Self-configuring high-speed multi-plane light conversion

TL;DR

This work addresses the fragility of traditional multi-plane light converters (MPLCs) by introducing a fully self-configuring, forward-only in-situ optimization that treats the MPLC as a complex medium and learns the phase profiles directly from transfer-matrix measurements. A fast-switching MEMS-based phase-only light modulator platform enables rapid exploration of millions of MPLC configurations, with phase drift stabilization ensuring reliable interferometric TM measurements. The method generalizes to multiple input modes, achieving simultaneous reshaping and universal mode sorting (e.g., Laguerre-Gaussian, Hermite-Gaussian) with high fidelity and reduced cross-talk, converging in minutes even for tens of thousands of parameters. This approach paves the way for ultra-fast, high-dimensional, high-fidelity free-space diffractive neural networks and has potential impact on optical communications, imaging through scattering media, and all-optical information processing.

Abstract

Multi-plane light converters (MPLCs) - also known as linear diffractive neural networks - are an emerging optical technology, capable of converting an orthogonal set of optical fields into any other orthogonal set via a unitary transformation. MPLC design is a non-linear problem typically solved by optimising a digital model of the optical system. However, inherently high levels of design complexity mean that even a minor mismatch between this digital model and the physically realised MPLC leads to a severe reduction in real-world performance. Here we address this challenge by creating a self-configuring free-space MPLC. Despite the large number of parameters to be optimised (typically tens of thousands or more), our proof-of-principle device converges in minutes using a method in which light only needs to be transmitted in one direction through the MPLC. Two innovations make this possible. Firstly, we devise an in-situ optimisation algorithm combining wavefront shaping with the principles of wavefront matching that would conventionally be used to inverse-design MPLCs offline in simulation. Secondly, we introduce a new MPLC platform incorporating a microelectromechanical system (MEMS) phase-only light modulator - allowing rapid MPLC switching at up to kiloHertz rates. Our scheme automatically accounts for the physical characteristics of all system components and absorbs any unknown misalignments and aberrations into the final design. We demonstrate self-configured MPLCs capable of mapping random orthogonal speckle input fields to well-defined Laguerre-Gaussian and Hermite-Gaussian output modes, as well as universal mode sorters. Our work paves the way towards large-scale ultra-high-fidelity fast-switching MPLCs and diffractive neural networks, which promises to unlock new applications in areas ranging from optical communications to optical computing and imaging.

Figures (7)

• Figure 1: Self-configuring multi-plane light conversion. (a) A schematic of a 4-plane MPLC based on a fast switching phase-only light modulator (PLM). Light reflects between different regions of the PLM and an opposing mirror. The PLM micro-mirror heights are optimised to simultaneously transform a set of input modes, such as the three orthogonal speckle modes shown, to a target set of output modes, such as the three Hermite-Gaussian modes at the output. (b) Experimental results showing the automatic in-situ optimisation of an MPLC designed to transform a single arbitrarily shaped input mode ($\mathbf{u}$) to a target output mode ($\mathbf{v}$), in this case converting a speckle pattern (left most panel) into a Laguerre-Gaussian beam, LG$_{p \ell}$, with a vortex charge of $\ell=1$ and radial index $p=1$ (target mode shown in right most panel). The central panels show experimental results of the progression of the output mode throughout the MPLC optimisation process. (c) The same as in (b), but here showing experimental results of the design of an MPLC to simultaneously transform three input orthogonal speckle modes into three Hermite-Gaussian output modes HG$_{ab}$ of mode order indexed by $a$ and $b$. Each speckle mode is formed from the complex weighted sum of a set of orthogonal step-index multi-mode fiber eigenmodes, which ensures that the speckle modes are spatially localised. Supplementary information (SI) §1 shows the fidelity as a function for mask update number for the experiments in (b) and (c).
• Figure 2: In-situ MPLC optimisation algorithm. A flow chart depicting the steps to calculate a single phase mask update.
• Figure 3: Experimental setup and progression of phase mask design. (a) A schematic of our experiment, which is based on a Mach-Zehnder interferometer. A 1 mW linearly polarised laser beam of wavelength $\lambda=633$ nm is split into two paths by a polarising beamsplitter (PBS). Light in the upper path is shaped by a liquid crystal SLM (Hamamatsu X13138-01), and transmitted through the MPLC, consisting of a PLM (Texas Instruments DLP6750 EVM) placed opposite a mirror, with a plane spacing of $\sim$6 cm. A flip mirror enables the shaped light incident on plane 1 of the MPLC to be directly imaged (using Cam 1, Basler acA640-300gm). Light exiting the MPLC is combined with the reference beam (which takes the lower path of the interferometer) via a beamsplitter (BS) and is imaged onto a camera (Cam 2, Basler acA640-300gm). The field is reconstructed using single-shot off-axis digital holography. (b) Examples of MPLC phase masks displayed throughout the in-situ optimisation procedure -- in this case the MPLC is designed to sort 7 orthogonal speckle modes. Top row: first mask update (Plane 1). Middle row: MPLC design after four mask updates (planes 1-4). Bottom row: final MPLC design after 40 mask updates (i.e., each of the four planes updated 10 times).
• Figure 4: Self-configured Hermite-Gaussian and speckle mode sorters. Upper panels (a-e): a self-configured 10-mode Hermite-Gaussian (HG) mode sorter. (a) Examples of individual input modes being focussed into specific output channels. (b) All input modes, here shown in the arrangement they will be sorted into. (c) A view of the output channels. Here we plot the incoherent sum of the intensity at the output when the MPLC is illuminated with each mode in turn. (d) The mean total cross-talk throughout the optimisation process ($M=4$ planes with $C=5$ cycles yields $M\times C=20$ mask updates). The mode-dependent cross-talk is given by the total intensity of light transmitted into the wrong output channels, divided by the total intensity of light transmitted into all channels, when the MPLC is illuminated with a given mode. The mean total cross-talk is the mode-dependent cross-talk averaged over all input modes. (e) The cross-talk matrix. Column $n$ shows the intensity of light transmitted into all output channels when the MPLC is illuminated with mode $n$. The average cross-talk is -21 dB. Lower panels (f-j): equivalent plots as the upper row, here showing a self-configured 7-mode speckle sorter. In this case the average cross-talk is -15 dB.
• Figure 5: Fidelity progression during self-configuring MPLC optimisation. Data on the left corresponds to Figure 1(b), and data on the right - to Figure 1(c).