1,474 research outputs found

    Indifferent electromagnetic modes: bound states and topology

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    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 figure

    Unidirectional wave propagation in media with complex principal axes

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    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 figure

    The cutoff-dependence of the Casimir force within an inhomogeneous medium

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    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 figure

    Scattering of accelerated wave packets

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    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.