Programmable Photonic Circuits with Embedded Feedback for Parallel Multi-Wavelength Operations

Linear transformations are cornerstone operations utilized in modern computing, but are computationally expensive on current electronic platforms. Optical computing has been positioned as a new computing solution, promising high speed and energy efficiency by exploiting the available degrees of freedom of light. Although solutions exist in the optical domain, there is a continuous search for compact solutions that properly utilize the limited chip space and exploit various degrees of freedom of light. Here, we introduce and experimentally demonstrate a compact, programmable photonic integrated circuit (PIC) architecture that operates on both spatial and frequency degrees of freedom by leveraging embedded optical feedback loops. This architecture enables universal linear unitary transforms by combining resonators with passive linear mixing layers and tunable active phase layers. The strong dispersion achieved from the resonant loops enables multi-frequency operation and reduces the number of required active layers to achieve universality. This solution reduces the optical port requirements, minimizes power losses, and leverages resonances to enable massive parallel computing in the frequency domain. The fabricated samples are compatible with silicon-on-insulator platforms and operate at single- and dual-frequency modes. The experimental setup demonstrates the ability to perform in situ training in both cases, validating the parallel-computing capabilities of the PICs. This work highlights the potential of feedback-loop PICs for scalable, compact, and energy-efficient linear optical computing.