58 research outputs found

    Quantum electrodynamics in the presence of moving bodies

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    Progress In Electromagnetics Research SymposiumPIERS 2013, Stockholm, Sweden, 12-15 August 2013This is the final version of the article. Available from the publisher via the URL in this record.The vacuum state of the electromagnetic field close to a dielectric body is not the same in all reference frames. Here we show that this has some surprising consequences. For instance, if we attempt to quantize electromagnetism interacting with a uniformly moving medium (properly including effects of dispersion and dissipation), then the resulting Hamiltonian lacks a lower bound. Consequently, a detector placed close to a moving surface can be excited by the vacuum! It is shown that when the dielectric is allowed to change velocity then the Hamiltonian again becomes bounded from below, thus demonstrating that the source of the energy exciting the detector is the kinetic energy of the dielectric.The author thanks the EPSRC for financial suppor

    The KdV hierarchy in optics

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    ArticleThis is an open access article.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 indicesSARH acknowledges financial support from program grant EP/I034548/1

    Spatiotemporal deformations of reflectionless potentials

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    This is the author accepted manuscript. The final version is available from American Physical Society via the DOI in this record.Reflectionless potentials for classical or matter waves represent an important class of scatteringless systems encountered in different areas of physics. Here we mathematically demonstrate that there is a family of non-Hermitian potentials that, in contrast to their Hermitian counterparts, remain reflectionless even when deformed in space or time. These are the profiles that satisfy the spatial Kramers-Kronig relations. We start by considering scattering of matter waves for the Schrödinger equation with an external field, where a moving potential is observed in the Kramers-Henneberger reference frame. We then generalize this result to the case of electromagnetic waves, by considering a slab of reflectionless material that both is scaled and has its center displaced as an arbitrary function of position. We analytically and numerically demonstrate that the backscattering from these profiles remains zero, even for extreme deformations. Our results indicate the supremacy of non-Hermitian Kramers-Kronig potentials over reflectionless Hermitian potentials in keeping their reflectionless property under deformation and could find applications to, e.g., reflectionless optical coatings of highly deformed surfaces based on perfect absorption.S.A.R.H. acknowledges financial support through a Royal Society TATA University Research Fellowship (Grant No. RPG-2016-186)

    One-way invisibility in isotropic dielectric optical media

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    This is the final version of the article. Available from American Association of Physics Teachers via the DOI in this record.Optical materials with a distribution of loss and gain can be used to manipulate waves in fascinating ways, seemingly impossible with ordinary lossless materials. Some recent results have shown that (for planar media) if the spatial distributions of the real and imaginary parts of the permittivity are related to one another by the Kramers-Kronig relations, then reflection can be eliminated. Moreover, if an additional “cancellation condition” is satisfied, then a material can be made invisible for incidence from one side. Here, we give a simple demonstration of these results that should be accessible to undergraduates. In addition, we show how this simple method can be used to prove results about the reflection from permittivity profiles, without ever requiring an exact solution of the Helmholtz equation.S.A.R.H. acknowledges financial support from the Royal Society and TATA

    Negative frequencies in wave propagation: A microscopic model

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    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=ω, 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 can be 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 the phase of the periodic force experienced by the oscillator due to the relative motion of the lattice.EPSRC programme grant EP/1034548/1

    Wave propagation in complex coordinates

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    ArticleWe give an interpretation for the use of complex spatial coordinates in electromagnetism, in terms of a family of closely related inhomogeneous media. Using this understanding we find that the phenomenon of reflection can be related to branch cuts in the wave that originate from poles of ϵ (z) at complex positions. Demanding that these branch cuts disappear, we derive a new 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 that in general include regions of loss and gain. We conclude by analyzing our findings within the phase integral (WKB) method, and find another very large family of isotropic planar media that from one side have a transmission of unity and reflection of zero, for all angles of incidence.SARH and TGP acknowledge financial support from EPSRC program grant EP/I034548/1

    Perfect transmission through disordered media

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    This is the author accepted manuscript. The final version is available from American Physical Society via the DOI in this record.The transmission of a wave through a randomly chosen `pile of plates' typically decreases expo- nentially with the number of plates, a phenomenon closely related to Anderson localisation. In ap- parent contradiction we construct disordered planar permittivity pro les which are complex-valued (i.e. have reactive and dissipative properties) that appear to vary randomly with position, yet are one-way re ectionless for all angles of incidence and exhibit a transmission coe cient of unity. In addition to these complex-valued 'random' planar permittivity pro les, we construct a family of real-valued, two-way re ectionless and perfectly transmitting disordered permittivity pro les that function only for a single angle of incidence and a narrow frequency range.C. G. K. acknowledges financial support from the EPSRC Centre for Doctoral Training in Electromagnetic Metamaterials Grant No. EP/L015331/1. S. A. R. H. acknowledges financial support from EPSRC program Grant No. EP/I034548/1, the Royal Society, and TATA. T. G. P. acknowledges financial support from EPSRC program Grant No. EP/I034548/1. The authors acknowledge useful discussions about localization in disordered media with J. Bertolotti

    Invisibility cloaking using pseudomagnetic field for photon

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    This is the final version of the article. Available from American Physical Society via the DOI in this record.A cylindrical cloak can be interpreted as a controlled mirage upon a transformation from cylindrical to planar stratified layers. Here, we show that such mirage can be obtained using a pseudomagnetic field instead of a gradient index profile, thus enabling an alternative route towards invisibility cloaking. While working equivalently to a conventional cloak, the asymmetry of light bending direction from a pseudomagnetic field enables the cloak to demonstrate an asymmetric transmission property subject to a truncation of the materials near the inner surface of the cloak. Furthermore, such an asymmetry allows us to design transformation optical devices, such as a one-way retroreflector, with asymmetric transmission.This work is supported by the European Union's Seventh Framework Programme under Grant Agreement No. 630979 (NHermPhoton)

    Scattering of accelerated wave packets

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    This is the final version of the article. Available from American Physical Society via the DOI in this record.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

    Graded index lenses for spin wave steering

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    This is the final version. Available from the American Physical Society via the DOI in this record. 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.Royal Society (Charity)Engineering and Physical Sciences Research Council (EPSRC
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