Physics
Scientific paper
Apr 2000
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2000phrve..61.4462b&link_type=abstract
Physical Review E (Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics), Volume 61, Issue 4, April 2000,
Physics
11
Classical Electromagnetism, Maxwell Equations, Electromagnetic Wave Propagation, Radiowave Propagation, Gravitational Waves: Theory, Mechanical And Elastic Waves, Vibrations
Scientific paper
Vector plane-wave superpositions defined by a given set of orthonormal scalar functions on a two- or three-dimensional manifold-beam manifold-are treated. We present a technique for composing orthonormal beams and some other specific types of fields such as three-dimensional standing waves, moving and evolving whirls. It can be used for any linear fields, in particular, electromagnetic fields in complex media and elastic fields in crystals. For electromagnetic waves in an isotropic medium or free space, unique families of exact solutions of Maxwell's equations are obtained. The solutions are illustrated by calculating fields, energy densities, and energy fluxes of beams defined by the spherical harmonics. It is shown that the obtained results can be used for a transition from the plane-wave approximation to more accurate models of real incident beams in free-space techniques for characterizing complex media. A mathematical formalism convenient for the treatment of various beams defined by the spherical harmonics is presented.
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