## Electromagnetic Gaussian beam

JOSA A, Vol. 15, Issue 10, pp. 2712-2719 (1998)

http://dx.doi.org/10.1364/JOSAA.15.002712

Enhanced HTML Acrobat PDF (368 KB)

### Abstract

The governing equations for the paraxial approximation are deduced from Maxwell’s equations. The plane wave, in the paraxial approximation, is found to be transverse electromagnetic. For a field distribution at the input plane having a general azimuthal variation and a radial variation in the form of a Bessel function of an integer order with a Gaussian envelope of a given waist size, the spreading due to the Fresnel diffraction is determined as the paraxial beam is transported in the axial direction. The effects of Fresnel diffraction are illustrated with examples for a beam transporting unit power. Diffraction patterns of azimuthally symmetrical and dipolar modes are presented.

© 1998 Optical Society of America

**OCIS Codes**

(090.1970) Holography : Diffractive optics

(260.1960) Physical optics : Diffraction theory

**History**

Original Manuscript: March 24, 1998

Revised Manuscript: June 29, 1998

Manuscript Accepted: June 2, 1998

Published: October 1, 1998

**Citation**

S. R. Seshadri, "Electromagnetic Gaussian beam," J. Opt. Soc. Am. A **15**, 2712-2719 (1998)

http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-15-10-2712

Sort: Year | Journal | Reset

### References

- D. Marcuse, Light Transmission Optics (Van NostrandReinhold, New York, 1972), Chap. 6.
- J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), Chap. 4.
- A. Yariv, Quantum Electronics, 2nd ed. (Wiley, New York, 1967), Chap. 6.
- R. H. Jordan, D. G. Hall, “Free-space azimuthal paraxial wave equation: the azimuthal Bessel–Gauss beam solution,” Opt. Lett. 19, 427–429 (1994). [CrossRef] [PubMed]
- D. G. Hall, “Vector-beam solutions of Maxwell’s wave equation,” Opt. Lett. 21, 9–11 (1996). [CrossRef] [PubMed]
- M. Lax, W. H. Louisell, W. B. McKnight, “From Maxwell to paraxial wave optics,” Phys. Rev. A 11, 1365–1370 (1975). [CrossRef]
- J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941), Chaps. 1 and 6.
- N. N. Bogoliubov, Y. A. Mitropolsky, Asymptotic Methods in the Theory of Nonlinear Oscillations (Hindustan, Delhi, India, 1961), Chap. 1.
- G. N. Watson, Theory of Bessel Functions, 2nd ed. (Cambridge U. Press, New York, 1966), Chaps. 2 and 13.
- M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1984), Chap. 8.
- L. Mandel, E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, New York, 1995), pp. 263–285.
- F. Gori, “Fresnel transform and sampling theorem,” Opt. Commun. 39, 293–297 (1981). [CrossRef]
- F. Gori, “Why is Fresnel transform so little known?” in Current Trends in Optics, J. C. Dainty, ed. (Academic, New York, 1994), pp. 139–148.
- F. Gori, G. Guattari, C. Padovani, “Bessel–Gauss beams,” Opt. Commun. 64, 491–495 (1987). [CrossRef]
- C. Palma, R. Borghi, G. Cincotti, “Beams originated by J0-correlated Schell-model planar sources,” Opt. Commun. 125, 113–121 (1996). [CrossRef]
- A. A. Tovar, G. H. Clark, “Concentric-circle-grating, surface-emitting laser beam propagation in complex optical systems,” J. Opt. Soc. Am. A 14, 3333–3340 (1997). [CrossRef]

## 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.