A Fabrication-Tolerant RGB Laser Combiner Based on a Shallow-Etched Rib-Waveguide Directional Coupler

Full-color holographic optical element (HOE) fabrication requires accurate spatial overlap of red, green, and blue laser beams, which is difficult to maintain with conventional free-space beam-combining systems, particularly for high-resolution near-eye displays. In this work, we propose the numerical design of a fabrication-tolerant RGB laser combiner based on a shallow-etched rib-waveguide directional coupler on a 150-nm-thick silicon nitride platform. The device is designed using supermode analysis and coupled-mode theory for operation at 450, 520, and 640 nm in the transverse-electric (TE) mode. Compared with a strip-waveguide RGB combiner, the rib-waveguide design exhibits lower sensitivity to sidewall-angle deviations: for a deviation of up to 8°, coupled-mode-theory calculations at the blue adding stage show that the average output power decreases by 0.6%, compared with 2.5 % for the strip-waveguide design. At the nominal geometry, separate three-dimensional finite-difference time-domain simulations of the two combining stages, including input and output S-bends, predict overall red, green, and blue output powers of 97.8%, 99.6%, and 99.9%, respectively, for an optimized RGB combiner with a footprint of 128.15×6.22 μm2. The device also exhibits low sensitivity to wavelength deviations. These results demonstrate the potential of a shallow-etched rib-waveguide RGB combiner for compact, efficient, and fabrication-tolerant RGB beam combining in HOE prototyping and related multicolor optical systems.