arXiv subjects

William Tuxbury

Publications and source records attributed to William Tuxbury.

9 recordsLinked to original sources

arXiv2026

Physical policy gradient theorem for in situ stochastic-adjoint training

In situ adjoint training extracts parameter gradients directly from measurement, but has so far been limited to reciprocal or restricted systems. Here, we introduce the physical counterpart of the policy gradient theorem: a stochastic-adjoint gradient estimator that lifts these constraints by trading reciprocity for nondegenerate diffusion. As validation, we train a nonlinear resonator network, whose own dynamics supply the policy, against antagonistic temporal modulations with gradients from measured stochastic trajectories alone, without finite differences or a separate adjoint experiment.

physics.optics↗

arXiv2026

In-situ Adjoint Wave Control in Reconfigurable Non-Hermitian Nonlinear Systems

Complex multipath environments are usually avoided in wave-based information processing because repeated scattering creates many interfering propagation paths, obscuring controllability and generating extreme sensitivity to perturbations. The addition of nonlinear mechanisms fundamentally alters the wave-control landscape by breaking the superposition principle that underpins most wave-management strategies. Here, we show that these two apparent impediments -- multipath complexity and nonlinearity -- can instead be harnessed as key resources for physical optimization. We demonstrate an in-situ adjoint optimization protocol in a wave-chaotic platform incorporating a single localized nonlinear defect, in which the system itself performs both the forward and the adjoint propagations required for gradient evaluation. Recurrent multipath returns repeatedly expose the wave to the defect, producing from a minimal hardware a rich nonlinear input-output map with many pathway-mediated degrees of freedom. At the same time, a suitable adjoint excitation enables direct extraction of the sensitivities from measurements alone, without a digital twin or conventional numerical backpropagation. We experimentally validate the protocol on a minimal nonlinear multipath platform composed of incommensurate coaxial cables connected via T-junctions, one of which hosts a diode-loaded cavity. Our approach opens a route to adaptive wireless communications, imaging and analog intelligence in complex, partially unknown environments where conventional modeling is impractical.

physics.optics↗

arXiv2026

Differentiable Fast Far-Field Transform in Cylindrical Coordinates for Large-Area Cascaded Metalens Optics

We present a fully differentiable far-field transform in cylindrical coordinates for full-area point spread function (PSF) evaluation and optimization of large axisymmetric metalenses. The method computes wave-optical responses of apertures spanning thousands to tens of thousands of wavelengths in diameter (millimeter scales in the visible, centimeter scales in the infrared) in seconds, achieving three to four orders of magnitude speedup over Green's function integration while avoiding the prohibitive memory of two-dimensional FFTs. The approach decomposes vectorial near fields into parallel angular-momentum channels, applies FFTLog-accelerated Hankel transforms, and uses Graf's addition theorem to recenter focal fields under oblique illumination. Analytic adjoint gradients enable optimization with only ~65% overhead relative to a forward simulation. For a 4 mm-diameter aperture (~8000 wavelengths, ~12,600 azimuthal modes) at 30-degree incidence, a forward-adjoint iteration requires only ~12 s on a 350-thread CPU, making oblique optimization practical without ray-tracing approximations. Applied to polychromatic RGB (446/530/650 nm) metalens design at normal incidence, full-area PSF evaluation exposes efficiency limits hidden by conventional cropped-focal-spot analysis: a mono-pillar metalens that appears diffraction-limited achieves only ~6% average absolute focusing efficiency, while direct far-field optimization raises this to 37% (locally periodic approximation) and 51% (zoned discrete axisymmetry). A cascaded double-metasurface design reaches 63%, while a four-metasurface architecture attains 96% average relative efficiency. We also demonstrate millimeter-scale, oblique-incidence optimization of single-surface and doublet architectures; cascaded doublets enable partial coma correction inaccessible to a single rotationally symmetric surface.

physics.optics↗

arXiv2026

Adaptive Sensing beyond Non-Adaptive Information Limits: End-to-End Co-Design of Geometry, Policy, and Inference

Inverse design has transformed vast physical parameter spaces into a substrate for emergent functionality, raising the tantalizing prospect of relocating intelligence from the digital domain into the physical world itself. Nowhere is this prospect more consequential than in sensing, where the analog-to-digital interface imposes a fundamental bottleneck: information not captured by the hardware is irrevocably lost to any downstream algorithm. Existing approaches improve information capture through either sensor hardware optimization or adaptive measurement strategies operating on fixed hardware, but rarely both in concert. A principled migration of intelligence from digital to physical demands their joint optimization: the sensing geometry must be co-designed with a policy that determines what to measure next. We formulate this co-design as joint dynamic programming (joint-DP), a unified optimization over sensor geometry and a Bellman-optimal adaptive measurement policy. The outer hardware gradient is obtained through differentiable dynamic programming with a sharp Bellman maximum. A hierarchy of relaxations extends the framework from small discrete POMDPs to freeform photonic topologies with more than $10^5$ design pixels.

physics.optics↗

arXiv2025

Synthetic Reflectionless Mode Exceptional Degeneracies via Emergent Local Symmetries

We propose a new kind of physically realizable exceptional point degeneracies (EPDs) corresponding to synthetic reflectionless modes (SRM). These are solutions of an auxiliary wave operator that is defined in synthetic frequency dimensions and describe incoming reflectionless waves onto a Floquet-driven cavity. The SRM-EPD emerges as a consequence of a spontaneous local PT-symmetry imposed on the auxiliary operator via appropriate Floquet driving. Its presence signifies the possibility to design wavefronts and time-modulated schemes with up/down targeted frequency conversion and flat transmission spectra. The theory is validated via simulations with driven RF resonators.

physics.optics↗

arXiv2024

Unidirectional Amplification in the Frozen Mode Regime Enabled by a Nonlinear Defect

A stationary inflection point (SIP) is a spectral singularity of the Bloch dispersion relation $\omega(k)$ of a periodic structure where the first and the second derivatives of $\omega$ with respect to $k$ vanish. An SIP is associated with a third order exceptional point degeneracy in the spectrum of the unit-cell transfer matrix, where there is a collapse of one propagating and two evanescent Bloch modes. At the SIP frequency, the incident wave can be efficiently converted into the frozen mode with greatly enhanced amplitude and vanishing group velocity. This can be very attractive for applications, including light amplification. Due to its non-resonant nature, the frozen mode regime (FMR) has fundamental advantages over common cavity resonances. Here, we propose a novel scheme for FMR-based unidirectional amplifiers by leveraging a tailored amplification/attenuation mechanism and a single nonlinear defect. The defect breaks the directional symmetry of the periodic structure and enables nonlinearity-related unidirectional amplification/ attenuation in the vicinity of the SIP frequency. We demonstrate the robustness of the amplification mechanism to local impurities and parasitic nonlinearity.

physics.optics↗

arXiv2024

Damping Reveals Hidden Dimensions in Elastic Metastructures Through Induced Transparency

Damping typically results in attenuation of vibrations and elastic wave propagation in mechanical systems. Contrary to this conventional understanding, we demonstrate experimentally and explain theoretically the revival of an elastic wave transmitted through a periodic metastructure when a weak non-Hermitian defect (damping mechanism) induces violation of time-reversal symmetry. Damping alters the nature of the system's resonant modes, instigating interference in the scattering field. This leads to transmission revival, revealing the presence of hidden modes which are otherwise masked by the symmetry. Our findings offer an innovative approach for designing dissipation-driven switches and controllers and non-destructive structural health monitoring systems.

physics.app-ph↗

arXiv2024

Nonlinearity-induced Scattering Zero Degeneracies for Spectral Management of Coherent Perfect Absorption in Complex Systems

We develop a Coherent Perfect Absorption (CPA) protocol for cases where scale invariance is violated due to the presence of nonlinear mechanisms. We demonstrate, using a microwave setting that lacks geometrical symmetries, that the nonlinearity offers new reconfigurable modalities: the destruction or formation of nonlinear CPAs (NL-CPAs), and their frequency positioning and bandwidth management using the incident power as a control knob. The latter occurs via the formation of exceptional point degeneracies of the zeroes of nonlinear scattering processes. Our results establish NL-CPA protocols as a versatile scheme for the creation of reconfigurable hot/cold-spots in complicated enclosures (e.g. buildings or vessels) with applications to next-generation telecommunications, long-range wireless power transfer, and electromagnetic warfare.

physics.optics↗

arXiv2023

Nonlinear Wavepacket Dynamics in Proximity to a Stationary Inflection Point

A stationary inflection point (SIP) in the Bloch dispersion relation of a periodic waveguide is an exceptional point degeneracy where three Bloch eigenmodes coalesce forming the so-called frozen mode with a divergent amplitude and vanishing group velocity of its propagating component. We have developed a theoretical framework to study the time evolution of wavepackets centered at an SIP. Analysis of the evolution of statistical moments distribution of linear pulses shows a strong deviation from the conventional ballistic wavepacket dynamics in dispersive media. The presence of nonlinear interactions dramatically changes the situation, resulting in a mostly ballistic propagation of nonlinear wavepackets with the speed and even the direction of propagation essentially dependent on the wavepacket amplitude. Such a behavior is unique to nonlinear wavepackets centered at an SIP and can be used for the realization of a novel family of beam power routers for classical waves.

physics.optics↗