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