Enhanced light extraction through randomly nano-textured interfaces

The use of micro-structured interfaces has been shown to increase the extracted light portion far beyond the total reflection cone that limits extraction from flat surfaces. However, earlier theoretical treatments based on ray tracing, break down for nano-structured features smaller than the material wavelength. We apply a new analytic method converting the boundary conditions at the interface into surface currents following from the surface discontinuity in the perpendicular electric and parallel displacement vectors. These currents serve as source terms driving the transmitted radiation, computed by applying the full wave propagator. Analytic formulae yield the transmitted fraction for quasi-periodic surface features involving random variation of the feature size and period. A single incidence of an incoming plane wavefront suffices for transmission, while, in the ray tracing approach, many bounces with an opposing surface are required until the randomly changing angle of incidence falls within the extraction cone.