Wave optics light-trapping theory: mathematical justification and ultimate limit on enhancement

This paper addresses a number of important and underlying theoretical and practical questions regarding the recently developed wave optics light-trapping theory for solar cells. We provide a rigorous and complete justification of its mathematical validity, using the second law of thermodynamics as well as fundamental properties of resonant scattering as described by the temporal coupled-mode theory. For maximal absorption, all optical modes supported by a solar cell structure must couple and only couple to the incident channel of sunlight radiation. For the first time to the best of our knowledge, we derive the ultimate limit of light trapping, which depends positively on the number of optical modes and hence on the periodicity of the structure. The ultimate limit is reached when every mode in the structure can couple only to the incident channel. Furthermore, we predict the theoretical optimal operating regimes of nanophotonic solar cells under practical scenarios. Our work reveals significant gaps between state-of-the-art nanophotonic solar cell designs and the ultimate limit, pointing to important future opportunities for nanophotonic light management for efficiency enhancement and cost reduction of solar cells.