## Higher-order corrections to the electric field vector of a Gaussian beam

JOSA A, Vol. 16, Issue 9, pp. 2232-2238 (1999)

http://dx.doi.org/10.1364/JOSAA.16.002232

Acrobat PDF (182 KB)

### Abstract

The higher-order correction terms of the electric field vector of a Gaussian beam are derived explicitly from the magnetic vector potential that is assumed to be Gaussian and linearly polarized at the z=0 plane. The correction terms are proved to satisfy exactly Lax’s recurrence equations [Phys. Rev. A11, 1365 (1975)]. The electric field vector with correction terms of orders up to 3 is compared with the exact electric field vector of an integral form that is also derived from the magnetic vector potential.

© 1999 Optical Society of America

**OCIS Codes**

(260.2110) Physical optics : Electromagnetic optics

(350.5500) Other areas of optics : Propagation

**History**

Original Manuscript: February 8, 1999

Revised Manuscript: April 19, 1999

Manuscript Accepted: April 19, 1999

Published: September 1, 1999

**Citation**

Hyo-Chang Kim and Yeon H. Lee, "Higher-order corrections to the electric field vector of a Gaussian beam," J. Opt. Soc. Am. A **16**, 2232-2238 (1999)

http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-16-9-2232

Sort: Year | Journal | Reset

### References

- M. Lax, W. H. Louisell, W. B. McKnight, “From Maxwell to paraxial wave optics,” Phys. Rev. A 11, 1365–1370 (1975). [CrossRef]
- G. P. Agrawal, D. N. Pattanayak, “Gaussian beam propagation beyond the paraxial approximation,” J. Opt. Soc. Am. 69, 575–578 (1979). [CrossRef]
- M. Couture, P. Belanger, “From Gaussian beam to complex-source-point spherical wave,” Phys. Rev. A 24, 355–359 (1981). [CrossRef]
- G. A. Deschamps, “Ray techniques in electromagnetics,” Proc. IEEE 60, 1022–1035 (1972). [CrossRef]
- T. Takenaka, M. Yokota, O. Fukumitsu, “Propagation of light beams beyond the paraxial approximation,” J. Opt. Soc. Am. A 2, 826–829 (1985). [CrossRef]
- A. E. Siegman, “Hermite–Gaussian functions of complex argument as optical-beam eigenfunctions,” J. Opt. Soc. Am. 63, 1093–1094 (1973). [CrossRef]
- B. T. Landesman, H. H. Barrett, “Gaussian amplitude functions that are exact solutions to the scalar Helmholtz equation,” J. Opt. Soc. Am. A 5, 1610–1619 (1988). [CrossRef]
- A. Wünsche, “Transition from the paraxial approximation to exact solutions of the wave equation and application to Gaussian beams,” J. Opt. Soc. Am. A 9, 765–774 (1992). [CrossRef]
- H. Laabs, “Propagation of Hermite–Gaussian-beams beyond the paraxial approximation,” Opt. Commun. 147, 1–4 (1998). [CrossRef]
- Q. Cao, X. Deng, “Corrections to the paraxial approximation of an arbitrary free-propagation beam,” J. Opt. Soc. Am. A 15, 1144–1148 (1998). [CrossRef]
- L. W. Davis, “Theory of electromagnetic beams,” Phys. Rev. A 19, 1177–1179 (1979). [CrossRef]
- A. L. Cullen, P. K. Yu, “Complex source-point theory of the electromagnetic open resonator,” Proc. R. Soc. London, Ser. A 366, 155–171 (1979). [CrossRef]
- D. N. Pattanayak, G. P. Agrawal, “Representation of vector electromagnetic beams,” Phys. Rev. A 22, 1159–1164 (1980). [CrossRef]
- R. Simon, E. C. G. Sudarshan, N. Mukunda, “Cross polarization in laser beams,” Appl. Opt. 26, 1589–1593 (1987). [CrossRef] [PubMed]
- W. L. Erikson, S. Singh, “Polarization properties of Maxwell–Gaussian laser beams,” Phys. Rev. E 49, 5778–5786 (1994). [CrossRef]
- P. Varga, P. Török, “Exact and approximate solutions of Maxwell’s equations for a confocal cavity,” Opt. Lett. 21, 1523–1525 (1996). [CrossRef] [PubMed]
- P. Varga, P. Török, “The Gaussian wave solution of Maxwell’s equations and the validity of scalar wave approximation,” Opt. Commun. 152, 108–118 (1998). [CrossRef]
- G. N. Watson, A Treatise on the Theory of Bessel Functions, 2nd ed. (Cambridge U. Press, London, 1966), p. 140.
- G. P. Agrawal, M. Lax, “Free-space wave propagation beyond the paraxial approximation,” Phys. Rev. A 27, 1693–1695 (1983). [CrossRef]
- S. Ramo, J. R. Whinnery, T. V. Duzer, Fields and Waves in Communication Electronics, 3rd ed. (Wiley, New York, 1994), p. 589.
- H. A. Haus, Waves and Fields in Optoelectronics (Prentice-Hall, Englewood Cliffs, N.J., 1984), pp. 113–118.
- B. E. A. Saleh, M. C. Teich, Fundamentals of Photonics (Wiley, New York, 1991), pp. 169–174.
- G. D. Boyd, J. P. Gordon, “Confocal multimode resonator for millimeter through optical wavelength masers,” Bell Syst. Tech. J. 40, 489–508 (1961). [CrossRef]
- H. Kogelnik, T. Li, “Laser beams and resonators,” Proc. IEEE 54, 1312–1329 (1966). [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.