arXiv subjects

Michael T. M. Woodley

Publications and source records attributed to Michael T. M. Woodley.

14 recordsLinked to original sources

arXiv2026

Applying the convolution theorem to the two-dimensional magnetic inverse problem

A collection and clarification is given of the key mathematical details of the method of applying the convolution theorem as part of the solution to the two-dimensional magnetic inverse problem: reconstructing current density from magnetic field data. Particular emphasis is given to obtaining a closed-form solution for the Fourier transform of the convolution kernel that features in the Biot-Savart law. Having done this, the Fourier-transformed current density is obtained, via the convolution theorem, as a function of Fourier-transformed magnetic field data and other variables.

math-ph↗

arXiv2025

The magnetic inverse problem for two stacked layers of sources

We present calculations that reconstruct electronic current densities in two stacked layers at known depths, using magnetic field data. Solving this inverse problem requires knowledge of the magnetic field in two planes -- one above both current layers, one below -- corresponding to non-invasive measurements of the field. We corroborate the accuracy of current density reconstruction from the resulting system of equations using a numerical simulation. This method is anticipated to be applicable to non-destructive current imaging for quality assurance in a range of applications featuring two-layer geometries, including printed circuit boards, capacitors, fuel cells, and battery cells; we focus particularly here on battery cells, due to their rapidly increasing relevance for automotive applications. This method also offers a framework for generalising the model to more than two layers in future work.

math-ph↗

arXiv2025

Computation and Verification of Spectra for Non-Hermitian Systems

We establish a connection between quantum mechanics and computation, revealing fundamental limitations for algorithms computing spectra, especially in non-Hermitian settings. Introducing the concept of locally trivial pseudospectra (LTP), we show such assumptions are necessary for spectral computation. LTP adapts dynamically to system energies, enabling spectral analysis across a broad class of challenging non-Hermitian problems. Exploiting this framework, we overcome a longstanding obstacle by computing the eigenvalues and eigenfunctions of the imaginary cubic oscillator $H_{\mathrm{B}} = p^2 + i x^3$ with error bounds and no spurious modes -- yielding, to our knowledge, the first such error-controlled result. We confirm, for instance, the 100th eigenvalue as $627.6947122484365113526737029011536\ldots$. Here, truncation-induced $\mathcal{PT}$-symmetry breaking causes spurious eigenvalues -- a pitfall our method avoids, highlighting the link between truncation and physics. Finally, we illustrate the approach's generality via spectral computations for a range of physically relevant operators. This letter provides a rigorous framework linking computational theory to quantum mechanics and offers a precise tool for spectral calculations with error bounds.

quant-ph↗

arXiv2024

A modular optically pumped magnetometer system

To address the demands in healthcare and industrial settings for spatially resolved magnetic imaging, we present a modular optically pumped magnetometer (OPM) system comprising a multi-sensor array of highly sensitive quantum magnetometers. This system is designed and built to facilitate fast prototyping and testing of new measurement schemes by enabling quick reconfiguration of the self-contained laser and sensor modules as well as allowing for the construction of various array layouts with a shared light source. The modularity of this system facilitates the development of methods for managing high-density arrays for magnetic imaging. The magnetometer sensitivity and bandwidth are first characterised in both individual channel and differential gradiometer configurations before testing in a real-world magnetoencephalography environment by measuring alpha rhythms from the brain of a human participant. We demonstrate the OPM system in a first-order axial gradiometer configuration with a magnetic field gradient sensitivity of 10 $\mathrm{fT/cm/\sqrt{Hz}}$. Bandwidths exceeding 200 Hz were achieved for two independent modules. The system's increased temporal resolution allows for the measurement of spinal cord signals, which we demonstrate by using phantom signal trials and comparing with an existing commercial sensor.

physics.atom-ph↗

arXiv2021

A Kerr Polarization Controller

Kerr-effect-induced changes of the polarization state of light are well known in pulsed laser systems. An example is nonlinear polarization rotation, which is critical to the operation of many types of mode-locked lasers. Here, we demonstrate that the Kerr effect in a high-finesse Fabry-Pérot resonator can be utilized to control the polarization of a continuous wave laser. It is shown that a linearly-polarized input field is converted into a left- or right-circularly-polarized field, controlled via the optical power. The observations are explained by Kerr-nonlinearity induced symmetry breaking, which splits the resonance frequencies of degenerate modes with opposite polarization handedness in an otherwise symmetric resonator. The all-optical polarization control is demonstrated at threshold powers down to 7 mW. The physical principle of such Kerr effect-based polarization controllers is generic to high-Q Kerr-nonlinear resonators and could also be implemented in photonic integrated circuits. Beyond polarization control, the spontaneous symmetry breaking of polarization states could be used for polarization filters or highly sensitive polarization sensors when operated close to the symmetry-breaking point.

physics.optics↗

arXiv2021

Kerr-Nonlinearity-Induced Mode-Splitting in Optical Microresonators

The Kerr effect in optical microresonators plays an important role for integrated photonic devices and enables third harmonic generation, four-wave mixing, and the generation of microresonator-based frequency combs. Here we experimentally demonstrate that the Kerr nonlinearity can split ultra-high-Q microresonator resonances for two continuous-wave lasers. The resonance splitting is induced by self- and cross-phase modulation and counter-intuitively enables two lasers at different wavelengths to be simultaneously resonant in the same microresonator mode. We develop a pump-probe spectroscopy scheme that allows us to measure power dependent resonance splittings of up to 35 cavity linewidths (corresponding to 52 MHz) at 10 mW of pump power. The required power to split the resonance by one cavity linewidth is only 286$μ$W. In addition, we demonstrate threefold resonance splitting when taking into account four-wave mixing and two counterpropagating probe lasers. These Kerr splittings are of interest for applications that require two resonances at optically controlled offsets, eg. for opto-mechanical coupling to phonon modes, optical memories, and precisely adjustable spectral filters.

physics.optics↗

arXiv2021

Coherent suppression of backscattering in optical microresonators

As light propagates along a waveguide, a fraction of the field can be reflected by Rayleigh scatterers. In high-quality-factor whispering-gallery-mode microresonators, this intrinsic backscattering is primarily caused by either surface or bulk material imperfections. For several types of microresonator-based experiments and applications, minimal backscattering in the cavity is of critical importance, and thus, the ability to suppress backscattering is essential. We demonstrate that the introduction of an additional scatterer into the near field of a high-quality-factor microresonator can coherently suppress the amount of backscattering in the microresonator by more than 30 dB. The method relies on controlling the scatterer position such that the intrinsic and scatterer-induced backpropagating fields destructively interfere. This technique is useful in microresonator applications where backscattering is currently limiting the performance of devices, such as ring-laser gyroscopes and dual frequency combs, which both suffer from injection locking. Moreover, these findings are of interest for integrated photonic circuits in which back reflections could negatively impact the stability of laser sources or other components.

physics.optics↗

arXiv2020

Self-switching Kerr oscillations of counter-propagating light in microresonators

We report the experimental observation of oscillatory antiphase switching between counter-propagating light beams in Kerr ring microresonators, including the emergence of periodic behaviour from a chaotic regime. Self-switching occurs in balanced regimes of operation and is well captured by a simple coupled dynamical system featuring only the self- and cross-phase Kerr nonlinearities. Switching phenomena are due to temporal instabilities of symmetry-broken states combined with attractor merging that restores the broken symmetry on average. Self-switching of counter-propagating light is robust for realising controllable, all-optical generation of waveforms, signal encoding and chaotic cryptography.

physics.optics↗

arXiv2020

Logic Gates based on Interaction of Counterpropagating Light in Microresonators

Optical logic has the potential to replace electronics with photonic circuits in applications for which optic-to-electronic conversion is impractical and for integrated all-optical circuits. Nonlinear optics in whispering gallery mode resonators provides low power, scalable methods to achieve optical logic. We demonstrate, for the first time, an all-optical, universal logic gate using counterpropagating light in which all signals have the same operating optical frequency. Such a device would make possible the routing of optical signals without the need for conversion into the electronic domain, thus reducing latency. The operating principle of the device is based on the Kerr interaction between counter-propagating beams in a whispering gallery mode resonator which induces a splitting between the resonance frequencies for the two propagating directions. Our gate uses a fused silica microrod resonator with a \textit{Q}-factor of $\SI{2e8}{}$. This method of optical logic gives a practical solution to the on-chip routing of light.

physics.optics↗

arXiv2020

A Nonlinear Enhanced Microresonator Gyroscope

We demonstrate a novel optical microresonator gyroscope whose responsivity to rotation is enhanced by a factor of around $10^4$ by operating close to the critical point of a spontaneous symmetry breaking transition between counterpropagating light. We present a proof-of-principle rotation measurement using a resonator with a diameter of 3 mm. In addition, we characterise the dynamical response of the system to a sinusoidally varying rotation, and show this to be well described by a simple theoretical model. We observe the universal critical behaviors of responsivity enhancement and critical slowing down, both of which are beneficial in an optical gyroscope.

physics.optics↗

arXiv2019

Effects of self- and cross-phase modulation on the spontaneous symmetry breaking of light in ring resonators

We describe spontaneous symmetry breaking in the powers of two optical modes coupled into a ring resonator, using a pair of coupled Lorentzian equations, featuring tunable self- and cross-phase modulation terms. We investigate a wide variety of nonlinear materials by changing the ratio of the self- and cross-phase interaction coefficients. Static and dynamic effects range from the number and stability of stationary states to the onset and nature of oscillations. Minimal conditions to observe symmetry breaking are provided in terms of the ratio of the self-/cross-phase coefficients, detuning, and input power. Different ratios of the nonlinear coefficients also influence the dynamical regime, where they can induce or suppress bifurcations and oscillations. A generalised description on this kind is useful for the development of all-optical components, such as isolators and oscillators, constructed from a wide variety of optical media in ring resonators.

physics.optics↗

arXiv2018

Universal Symmetry Breaking Dynamics for the Kerr Interaction of Counter-Propagating Light in Dielectric Ring Resonators

Spontaneous symmetry breaking is an important concept in many areas of physics. A fundamentally simple symmetry breaking mechanism in electrodynamics occurs between counter-propagating electromagnetic waves in ring resonators, mediated by the Kerr nonlinearity. The interaction of counter-propagating light in bi-directionally pumped microresonators finds application in the realisation of optical non-reciprocity (for optical diodes), studies of PT-symmetric systems, and the generation of counter-propagating solitons. Here, we present comprehensive analytical and dynamical models for the nonlinear Kerr-interaction of counter-propagating light in a dielectric ring resonator. In particular, we study discontinuous behaviour in the onset of spontaneous symmetry breaking, indicating divergent sensitivity to small external perturbations. These results can be applied to realise, for example, highly sensitive near-field or rotation sensors. We then generalise to a time-dependent model, which predicts new types of dynamical behaviour, including oscillatory regimes that could enable Kerr-nonlinearity-driven all-optical oscillators. The physics of our model can be applied to other systems featuring Kerr-type interaction between two distinct modes, such as for light of opposite circular polarisation in nonlinear resonators, which are commonly described by coupled Lugiato-Lefever equations.

physics.optics↗

arXiv2018

Interplay of Polarization and Time-Reversal Symmetry Breaking in Synchronously Pumped Ring Resonators

Optically induced breaking of symmetries plays an important role in nonlinear photonics, with applications ranging from optical switching in integrated photonic circuits to soliton generation in ring lasers. In this work we study for the first time the interplay of two types of spontaneous symmetry breaking that can occur simultaneously in optical ring resonators. Specifically we investigate a ring resonator (e.g. a fiber loop resonator or whispering gallery microresonator) that is synchronously pumped with short pulses of light. In this system we numerically study the interplay and transition between regimes of temporal symmetry breaking (in which pulses in the resonator either run ahead or behind the seed pulses) and polarization symmetry breaking (in which the resonator spontaneously generates elliptically polarized light out of linearly polarized seed pulses). We find ranges of pump parameters for which each symmetry breaking can be independently observed, but also a regime in which a dynamical interplay takes place. Besides the fundamentally interesting physics of the interplay of different types of symmetry breaking, our work contributes to a better understanding of the nonlinear dynamics of optical ring cavities which are of interest for future applications including all-optical logic gates, synchronously pumped optical frequency comb generation, and resonator-based sensor technologies.

physics.optics↗

arXiv2018

Microresonator Isolators and Circulators Based on the Intrinsic Nonreciprocity of the Kerr Effect

Nonreciprocal light propagation is important in many applications, ranging from optical telecommunications to integrated photonics. A simple way to achieve optical nonreciprocity is to use the nonlinear interaction between counterpropagating light in a Kerr medium. Within a ring resonator, this leads to spontaneous symmetry breaking, with the result that light of a given frequency can circulate in one direction, but not in both directions simultaneously. In this work, we demonstrate that this effect can be used to realize optical isolators and circulators based on a single ultra- high-Q microresonator. We obtain isolation of more than 24 dB and develop a theoretical model for the power scaling of the attainable nonreciprocity.

physics.optics↗