On-chip micro-ring resonator array spectrum detection system based on convex optimization algorithm.

We propose an all on-chip micro-ring resonator array spectrum detection system (MRRAS). Micro-ring resonator array as the core is used to construct the transmission matrix of the system. The theoretical analysis of the spectrum detection system is completed with waveguide transmission theory and spectrum construction method based on convex optimization algorithm. In the experiment, we obtain the priori information of the transmission matrix of the system, then detect the output intensity of unknown spectrum through MRRAS, and construct the under-determined matrix equations when the number of micro-rings is much smaller than that of reconstructed wavelengths. Convex optimization algorithm is employed to obtain the least norm solution of the under-determined matrix equations, which enables fast spectrum reconstruction. The experimental results show that the spectrum detection system is constructed using three micro-ring resonators with 4 μm radius, enabling the compact footprint. In addition, the silicon nitride based photonic platform is fully compatible with standard complementary metal oxide semiconductor (CMOS) processes. The system operating bandwidth is more than 12 nm and the resolution is better than 0.17 nm.