Thermodynamics of Light Extraction from Luminescent Materials

Abstract

Light extraction from luminescent materials, where luminescence generated in a high refractive index medium must be coupled to a lower index medium, is a complex problem with significant ramifications for efficient LED and phosphor converted LED lighting. We derive thermodynamic arguments which show that light transmission for incident Lambertian light through arbitrary structured or non-structured surfaces is always limited by the ratio of incident to output étendues. Numerical simulations of various strongly scattering surfaces in the wave-optic regime are made to confirm the surface extraction results. The results are also extended to arbitrary angular radiance distributions of incident light as in Lenef, et al. [Opt. Lett., 39, 3058 (2014)], but also generalized to cases of restricted angular output emission. Furthermore, we show how cavity effects and scattering are both needed to overcome the thermodynamic surface extraction limits. Examples of both surface scattering and a converted LED with volume scattering are given. Finally, a derivation of the Lambertian light transmission theorem is developed from scalar wave-optics to highlight the physics of the thermodynamic result and to provide limits of applicability of the surface extraction limit.