Low-Loss Silicon Directional Coupler with Arbitrary Coupling Ratios for Broadband Wavelength Operation Based on Bent Waveguides

The wavelength-insensitive response of the bent directional coupler (DC) is rigorously studied by means of coupled mode theory analysis. On that basis, we demonstrate an experimental-based coupling model for the bent DC capable of achieving wavelength-insensitive coupling for arbitrary coupling ratios. The measured devices exemplify wavelength-insensitive coupling at key ratios: 0.4, 0.5, 0.6, and 0.7. As a benchmark, we demonstrate a 0.5:0.5 splitter that significantly reduces coupling variation from 0.391 in the traditional DC to just 0.051 over an 80 nm wavelength span. This represents a remarkable 7.67 times reduction in coupling variation. Further, newly-invented low loss bends were used in the proposed design leading to a lossless design with negligible excess loss ( $<0.01$ 0.01 dB). The proposed 0.5:0.5 design is tolerant and shows consistently low cross coupling variation over the 300 mm wafer showcasing a maximum cross coupling variation of 0.112 with a corresponding average cross coupling of 0.531 over 80 nm wavelength range, at the extreme edge of the wafer. Futhermore, we augmented the wafer mapping with a waveguide width fabrication tolerance study, confirming the tolerance of the device with a mere 0.061 maximum coupling variation with a waveguide width deviation of ±20 nm over 80 nm wavelength range. The proposed splitter meets essential requirements for 2 × 2 splitters such as wavelength-insensitivity, support for arbitrary coupling ratios, lossless coupling, fabrication tolerance, and compact footprint, offering a promising application prospect for mass production.