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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 17, Iss. 21 — Oct. 12, 2009
  • pp: 19181–19189

On the Interference of two Gaussian beams and their ABCD Matrix Representation

Muzammil A. Arain and Guido Mueller  »View Author Affiliations

Optics Express, Vol. 17, Issue 21, pp. 19181-19189 (2009)

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Gaussian beam propagation is well described by the q-parameter and the ABCD matrices. A variety of ABCD matrices are available that represent commonly occurring scenarios/components in optics. One important phenomenon that has not been studied in detail is the interference of two optical beams with different q-parameters undergoing interference. In this paper, we describe the effect of interference of two Gaussian beams. We derive an ABCD matrix for the addition of two beams that takes into account both the amplitude and phase difference between two beams. This ABCD matrix will help greatly in determining the propagation of beams inside complex interferometers and finding the solutions for the coupled cavity Eigenmodes.

© 2009 OSA

OCIS Codes
(070.2590) Fourier optics and signal processing : ABCD transforms
(080.0080) Geometric optics : Geometric optics
(080.2730) Geometric optics : Matrix methods in paraxial optics
(260.0260) Physical optics : Physical optics
(260.3160) Physical optics : Interference

ToC Category:
Physical Optics

Original Manuscript: July 27, 2009
Revised Manuscript: October 5, 2009
Manuscript Accepted: October 7, 2009
Published: October 8, 2009

Muzammil A. Arain and Guido Mueller, "On the Interference of two Gaussian Beams and their ABCD Matrix Representation," Opt. Express 17, 19181-19189 (2009)

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  1. A. E. Siegman, Lasers, University Science books, Sausalito, CA (1984).
  2. R. P. Herloski, S. Marshall, and R. L. Antos, “Gaussian Beam Ray-Equivalent Modeling and Optical Design—Erratum,” Appl. Opt. 22(8), 1168–1174 (1983). [CrossRef] [PubMed]
  3. J. Arnaud, “Representation of Gaussian beams by complex rays,” Appl. Opt. 24(4), 538–543 (1985). [CrossRef] [PubMed]
  4. A. W. Greynolds, “Vector Formulation of the Ray-Equivalent Method for General Gaussian Beam Propagation,” Proceedings of SPIE, Current Developments in Optical Engineering and Diffractive Phenomena 679, 129–133 (1986).
  5. G. W. Forbes and M. A. Alonso, “Using rays better. I. Theory for smoothly varying media,” J. Opt. Soc. Am. A 18(5), 1132–1145 (2001). [CrossRef]
  6. M. A. Alonso and G. W. Forbes, “Using rays better. II. Ray families to match prescribed wave fields,” J. Opt. Soc. Am. A 18(5), 1146–1159 (2001). [CrossRef]
  7. M. Born, and E. Wolf, Principles of Optics, 7th (expanded)ed., Cambridge U. Press, Cambridge, UK, (1999).
  8. D. Z. Anderson, “Alignment of resonant optical cavities,” Appl. Opt. 23(17), 2944–2949 (1984). [CrossRef] [PubMed]
  9. H. Yamamoto, M. Barton, B. Bhawal, M. Evans, and S. Yoshida, “Simulation tools for future interferometers,” J. Phys.: Conf. Ser. 32, 398–403 (2006). [CrossRef]
  10. S. A. Collins., “Lens-system diffraction integral written in terms of matrix optics,” J. Opt. Soc. Am. 60(9), 1168–1177 (1970). [CrossRef]
  11. J. Arnaud, “Nonorthogonal optical Waveguides and Resonators,” Bell Syst. Tech. J. (November), 2311–2348 (1970).
  12. M. J. Bastiaans, “The Expansion of an Optical Signal into a Discrete Set of Gaussian Beams,” Optik (Stuttg.) 57, 95–101 (1980).
  13. M. A. Arain and G. Mueller, “Design of the Advanced LIGO recycling cavities,” Opt. Express 16(14), 10018–10032 (2008), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-14-10018 . [CrossRef] [PubMed]

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