OSA's Digital Library

Applied Optics

Applied Optics


  • Editor: Joseph N. Mait
  • Vol. 52, Iss. 24 — Aug. 20, 2013
  • pp: 6030–6040

Modeling of the general astigmatic Gaussian beam and its propagation through 3D optical systems

Evgenia Kochkina, Gudrun Wanner, Dennis Schmelzer, Michael Tröbs, and Gerhard Heinzel  »View Author Affiliations

Applied Optics, Vol. 52, Issue 24, pp. 6030-6040 (2013)

View Full Text Article

Enhanced HTML    Acrobat PDF (656 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



The paper introduces the complete model of the general astigmatic Gaussian beam as the most general case of the Gaussian beam in the fundamental mode. This includes the laws of propagation, reflection, and refraction as well as the equations for extracting from the complex-valued beam description its real-valued parameters, such as the beam spot radii and the radii of curvature of the wavefront. The suggested model is applicable to the case of an oblique incidence of the beam at any 3D surface that can be approximated by the second-order equation at the point of incidence. Thus it can be used in simulations of a large variety of 3D optical systems. The provided experimental validation of the model shows good agreement with simulations.

© 2013 Optical Society of America

OCIS Codes
(000.3860) General : Mathematical methods in physics
(350.5500) Other areas of optics : Propagation
(080.2468) Geometric optics : First-order optics
(140.3295) Lasers and laser optics : Laser beam characterization

ToC Category:
Geometric Optics

Original Manuscript: May 3, 2013
Revised Manuscript: July 17, 2013
Manuscript Accepted: July 21, 2013
Published: August 19, 2013

Evgenia Kochkina, Gudrun Wanner, Dennis Schmelzer, Michael Tröbs, and Gerhard Heinzel, "Modeling of the general astigmatic Gaussian beam and its propagation through 3D optical systems," Appl. Opt. 52, 6030-6040 (2013)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. H. Kogelnik and T. Li, “Laser beams and resonators,” Appl. Opt. 5, 1550–1567 (1966). [CrossRef]
  2. J. Alda, “Laser and Gaussian beam propagation and transformation,” in Encyclopedia of Optical Engineering (Marcel Dekker, 2003), pp. 999–1013.
  3. G. A. Massey and A. E. Siegman, “Reflection and refraction of Gaussian light beams at tilted ellipsoidal surfaces,” Appl. Opt. 8, 975–978 (1969). [CrossRef]
  4. J. A. Arnaud and H. Kogelnik, “Gaussian light beams with general astigmatism,” Appl. Opt. 8, 1687–1694 (1969). [CrossRef]
  5. A. Rohani, A. A. Shishegar, and S. Safavi-Naeini, “A fast Gaussian beam tracing method for reflection and refraction of general vectorial astigmatic Gaussian beams from general curved surfaces,” Opt. Commun. 232, 1–10 (2004). [CrossRef]
  6. E. Kochkina, G. Heinzel, G. Wanner, V. Müller, C. Mahrdt, B. Sheard, S. Schuster, and K. Danzmann, “Simulating and optimizing laser interferometers,” in 9th LISA Symposium, Paris, ASP Conference Series (Astronomical Society of the Pacific, 2013), vol. 467, pp. 291–292.
  7. G. Wanner, G. Heinzel, E. Kochkina, C. Mahrdt, B. Sheard, S. Schuster, and K. Danzmann, “Methods for simulating the readout of lengths and angles in laser interferometers with Gaussian beams,” Opt. Commun. 285, 4831–4839 (2012). [CrossRef]
  8. J. Alda, S. Wang, and E. Bernabeu, “Analytical expression for the complex radius of curvature tensor Q for generalized Gaussian beams,” Opt. Commun. 80, 350–352 (1991). [CrossRef]
  9. A. E. Siegman, Lasers (University Science, 1986), pp. 626–697.
  10. A. B. Plachenov, V. N. Kudashov, and A. M. Radin, “Simple formula for a Gaussian beam with general astigmatism in a homogeneous medium,” Opt. Spectrosc. 106, 910–912 (2009). [CrossRef]
  11. J. Serna and G. Nemes, “Decoupling of coherent Gaussian beams with general astigmatism,” Opt. Lett. 18, 1774–1776 (1993). [CrossRef]
  12. G. A. Deschamps, “Ray techniques in electromagnetics,” Proc. IEEE 60, 1022–1035 (1972). [CrossRef]
  13. G. J. James, Geometrical Theory of Diffraction for Electromagnetic Waves, 3rd ed. (Peter Peregrinus, 1986), pp. 96–116.
  14. E. Hecht, Optics (Addison-Wesley, 1974), pp. 60–98.

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