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

Abstract

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.

Figures (5)

• Figure 1: Concept and fabricated samples.a Illustration of one of the programmable looped architectures. This comprises evanescently coupled waveguides used for wave mixing and metal heaters for the phase control required to produce interference. The input and output are coupled to grating couplers to excite and gather the PIC through lensed fibers (left and right side), respectively. b Microscopic image of the fabricated three-port device with three microheater layers and two embedded loops. Insets show the scanning electron microscope (SEM) images of the coupled WGAs (red-dashed area) and the circular bends (blue-dotted area) used to close the loops. e Microscopic image of a second fabricated feedback PIC showcasing a two-port device with two microheater layers and a single loop design.
• Figure 2: Experimental setup and training results.a Experimental setup used for characterization of the feedback-loop chip. A wavelength-tunable laser source (upper left) interconnects with a programmable 1x8 optical switch (OS), the outputs of which feed into a V-groove fiber array that injects light into the device under test (DUT). A second fiber array couples lights out of the DUT and interconnects with a multiport power meter (MPM) that gathers the optical signal. The DUT is connected to a thermoelectric cooler (TEC) unit for temperature control and to a standard measure unit (SMU) that provides currents to the microheaters in the DUT. A personal computer interfaces with the laser, OS, MPM, SMU, and TEC for control and monitoring. b-c Dispersion response of a single waveguide guide array ($N=3$) b and a feedback-loop circuit c. The former showcases an almost flat response, whereas the latter depicts the effects of the embedded loops.
• Figure 3: Single-frequency training results.a-b In-situ training and target normalized intensities for the $K=2$ (a) and $K=3$ (b) structures shown in Fig. \ref{['fig:FigX1']}b-c. The bar, cross, uniform-power, and random unitaries have been tested in both structures. c-d Training history of the in-situ optimized identity targets and the corresponding figure of merit $\mathcal{L}$.
• Figure 4: Parallel linear transforms.a-b Parallel and arbitrary spatial photonic state generation from a single excitation at the upper-most port for the $K=2$ (a) and $K=3$ (b) structures at 1549.5 nm and 1550.5 nm. The lower-left and lower-right panels show the training history and figure of merit history, respectively, for the uniform photonic state generation. c Parallel matrix-vector operations by simultaneously embedding two $2\times 2$ unitaries in the $K=3$ structure at 1549.5 nm and 1550.5 nm wavelengths.
• Figure 5: Theoretical model and predictions of the looped structures.a Schematic depiction of the transmission matrix of a straight structure (upper panel) and its decomposition (lower panel) into the smaller-dimensional matrices $\mathbb{M}_{1,2,3,4}$. The latter builds up the looped structure $\overline{\mathbb{M}}$. b Examples of the straight and feedback-loop structures for $N=3$ and $P=1$ (one loop). c Predicted wavelength response for the straight and resonant structures. This indicates an FSR of approximately 282 pm. d Single-wavelength numerical optimizations of the feedback-loop structure using the dispersive model introduced in the text for $\{N=3,P=1\}$ and $\{N=5, P=2\}$, and several numbers of layers. In this test, 100 random unitary and non-unitary matrices are randomly generated and used as targets. e Numerical optimization for random vectors as targets in the dual wavelength operation at 1549.5 nm and 1550.5 nm. Here, 100 random normalized vectors for $\{N=3,P=1\}$ and $\{N=5, P=2\}$, and various number of layers.