Integrated ray-wave optics modeling for macroscopic diffractive lighting devices.

We studied a high-accuracy hybrid optics modeling for macroscopic lighting devices containing highly diffractive elements. For a two-dimensional (2D) grating, we achieved forward and backward diffraction distributions at omnidirectional incidence by conducting rigorous coupled-wave analysis and then assigned the diffuse information to a virtual, planar surface in a ray-optics model. By using the integrated ray-wave optics simulation, we obtained extraction efficiencies and far-field distributions of millimeter-scale (0.5 × 0.5 × 0.1 mm3) flip-chip GaN-based light-emitting diodes (LEDs) with embedded 2D gratings. The increased index contrast of 2D gratings progressively improved the extraction of light via the top face of the substrates, thus inducing a vertical beaming effect that strongly supported measured data. The outcoupling features related to the index contrast of gratings were understood by performing Fourier analysis; a high-index-contrast grating preferred to excite high-order diffraction modes, thereby effectively converting tightly bound waveguide modes into leaky light through the top escape route. The simulation strategy developed herein will be essential for designing directional illuminations and micro-LED displays.