Lattice-parameter effects on diffracted transmission of GaN two-dimensional square-lattice photonic crystals

The lattice-parameter effects on the diffracted transmission of GaN square-lattice photonic crystals （2PhC） at the wavelength of 460 nm were studied by using a rigorous coupled wave analysis （RCWA）. The impacts of lattice parameters on the diffracted transmission are calculated in the ranges for lattice pitch from 100 nm to 2000 nm, fill factor from 0.1 to 0.9 and grat- ing height from 100 nm to 1000 rim, respectively. Our simulation results confirm that the lattice pitch is the dominant factor of the diffraction. It determines how many orders of diffraction occur by the 2PhCs. The larger the lattice pitch, the higher the diffraction orders come into play. Moreover, besides the first-order Bragg diffraction, higher diffraction orders from large pitches of PhCs are also beneficial to the light extraction improvement. The higher enhancement factors of the integrated transmission were obtained from a wide range of pitches with micro-scale GaN 2PhCs. Three different diffraction mechanisms through wave vector analysis were used to discuss the simulation results.