Scalable programmable silicon photonic processor for solving differential equations

We propose and experimentally demonstrate a scalable programmable silicon photonic processor for solving differential equations. This processor is composed of an array of ellipital microrings (MRRs) and 16-channels of tunable delaylines. The MRRs is cascaded to offer flat-top filtering response to select/combine/amplitude control the carrier wavelength of the input optical signal. The following sixteen-channel delaylines are realized by 7-bit ultra-low-loss broadened waveguides and low-phase-error Mach-Zehnder interferometer for 0~330.2 ps time-delay with a step of 2.6 ps. By using wavelength division multiplexing and amplitude/phase control techniques, the processor enables parallel signal processing in each channel, offering scalability and programming flexibility. By programming the silicon photonic processor, a reconfigurable intensity differentiator with variable differentiation orders can be achieved. The operation principle is theoretically analyzed and this programmable silicon photonic processor has been demonstrated successfully to verify the first-, second- and third-order intensity differentiator functionality, which can be used in the field of optical computing.