Common Aspects of Gaussian Beams, Ellipsoidal Waves and Multipole Radiation

Abstract

A close connection is found among spheroidal waves, light beams with the Gaussian amplitude profile or the resonant mode of Fabry-Perot resonators and the multipole expansion of electro-magnetic radiation. For usual applications where aberrations are ignored, the dipole radiation term aR-1exp jγ0nR is sufficient to represent those beam waves, where R is defined through R2=( r- r0+j q0), 2 in which r is the radius vector and r0, q0, a are constant vectors specifying the position of waist, direction of propagation as well as the waist size, and polarization, respectively. Two beams, each consisting of electric dipole, magnetic dipole and electric quadrupole radiation terms, are found necessary and sufficient to match the magnetic field and tangential electric field on both sides of a spherical surface up to the fourth order.