Dispersion of electromagnetic waves in linear, homogeneous, and isotropic media

An electromagnetic wave-packet propagating in a linear, homogeneous, and isotropic medium changes shape while its envelope travels with different velocities at different points in spacetime. In general, a wave-packet can be described as a superposition of plane-waves having different frequencies omega and different propagation vectors kappa. While the angular spread of the k-vectors gives rise to diffractive effects, it is the frequency-dependence of the refractive index of the host medium that is commonly associated with optical dispersion. When the spectral distribution of the wave-packet is confined to a narrow band of frequencies, and also when the spread of the k-vectors is not too broad, it is possible, under certain circumstances, to obtain analytical expressions for the local and/or global trajectory of the packet's envelope as it evolves in time. This paper is an attempt at a systematic description of the underlying physical assumptions and mathematical arguments leading to certain well-known properties of narrowband electromagnetic wave-packets in the presence of diffractive as well as (temporally) dispersive effects.This item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at repository@u.library.arizona.edu