Abstract

Focus wave modes are embedded into a wider class of solutions of the wave equation in the paraxial approximation. The generalizations of focus wave modes are made in regard to the following attributes: (1) a wave-packet envelope is admitted that moves with the group velocity in the direction opposite that of the focus envelope and (2) the velocity of the focus envelope can be chosen arbitrarily, in contrast to the group velocity. The Fourier spectrum of the generalized approximate solutions of the wave equation is calculated. This Fourier spectrum becomes singular on the dispersion surface with a strong correlation between frequencies and longitudinal components of the wave vectors in case of focus wave modes. The well-known Gaussian beam solutions with resting focus appear as another special case of the considered class of approximate solutions of the wave equation.

© 1989 Optical Society of America

Generalized Gaussian beam solutions of paraxial optics and their connection to a hidden symmetry

A. Wünsche
J. Opt. Soc. Am. A 6(9) 1320-1329 (1989)

Approximation of the scalar focus wave modes

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Transition from the paraxial approximation to exact solutions of the wave equation and application to Gaussian beams

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Backscatter corrections to the parabolic wave equation

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J. Opt. Soc. Am. A 6(2) 174-179 (1989)