Ultra-broadband and compact 2$\times$2 3-dB silicon adiabatic coupler based on supermode-injected adjoint shape optimization

The 2$\times$2 3-dB couplers are one of the most widely used and important components in silicon photonics. We propose an ultra-broadband and compact 2$\times$2 3-dB adiabatic coupler defined by b-splines and optimized with an efficient supermode-injected adjoint shape optimization. By employing mode adiabatic evolution and mode coupling at two different wavelength ranges, respectively, we achieve an ultra-broad bandwidth of 530 nm from 1150nm to1680nm with a power imbalance below $\pm$0.76 dB in a compact coupling length of 30 $\mu m$ according to our simulation results. The supermode-injected adjoint shape optimization can also be applied to the design of other photonic devices based on supermode manipulation.