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AI and Optical Data Sciences

Design of asymptotically perfect linear photonic circuits

Ryan Hamerly, Saumil Bandyopadhyay, Alexander Sludds, Dirk Englund

Published Mar 3, 2022• 0 citations
Publisher

Abstract

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.

DOI
10.1117/12.2610494

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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.
Component errors limit the scaling of programmable coherent photonic circuits. These errors arise because the standard tunable photonic coupler-the Mach-Zehnder interferometer (MZI)-cannot be perfectly programmed to the cross state. Here, we introduce two modified circuit architectures that overcome this limitation: (1) a 3-splitter MZI mesh for generic errors, and (2) a broadband MZI+Crossing design for correlated errors. Because these designs allow for perfect realization of the cross state, the matrix fidelity no longer degrades with increased mesh size, allowing scaling to arbitrarily large meshes. The proposed architectures support progressive self-configuration, are more compact than previous MZI-doubling schemes, and do not require additional phase shifters. This removes a key limitation to the development of very-large-scale programmable photonic circuits.
Universal linear programmable photonic circuits, composed of an array of Mach-Zehnder interferometers (MZIs), are fidelity-limited devices and are prohibitively difficult to scale. To address these limitations, we propose a compact and non-feedforward recurrent MZI topology wherein light can propagate in both directions. Our recurrent mesh achieves O ( N ) scaling by building imperfect beamsplitters in series to build perfect transformations. We theoretically examine the error tolerance of our proposed recurrent interferometer under imperfect mesh parameters. Our numerical results indicate that our proposed recurrent mesh permits more than an order of magnitude reduction in implementing unitary transformations.
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.
Realistic multiport interferometers (beamsplitter meshes) are sensitive to component imperfections, and this sensitivity increases with size. Self-configuration techniques can be employed to correct these imperfections, but not all techniques are equal. This paper highlights the importance of algorithmic stability in self-configuration. Na\"{\i}ve approaches based on sequentially setting matrix elements are unstable and perform poorly for large meshes, while techniques based on power ratios perform well in all cases, even in the presence of large errors. Based on this insight, we propose a self-configuration scheme for triangular meshes that requires only external detectors and works without prior knowledge of the component imperfections. This scheme extends to the rectangular mesh by adding a single array of detectors along the diagonal.
Photonic information processing demands programmable multiport interferometers capable of implementing arbitrary transfer matrices, for which planar meshes of error-sensitive Mach-Zehnder interferometers are usually exploited. We propose an alternative design that uses a single-static beam splitter (BS) and a variable phase shift as the building blocks. The design possesses superior resilience to manufacturing errors and losses without extra elements added into the scheme. Namely, the power transmissivities of the static BSs can take arbitrary values in the range from ≈1/2 to ≈4/5. In this Letter, we show that the fraction of transfer matrices non-implementable by the interferometers of our design diminishes rapidly with its size.