## End correction in the quasi-fast Hankel transform for optical-propagation problems

Optics Letters, Vol. 6, Issue 4, pp. 171-173 (1981)

http://dx.doi.org/10.1364/OL.6.000171

Enhanced HTML Acrobat PDF (350 KB)

### Abstract

An explicit evaluation is made of a simple end correction to the quasi-fast Hankel-transform algorithm. Application to a Gaussian beam shows that for a given accuracy, the use of this end correction permits a reduction of a factor of 8 in storage as well as a factor of 8 in running time.

© 1981 Optical Society of America

**History**

Original Manuscript: January 15, 1981

Published: April 1, 1981

**Citation**

G. P. Agrawal and M. Lax, "End correction in the quasi-fast Hankel transform for
optical-propagation problems," Opt. Lett. **6**, 171-173 (1981)

http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-6-4-171

Sort: Year | Journal | Reset

### References

- R. W. Hockney, “A fast direct solution of Poisson’s equation using Fourier analysis,” J. Assoc. Comput. Mach. 17, 95–113 (1965). [CrossRef]
- R. C. Le Bail, “Use of fast Fourier transform for solving partial differential equations,” J. Comput. Phys. 9, 440–465 (1972). [CrossRef]
- A. E. Siegman, E. A. Sziklas, “Mode calculations in unstable resonator with flowing saturable gain. 2: Fast Fourier transform method,” Appl. Opt. 14, 1874–1889 (1975). [CrossRef] [PubMed]
- J. A. Fleck, J. R. Morris, M. D. Feit, “Time-dependent propagation of high energy laser beams through the atmosphere,” Appl. Phys. 10, 129–160 (1976). [CrossRef]
- M. Lax, G. P. Agrawal, W. H. Louisell, “Continuous Fourier-transform spline solution of unstable resonator field-distribution,” Opt. Lett. 4, 303–305 (1979). [CrossRef] [PubMed]
- M. Lax, J. H. Batteh, G. P. Agrawal, “Channeling of intense electromagnetic beams,” J. Appl. Phys. (in press); G. P. Agrawal, M. Lax, J. H. Batteh, “Laser-induced channel for atmospheric transmission,” Opt. News 6(3), 37 (1980); G. P. Agrawal, M. Lax, J. H. Batteh, presented at the Optical Society of America Annual Meeting, October 1980.
- J. W. Cooley, J. W. Tukey, “An algorithm for the machine calculation of complex Fourier series,” Math. Comput. 19, 297–301 (1965). [CrossRef]
- R. C. Singleton, “An algorithm for computing the mixed radix fast Fourier transform,” IEEE Trans. Audio Electroacoust. AE-17, 93–103 (1969). [CrossRef]
- A. E. Siegman, “Quasi-fast Hankel transform,” Opt. Lett. 1, 13–15 (1977). [CrossRef] [PubMed]
- The exponential transformation r = r0eαx is attributed to Gardner by Siegman in Ref. 9: D. G. Gardner, J. C. Gardner, G. Lausch, W. W. Meinke, “Method for the analysis of multi-component exponential decays,” J. Chem. Phys. 31, 987 (1959). However, its usefulness in connection with the solution of the radial Sehrödinger equation was recognized much earlier by Langer: see R. E. Langer, “On the connection formulas and the solution of the wave equation,” Phys. Rev. 51, 669–676 (1937). [CrossRef]
- W. D. Murphy, M. L. Bernabe, “Numerical procedures for solving nonsymmetric eigenvalue problems associated with optical resonators,” Appl. Opt. 17, 2358–2365 (1978). [CrossRef] [PubMed]
- W. P. Latham, T. C. Salvi, “Resonator studies with the Gardner–Fresnel–Kirchhoff propagator,” Opt. Lett. 5, 219–221 (1980). [CrossRef] [PubMed]

## Cited By |
Alert me when this paper is cited |

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article | Next Article »

OSA is a member of CrossRef.