Abstract
A treatment of the higher-order hollow Gaussian beam is presented. The required higher-order point source in the complex space is introduced. The higher-order hollow full Gaussian wave generated by the complex space source is derived. The basic full Gaussian wave is obtained as a special case of the higher-order hollow full Gaussian wave. The cosh-Gauss paraxial beam is deduced by the two-dimensional Fourier transform technique. The required array of point sources situated on the corners of a square in the complex space is introduced. The full-wave generalization of the cosh-Gauss beam is determined. The basic full Gaussian wave is obtained as a special case of the full cosh-Gauss wave as the side of the square reduces to zero.
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