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Andrew Forbes

Publications and source records attributed to Andrew Forbes.

At least 19 recordsLinked to original sources
arXiv2026

Recovering topological information of light by topological learning

The evolution of modern-day communication networks towards optical solutions with enhanced capacity and robustness is driving interest in topological light waves, exploiting their stability against perturbations through a topological invariant, e.g., the skyrmion number. However, detecting the underlying topology remains a computationally intense process even under ideal conditions, becoming intractable after passing through strongly disordered channels, where the degradation into unrecognisable speckle appears to destroy the topology. Here, we propose and demonstrate a topology-enhanced artificial intelligence (AI) approach to recover and classify such apparently lost topological information by computationally leveraging topological invariants in the data across many length scales. By aligning the topological classification of information with the topology of light, our topology-enhanced learning protocol, termed TOPO$^{2}$, achieves highly efficient recognition of the topological states of light, even from speckle, without the need for any prior learning. Our approach outperforms benchmark tests against standard computational algorithms and has the benefit of requiring just a single intensity pattern as the input, facilitating single-shot operation. To demonstrate this, we leverage the skyrmion number as a robust data carrier of images through a disordered channel, using TOPO$^{2}$ to accurately reconstruct the transmitted images. This work synergises topological photonics and topological AI for unravelling hidden topological signatures in light, opening a pathway towards robust communications even in extreme disordered environments.

physics.optics↗
arXiv2026

Cluster randomized crossover trials with very few clusters but multiple periods: which analyses for continuous outcomes should be used?

Cluster randomized crossover (CRXO) trials are often used when individual randomization is impractical and the number of available clusters is limited. However, statistical analysis of CRXO trials is complex because of the need to account for complex correlation structures over time. It becomes especially challenging when very few clusters are used because standard modeling assumptions may lead to unstable variance estimates, poor confidence interval coverage, and inflated type I error. This study evaluates individual-level mixed-effects and fixed-effects models with and without a cluster-period random effect, cluster-period summary analysis using normal- or \(t\)-based inference, and two-period crossover-difference estimators. Using extensive simulation studies under both nested exchangeable and discrete time decay correlation structures, we compare model performance in terms of bias, root mean squared error, coverage probability, type I error, and convergence. Across scenarios, all models produced approximately unbiased treatment effect estimates, but their inferential performance differed substantially. Models that explicitly accounted for cluster-period heterogeneity generally provided the most reliable control of coverage and type I error, whereas simpler exchangeable models performed adequately only when the true correlation structure closely matched their assumptions. Cluster-period level analysis performance improved with increasing numbers of periods but was unreliable in the sparsest designs. Overall, the findings suggest that in CRXO trials with very few clusters, accurate modeling of cluster-period correlation is more important than the choice between fixed and random cluster intercepts, and that results from extremely sparse designs should be interpreted with caution.

stat.ME↗
arXiv2026

Nonlocal wavefront shaping through complex media

Wavefront shaping is a key technique for mitigating scattering in complex media, enabling advanced imaging and optical communication. Yet existing approaches are inherently local, requiring active correction elements - such as spatial light modulators or deformable mirrors - to lie directly in the optical path of the scattered light, which limits their integration into compact imaging systems. Here, we experimentally demonstrate nonlocal wavefront shaping using spatially entangled photon pairs. By applying a phase correction to a photon that never interacts with the scattering medium, we compensate for the distortions experienced by its entangled partner and restore their initial spatial correlations. Our approach physically decouples the wavefront correction from the scattering medium, paving the way for imaging through complex media in compact and otherwise inaccessible systems.

quant-ph↗
arXiv2026

Quantum skyrmion parallelism via metasurface-tailored high-dimensional entanglement

Quantum skyrmions are topological structures that have garnered significant interest due to their demonstrated robustness and versatility across diverse optical platforms. However, existing approaches for their generation are limited to producing pre-determined two dimensional qubit states with a single topology. Here we create multi-dimensional topological states by introducing a non-local interaction between high-dimensional photonic entanglement and a metasurface, where the topological transformation induced by the metasurface is made non-deterministic by the probabilistic nature of the interfacing entangled state. Within this framework, we demonstrate that individual quantum states can host multiple co-existing topologies that are only revealed upon measurement, allowing for their parallel transport within distinct spatial mode channels. We confirm this by revealing the rich topological landscape within our modified Hilbert space while controlling the desired output topology by orbital angular momentum (OAM) projections on one of the entangled photons, producing multiple non-local polarization-OAM entangled states characterized by distinct topological classes, all from a single metasurface device. Our results reveal new capability when structured high-dimensional entanglement is interfaced with structured matter capable of coupling photonic degrees of freedom, establishing a new pathway for the compact generation of complex quantum states.

quant-ph↗
arXiv2026

Topological space-time waves in complex channels

Structured light in space and time has become a powerful playground in which to explore the fundamental physics of wave systems, while simultaneously introducing new exotic forms of light, from spatio-temporal vortices to toroidal pulses of light. Yet their creation remains restricted by complex optical systems while directly observing their evolution in arbitrary channels remains elusive, complicated by the interplay of dispersion and diffraction and exacerbated by the lack of suitable detection tools. Here we create topological space-time beams in a single step by a resonant response of a symmetry-broken metasurface, mixing spatial, temporal and polarisation degrees of freedom in a single microwave field. Our realisation in the microwave regime allows us to directly observe their dynamics in arbitrary channels, from free-space to complex random media, showing the preservation of topology while the foundational degrees of freedom are scrambled. We use our control to show how to unscramble the space-time properties for the first crosstalk-free transmission of space-time waves. Our work advances the physics of space-time waves, introduces a new toolkit for their creation and control, and offers an exciting roadmap to their exploitation in real-world scenarios, e.g., for robust communications through noisy channels.

physics.optics↗
arXiv2026

VortexChat: An agentic framework for autonomous multi-objective integrated photonic design

The advancement of modern integrated photonics is frequently bottlenecked by device design workflows that rely heavily on manual simulation and expert intuition. While inverse design offers an alternative, it remains constrained by expert supervision and a lack of end-to-end automation. To address these issues, we present VortexChat, an agentic framework for the autonomous, end-to-end inverse design of integrated photonic devices directly from natural language specifications. VortexChat couples a large language model (LLM) decision agent with topology generation, gradient-based refinement, and full-wave electromagnetic simulation. This closed-loop architecture enables the system to iteratively decompose design objectives, orchestrate computational tools, and update strategies based on feedback with minimal human intervention. Constrained by the absolute metrics of the Vortex100 Benchmark, VortexChat autonomously generates devices that strictly meet all predefined performance thresholds without any human-in-the-loop. As an experimental demonstration, we fabricated a broadband terahertz perfect vortex beam multiplexer, autonomously designed by VortexChat, with measurements confirming high-efficiency operation, high mode purity and low inter-channel crosstalk in agreement with full-wave simulations. These results demonstrate that an LLM agent can assume key aspects of expert decision-making in photonic inverse design while maintaining physical fidelity and fabrication feasibility, providing a scalable route towards autonomous design of complex integrated photonic systems.

cs.AI↗
arXiv2026

Real-time estimation of the transmission matrix of an atmospheric channel

Optical wavelengths have received significant attention in free-space channels and are vital for applications in communications, imaging and sensing. Their widespread implementation is motivated by a variety of factors including improved bandwidths, increased security and higher energy efficiency. However, these advantages cannot be fully brought to bear in real-world scenarios due to the deleterious effects of atmospheric turbulence. Induced by small temperature and pressure fluctuations in the environment that vary rapidly in space and time, these effects cause significant power losses which decrease SNR, induce severe crosstalk in communication links, and greatly limit resolution of long-range imaging systems. To overcome this, we numerically and experimentally investigate the reconstruction of the transmission matrix of a time-evolving atmospheric channel with a real-time recursive optimization routine. We demonstrate that this estimation technique is able to keep up with the evolution of the channel and enables a significant improvement of communication-relevant quantities such as the coupling of the received light into a single-mode fiber while notably reducing the probability and duration of power outages, even in strong turbulence. Our results have immediate applications in free-space optical communication in both the classical and quantum regimes.

physics.optics↗
arXiv2026

Imprinting topology on thermal light

Topological structuring of light inevitably leverages on optical coherence to ensure that the imparted spatial phases are preserved, requiring highly coherent sources or coherence engineering embedded in the design. Now we show that thermal light can be spatially engineered to carry optical topologies in the form of Skyrmions. Such topologies are immune to time averaged decoherence, a fact we leverage on in reverse to create metasurface mediated incoherent topologies from a thermal source. The pristine nature of our measured Skyrmions validates the approach, while simulations reveal how coherence management in the metasurface design would further enhance the functionality. Remarkably, the generation stage inherits robustness from the topology, remaining immune to material and fabrication defects. Our work reports the first topologies from purely thermal light, opening a path to exploiting topology in ubiquitous everyday light sources.

physics.optics↗
arXiv2026

Tunable spatio-spectral Target Skyrmions and topological multiplexing

Optical Skyrmions have recently garnered much interest providing a potential avenue for high capacity, robust topological information transfer. Typically, Skyrmions are derived from the coupling of just two degrees of freedom (DoFs) limiting their versatility. In this work we realize spatio-spectral Skyrmions derived from the non-separability between three DoFs: wavelength, space and polarization. A compact and simple technique is used to generate the spatio-spectral vector beams (SSVB) carrying the desired Skyrmionic structure, offering simple pathways for complex Skyrmionic beam design. The topological structure, witnessed through a map between the spatio-spectral plane and the Poincar\'e sphere, exhibits an additional tunable $k\pi$ parameter thereby enhancing the number of controllable DoFs. Our three DoF construction allows us to propose a novel topological multiplexing strategy that independently encodes different Skyrmion numbers at different radii of the field. We experimentally demonstrate the practicality of this approach by transmitting and receiving three distinct Skyrmion numbers encoded into a single topological field, for the first form of mode division multiplexing with Skyrmion topology. This work opens up new avenues for dense information encoding using multiple topological channels encoded in a single light field.

physics.optics↗
arXiv2026

Towards digital phantoms: emulating scattering with a spatial light modulator

The distortion of light's degrees of freedom when passing through complex random media is of great interest across a diversity of fields, e.g., scattering in biological studies. Emulating such media in a controlled laboratory setting conventionally relies on real-world physical samples (e.g., white paint), inhomogeneous mixtures with embedded scatterers, or biological tissue-mimicking phantoms. Such methods, while effective in certain contexts, are not without complexity and limitations: the exact medium properties are challenging to control and often require laborious preparation, external characterisation techniques, are not easily reproducible between studies and cannot be matched precisely by numerical simulations. Here, we propose a simple all-digital implementation of random scattering which can be readily implemented on any setup capable of producing digital holograms. Our approach employs binary random phase masks encoded onto a spatial light modulator which perturbs the input beam's phase and amplitude. We highlight two methods to precisely tune distortion strengths which show excellent agreement between simulated and measured results. We demonstrate distortion strengths comparable to real-world scattering samples and illustrate two example applications to emulate scattering of scalar and vectorial structured light. Finally we showcase the versatility of this toolkit for emulating various amplitude and phase profiles and suggest several easy to implement alternative modalities accessible with this method. This digital phantom circumvents many of the practical challenges of physical samples, making it ideally suited for applications at the intersection of structured light, biological imaging and optical communications.

physics.optics↗
arXiv2026

Optical hopfions with arbitrary two winding numbers

Hopfions, as three-dimensional topologically nontrivial structures described by poloidal and toroidal winding numbers, hold promise as robust information carriers in spintronics, functional materials, and optical communications. Although they have been experimentally realized in various physical systems, such realizations have been restricted to low orders, with the winding numbers lacking tunability. Here, using optical fields as our platform, we outline how to make tunable hopfions in any order with any winding number. We use tailored superpositions of Laguerre-Gaussian modes in free-space as our construction, achieving effective control for arbitrary-order poloidal and toroidal winding numbers, which we demonstrate up to orders 5 and 3, respectively, for a new state-of-the-art. The resulting torus-knot structures are visualized experimentally via polarization filaments, confirming the designed topological textures. Our work reports an exotic optical topologies observed in free space, provides a systematic route hopfions of any order, with implications for topological photonics, optical communications, and analogies in magnetic and condensed-matter systems.

physics.optics↗
arXiv2026

Orthogonalised Self-Guided Quantum Tomography: Insights from Single-Pixel Imaging

We introduce the concept of self-guided imaging (SGI) as a linear analogue of self-guided quantum tomography (SGQT). We show that SGI is mathematically equivalent to single-pixel imaging (SPI). Taking inspiration from orthogonalised ghost imaging, a recent advance in SPI, we introduce orthogonalised SGQT. This requires no additional experimental overhead and leads to faster and more accurate final convergence, as we demonstrate numerically (fidelity $95.2\% \rightarrow 99.17\%$) and experimentally (fidelity $92.1\% \rightarrow 95.3\%$). This work suggests that further routines from SPI and SGQT can be interchanged to optimise measurements and convergence.

quant-ph↗
arXiv2026

High-Dimensional Quantum Photonics: Roadmap

The field of high-dimensional quantum photonics involves the use of multimode photonic degrees-of-freedom such as the spatial, temporal, or spectral structure of light to encode multi-level quantum states. Recent years have seen rapid progress in the development of methods to generate, manipulate, and distribute such quantum states of light and their use in a range of quantum technology applications that offer practical advantages over conventional qubit-based approaches. High-dimensional quantum states of light encoded in photonic time-bins, frequency-bins, transverse-spatial modes, waveguide paths, and temporal modes have enabled noise-robust fundamental tests of quantum mechanics, error-resilient and high-capacity quantum communication protocols, andas well as efficient approaches for quantum information processing, to name just a few examples. However, research in this field has progressed fairly independently, with little exchange across different photonic degrees-of-freedom or between experiment and theory and no comprehensive comparison between degrees-of-freedom. This roadmap aims to bridge this gap by surveying progress in each area and identifying shared challenges and opportunities that cut across two or more photonic degrees-of-freedoms. We review early work and state-of-the-art experimental techniques under development for high-dimensional quantum states encoded in single and entangled photons, as well as theoretical tools for their measurement and certification. We outline the main outstanding challenges for theory and each experimental degree-of-freedom, identifying promising future directions of research that may enable these to be overcome. We end by discussing interconnections and shared challenges centered around their distribution, measurement, and manipulation, with a view towards their integration into next-generation quantum technology platforms and applications.

quant-ph↗
arXiv2026

Reconfigurable circuit for mode tunable topological quantum structured light

Structured light in the quantum regime has garnered considerable attention due to the opportunities it offers when mixing light's internal degrees of freedom, for high-dimensional and multi-dimensional quantum states of light. A popular example is to harness polarisation and spatial entangled photons with a shared topological invariant that is robust against numerous families of noisy quantum channels. Yet, producing such states with high purity and adaptability remains challenging. Here we introduce a compact, self-locking Mach-Zehnder interferometer that integrates digital spatial light modulators with static beam displacers to map spatial-mode entanglement from a parametric down-conversion source onto topological entanglement with high fidelity. The device also mimics the action of a reprogrammable controlled-unitary gate, digitally driven by the spatial light modulator. This approach is an enabling platform and provides a practical route to generating reliable, high-purity quantum-structured light with topological features, both at the single-photon level and as entangled states, a direction of growing topical interest.

quant-ph↗
arXiv2026

Remote engineering of particle-like topologies to visualise entanglement dynamics

Skyrmions are a particle-like topology with a quantised skyrmion number, realised across condensed matter and photonic platforms alike. In quantum photonics, they constitute an emerging resource, promising robust quantum information encoding, so far realised as single photon and bi-photon entangled states. Here we report the first visualisation of tripartite entanglement dynamics through topological structure using spin-skyrmion entangled states, where the topology of a single photon is remotely controlled through the spin of its entangled partner. We visualise our tripartite state theoretically by introducing the notion of a topological Bloch sphere that completely captures the entanglement and topolological features of the state. By leveraging this state, we realise the first quantum multiskyrmions, comprising multiple localised skyrmions within a single structure, that emulate signatures of their magnetic counterparts. We verify this experimentally and show that traversing our topological sphere reveals entanglement-driven particle-like motion of the localised topological structures. These dynamics unveil a physical manifestation of tripartite entanglement correlations which we illustrate by example of GHZ-like states, enabling a visualisation of multiple Bell states encoded within our system. Our work opens exciting possibilities for quantum sensing by mapping complex quantum channel features onto topological observables of multipartite states and offers a promising avenue for harnessing quantum topologies for multi-level encoding quantum communication schemes.

quant-ph↗
arXiv2026

Topological robustness of orbital angular momentum entanglement in stochastic channels

Orbital angular momentum (OAM) entanglement gives access to multiple qubit and high dimensional Hilbert spaces, but is unfortunately susceptible to disturbance, decaying in real-world noisy channels. Here, we show there is an underlying topology arising from OAM entanglement that is robust to such channels, which we demonstrate using atmospheric turbulence -- exemplary of stochastic or chaotic media. Using a quantum channel with various turbulence strengths, we find the OAM topological observable preserved even though the OAM itself is shown to be highly sensitive to the turbulence. We show this is true for mixed states too, with the OAM topology intact even as the purity of the state decreases due to decoherence. Our work offers a new perspective on OAM entanglement preservation, and may easily be extended to other spatial bases, degrees of freedom, as well as complex channels, whether static or dynamic.

quant-ph↗
arXiv2026

Particle-like topologies of light in turbulent complex media

The basic building blocks of many forms of optical topologies are particle-like singularities in phase and polarisation, giving rise to lines of darkness that weave complex threads in 3D space. Although known for half a century since seminal work on dislocations in wave trains, their behaviour in complex media remains under debate, especially with respect to their relative stability. Here we show that polarisation and phase vortices behave identically in one-sided turbulent complex channels. We perform complementary numerical and experimental studies using atmospheric turbulence as a test case, demonstrating agreement and equivalent dynamics. Our work addresses open questions on optical topologies and will be relevant to their harnessing for applications such as sensing, communication, imaging, and information transfer in noisy or complex environments.

physics.optics↗
arXiv2026

Fractional optical skyrmions

Optical topologies in the form of Skyrmions have attracted significant interest of late, where their integer Skyrmion number has been shown to be robust to complex media. Here we create the first fractional Skyrmions by structuring light as a vectorial superposition of non-integer orbital angular momentum. We unravel the map structure to reveal a new phenomenon, the abrupt transition jumps in skyrmion number, which serves to reinforce the integer nature of skyrmion topologies. Our experimental demonstration agrees well with simulation, opening a new spectrum of optical topologies to explore, with exciting possibilities in optical communication and sensing.

physics.optics↗