This paper presents two- and three-dimensional (2D and 3D) finite difference time domain modeling and plane wave expansion results for 2D photonic crystal waveguides in GaN-on-sapphire with an AlN lattice matching layer. The low refractive index contrast between GaN and sapphire restricts operation to above the light line, and losses have been calculated to be in the region of , depending on hole depth, which in short devices could be acceptable. A slow-light directional coupler is then designed that has an overall length of 5 μm for 50%–50% coupling at 800 nm. Device tuning is then discussed in terms of both thermo-optic and electro-optic effects, and tuning from 50%–50% to 93%–7% coupling is shown for a 0.1% change in refractive index.
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