2,693 research outputs found
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.Comment: 10 pages, 6 figure
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.Comment: 21 pages, 4 figure
The cutoff-dependence of the Casimir force within an inhomogeneous medium
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
The pi-N Sigma term - a lattice investigation
A lattice calculation of the pi-N sigma term is described using dynamical
staggered fermions. Preliminary results give a sea term comparable in magnitude
to the valence term.Comment: Latex article. 6 pages, uuencoded compressed tar file. Contribution
to the Kyffhaeuser Workshop (Leipzig, Germany, September 1993). HLRZ preprint
93-6
The ``Spin'' Structure of the Nucleon - a lattice investigation
We will discuss here an indirect lattice evaluation of the baryon axial
singlet current matrix element. This quantity may be related to the fraction of
nucleon spin carried by the quarks. The appropriate structure function has
recently been measured (EMC experiment). As in this experiment, we find that
the quarks do not appear to carry a large component of the nucleon spin.Comment: Latex article. 3 pages. Contribution to the Second IMACS Conference
on Computational Physics, Cahokia, U.S.A. October 1993. HLRZ preprint 93-7
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