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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 ${\epsilon}({\omega}) {\to} {\epsilon}(t,{\omega})$ 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., Comment: 10 pages, 8 figures

We show that a large family of tensorial metasurfaces can be found that perform an identical wave transformation, showing that even when the conditions of reciprocity and passivity are imposed, there still remain many solutions to the design problem. As an example, we explore the case of a metasurface that rotates a single input polarization, showing we can parameterize the set of equivalent reciprocal metasurfaces in terms of a single complex parameter. 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.

The interaction of light with superluminally moving matter entails unconventional phenomena, from Fresnel drag to Hawking radiation and to light amplification. While relativity makes these effects inaccessible using objects in motion, synthetic motion - enabled via space-time modulated internal degrees of freedom - is free from these constraints. Here we observe synthetic velocity of a reflectivity modulation travelling on an Indium-Tin-Oxide (ITO) interface, generated by ultrafast laser illumination at multiple positions and times. The interaction of the moving reflectivity modulation with a probe light beam acts as a non-separable spatio-temporal transformation that diffracts the light, changing its frequency and momentum content. The recorded frequency-momentum diffraction pattern is defined by the velocity of the diffracted probe wave relative to the modulation. Our experiments open a path towards mimicking relativistic mechanics and developing programmable spatio-temporal transformations of light., Comment: 9 pages, 3 figures

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.

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., Comment: 6 pages, 5 figures

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.

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.

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., Comment: 24 pages, 6 figures

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., Comment: 6 pages, 3 figures

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.

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.

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., Comment: 66 pages, 6 figures

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., Comment: 82 pages, 20 figures

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., Comment: 18 pages. 5 figures

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., Comment: 20 pages, 19 figures

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., Comment: 15 pages, 6 figures

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., Comment: 22 pages, 5 figures

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., Comment: substantially updated version, 5 figures, 12 pages+refs+appendix, comments welcome (previous title: Versatile three-dimensional quantum spin dynamics equation with guaranteed fluctuation-dissipation link)

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., Comment: 26 pages, 7 figures

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.

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., Comment: 10 pages, 6 figures

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.

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., Comment: 14 pages, 4 figures

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., Comment: 13 pages, 4 figures, to appear in Phys. Rev. A

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., Comment: 21 pages, 4 figures

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 Schr\"odinger-like equation with a P\"oschl-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 P\"oschl-Teller profile for a domain wall is found to correspond to a local maximum of the emission efficiency. Furthermore, for a tailored P\"oschl-Teller potential with a variable aspect ratio, particular values of the latter can lead to enhanced or even completely suppressed emission., Comment: added ancillary files

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., Comment: 18 pages, 4 figs

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., Comment: 16 pages, 4 figures

There is a well explored relationship between quantum mechanical scattering from a potential and the Korteweg-de Vries (KdV) equation of fluid dynamics: if the potential is 'evolved' according to the KdV equation then it will have the same reflectivity and transmissivity as a function of energy, for each snapshot in time. In this work we explore this connection in optics, where the permittivity plays the role of the potential. We begin by deriving the relationship between the Helmholtz equation and the KdV equation in terms of the current induced in a material when a permittivity profile is changed slightly. It is then shown that the KdV equation can be used to design a plethora of bounded complex potentials that are relfectionless from both sides for all angles of incidence, and planar periodic media that exhibit a real Bloch vector for all angles of propagation. Finally we apply the KdV equation to reduce the reflection of a wave from an interface between two media of differing refractive indices., Comment: 15 pages, 5 figures

A change in the sign of the frequency of a wave between two inertial reference frames corresponds to a reversal of the phase velocity. Yet from the point of view of the relation $E=\hbar\omega$, a positive quantum of energy apparently becomes a negative energy one. This is physically distinct from a change in the sign of the wave-vector, and has been associated with various effects such as Cherenkov radiation, quantum friction, and the Hawking effect. In this work we provide a more detailed understanding of these negative frequency modes based on a simple microscopic model of a dielectric medium as a lattice of scatterers. We calculate the classical and quantum mechanical radiation damping of an oscillator moving through such a lattice and find that the modes where the frequency has changed sign contribute negatively. In terms of the lattice of scatterers we find that this negative radiation damping arises due to phase of the periodic force experienced by the oscillator due to the relative motion of the lattice., Comment: 14 pages, 6 figures

We investigate the analytic continuation of wave equations into the complex position plane. For the particular case of electromagnetic waves we provide a physical meaning for such an analytic continuation in terms of a family of closely related inhomogeneous media. For bounded permittivity profiles we find the phenomenon of reflection can be related to branch cuts in the wave that originate from poles of the permittivity at complex positions. Demanding that these branch cuts disappear, we derive a large family of inhomogeneous media that are reflectionless for a single angle of incidence. Extending this property to all angles of incidence leads us to a generalized form of the Poschl Teller potentials. We conclude by analyzing our findings within the phase integral (WKB) method., Comment: 18 pages, 8 figures

We show that if the permittivity profile of a planar dielectric medium is an analytic function in the upper (lower) half complex position plane then it won't reflect radiation from the left (right), whatever the angle of incidence. Consequently, using the spatial Kramers-Kronig relations one can derive a real part of a permittivity profile from some given imaginary part (or vice versa), such that the reflection is guaranteed to be zero. This result is valid for both scalar and vector wave theories, and may have relevance for efficiently absorbing radiation, or reducing reflection from bodies., Comment: 10 pages, 3 figures

We show that a pulse of electromagnetic radiation launched into a cavity can be completely absorbed into an infinitesimal region of space, provided one has a high degree of control over the current flowing through this region. We work out explicit examples of this effect in a cubic cavity and a cylindrical one, and experimentally demonstrate the effect in the microwave regime., Comment: 7 pages, 4 figures

We find the action that describes the electromagnetic field in a spatially dispersive, homogeneous medium. This theory is quantized and the Hamiltonian is diagonalized in terms of a continuum of normal modes. It is found that the introduction of nonlocal response in the medium automatically regulates some previously divergent results, and we calculate a finite value for the intensity of the electromagnetic field at a fixed frequency within a homogeneous medium. To conclude we discuss the potential importance of spatial dispersion in taming the divergences that arise in calculations of Casimir-type effects., Comment: 16 pages

Reciprocity is fundamental to light transport and is a concept that holds also in rather complex systems. Yet, reciprocity can be switched off even in linear, isotropic and passive media by setting the material structure into motion. In highly dispersive multilayers this leads to a fairly large forward-backward asymmetry in the pulse transmission. Moreover, in multilevel systems, this transport phenomenon can be all-optically enhanced. For atomic multilayer structures made of three-level cold Rubidium 87 atoms, for instance, forward-backward transmission contrast around 95 per cent can be obtained already at atomic speeds in the meter per second range. The scheme we illustrate may open up avenues for optical isolation that were not previously accessible., Comment: 5 pages, 4 figures

The physics of quantum electromagnetism in an absorbing medium is that of a field of damped harmonic oscillators. Yet until recently the damped harmonic oscillator was not treated with the same kind of formalism used to describe quantum electrodynamics in a arbitrary medium. Here we use the techniques of macroscopic QED, based on the Huttner--Barnett reservoir, to describe the quantum mechanics of a damped oscillator. We calculate the thermal and zero-point energy of the oscillator for a range of damping values from zero to infinity. While both the thermal and zero-point energies decrease with damping, the energy stored in the oscillator at fixed temperature increases with damping, an effect that may be experimentally observable. As the results follow from canonical quantization, the uncertainty principle is valid for all damping levels., Comment: 10 pages

We consider the ground state energy of the electromagnetic field in a piston geometry. In the idealised case, where the piston and the walls of the chamber are taken as perfect mirrors, the Casimir pressure on the piston is finite and independent of the small scale physics of the media that compose the mirrors; the Casimir-energy of the system can be regularised and is cutoff-independent. Yet we find that, when the body of the piston is filled with an inhomogeneous dielectric medium, the Casimir energy is cutoff-dependent, and the value of the pressure is thus inextricably dependent on the detailed behaviour of the mirror and the medium at large wave-vectors. This result is inconsistent with recent proposals for regularising Casimir forces in inhomogeneous media., Comment: 6 pages, 2 figures

A series of thin layers of alternating refractive index is known to make a good optical mirror over certain bands of frequency. Such a device - often termed the Bragg reflector - is usually introduced to students within the first years of an undergraduate degree, often in isolation from other parts of the course. Here we show that the basic physics of wave propagation through a stratified medium can be used to illustrate some more modern developments in optics as well as quantum physics; from transfer matrix techniques, to the optical properties of cold trapped atoms, optomechanical cooling, and a simple example of a system exhibiting an appreciable level of optical non-reciprocity., Comment: 24 pages, 9 figures

A theory is presented for calculating the effect of the electromagnetic field on the centre of mass of a macroscopic dielectric body that is valid in both quantum and classical regimes. We apply the theory to find the classical equation of motion for the centre of mass of a macroscopic object in a classical field, and the spreading of an initially localized wave-packet representing the centre of mass of a small object, in a quantum field. The classical force is found to be consistent with the identification of the Abraham momentum with the mechanical momentum of light, and the motion of the wave-packet is found to be subject to an acceleration due to the Casimir force, and a time dependent fluctuating motion due the creation of pairs of excitations within the object. The theory is valid for any dielectric that has susceptibilities satisfying the Kramers-Kronig relations, and is not subject to arguments regarding the form of the electromagnetic energy-momentum tensor within a medium., Comment: 15 pages, 2 figures

A general theory of optical forces on moving bodies is here developed in terms of generalized/4x4 transfer and scattering matrices. Results are presented for a planar dielectric multilayer of arbitrary refractive index placed in an otherwise empty space and moving parallel and perpendicular to the slab-vacuum interface. In both regimes of motion the resulting force comprises lateral and normal velocity-dependent components which may depend in a subtle way on the Doppler effect and TE-TM polarization mixing. For lateral displacements in particular, polarization mixing, which is here interpreted as an effective magneto-electric effect due to the reduced symmetry induced by the motion of the slab, gives rise to a velocity dependent force contribution that is sensitive to the phase difference between the two polarization amplitudes. This term gives rise to a rather peculiar optical response on the moving body and specific caseses are illustrated for incident radiation of arbitrarily directed linear polarization. The additional force due to polarization mixing may cancel to first order in V/c with the first order Doppler contribution yielding an overall vanishing of the velocity-dependent component of the force on the body. The above findings bare some relevance to modern developments of nano-optomechanics as well as to the problem of a frictional component to the Casimir force., Comment: 14 pages, 4 figures

The electromagnetic field is canonically quantized in the presence of a linear, dispersive and dissipative medium that is in uniform motion. Specifically we calculate the change in the normal modes of the coupled matter-field system and find a Hamiltonian that contains negative energy normal modes. We interpret these modes as the origin of phenomena such as quantum friction, and find that a detector initially in its ground state and coupled to the electromagnetic field in the vicinity of, or within a uniformly moving medium has a non-zero probability of excitation at T=0K., Comment: 14 pages, 3 figures

The dependence of macroscopic radiation pressure on the velocity of the object being pushed is commonly attributed to the Doppler effect. This need not be the case, and here we highlight velocity dependent radiation pressure terms that have their origins in the mixing of s and p polarizations brought about by the Lorentz transformation between the lab and the material rest frame, rather than in the corresponding transformation of frequency and wavevector. The theory we develop is relevant to the nano-optomechanics of moving bodies., Comment: 5 pages, 2 figures

Recent work by Philbin [1] has provided a Lagrangian theory that establishes a general method for the canonical quantization of the electromagnetic field in any dispersive, lossy, linear dielectric. Working from this theory, we extend the Lagrangian description to reciprocal and non- reciprocal magnetoelectric (bi-anisotropic) media, showing that some versions of the constitutive relations are inconsistent with a real Lagrangian, and hence with quantization. This amounts to a restriction on the magnitude of the magnetoelectric coupling. Moreover from the point of view of quantization, moving media are shown to be fundamentally different from stationary magnetoelectrics, despite the formal similarity in the constitutive relations., Comment: 11 pages

The geometrical interpretation of electromagnetism in transparent media (transformation optics) is extended to include media with isotropic, inhomogeneous, chirality. It is found that such media may be described through introducing the non-Riemannian geometrical property of torsion into the Maxwell equations, and shown how such an interpretation may be applied to the design of optical devices., Comment: 11 pages, 2 figures

In quantum mechanics, asymptotic degeneracy is often considered in the context of a particle in a symmetric double-well potential, and is the phenomenon whereby pairs of energy levels come together to form doubly degenerate levels in response to an increase in the separation, or depth of the two wells. Here we highlight a new kind of asymptotic degeneracy that can arise when a particle is bound to a surface formed by the intersection of two planes, when the intersection angle is greater than pi. To demonstrate this effect we consider the bound states of a charged particle subject its own 'image' potential in a highly polarizable wedge, as a function of the wedge opening angle., Comment: 4 pages, 3 figures