OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Vol. 19, Iss. 2 — Feb. 1, 2002
  • pp: 404–412

Analyses of vector Gaussian beam propagation and the validity of paraxial and spherical approximations

Carl G. Chen, Paul T. Konkola, Juan Ferrera, Ralf K. Heilmann, and Mark L. Schattenburg  »View Author Affiliations


JOSA A, Vol. 19, Issue 2, pp. 404-412 (2002)
http://dx.doi.org/10.1364/JOSAA.19.000404


View Full Text Article

Acrobat PDF (402 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

The analysis of many systems in optical communications and metrology utilizing Gaussian beams, such as free-space propagation from single-mode fibers, point diffraction interferometers, and interference lithography, would benefit from an accurate analytical model of Gaussian beam propagation. We present a full vector analysis of Gaussian beam propagation by using the well-known method of the angular spectrum of plane waves. A Gaussian beam is assumed to traverse a charge-free, homogeneous, isotropic, linear, and nonmagnetic dielectric medium. The angular spectrum representation, in its vector form, is applied to a problem with a Gaussian intensity boundary condition. After some mathematical manipulation, each nonzero propagating electric field component is expressed in terms of a power-series expansion. Previous analytical work derived a power series for the transverse field, where the first term (zero order) in the expansion corresponds to the usual scalar paraxial approximation. We confirm this result and derive a corresponding longitudinal power series. We show that the leading longitudinal term is comparable in magnitude with the first transverse term above the scalar paraxial term, thus indicating that a full vector theory is required when going beyond the scalar paraxial approximation. In spite of the advantages of a compact analytical formalism, enabling rapid and accurate modeling of Gaussian beam systems, this approach has a notable drawback. The higher-order terms diverge at locations that are sufficiently far from the initial boundary, yielding unphysical results. Hence any meaningful use of the expansion approach calls for a careful study of its range of applicability. By considering the transition of a Gaussian wave from the paraxial to the spherical regime, we are able to derive a simple expression for the range within which the series produce numerically satisfying answers.

© 2002 Optical Society of America

OCIS Codes
(000.4430) General : Numerical approximation and analysis
(260.2110) Physical optics : Electromagnetic optics
(350.5500) Other areas of optics : Propagation

Citation
Carl G. Chen, Paul T. Konkola, Juan Ferrera, Ralf K. Heilmann, and Mark L. Schattenburg, "Analyses of vector Gaussian beam propagation and the validity of paraxial and spherical approximations," J. Opt. Soc. Am. A 19, 404-412 (2002)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-19-2-404


Sort:  Author  |  Year  |  Journal  |  Reset

References

  1. H. Kogelnik, “On the propagation of Gaussian beams of light through lenslike media including those with a loss and gain variation,” Appl. Opt. 4, 1562–1569 (1965).
  2. D. C. O’Shea, Elements of Modern Optical Design (Wiley-Interscience, New York, 1985), pp. 247–252.
  3. A. Yariv, Optical Electronics in Modern Communications, 5th ed. (Oxford U. Press, New York, 1997), Chap. 2.
  4. G. P. Agrawal and D. N. Pattanayak, “Gaussian beam propagation beyond the paraxial approximation,” J. Opt. Soc. Am. 69, 575–578 (1979).
  5. M. Lax, W. H. Louisell, and W. B. McKnight, “From Maxwell to paraxial wave optics,” Phys. Rev. A 11, 1365–1370 (1975).
  6. W. H. Carter, “Electromagnetic field of a Gaussian beam with an elliptical cross section,” J. Opt. Soc. Am. 62, 1195–1201 (1972).
  7. C. G. Chen, P. T. Konkola, R. K. Heilmann, G. S. Pati, and M. L. Schattenburg, “Image metrology and system controls for scanning beam interference lithography,” J. Vac. Sci. Technol. B (to be published).
  8. M. H. Lim, J. Ferrera, K. P. Pipe, and H. I. Smith, “A holo-graphic phase-shifting interferometer technique to measure in-plane distortion,” J. Vac. Sci. Technol. B 17, 2703–2706 (1999).
  9. G. E. Sommargren, “Phase shifting diffraction interferometry for measuring extreme ultraviolet optics,” in Extreme Ultraviolet Lithography, G. D. Kubiak and D. R. Kania, eds., Vol. 4 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 1996), pp. 108–112.
  10. D. R. Rhodes, “On the stored energy of planar apertures,” IEEE Trans. Antennas Propag. AP-14, 676–683 (1966).
  11. D. R. Rhodes, “On a fundamental principle in the theory of planar antennas,” Proc. IEEE 52, 1013–1021 (1964).
  12. I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products, 5th ed. (Academic, San Diego, 1994), p. 978.
  13. I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products, 5th ed. (Academic, San Diego, 1994), pp. 737 [Eq. (6.631)(1)], 1062 [Eq. (8.972)(1)], 1087 [Eq. (9.220)(2)].
  14. W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in Fortran 77: The Art of Scientific Computing, Vol. 1 of Fortran Numerical Recipes, 2nd ed. (Cambridge U. Press, Cambridge, UK, 1999), Chap. 16.
  15. M. Born and E. Wolf, Principles of Optics, 6th ed. (Cambridge U. Press, Cambridge, UK, 1980), p. 752.

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.

CrossCheck Deposited