Volume 81, Number 1, January 2008
Article Number 10007
Number of page(s) 6
Section General
Published online 29 November 2007
EPL, 81 (2008) 10007
DOI: 10.1209/0295-5075/81/10007

Propagation of electromagnetic waves in linear media and pseudo-hermiticity

A. Mostafazadeh1 and F. Loran2

1  Department of Mathematics, Koç University - Sariyer 34450, Istanbul, Turkey
2  Department of Physics, Isfahan University of Technology - Isfahan, Iran

received 7 July 2007; accepted in final form 2 November 2007; published January 2008
published online 29 November 2007

We express the electromagnetic field propagating in an arbitrary time-independent non-dispersive medium in terms of an operator that turns out to be pseudo-Hermitian for Hermitian dielectric and magnetic permeability tensors ${\stackrel{\leftrightarrow}{\mbox{\large {$\varepsilon$ }}}} $ and ${\stackrel{\leftrightarrow}{\mbox{\large {$\mu$ }}}} $. We exploit this property to determine the propagating field. In particular, we obtain an explicit expression for a planar field in an isotropic medium with ${\stackrel{\leftrightarrow}{\mbox{\large {$\varepsilon$ }}}}=\varepsilon{\stackrel{\leftrightarrow}{1}} $ and ${\stackrel{\leftrightarrow}{\mbox{\large {$\mu$ }}}}=\mu{\stackrel{\leftrightarrow}{1}} $ varying along the direction of the propagation. We also study the scattering of plane waves due to a localized inhomogeneity.

03.50.De - Classical electromagnetism, Maxwell equations.
41.20.Jb - Electromagnetic wave propagation; radiowave propagation.
02.70.Hm - Spectral methods.

© EPLA 2008