arXiv subjects

Matthew R. Foreman

Publications and source records attributed to Matthew R. Foreman.

At least 19 recordsLinked to original sources

arXiv2026

Role of Spatial Coherence in Single-Shot Lensless Image Reconstruction

Lensless imaging is a technique that recovers object information computationally from diffraction patterns recorded without imaging optics, making its performance strongly dependent on the forward model used during image reconstruction. A common source of reconstruction error is the assumption of fully coherent propagation, even when the illumination exhibits partial spatial coherence in practice. Here, the role of spatial coherence is examined for assorted object classes using a coherence-aware forward model based on generalised van Cittert-Zernike Schell propagation. Simulated measurements are generated over a controlled range of effective source spatial coherence lengths and reconstructed using either a partially coherent forward model or a conventional coherent propagation model. Our results show that decreasing spatial coherence progressively degrades reconstructions under the coherent assumption, whereas incorporating partial coherence can preserve object structure and improve image quality, particularly for dense high-spatial-frequency features. Reconstructions from experimental measurements further confirm the practical need to use coherence-aware inversion under partially spatially coherent illumination. These findings establish spatial coherence as a defining component of the inverse problem in lensless imaging and provide a route to optimization of partially coherent lensless imaging systems.

physics.optics↗

arXiv2026

Programmable Hybrid Exceptional Points in Passive Scattering Networks

Exceptional points (EPs) have long promised enhanced sensing of physical signals, but have practically been limited by simultaneous enhancement of noise. Aligning an EP's non-analytic response with target perturbations while suppressing noise has, however, remained challenging. Here we show that fully passive, phase-tuned multi-port scattering networks enable scattering EPs with tailored anisotropic response to perturbations. We leverage projection-induced non-unitarity to realize effective non-Hermitian behavior when measuring only a subset of system ports. By formulating EP design in terms of the discriminant of the projected scattering sub-block and its directional derivatives, we give control-counting rules relating the number of programmable link phases to achievable Riemann surface topologies. We demonstrate our framework in a four-port photonic network by designing both an anisotropic EP and a Dirac-type EP with linear splitting along two parametric directions. We further suppress the global thermal drift response of a network-based sensor to a 3/2 power-law scaling while retaining square-root sensitivity to localized signals. Since the effective non-Hermiticity arises purely from port projection, our approach transfers to integrated photonic and microwave meshes, acoustic circuits, and projected metasurfaces, offering a phase-only route to reconfigurable non-Hermitian response and noise-robust EP sensing.

physics.optics↗

arXiv2026

Anisotropy in Fourier space optical memory effect correlations

We investigate anisotropy in Fourier-domain speckle correlations associated with the optical memory effect in disordered scattering media. Within a single scattering framework, we show that while the conventional memory effect constrains transverse wavevector shifts, the correlation strength also depends non-trivially on differences in the axial wavevector components. Our theory is supported by numerical simulations of a three-dimensional, single scattering medium, which show excellent agreement with theory. We extend the analysis to pseudo-correlations, demonstrating that analogous anisotropic behavior arises in the conjugate memory effect. Our results highlight the often neglected role of axial disorder in scattered field correlations.

physics.optics↗

arXiv2026

Single-Shot Lensless Imaging with Physics Guided Genetic Programming

Lensless optical imaging eliminates the need for refractive optics, enabling compact and low-cost cameras with a large field-of-view, supporting point-of-care diagnostics and industrial monitoring. Practical deployments, however, remain constrained by ill-posed image reconstruction pipelines that require multiple measurements, careful calibration or object-specific training, thus limiting robustness and scalability. In this work, we introduce a single-shot lensless imaging framework that reconstructs complex objects from only a single recorded intensity pattern using a genetically programmed iterative algorithm. Our method couples a wave-propagation model with an adaptive meta-optimisation strategy to jointly estimate the object amplitude, object phase, and effective object-detector distance. Experiments demonstrate high-fidelity recovery of amplitude objects, including a USAF target and 2~$\mu$m silicon beads on a glass slide, as well as a phase-dominant biological sample consisting of U2OS cells on a glass slide. Across multiple object types, wavelengths, and propagation distances, the same learned policy maintains high reconstruction quality with minimal retuning, indicating strong out-of-distribution generalisation. As a practical demonstration, the framework is integrated with a $\beta$-amyloid-based optical digital bead assay under wide field-of-view acquisition. The resulting platform combines single-shot capture, compact hardware, and accurate reconstruction of complex fields, enabling rapid, portable assays in which throughput, alignment tolerance, and cost are critical.

physics.optics↗

arXiv2026

Extended scattering channels for random matrix simulations of polarized light transport

Modeling the propagation of light through disordered media is central to understanding and controlling wave transport in diverse optical and mesoscopic applications. Here, we present a random matrix simulation framework for modeling the transport of polarized light through random media composed of arbitrary particulate scatterers. Our approach employs extended scattering channels applied to angular spectral decompositions of the underlying fields, enabling flexible representations of arbitrary illumination and detection profiles. In contrast to previous work, this framework provides a rigorous treatment of scattering matrix correlations and offers novel geometric insights into the optical memory effect. We provide a detailed exposition of the underlying theory and illustrate several key features through numerical simulations. Our work is supported by a free accompanying codebase.

physics.optics↗

arXiv2025

Hypothesis-Based Particle Detection for Accurate Nanoparticle Counting and Digital Diagnostics

Digital assays represent a shift from traditional diagnostics and enable the precise detection of low-abundance analytes, critical for early disease diagnosis and personalized medicine, through discrete counting of biomolecular reporters. Within this paradigm, we present a particle counting algorithm for nanoparticle based imaging assays, formulated as a multiple-hypothesis statistical test under an explicit image-formation model and evaluated using a penalized likelihood rule. In contrast to thresholding or machine learning methods, this approach requires no training data or empirical parameter tuning, and its outputs remain interpretable through direct links to imaging physics and statistical decision theory. Through numerical simulations we demonstrate robust count accuracy across weak signals, variable backgrounds, magnification changes and moderate PSF mismatch. Particle resolvability tests further reveal characteristic error modes, including under-counting at very small separations and localized over-counting near the resolution limit. Practically, we also confirm the algorithm's utility, through application to experimental dark-field images comprising a nanoparticle-based assay for detection of DNA biomarkers derived from SARS-CoV-2. Statistically significant differences in particle count distributions are observed between control and positive samples. Full count statistics obtained further exhibit consistent over-dispersion, and provide insight into non-specific and target-induced particle aggregation. These results establish our method as a reliable framework for nanoparticle-based detection assays in digital molecular diagnostics.

physics.comp-ph↗

arXiv2025

Generalized Wigner-Smith theory for perturbations at exceptional and diabolic point degeneracies

Spectral degeneracies, including diabolic (DP) and exceptional (EP) points, exhibit unique sensitivity to external perturbations, enabling powerful control and engineering of wave phenomena. We present a residue-based perturbation theory that quantifies complex resonance splitting of DP and EP type spectral degeneracies using generalized Wigner-Smith operators. We validate our theory using both analytic Hamiltonian models and numerical electromagnetic simulations, demonstrating excellent agreement across a range of cases. Our approach accurately predicts degenerate resonance splitting using only scattering data, offering a powerful framework for precision tuning, inverse design, and practical exploitation of non-Hermitian phenomena.

physics.optics↗

arXiv2025

Topological Engineering of High-Order Exceptional Points through Transformation Optics

Exceptional points (EPs) in non-Hermitian photonic systems have attracted considerable research interest due to their singular eigenvalue topology and associated anomalous physical phenomena. These properties enable diverse applications ranging from enhanced quantum metrology to chiral light-matter interactions. Practical implementation of high order EPs in optical platforms however remains fundamentally challenging, requiring precise multi-parameter control that often exceeds conventional design capabilities. This work presents a novel framework for engineering high order EPs through transformation optics (TO) principles, establishing a direct correspondence between mathematical singularities and physically controllable parameters. Our TO-based paradigm addresses critical limitations in conventional Hamiltonian approaches, where abstract parameter spaces lack explicit connections to experimentally accessible degrees of freedom, while simultaneously providing full-field mode solutions. In contrast to prevailing parity-time-symmetric architectures, our methodology eliminates symmetry constraints in EP design, significantly expanding the possibilities in non-Hermitian photonic engineering. The proposed technique enables unprecedented control over EP formation and evolution in nanophotonic systems, offering new pathways for developing topological optical devices with enhanced functionality and robustness.

physics.optics↗

arXiv2024

Generalized Wigner-Smith analysis of resonance perturbations in arbitrary $Q$ non-Hermitian systems

Perturbing resonant systems causes shifts in their associated scattering poles in the complex plane. In a previous study [arXiv: 2408.11360], we demonstrated that these shifts can be calculated numerically by analyzing the residue of a generalized Wigner-Smith operator associated with the perturbation parameter. In this work, we extend this approach by connecting the Wigner-Smith formalism with results from standard electromagnetic perturbation theory applicable to open systems with resonances of arbitrary quality factors. We further demonstrate the utility of the method through several numerical examples, including the inverse design of a multi-layered nanoresonator sensor and an analysis of the enhanced sensitivity of scattering zeros to perturbations.

quant-ph↗

arXiv2024

Perturbing scattering resonances in non-Hermitian systems: a generalized Wigner-Smith operator formulation

Resonances of open non-Hermitian systems are associated with the poles of the system scattering matrix. Perturbations of the system cause these poles to shift in the complex frequency plane. In this work, we introduce a novel method for calculating shifts in scattering matrix poles using generalized Wigner-Smith operators. We link our method to traditional cavity perturbation theory and validate its effectiveness through application to complex photonic networks. Our findings underscore the versatility of generalized Wigner-Smith operators for analyzing a broad spectrum of resonant systems and provides new insight into resonant properties of non-Hermitian systems.

physics.optics↗

arXiv2024

Bootstrapping cascaded random matrix models: correlations in permutations of matrix products

Random matrix theory is a useful tool in the study of the physics of multiple scattering systems, often striking a balance between computation speed and physical rigour. Propagation of waves through thick disordered media, as arises in for example optical scattering or electron transport, typically necessitates cascading of multiple random matrices drawn from an underlying ensemble for thin media, greatly increasing computational burden. Here we propose a dual pool based bootstrapping approach to speed up statistical studies of scattering in thick random media. We examine how potential matrix reuse in a pool based approach can impact statistical estimates of population averages. Specifically, we discuss how both bias and additional variance in the sample mean estimator are introduced through bootstrapping. In the diffusive scattering regime, the extra estimator variance is shown to originate from samples in which cascaded transfer matrices are permuted matrix products. Through analysis of the combinatorics and cycle structure of permutations we quantify the resulting correlations. Proofs of several analytic formulae enumerating the frequency with which correlations of different strengths occur are derived. Extension to the ballistic regime is briefly considered.

math-ph↗

arXiv2022

Random matrix theory of polarized light scattering in disordered media

In this work we present a method for generating random matrices describing electromagnetic scattering from disordered media containing dielectric particles with prescribed single particle scattering characteristics. Resulting scattering matrices automatically satisfy the physical constraints of unitarity, reciprocity and time reversal, whilst also incorporating the polarization properties of electromagnetic waves and scattering anisotropy. Our technique therefore enables statistical study of a variety of polarization phenomena, including depolarization rates and polarization-dependent scattering by chiral particles. In this vein, we perform numerical simulations for media containing isotropic and chiral spherical particles of different sizes for thicknesses ranging from the single to multiple scattering regime and discuss our results, drawing comparisons to established theory.

physics.optics↗

arXiv2021

Theory of Multiple Scattering Enhanced Single Particle Plasmonic Sensing

Methods to increase the light scattered from small particles can help improve the sensitivity of many sensing techniques. Here, we investigate the role multiple scattering plays in perturbing the scattered signal when a particle is added to a random scattering environment. Three enhancement factors, parametrising the effect of different classes of multiple scattering trajectories on the field perturbation, are introduced and their mean amplitudes explored numerically in the context of surface plasmon polariton scattering. We demonstrate that there exists an optimum scatterer density at which the sensitivity enhancement is maximised, with factors on the order of $10^2$ achievable. Dependence of the enhancement factors on scatterer properties are also studied.

physics.optics↗

arXiv2021

Role of Multiple Scattering in Single Particle Perturbations in Absorbing Random Media

Speckle patterns produced by disordered scattering systems exhibit a sensitivity to addition of individual particles which can be used for sensing applications. Using a coupled dipole model we investigate how multiple scattering can enhance field perturbations arising in such random scattering based sensors. Three distinct families of multiple scattering paths are shown to contribute and the corresponding complex enhancement factors derived. Probability distributions of individual enhancement factors over the complex plane are characterised numerically within the context of surface plasmon polariton scattering in which absorption is shown to play an important role. We show that enhancements become more strongly dependent on individual scatterer properties when absorption losses are larger, however, amplitude enhancements $\sim 10^2$, comparable to low loss surface plasmons, are achievable through sensor optimisation. Approximate analytic expressions for the complex mean enhancements are also found, which agree well with simulations when loop contributions are negligible.

physics.optics↗

arXiv2020

Dielectric perturbations: anomalous resonance frequency shifts in optical resonators

Small perturbations in the dielectric environment around a high quality whispering gallery mode resonator usually lead to a frequency shift of the resonator modes directly proportional to the polarizability of the perturbation. Here, we report experimental observations of strong frequency shifts that can be opposite and even exceed the contribution of the perturbations' polarizability. The mode frequencies of a lithium niobate whispering gallery mode resonator are shifted using substrates of refractive indices ranging from 1.50 to 4.22. Both blue- and red-shifts are observed, as well as an increase in mode linewidth, when substrates are moved into the evanescent field of the whispering gallery mode. We compare the experimental results to a theoretical model by Foreman et al. and provide an additional intuitive explanation based on the Goos-Hänchen shift for the optical domain.

physics.optics↗

arXiv2020

Symmetry constraints for vector scattering and transfer matrices containing evanescent components: energy conservation, reciprocity and time reversal

In this work we study the scattering and transfer matrices for electric fields defined with respect to an angular spectrum of plane waves. For these matrices, we derive the constraints that are enforced by conservation of energy, reciprocity and time reversal symmetry. Notably, we examine the general case of vector fields in three dimensions and allow for evanescent field components. Moreover, we consider fields described by both continuous and discrete angular spectra, the latter being more relevant to practical applications, such as optical scattering experiments. We compare our results to better-known constraints, such as the unitarity of the scattering matrix for far-field modes, and show that previous results follow from our framework as special cases. Finally, we demonstrate our results numerically with a simple example of wave propagation at a planar glass-air interface, including the effects of total internal reflection. Our formalism makes minimal assumptions about the nature of the scattering medium and is thus applicable to a wide range of scattering problems.

physics.optics↗

arXiv2020

Tracking Single Particles using Surface Plasmon Leakage Radiation Speckle

Label free tracking of small bio-particles such as proteins or viruses is of great utility in the study of biological processes, however such experiments are frequently hindered by weak signal strengths and a susceptibility to scattering impurities. To overcome these problems we here propose a novel technique leveraging the enhanced sensitivity of both interferometric detection and the strong field confinement of surface plasmons. Specifically, we show that interference between the field scattered by an analyte particle and a speckle reference field, derived from random scattering of surface plasmons propagating on a rough metal film, enables particle tracking with sub-wavelength accuracy. We present the analytic framework of our technique and verify its robustness to noise through Monte Carlo simulations.

physics.optics↗

arXiv2020

Universal bounds for imaging in scattering media

In this work we establish universal ensemble independent bounds on the mean and variance of the mutual information and channel capacity for imaging through a complex medium. Both upper and lower bounds are derived and are solely dependent on the mean transmittance of the medium and the number of degrees of freedom $N$. In the asymptotic limit of large $N$, upper bounds on the channel capacity are shown to be well approximated by that of a bimodal channel with independent identically Bernoulli distributed transmission eigenvalues. Reflection based imaging modalities are also considered and permitted regions in the transmission-reflection information plane defined. Numerical examples drawn from the circular and DMPK random matrix ensembles are used to illustrate the validity of the derived bounds. Finally, although the mutual information and channel capacity are shown to be non-linear statistics of the transmission eigenvalues, the existence of central limit theorems is demonstrated and discussed.

physics.optics↗