struc tures applied to the surfaces, geometrical optics approaches have been successfully applied for evaluating and understanding the absorption efficiency of materials. Our ray model takes into account the phases and describes exactly the wave properties of the light in effectively one-dimensional systems, i.e. layered optically thin solar cells with perpendicular incidence [15]. In the paper at hand, we present a ray model that describes exactly the absorption and reso nance properties for the situation when a plane wave is incident on a three-dimensional layered system with plane surfaces and with an arbitrary angle of incidence. This three-dimensional system is transla tionally invariant in one dimension and can be simplified to a two-dimensional problem.
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