arXiv subjects

S. A. R. Horsley

Publications and source records attributed to S. A. R. Horsley.

At least 37 records · Page 2Linked to original sources

arXiv2022

Designing Multi-functional Metamaterials

The ability to design passive structures that perform different operations on different electromagnetic fields is key to many technologies, from beam-steering to optical computing. While many techniques have been developed to optimise structure to achieve specific functionality through inverse design, designing multi-function materials remains challenging. We present a semi-analytic method, based on the discrete dipole approximation, to design multi-functional metamaterials. To demonstrate the generality of our method, we design a device that operates at optical wavelengths and beams light into different directions depending on the source polarisation and a device that works at microwave wavelengths and sorts plane waves by their angle of incidence.

physics.app-ph↗

arXiv2022

Tutorial: Macroscopic QED and vacuum forces

This tutorial introduces the theory of macroscopic QED, where a Hamiltonian is found that represents the electromagnetic field interacting with a dispersive, dissipative material. Using a one dimensional theory as motivation, we build up the more cumbersome three dimensional theory. Then considering the extension of this theory to moving materials, where the material response changes due to both the Doppler effect and the mixing of electric and magnetic responses, it is shown that one gets the theory of quantum electromagnetic forces for free. We finish by applying macroscopic QED to reproduce Pendry's expression for the quantum friction force between sliding plates.

quant-ph↗

arXiv2022

Tutorial: Topology, waves, and the refractive index

This tutorial is divided into two parts: the first examines the application of topology to problems in wave physics. The origins of the Chern number are reviewed, where it is shown that this counts the number of critical points of a complex tangent vector field on the surface. We then show that this quantity arises naturally when calculating the dispersion of modes in any linear system, and give examples of its application to find one--way propagating interface modes in both continuous and periodic materials. The second part offers a physical interpretation for the Chern number, based on the idea that the critical points which it records can be understood as points where the refractive index vanishes. Using the theory of crystal optics, we show that when the refractive index vanishes in a complex valued direction, the wave is forced to circulate in only one sense, and this is the origin of the one-way propagation of topological interface states. We conclude by demonstrating that this idea of `zero refractive index in a complex direction' can be used as a shortcut to find acoustic and electromagnetic materials supporting one-way interface states.

physics.optics↗

arXiv2021

Time modulated media with digital meta-atoms

We develop the theory of acoustic wave propagation in a waveguide containing an array of time modulated digital meta-atoms, showing the equivalence between this array and a homogeneous, time varying, dispersive material. In the limit of an adiabatic time variation we find some choices of meta-atom coupling strength lead to exceptional points, where one mode is exponentially amplified and the adiabatic approximation breaks down. In the highly non--adiabatic limit we derive the analogue of reflection coefficients for an abrupt change in the meta-atom coupling. Due to dispersion we have both conversion between different types of modes, and different directions of propagation, which can be tuned through modifying the programmed response of the digital meta--atoms.

physics.class-ph↗

arXiv2021

Quantum Brownian Motion for Magnets

Spin precession in magnetic materials is commonly modelled with the classical phenomenological Landau-Lifshitz-Gilbert (LLG) equation. Based on a quantized spin+environment Hamiltonian, we here derive a general spin operator equation of motion that describes three-dimensional precession and damping and consistently accounts for effects arising from memory, coloured noise and quantum statistics. The LLG equation is recovered as its classical, Ohmic approximation. We further introduce resonant Lorentzian system--reservoir couplings that allow a systematic comparison of dynamics between Ohmic and non--Ohmic regimes. Finally, we simulate the full non-Markovian dynamics of a spin in the semi--classical limit. At low temperatures, our numerical results demonstrate a characteristic reduction and flattening of the steady state spin alignment with an external field, caused by the quantum statistics of the environment. The results provide a powerful framework to explore general three-dimensional dissipation in quantum thermodynamics.

quant-ph↗

arXiv2020

Superfluid Optomechanics with Phononic Nanostructures

In quantum optomechanics, finding materials and strategies to limit losses has been crucial to the progress of the field. Recently, superfluid 4He was proposed as a promising mechanical element for quantum optomechanics. This quantum fluid shows highly desirable properties (e.g. extremely low acoustic loss) for a quantum optomechanical system. In current implementations, superfluid optomechanical systems suffer from external sources of loss, which spoils the quality factor of resonators. In this work, we propose a new implementation, exploiting nanofluidic confinement. Our approach, based on acoustic resonators formed within phononic nanostructures, aims at limiting radiation losses to preserve the intrinsic properties of superfluid 4He. In this work, we estimate the optomechanical system parameters. Using recent theory, we derive the expected quality factors for acoustic resonators in different thermodynamic conditions. We calculate the sources of loss induced by the phononic nanostructures with numerical simulations. Our results indicate the feasibility of the proposed approach in a broad range of parameters, which opens new prospects for more complex geometries.

physics.app-ph↗

arXiv2020

Supersymmetry, half-bound states, and grazing incidence reflection

Electromagnetic waves at grazing incidence onto a planar medium are analogous to zero energy quantum particles incident onto a potential well. In this limit waves are typically completely reflected. Here we explore dielectric profiles supporting optical analogues of `half-bound states', allowing for zero reflection at grazing incidence. To obtain these profiles we use two different theoretical approaches: supersymmetric quantum mechanics, and direct inversion of the Helmholtz equation.

physics.optics↗

arXiv2020

Designing Collective Non-local Responses of Metasurfaces

We propose a numerically efficient `adjoint' inverse design method to optimize a planar structure of dipole scatterers, to manipulate the radiation from an electric dipole emitter. Several examples are presented: modification of the near-field to provide a 3 fold enhancement in power emission; re-structuring the far-field radiation pattern to exhibit chosen directivity; and the design of a discrete `Luneburg lens'. Additionally, we develop a clear physical interpretation of the optimized structure, by extracting `eigen-polarizabilities' of the system. We find that large `eigen-polarizability' corresponds to a large collective response of the scatterers. This framework may find utility in wavefront shaping as well as in the design and characterisation of non-local metasurfaces.

physics.optics↗

arXiv2019

Zero index electromagnetic materials

Here we re-examine one of the most basic quantities in optics: the refractive index. Considering propagation in a plane, we first develop a general formalism for calculating the direction dependent refractive index in a general bi-anisotropic material. From this we derive the general condition for achieving zero refractive index in a given direction. We show that when the zero-index direction is complex valued the material supports waves that can propagate in only one sense, e.g. in only a clockwise direction. We dub such materials complex axis nihility (CAN) media. Our condition shows that there are an infinite family of both time reversible and time irreversible homogeneous electromagnetic media that support unidirectional propagation for a particular polarization. We give examples showing that scattering from such media results in the complete exclusion of partial waves with one sign of the angular momentum, and that interfaces between such media generally support one-way interface states. As well as giving new sets of material parameters, our simple condition reproduces many of the findings derived using topology, such as unidirectional propagation in gyrotropic media, and spin-momentum locking of evanescent waves.

physics.optics↗

arXiv2019

Graded index lenses for spin wave steering

We use micromagnetic modelling to demonstrate the operation of graded index lenses designed to steer forward-volume magnetostatic spin waves by 90 and 180 degrees. The graded index profiles require the refractive index to diverge in the lens center, which, for spin waves, can be achieved by modulating the saturation magnetization or external magnetic field in a ferromagnetic film by a small amount. We also show how the 90$^\circ$ lens may be used as a beam divider. Finally, we analyse the robustness of the lenses to deviations from their ideal profiles.

physics.app-ph↗

arXiv2019

Indifferent electromagnetic modes: bound states and topology

At zero energy the Dirac equation has interesting behaviour. The asymmetry in the number of spin up and spin down modes is determined by the topology of both space and the gauge field in which the system sits. An analogous phenomenon also occurs in electromagnetism. Writing Maxwell's equations in a Dirac-like form, we identify cases where a material parameter plays the role of energy. At zero energy we thus find electromagnetic modes that are indifferent to local changes in the material parameters, depending only on their asymptotic values at infinity. We give several examples, and show that this theory has implications for non-Hermitian media, where it can be used to construct permittivity profiles that are either reflectionless, or act as coherent perfect absorbers, or lasers.

physics.optics↗

arXiv2018

Topology and the optical Dirac equation

Through understanding Maxwell's equations as an effective Dirac equation (the `optical Dirac equation'), we re--examine the relationship between electromagnetic interface states and topology. We illustrate a simple case where electromagnetic material parameters play the roles of `mass' and `energy' in an equivalent Dirac equation. The modes trapped between a gyrotropic medium and a mirror are then the counterpart of those at a `domain wall', where the mass of the Dirac particle changes sign. Considering the general case of arbitrary electromagnetic media, we provide an analytical proof relating the integral of the Berry curvature (the Chern number) to the number of interface states. We show that this reduces to the usual result for periodic media, and also that the Chern number can be computed without knowledge of how the material parameters depend on frequency.

physics.optics↗

arXiv2018

A Luneburg lens for spin waves

We report on the theory of a Luneburg lens for forward-volume magnetostatic spin waves, and verify its operation via micromagnetic modelling. The lens converts a plane wave to a point source (and vice versa) by a designed graded index, realised here by either modulating the thickness or the saturation magnetization in a circular region. We find that the lens enhances the wave amplitude by 5 times at the lens focus, and 47% of the incident energy arrives in the focus region. Furthermore, small deviations in the profile can still result in good focusing, if the lens index is graded smoothly.

physics.app-ph↗

arXiv2018

Scattering of accelerated wave packets

Wave-packet scattering from a stationary potential is significantly modified when the wave-packet is subject to an external time-dependent force during the interaction. In the semiclassical limit, wave--packet motion is simply described by Newtonian equations and the external force can, for example, cancel the potential force making a potential barrier transparent. Here we consider wave-packet scattering from reflectionless potentials, where in general the potential becomes reflective when probed by an accelerated wave-packet. In the particular case of the recently-introduced class of complex Kramers-Kronig potentials we show that a broad class of time dependent forces can be applied without inducing any scattering, while there is a breakdown of the reflectionless property when there is a broadband distribution of initial particle momentum, involving both positive and negative components.

quant-ph↗

arXiv2018

Unidirectional wave propagation in media with complex principal axes

In an anisotropic medium, the refractive index depends on the direction of propagation. Zero index in a fixed direction implies a stretching of the wave to uniformity along that axis, reducing the effective number of dimensions by one. Here we investigate two dimensional gyrotropic media where the refractive index is zero in a complex valued direction, finding that the wave becomes an analytic function of a single complex variable z. For simply connected media this analyticity implies unidirectional propagation of electromagnetic waves, similar to the edge states that occur in photonic 'topological insulators'. For a medium containing holes the propagation is no longer unidirectional. We illustrate the sensitivity of the field to the topology of the space using an exactly solvable example. To conclude we provide a generalization of transformation optics where a complex coordinate transformations can be used to relate ordinary anisotropic media to the recently highlighted gyrotropic ones supporting one-way edge states.

physics.optics↗

arXiv2017

Direct manipulation of wave amplitude and phase through inverse design of isotropic media

In this article we propose a new design methodology allowing us to control both ampli- tude and phase of electromagnetic waves from a cylindrical incident wave. This results in isotropic materials and does not resort to transformation optics or its quasi-conformal approximations. Our method leads to two-dimensional isotropic, inhomogeneous material profiles of permittivity and permeability, to which a general class of scattering-free wave solutions arise. Our design is based on the separation of the complex wave solution into amplitude and phase. We give two types of examples to validate our methodology.

physics.class-ph↗

arXiv2017

Theory of Linear Spin Wave Emission from a Bloch Domain Wall

We report an analytical theory of linear emission of exchange spin waves from a Bloch domain wall, excited by a uniform microwave magnetic field. The problem is reduced to a one-dimensional Schrödinger-like equation with a Pöschl-Teller potential and a driving term of the same profile. The emission of plane spin waves is observed at excitation frequencies above a threshold value, as a result of a linear process. The height-to-width aspect ratio of the Pöschl-Teller profile for a domain wall is found to correspond to a local maximum of the emission efficiency. Furthermore, for a tailored Pöschl-Teller potential with a variable aspect ratio, particular values of the latter can lead to enhanced or even completely suppressed emission.

cond-mat.mtrl-sci↗

arXiv2016

Polariton excitation rates from time dependent dielectrics

In recent years, a rigorous quantum mechanical model for the interaction between light and macroscopic dispersive, lossy dielectrics has emerged -macroscopic QED- allowing the application of the usual methods of quantum field theory. Here, we apply time dependent perturbation theory to a general class of problems involving time dependent lossy, dispersive dielectrics. The model is used to derive polariton excitation rates in three illustrative cases, including that of a travelling Gaussian perturbation to the susceptibility of an otherwise infinite homogeneous dielectric, motivated by recent experiments on analogue Hawking radiation. We find that the excitation rate is increased when the wave--vector and frequency of each polariton in the pair either satisfies (or nearly satisfies) the dispersion relation for electromagnetic waves, or is close to a material resonance.

quant-ph↗