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arXiv:2106.03249 · Physical Review Applied

Accurate Self-Configuration of Rectangular Multiport Interferometers

Ryan Hamerly, Saumil Bandyopadhyay, Dirk Englund

Published Aug 5, 2022• 51 citations

Abstract

Multiport interferometers based on integrated beamsplitter meshes are widely used in photonic technologies. While the rectangular mesh is favored for its compactness and uniformity, its geometry resists conventional self-configuration approaches, which are essential to programming large meshes in the presence of fabrication error. Here, we present a configuration algorithm, related to the $2\ifmmode\times\else\texttimes\fi{}2$ block decomposition of a unitary matrix, that overcomes this limitation. Our proposed algorithm is robust to errors, requires no prior knowledge of the process variations, and relies only on external sources and detectors. We show that self-configuration using this technique reduces the effect of fabrication errors by the same quadratic factor observed in triangular meshes. This relaxes a significant limit to the size of multiport interferometers, removing a major roadblock to the scaling of optical quantum and machine-learning hardware.

DOI: 10.1103/physrevapplied.18.024019

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Multiport interferometers based on integrated beamsplitter meshes are widely used in photonic technologies. While the rectangular mesh is favored for its compactness and uniformity, its geometry resists conventional self-configuration approaches, which are essential to programming large meshes in the presence of fabrication error. Here, we present a configuration algorithm, related to the

2\ifmmode\times\else\texttimes\fi{}2

block decomposition of a unitary matrix, that overcomes this limitation. Our proposed algorithm is robust to errors, requires no prior knowledge of the process variations, and relies only on external sources and detectors. We show that self-configuration using this technique reduces the effect of fabrication errors by the same quadratic factor observed in triangular meshes. This relaxes a significant limit to the size of multiport interferometers, removing a major roadblock to the scaling of optical quantum and machine-learning hardware.

Multiport interferometer meshes can be used to implement unitary transformations on input vectors of light in both the classical and quantum domain. In practice, the phase-shifters in a mesh photonic circuit must be calibrated to compensate for phase errors due to fabrication variations. Calibration using photodetectors external to the mesh has been demonstrated for triangular meshes, but not rectangular meshes. Here, we propose an algorithm for the calibration of rectangular meshes using only external photodetectors and simulate it to evaluate its feasibility.

Multiport interferometers based on integrated beamsplitter meshes have recently captured interest as a platform for many emerging technologies. In this paper, we present a novel architecture for multiport interferometers based on the Sine-Cosine fractal decomposition of a unitary matrix. Our architecture is unique in that it is self-similar, enabling the construction of modular multi-chiplet devices. Due to this modularity, our design enjoys improved resilience to hardware imperfections as compared to conventional multiport interferometers. Additionally, the structure of our circuit enables systematic truncation, which is key in reducing the hardware footprint of the chip as well as compute time in training optical neural networks, while maintaining full connectivity. Numerical simulations show that truncation of these meshes gives robust performance even under large fabrication errors. This design is a step forward in the construction of large-scale programmable photonics, removing a major hurdle in scaling up to practical machine learning and quantum computing applications.

Universal multiport interferometers, which can be programmed to implement any linear transformation between multiple channels, are emerging as a powerful tool for both classical and quantum photonics. These interferometers are typically composed of a regular mesh of beam splitters and phase shifters, allowing for straightforward fabrication using integrated photonic architectures and ready scalability. The current, standard design for universal multiport interferometers is based on work by Reck et al. [Phys. Rev. Lett.73, 58 (1994)PRLTAO0031-900710.1103/PhysRevLett.73.58]. We demonstrate a new design for universal multiport interferometers based on an alternative arrangement of beam splitters and phase shifters, which outperforms that by Reck et al. Our design requires half the optical depth of the Reck design and is significantly more robust to optical losses.

Conventional multiport interferometers based on MZI meshes suffer from component imperfections, which limit their scaling. We introduce two new designs that overcome this limitation: a 3-splitter MZI for generic errors and a broadband MZI+Crossing design for more realistic correlated errors. These architectures, motivated by the correspondence between SU(2) and the Riemann sphere, are more error tolerant than the standard MZI mesh and support progressive self-configuration. Numerical simulations reveal orders-of-magnitude error reductions compared to the standard MZI mesh; moreover, the mesh is asymptotically perfect: the matrix error decreases with mesh size.

Coherent multiport interferometers are a promising approach to realize matrix multiplication in integrated photonics. However, most known architectures - such as MZI and beamsplitter meshes, as well as more general interferometers - suffer from complicated procedures for mapping the matrix elements of the desired transformation to specific phaseshifts in the device. We point out that the high programming complexity is intrinsic, rather than accidental. At the same time, we argue that interferometers admitting efficient programming algorithms in general yield a much lower useful output energy, which ultimately limits their accuracy and energy efficiency.