Propagation of axisymmetric beams by means of Gauss-Fourier expansion

Shlomo Ruschin

doi:10.1117/12.143851

22 April 1993 Propagation of axisymmetric beams by means of Gauss-Fourier expansion

Shlomo Ruschin

Proceedings Volume 1834, Laser Energy Distribution Profiles: Measurement and Applications; (1993) https://doi.org/10.1117/12.143851
Event: Applications in Optical Science and Engineering, 1992, Boston, MA, United States

Abstract

A method is presented for describing the propagation of axisymmetric beams by expansion into Gaussian beams which are displaced axially relative to the entrance plane. If the position of the Gaussian beams' waists and their widths are properly chosen, the coefficients of the expansion can be found by means of fast Fourier transform (FFT) procedures. One disadvantage of propagation algorithms based on FFTs is that their range is limited by aliasing effects. The propagation length is then enhanced usually by enlarging the entrance plane and padding with zeros the transverse field range thus enlarging the size of vectors without increasing field details. An alternative approach is that of subdividing the propagation length into smaller steps and eliminating the leaking aliased field by introducing absorbing layers close to the boundaries of the transverse range. The method described here has significantly reduced aliasing effects due to the bound character of the Gaussian functions, thus enlarging the range of propagation of a single step. Another advantage of the method is that the sampling points are evenly distributed in the r² coordinate, following linearly the power distribution across the radius of axisymmetric beams.

Citation Download Citation

Shlomo Ruschin "Propagation of axisymmetric beams by means of Gauss-Fourier expansion", Proc. SPIE 1834, Laser Energy Distribution Profiles: Measurement and Applications, (22 April 1993); https://doi.org/10.1117/12.143851

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KEYWORDS

Gaussian beams

Wave propagation

Beam propagation method

Laser energy

Electrical engineering

Fourier transforms

Free space

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