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Optics Express

Reconfigurable unitary transformations of optical beam arrays

Aldo C. Martinez-Becerril, Siwei Luo, Liu Li, Jordan T. R. Pagé, Lambert Giner, Raphael A. Abrahão, Jeff S. Lundeen

Published Oct 8, 2024• 4 citations
Publisher

Abstract

Spatial transformations of light are ubiquitous in optics, with examples ranging from simple imaging with a lens to quantum and classical information processing in waveguide meshes. Multi-plane light converter (MPLC) systems have emerged as a platform that promises completely general spatial transformations, i.e., a universal unitary. However, until now, MPLC systems have demonstrated transformations that are far from general, e.g., converting from a Gaussian to Laguerre-Gauss mode. Here, we demonstrate the promise of an MLPC, the ability to impose an arbitrary unitary transformation that can be reconfigured dynamically. Specifically, we consider transformations on superpositions of parallel free-space beams arranged in an array, which is a common information encoding in photonics. We experimentally test the full gamut of unitary transformations for a system of two parallel beams and make a map of their fidelity. We obtain an average transformation fidelity of 0.85 ± 0.03. This high-fidelity suggests that MPLCs are a useful tool for implementing the unitary transformations that comprise quantum and classical information processing.

DOI
10.1364/oe.535204

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Spatial transformations of light are ubiquitous in optics, with examples ranging from simple imaging with a lens to quantum and classical information processing in waveguide meshes. Multi-plane light converter (MPLC) systems have emerged as a platform that promises completely general spatial transformations, i.e., a universal unitary. However, until now, MPLC systems have demonstrated transformations that are far from general, e.g., converting from a Gaussian to Laguerre-Gauss mode. Here, we demonstrate the promise of an MLPC, the ability to impose an arbitrary unitary transformation that can be reconfigured dynamically. Specifically, we consider transformations on superpositions of parallel free-space beams arranged in an array, which is a common information encoding in photonics. We experimentally test the full gamut of unitary transformations for a system of two parallel beams and make a map of their fidelity. We obtain an average transformation fidelity of 0.85 ± 0.03. This high-fidelity suggests that MPLCs are a useful tool for implementing the unitary transformations that comprise quantum and classical information processing.
Spatial transformations of light are ubiquitous in optics, with examples ranging from simple imaging with a lens to quantum and classical information processing in waveguide meshes. Multi-plane light converter (MPLC) systems have emerged as a platform that promises completely general spatial transformations, i.e., a universal unitary. However until now, MPLC systems have demonstrated transformations that are far from general, e.g., converting from a Gaussian to Laguerre-Gauss mode. Here, we demonstrate the promise of an MLPC, the ability to impose an arbitrary unitary transformation that can be reconfigured dynamically. Specifically, we consider transformations on superpositions of parallel free-space beams arranged in an array, which is a common information encoding in photonics. We experimentally test the full gamut of unitary transformations for a system of two parallel beams and make a map of their fidelity. We obtain an average transformation fidelity of 0.85±0.030.85 \pm 0.030.85±0.03. This high-fidelity suggests MPLCs are a useful tool implementing the unitary transformations that comprise quantum and classical information processing.
Programmable linear optical interferometers are a core primitive in optical signal processing, quantum information processing, and photonic computing. Existing photonic-integrated implementations realize arbitrary MMM-mode unitaries using Mach--Zehnder-interferometer meshes whose footprint and accumulated loss scale with O(M2)O(M^2)O(M2) optical components. Here we analyze and experimentally demonstrate a programmable architecture for implementing linear optical transformations directly on spatially tiled free-space {\em pixel modes} using multi-plane light conversion (MPLC). In this architecture, MMM spatial modes arranged on a transverse lattice undergo a unitary transformation and are mapped to MMM output modes of identical geometry through a sequence of programmable phase masks separated by free-space propagation segments. Numerical simulations show that arbitrary MMM-mode unitaries can be compiled to a desired high fidelity using a number of phase planes that scales approximately linearly with MMM. Using a spatial-light-modulator-based MPLC, we experimentally demonstrate programmable interferometers acting on up to 161616 spatial pixel modes, including tunable beamsplitters, Hadamard unitaries, spatial permutations, and partial unitaries on select subsets of modes. These results establish MPLC-based pixel-mode interferometers as a promising architecture for programmable linear optics with applications in classical and quantum optical interconnects, photonic switching, and quantum information processing.
High-dimensional entangled photons are a key resource for advanced quantum information processing. Efficient processing of high-dimensional entangled photons requires the ability to synthesize their state using general unitary transformations. The leading technology for processing photons in high-dimensions is integrated multiport interferometers. However, such devices are incompatible with free-space and fiber-based systems, and their architecture poses significant scaling challenges. Here we unlock these limitations by demonstrating a reconfigurable processor of entangled photons that is based on multi-plane light conversion (MPLC), a technology that was recently developed for multiplexing hundreds of spatial modes for classical free-space and fiber communication. To demonstrate the flexibility of MPLC, we perform four key tasks of quantum information processing using the same MPLC hardware: entanglement certification, tailored two-photon interference, arbitrary state transformations, and mode conversion. Based on the high degree of control we obtain, we expect MPLC will become a leading platform for future quantum technologies.
Abstract The ability to manipulate the spatial structure of light is fundamental for a range of applications, from classical communication to quantum information processing. Multi-plane light conversion (MPLC) addresses the limitations of single-plane modulation by enabling full control over multiple spatial modes of light through a series of phase masks separated by free-space propagation. In this tutorial, we present a step-by-step guide for building and aligning a 10-plane programmable light converter using a single spatial light modulator and standard optical components. Our method allows precise alignment, achieving single-pixel accuracy with a relatively simple setup. We hope that this guide will help other researchers to quickly adopt and adapt MPLC technology for their own experiments.
Multi-plane light converters (MPLCs) are an emerging beam shaping technology capable of deterministically mapping a basis of input spatial light modes to a different basis of output modes. The ability to perform such multi-modal spatial reformatting operations has many future applications in both classical and quantum photonics, spanning from optical communications to photonic computing and advanced imaging. In this work we fabricate miniaturised transmissive MPLCs fully-encapsulated within a fused silica glass chip using single-step 3D direct laser writing. Our approach relies on the formation of femto-second laser induced birefringent nanogratings with a spatially controllable slow-axis orientation. Multiple layers of these nanogratings are laser-written throughout the volume of the glass to create a sequence of axially separated geometric phase holograms which imprint controllable phase patterns onto circularly polarised read-out light propagating through them. We construct and test a range of proof-of-concept laser-written MPLCs operating in the visible (lambda = 633nm). These miniature beam multiplexers are formed from up to 5 separate phase masks of width ~260um, cascaded along a total length of ~2.7mm, thus occupying a compact volume of ~0.15 mm3. We first demonstrate Hermite-Gaussian (HG) mode sorters capable of diverting the energy carried by up to 28 overlapping HG modes into spatially separated output channels. We next create a 7-mode orthogonal speckle sorter, highlighting the universal nature of the spatial transformations it is possible to encode. Finally, we show analogue optical matrix multiplications achieved by passively scattering light through these 3D structured glass elements. Our work begins to merge the concepts of free-space optics with 3D integrated photonics in glass and plots a path towards the rapid prototyping of robust monolithic MPLC technology.
Structured light beams are essential in optical communications, quantum information processing, and light-matter interactions. The generation and conversion of high-purity structured light beams are crucial for these applications. In this study, we propose a bidirectional high-purity structured light beam transformation approach based on the multi-plane light conversion (MPLC) method. This approach enables mutual conversion of arbitrary orthogonal modes and precise control of system loss and mode purity. Using the proposed method, we demonstrate the conversion of 7-modes Gaussian beams array (GBA) and perfect vortex beams (PVB), achieving a bidirectional output modes signal-to-noise ratio (SNR) exceeding 30 dB and a loss of 5.23 dB. For generation of 13-modes, an SNR above 25 dB and an insertion loss below 5.45 dB are obtained. Furthermore, the validity of methods is confirmed by generating multi-wavelength and structured light beams with more complex field distribution. The work paves the way toward structured-light-beam-based optical communications, high-dimensional quantum communications, and advancements in MPLC.