Dynamics of the linearly polarized fundamental Gaussian light wave

Abstract

A continuous planar array of dipoles that are oriented in a particular direction and have an amplitude distribution that is Gaussian in the paraxial limit is introduced as a source for the fundamental Gaussian light wave. The radiation intensity of the Gaussian light wave is determined and its characteristics are analyzed. The universal Gaussian beam factor is deduced and identified as the radiation intensity of the scalar Gaussian wave. The total radiated power, the mean center of the localized wave, and the beam widths of the intensity distribution are obtained. The ratio of the power in the Gaussian wave to that in the corresponding paraxial Gaussian beam is used as a measure of the quality of the paraxial beam approximation. A limiting factor for the power ratio is introduced as an indicator for the acceptability of the paraxial beam approximation. The cross section and the beam widths of the localized light wave are investigated in the large and small kw0 limits, where k is the wavenumber and w0 is the beam waist at the input plane. The beam width of the full Gaussian wave is found to be less than that of the corresponding paraxial Gaussian beam both for the scalar Gaussian wave and for the Gaussian light wave.