Radio Science

The propagation of gaussian beams very near the source


  • L. Lewin


The field of a gaussian beam is examined in detail. It is shown that the usual formula for the field does not satisfy the wave equation within the Rayleigh distance except in the limit of large waist diameter. For small waist sizes the departure from the results of the usual formula can be substantial within a distance of about 1.3 wavelengths from the source. An exact formula is found for the on-axis radiation. In order to make this study, certain features such as the obliquity factor, which is commonly ignored, have to be considered in detail. This leads to the need for a physical characterization of the source, which is not capable of a unique specification. The choice is probably not critical—the usual formulas for the transformation of gaussian beams do not need to refer to it at all—and the one used here pertains closely to the condition of radiation from the dielectric-air interface of a solid state laser.