arXiv subjects

S. A. R. Horsley

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

At least 19 recordsLinked to original sources

arXiv2026

Minimum energy and photon content in PT symmetric metamaterials

In the context of waves in space time modulated materials, we ask two questions how much energy does it cost to break time reversal symmetry and transition to a PT symmetric state. and can a PT symmetric system have a ground state in the sense that no photons are present. Our model system is a periodic metamaterial set in virtual motion with velocity cg to become a space-time crystal. We find that the expectation of energy content is always increased on breaking symmetry. At the same time breaking T symmetry introduces photon-pairs even when we start from a T symmetric ground state empty of photons, except in certain pathological examples which we describe. For a range of velocities, PT symmetry is broken so that energy must be continuously invested to preserve motion, creating a trail of photon pairs. Here energy must be continuously invested to preserve motion. We make an analogy with acoustic radiation generated from breaking the sound barrier.

physics.optics↗

arXiv2026

Generalized Time-Varying Drude Model for Dispersive and Lossy Modulations

We develop a generalization of the time-varying Drude model, treating carrier density, effective mass, and collision rate as explicit functions of time. We derive expressions for polarization, susceptibility, displacement, and permittivity in different domains. Our analysis reveals that non-adiabatic modulations and time-dependent losses induce rich and distinct behaviors, leading to temporal blurring, selective gating and suppression, and low-frequency spectral reshaping. Besides underpinning and upgrading the current framework on photonics of time-varying media, this model may be useful in the design and fitting theoretical models with experimental realizations.

physics.optics↗

arXiv2025

Bound States to the Continuum: Time-varying Spoof Acoustic Surface Waves

We develop a theoretical framework for time-modulated acoustic metasurfaces comprising a line array of modulated cavities, and show that bound acoustic surface waves can undergo temporal diffraction from bound states localised at an interface into bulk waves. The dispersion relation is derived via an operator formalism that captures the spatio-temporal coupling between Floquet sidebands. We show that under periodic modulation of the cavity length sidebands spaced by the modulation frequency are produced (diffraction in time), enabling the coupling of bound surface acoustic waves with bulk radiation i.e. from a bound state \textit{to} the continuum. We observe the negative-frequency spectra as spatial reflections along the array via time-domain finite element simulations. Spectral $k$-gaps are observed at band crossings, with the width of the gap proportional to the modulation amplitude. The modulation enters solely through a time-dependent reflection phase, such that the framework applies generally to metasurfaces with programmable boundary conditions, beyond purely mechanical modulation.

physics.app-ph↗

arXiv2025

Finding passive, reciprocal metasurfaces for arbitrary wave transformations

We give a general design method for finding the passive, reciprocal surface impedance tensor required to enact any wave transformation. We do this through characterising the surface in terms of a tensorial surface impedance, showing that a large family of impedance distributions can be found that perform an identical wave transformation. Even when the conditions of reciprocity and passivity are imposed, there still remain many solutions to the design problem.} We exploit this as a design method for metasurfaces, giving two examples where the metasurface rotates the input polarization and reshapes the output field, showing we can parameterize the set of equivalent reciprocal metasurfaces in terms of a single complex parameter. \hl{In addition, through allowing dissipation and gain within the response, the surface can have many different functionalities in the orthogonal polarization, opening up a new route for the design of multiplexed metasurfaces.

physics.app-ph↗

arXiv2025

Calculating propagators for relativistic wave equations

Here we examine the propagation of relativistic fields in spacetime using the viewpoint applied to derive the Rayleigh--Sommerfeld diffraction integral in three--dimensional space. We use this theory to find the propagators for both the Klein--Gordon equation and the Dirac equation. Based on these results, we highlight some apparently overlooked aspects of the Feynman checkerboard model as it is usually applied to the Dirac equation.

physics.gen-ph↗

arXiv2025

Harnessing the frequency eigenchannels of ultrafast time-varying media

Control over the interaction of waves with ultrafast time-varying materials - those that change on a time-scale commensurate with the wave period - holds much promise for developing a raft of new technologies. Time-varying materials exchange energy with the waves passing through them, thus exhibiting entirely new phenomena not possible with static media. Work to date has largely considered the realisation of ultrafast time-varying materials, with much less attention paid to how their interaction depends upon the shape of the incident waves themselves. Here we experimentally demonstrate 'waveform shaping' within ultrafast time-varying media: temporal shaping of incident pulses to optimise specific dynamic material interactions. We create an ultrafast time-varying medium by rapidly modulating a waveguide termination, and measure the spectrally resolved reflection matrix. Analysis of this reflection matrix enables the identification of the incident waveforms that undergo a desired spectral transformation. Using this approach, we first characterise the medium's eigenpulses; temporal modes that reflect from the medium without spectral distortion. Next, we identify the waveforms that are either maximally or minimally reflected, enabling strong broadband absorption arising from the temporal modulation of the medium. Finally, we show how energy can be optimally concentrated into a user-defined set of frequency bands upon reflection. Our work paves the way towards new applications of ultrafast time-varying media, spanning from optics to microwaves and acoustics.

physics.optics↗

arXiv2025

Effects due to generation of negative frequencies during temporal diffraction

Temporal diffraction from rapidly time-modulated materials can generate new frequency components not present in an incident wave. In such an experiment, the spectral extent of these new frequencies is determined by the rate of modulation relative to the period of the oscillating field. Here we present a temporal diffraction experiment carried out in the far-infrared (THz) spectral region. Using graphene, a fast modulator for this spectral domain, we show that one can modulate the transmission significantly faster than the period of a narrow band THz field. This leads to a large bandwidth for the generated frequencies, including the generation of negative frequency components. We show that interference between negative and positive frequency components give rise to distinctive oscillatory features in the transmitted spectrum.

physics.optics↗

arXiv2025

Space-Time Optical Diffraction from Synthetic Motion

The interaction of light with objects and media moving at relativistic and superluminal speeds enables unconventional phenomena such as Fresnel drag, Hawking radiation, and light amplification. Synthetic motion, facilitated by modulated internal degrees of freedom, enables the study of relativistic phenomena unrestricted by the speed of light. In this study, we investigate synthetically moving apertures created by high-contrast reflectivity modulations, which are generated by ultrafast laser pulses on a subwavelength thin film of indium tin oxide. The space-time diffraction of a weaker probe beam reveals a complex, non-separable spatio-temporal transformation, where changes in the frequency of the wave are correlated to changes in its momentum. By using schemes of continuous or discrete modulation we demonstrate tunable frequency-momentum diffraction patterns with gradients that depend upon the relative velocity between the modulation and the probe wave. The diffraction patterns are matched by operator-based theory and the gradients are analytically predicted using a super-relativistic Doppler model, where the modulation is described as a superluminally moving scattering particle. Our experiments open a path towards mimicking relativistic mechanics and developing complex and programmable spatio-temporal transformations of light.

physics.optics↗

arXiv2025

Time Varying Resonators in Acoustic Waveguides: A Transfer Matrix Formalism for Space-time Modulated Metamaterials

The transfer matrix method remains a simple yet powerful tool for modeling acoustic systems, particularly in a closed waveguide geometry. Here we present a generalisation of this method based on the theory of mode matching, that incorporates the effect of ultra--fast temporal variations in the geometry, applying it to a system of side-branching resonant cavities (quarter wavelength resonators) fixed to an acoustic waveguide, modulated through alteration of the cavity length. We calculate propagation in a waveguide containing both a single resonator and a periodic array. In particular we predict the generation of additional Doppler-like terms in the reflected and transmitted fields that leads to modification of the band structure, comparing our results to finite element simulations of space-time modulated acoustic crystals.

physics.app-ph↗

arXiv2025

Spring-loaded: Engineering Dispersion Relations Using Complex Couplings

Motivated by recent theoretical and experimental interest in metamaterials comprising non-local coupling terms, we present an analytic framework to realise materials with arbitrary complex dispersion relations. Building on the inverse design method proposed by Kazemi \textit{et al}. [Phys. Rev. Lett. 131, 176101 (2023)], which demonstrated arbitrary real dispersion relations with real non-local coupling terms, we show that using \textit{complex} non-local couplings not only can band structures be drawn, but that arbitrary attenuation of the supported modes can be achieved by tuning their trajectory in the complex frequency plane. This is demonstrated using a canonical mass-spring lattice with higher-order spatial connections; we consider the energy velocity in such systems and show that competing loss and gain of the complex interactions can produce exotic wave dispersion.

physics.app-ph↗

arXiv2024

Macroscopic QED and noise currents in time-varying media

Macroscopic QED (MQED) is the field theory for computing quantum electromagnetic effects in dispersive media. Here we extend MQD to treat time-varying, dispersive media. For a time dependent Drude model, we find that the expected replacement $ε(ω) {\to} ε(t,ω)$ within standard MQED leads to nonphysical polarization currents, becoming singular in the limit of a step change in the carrier density. We show this singular behaviour can be removed through modifying the reservoir dynamics, quantizing the resulting theory and finding the non-equilibrium, time-varying noise currents, which exhibit extra correlations due to temporal reflections within the material dynamics.

physics.optics↗

arXiv2024

Moving impedance profiles make one--way, spectrum--reshaping mirrors

We find a new set of exact solutions to Maxwell's equations in space--time varying materials, where the refractive index is constant, while the impedance exhibits effective motion, i.e. it is a function of $x-vt$. We find that waves co--propagating with the modulation are not reflected within the material, while counter--propagating waves are continually reflected by the changing impedance. For a finite section of such a material we find analogues of transmission resonances, where specially shaped `eigenpulses' enter without reflection. We also find that there is a strong asymmetry in reflection from the medium when the impedance modulation is small but rapid, the material reflecting strongly from one side, and negligibly from the other. Unlike stationary media, the spectrum of the reflected wave can be significantly different from the incident one.

physics.optics↗

arXiv2024

Travelling wave amplification in stationary gratings

We show that a grating amplitude stationary in space but oscillating in time can be accurately modelled as a set of independent gratings travelling in opposite directions, interacting almost exclusively with waves travelling in the same direction. This structure reproduces the key features of travelling gratings: amplification of a wave at points where the local wave speed equals the grating velocity. The same field compression and photon production is evident when even a single Fourier component of the grating profile has a velocity that matches the local wave speed. We speculate that these stationary but oscillating gratings may prove easier to realise experimentally than travelling gratings.

physics.optics↗

arXiv2023

The Electronic and Electromagnetic Dirac Equations

Maxwell's equations and the Dirac equation are the first-order differential relativistic wave equation for electromagnetic waves and electronic waves respectively. Hence, there is a notable similarity between these two wave equations, which has been widely researched since the Dirac equation was proposed. In this paper, we show that the Maxwell equations can be written in an exact form of the Dirac equation by representing the four Dirac operators with $8\times8$ matrices. Unlike the ordinary $4\times4$ Dirac equation, both spin--1/2 and spin--1 operators can be derived from the $8\times8$ Dirac equation, manifesting that the $8\times8$ Dirac equation is able to describe both electrons and photons. As a result of the restrictions that the electromagnetic wave is a transverse wave, the photon is a spin--1 particle. The four--current in the Maxwell equations and the mass in the electronic Dirac equation also force the electromagnetic field to transform differently to the electronic field. We use this $8\times8$ representation to find that the Zitterbewegung of the photon is actually the oscillatory part of the Poynting vector, often neglected upon time averaging.

quant-ph↗

arXiv2023

Generalising the Yagi-Uda Antenna: Designing Disordered Metamaterials to Manipulate Antenna Radiation

Next generation microwave communications systems face several challenges, particularly from congested communications frequencies and complex propagation environments. Taking inspiration from the Yagi-Uda antenna, we present, and experimentally test, a framework based on the coupled dipole approximation for designing structures composed of a single simple emitter with a passive disordered scattering structure of rods that is optimised to provide a desired radiation pattern. Our numerical method provides an efficient way to model, and then design and test, otherwise inaccessibly large scattering systems.

physics.app-ph↗

arXiv2023

The theory of electromagnetic line waves

Whereas electromagnetic surface waves are confined to a planar interface between two media, line waves exist at the one-dimensional interface between three materials. Here we derive a non-local integral equation for computing the properties of line waves, valid for surfaces characterised in terms of a general tensorial impedance. We find a good approximation -- in many cases -- is to approximate this as a local differential equation, where line waves are one-dimensional analogues of surface plasmons bound to a spatially dispersive metal. For anisotropic surfaces we find the oscillating decay of recently discovered `ghost' line waves can be explained in terms of an effective gauge field induced by the surface anisotropy. These findings are validated using finite element simulations.

physics.optics↗

arXiv2022

Eigenpulses of dispersive time-varying media

We develop a compact theory that can be applied to a variety of time-varying dispersive materials. The continuous wave reflection and transmission coefficients are replaced with equivalent operator expressions. In addition to comparing this approach to existing numerical and analytical techniques, we find that the eigenfunctions of these operators represent pulses that do not change their spectra after interaction with the time-varying, dispersive material. In addition, the poles of these operators represent the non-time harmonic bound states of the system.

physics.optics↗

arXiv2022

Microwave Demonstration of Purcell Effect Enhanced Radiation Efficiency

We experimentally demonstrate a Purcell effect-based design technique for improved impedance matching, and thus enhanced radiation efficiency from a small microwave emitter. Using an iterative process centred on comparing the phase of the radiated field of the emitter in air with that of the emitter in a dielectric environment, we optimise the structure of a dielectric hemisphere above a ground plane surrounding a small monopolar microwave emitter in order to maximise its radiation efficiency. The optimised system shows very strong coupling between the emitter and two omnidirectional radiation modes at 2.00 GHz and 2.84 GHz, yielding Purcell enhancement factors of 8360 and 430 times increase respectively, and near perfect radiation efficiency.

physics.app-ph↗