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General in situ feedback control of cascaded liquid crystal spatial light modulators for structured field generation

An Aloysius Wang, Yuxi Cai, Zhenglin Li, Ruofu Liu, Yifei Ma, Patrick S Salter, Chao He

TL;DR

The work addresses robust, real-time generation of structured light and matter fields with cascaded LC-SLMs under environmental drift and component variability. It introduces a general in situ feedback framework that recasts the high-dimensional phase optimization as decoupled pixel-wise updates on manifolds $S^2$ and $\mathrm{SO}(3)$ using a Gauss–Seidel scheme, first-order local expansions, and area averaging. Experimental demonstrations show rapid convergence for polarization fields on the Poincaré sphere and for matter-field rotations, including scenarios with engineered vectorial aberrations, highlighting practical robustness and real-time operation. The approach is extensible to other optical-retarder-based platforms and arbitrary target manifolds, enabling reliable, cascaded architectures for structured-field generation in real-world settings.

Abstract

Cascaded liquid crystal spatial light modulators provide a versatile strategy for the generation of structured light and matter fields, with applications including optical communications, photonic computing, and topological field engineering. However, experimental imperfections, such as temperature-dependent liquid crystal response, variations between individual pixels, and alignment errors, present significant engineering challenges in generating high-quality fields. Moreover, changes in experimental conditions over time mean that calibrating each component once is insufficient for maintaining long-term, high-quality field generation. To address this, we present a general engineering approach based on a bespoke, physically informed, and manifold-constrained gradient-descent scheme that enables in situ feedback control, compensating for such errors in real time without the need to alter the experimental setup. We further demonstrate the correction efficacy of our proposed strategy through experiments in both spatially varying light and matter field generation, including scenarios in which complex vectorial aberrations are artificially introduced into the setup. Together, these demonstrations underscore the practicality of our method and its suitability for deployment in real-world experimental environments, paving the way for robust operation of cascaded architectures for structured field generation.

General in situ feedback control of cascaded liquid crystal spatial light modulators for structured field generation

TL;DR

The work addresses robust, real-time generation of structured light and matter fields with cascaded LC-SLMs under environmental drift and component variability. It introduces a general in situ feedback framework that recasts the high-dimensional phase optimization as decoupled pixel-wise updates on manifolds and using a Gauss–Seidel scheme, first-order local expansions, and area averaging. Experimental demonstrations show rapid convergence for polarization fields on the Poincaré sphere and for matter-field rotations, including scenarios with engineered vectorial aberrations, highlighting practical robustness and real-time operation. The approach is extensible to other optical-retarder-based platforms and arbitrary target manifolds, enabling reliable, cascaded architectures for structured-field generation in real-world settings.

Abstract

Cascaded liquid crystal spatial light modulators provide a versatile strategy for the generation of structured light and matter fields, with applications including optical communications, photonic computing, and topological field engineering. However, experimental imperfections, such as temperature-dependent liquid crystal response, variations between individual pixels, and alignment errors, present significant engineering challenges in generating high-quality fields. Moreover, changes in experimental conditions over time mean that calibrating each component once is insufficient for maintaining long-term, high-quality field generation. To address this, we present a general engineering approach based on a bespoke, physically informed, and manifold-constrained gradient-descent scheme that enables in situ feedback control, compensating for such errors in real time without the need to alter the experimental setup. We further demonstrate the correction efficacy of our proposed strategy through experiments in both spatially varying light and matter field generation, including scenarios in which complex vectorial aberrations are artificially introduced into the setup. Together, these demonstrations underscore the practicality of our method and its suitability for deployment in real-world experimental environments, paving the way for robust operation of cascaded architectures for structured field generation.
Paper Structure (3 sections, 19 equations, 3 figures, 2 algorithms)

This paper contains 3 sections, 19 equations, 3 figures, 2 algorithms.

Table of Contents

  1. Feedback control strategy
  2. Polarization field generation
  3. Matter field generation

Figures (3)

  • Figure 1: Experimental results (Light field generation). Measured Stokes fields and corresponding $\ell^2$-error distributions (pixelwise and histogram) for various target Stokes fields across five feedback-loop iterations. For each histogram, the $x$-axis represents the $\ell^2$-error, while the $y$-axis is implicitly defined so that the total count across all bins equals the total number of camera pixels. A four-SLM cascade is used, with the relevant experimental configuration shown above. Throughout this paper, Stokes fields are depicted using color to represent the azimuthal angle on the Poincaré sphere and saturation to represent height shen_optical_2023. (Top left) A lattice of randomly generated polarization states, which provides multiple analyzing channels and can thereby be used for applications such as one-shot polarization measurements. (Middle and bottom left) Color-encoded polarization images depicting a portrait and the Vectorial Optics and Photonics Group logo at the University of Oxford. (Right) Skyrmions of order 1, 10 and 20, respectively.
  • Figure 2: Experimental results (Light field generation with aberration). Measured Stokes fields and corresponding $\ell^2$-error distribution (pixelwise and histogram) for various target Stokes fields across feedback-loop iterations under different polarization aberrations. For each target field, four feedback-loop iterations are performed (with iterations 0, 2, and 4 shown), while nine different polarization aberrations are considered, each characterized by a distinct maximum spatial frequency and maximum retardance. (Top) Phase pattern applied to the fourth SLM, mimicking a band-limited polarization aberration. (Middle) Experimental results for a target field that is uniformly right-circularly polarized. (Bottom) Experimental results for a target field consisting of a lattice of randomly generated polarization states, identical to that presented in Fig. \ref{['fig:experiment1']}
  • Figure 3: Experimental results (Matter field). Measured Mueller matrices and corresponding Frobenius-norm error distributions (pixelwise and histogram) for various target matter fields across three feedback-loop iterations. (Top) An order-1 skyrmion photo-adder Wang2025PerturbationResilient (Bottom) A lattice of random elliptical retarders.