Programmable Space-Frequency Linear Transformations in Photonic Interlacing Architectures

TL;DR

This work addresses the challenge of performing linear transformations in both space and frequency domains within photonic hardware by implementing a 4×4 programmable photonic integrated circuit (PIC) that realizes space–frequency transformations through a parameterized unitary $\mathcal{U}(\Phi)\in U(N)$ built from passive dispersive arrays $F=e^{-i z H}$ interleaved with five active phase layers. The device is demonstrated to perform wavelength demultiplexing and filtering, and its parameters (20 tunable values across 5 layers) can be trained in-situ to target arbitrary unitary functions, including sparse permutation matrices, while compensating for fabrication defects. The architecture exhibits robustness to partial hardware faults and enables real-time reconfiguration for tasks such as wavelength routing on an SOI platform, highlighting a path toward versatile, programmable dispersion control and space–frequency processing. Overall, the work contributes a practical, open-foundry-compatible approach to programmable photonic computation with tangible benefits for high-speed optical switching and wavelength-division multiplexed signal processing.

Abstract

Programmable photonic circuits are versatile platforms that route light through multiple interference paths using reconfigurable optoelectronic elements to perform complex discrete linear operations. These circuits offer the potential for high-speed and low-power photonic information processing in various applications. The mainstream research on programmable photonics has focused on implementing linear operations on discrete signals encoded in the modal amplitudes of an array of spatially separated single-mode waveguides. However, many photonic device applications require simultaneous transformations in the space-frequency domain, where information is encoded in both the spatial modes of waveguides and their spectral content. Here, we experimentally demonstrate linear space-frequency transformations using a $4 \times 4$-port programmable silicon photonic circuit with an alternating architecture. This design leverages the limited dispersion of coupled waveguide arrays to enable linear operations with reconfigurable frequency-dependent matrix elements. We utilize this device to perform wavelength demultiplexing and filtering. This architecture platform can pave the way for versatile devices with applications ranging from wavelength routing to programmable dispersion control.

Figures (4)

• Figure 1: Reconfigurable programmable photonic integrated circuits design. a Block diagram of the proposed $4\times 4$ unitary and programmable device. This design features low-dispersive mixing layers that work together to create a richer dispersive response. b Schematic representation of the proposed PIC, illustrating the dispersive waveguide arrays (passive units) and the phase shifters (active units) utilized in the interlacing structure. c Image of the as-fabricated packaged chiplet on the PCB board assembled with the optical fiber array and electrical wiring. d Image of the fabricated PIC. Lines starting near the bottom are the electrical traces connecting the metal heaters. e SEM micrograph of a zoomed-in view of the four-port waveguide array section. f-i Electromagnetic wave simulations of the proposed PIC. The phase elements have been simulated by changing the effective index of the waveguide arms to introduce desired phase changes. The phases were tuned to achieve the cross configuration, which routes the excitations in the input ports $\{1,2,3,4\}$ to the output ports $\{4,3,2,1\}$, respectively.
• Figure 2: Experimental setup for in-situ training and wavelength-sweep measurements.a The measurement system consists of a laser source, an optical switch, polarization paddles, and an electrical source-measure unit (SMU) connected to the PIC to drive both optical and electrical signals. Starting with an initial random set of current values, the system generates a transmission matrix from the chip and then minimizes the error relative to the target matrix. The computer program automatically continues iterating until the error drops below a predefined threshold. b Simulated wavelength response of the coupled waveguide array used as the dispersive mixing layer ($F$) in the device. c Optimization error versus step for the target matrix shown in the lower-left inset. The transmission matrices obtained after various optimization methods are shown in the right insets. d Wavelength-sweep of system optimized for identity matrix permutation 2143 at 1550 nm.
• Figure 3: Port-selective wavelength demultiplexing.a Embedded 1x2 passthrough optimized for 1520 nm and 1580 nm through output 1, and not through output 2. b Embedded 1x2 demultiplexer optimized for 1530 nm through output 1 and 1570 nm through output 2. c Embedded bandpass filter optimized for 1550 nm through output 1, and 1540 and 1560 nm through output 2. d Embedded highpass filter optimized for 1530 nm through output 1, and 1540, 1550, 1560, and 1570 nm through output 2.
• Figure 4: Single wavelength optimization of the device for representing sparse matrices. Experimental measurements of the intensity transmission matrix of the device when programmed in-situ to represent $4\times 4$ permutation matrices at a single wavelength of $\lambda=1550$ nm. In this experiment, we considered the whole set of 24 permutation matrices.