We propose and experimentally demonstrate a feasible integrated scheme to solve all-optical differential equations using microring resonators (MRRs) that is capable of solving first- and second-order linear ordinary differential equations with different constant coefficients. Employing two cascaded MRRs with different radii, an excellent agreement between the numerical simulation and the experimental results is obtained. Due to the inherent merits of silicon-based devices for all-optical computing, such as low power consumption, small size, and high speed, this finding may motivate the development of integrated optical signal processors and further extend optical computing technologies.

We theoretically propose a silicon nitride (Si(3)N(4)) grating coupler (GC) with both ultrahigh efficiency and simplified fabrication processes. Instead of using a bottom distributed Bragg reflector (DBR) or metal reflector, a bottom Si grating reflector (GR) with comparable reflectivity is utilized to improve the coupling efficiency. The fully etched Si GR is designed based on an industrially standard silicon-on-insulator (SOI) wafer with 220 nm top Si layer. By properly adjusting the trench width and period length of the Si GR, a high reflectivity over 90% is obtained. The Si(3)N(4) GC is optimized based on a common 400 nm Si(3)N(4) layer sitting on the Si GR with a SiO(2) separation layer. With an appropriate distance between the Si(3)N(4) GC and bottom Si GR, a low coupling loss of -1.47 dB is theoretically obtained using uniform GC structure. A further record ultralow loss of -0.88 dB is predicted by apodizing the Si(3)N(4) GC. The specific fabrication processes and tolerance are also investigated. Compared with DBR, the bottom Si GR can be easily fabricated by single step of patterning and etching, simplifying the fabrication processes.

A compact silicon-on-insulator device used for conversions between polarization division multiplexing (PDM) and mode division multiplexing (MDM) signals is proposed and experimentally demonstrated by utilizing a structure combining the improved two-dimensional grating coupler and two-mode multiplexer. The detailed design of the proposed device is presented and the results show the extinction ratio of 16 and 20 dB for X- and Y-pol input, respectively. The processing of 40  Gb/s signal is achieved within the C-band with good performance. The proposed converter is capable of handling multiple wavelengths in wavelength division multiplexing (WDM) networks, enabling the conversions between WDM-PDM and WDM-MDM, which is promising to further increase the throughput at the network interface.