“…The majority of emitted light in a GaN LED, trapped by TIR, propagates in the form of guided modes, with 22% trapped in the sapphire substrate and 66% in the GaN. 15 PhCs patterned in the GaN couple the GaN guided modes into extracted modes by diffraction of the in-plane vector, k ʈ = k ʈ0 -G, where k ʈ and k ʈ0 are the modified and original in-plane wave vectors, respectively, and G is the reciprocal lattice vector, which depends on the PhC lattice constant. When the periodicity is chosen correctly, the modified in-plane wave vector falls within the air escape cone, resulting in extraction to air at an angle dependent on the specific lattice constant within this range.…”