Electromagnetic Gaussian beam

The governing equations for the paraxial approximation are deduced from Maxwell's equations. The plane wave, in the paraxial approximation, is found to be transverse electromagnetic. For a field distribution at the input plane having a general azimuthal variation and a radial variation in the form of a Bessel function of an integer order with a Gaussian envelope of a given waist size, the spreading due to the Fresnel diffraction is determined as the paraxial beam is transported in the axial direction. The effects of Fresnel diffraction are illustrated with examples for a beam transporting unit power. Diffraction patterns of azimuthally symmetrical and dipolar modes are presented. (C) 1998 Optical Society America.