Inverse-designed ultra-compact hexagonal/square/circular silicon on-chip wavelength routers

Wavelength routers (WRs) are important in on-chip photonic integrated circuits. A modified sequential quadratic programming (MSQP) inverse design method is proposed to design multi-shape WRs. In this method, fabrication constraints are considered by quoting projection functions, while the finite element method (FEM) is used for optical field simulation during the iterative optimization process. By the MSQP method, the 10-channel hexagonal, square, and circular WRs are designed with footprints of 3.74 μm², 4.00 μm², and 4.52 μm², respectively. Their average transmission efficiencies are 81.0 %, 77.4 %, and 76.4 % in the 1070–1600 nm, 1070–1620 nm, and 1070–1620 nm bands, respectively. Additionally, 11- and 12-channel square WRs are designed with footprints of 4.00 μm². Their average transmission efficiencies are 75.6 % and 72.0 %, within the 1070–1690 nm and 1070–1640 nm bands. Furthermore, the fabrication tolerances of the hexagonal WR are analyzed. The results show that it has the tolerant capabilities of a silicon layer thickness variation of ±50 nm, an etching line width deviation of ±10 nm, an edge roughness of 1–10 nm, and a misalignment of 20 nm. This study provides new ideas for the design of ultra-compact integrated devices and lays the foundation for high-volume optical computing.