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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 27 — Dec. 19, 2011
  • pp: 25944–25953

Effect of ABCD transformations on beam paraxiality

Pablo Vaveliuk and Oscar Martinez-Matos  »View Author Affiliations

Optics Express, Vol. 19, Issue 27, pp. 25944-25953 (2011)

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The limits of the paraxial approximation for a laser beam under ABCD transformations is established through the relationship between a parameter concerning the beam paraxiality, the paraxial estimator, and the beam second-order moments. The applicability of such an estimator is extended to an optical system composed by optical elements as mirrors and lenses and sections of free space, what completes the analysis early performed for free-space propagation solely. As an example, the paraxiality of a system composed by free space and a spherical thin lens under the propagation of Hermite-Gauss and Laguerre-Gauss modes is established. The results show that the the paraxial approximation fails for a certain feasible range of values of main parameters. In this sense, the paraxial estimator is an useful tool to monitor the limits of the paraxial optics theory under ABCD transformations.

© 2011 OSA

OCIS Codes
(070.2590) Fourier optics and signal processing : ABCD transforms
(120.4820) Instrumentation, measurement, and metrology : Optical systems
(200.4740) Optics in computing : Optical processing

ToC Category:
Fourier Optics and Signal Processing

Original Manuscript: August 1, 2011
Revised Manuscript: October 30, 2011
Manuscript Accepted: October 31, 2011
Published: December 6, 2011

Pablo Vaveliuk and Oscar Martinez-Matos, "Effect of ABCD transformations on beam paraxiality," Opt. Express 19, 25944-25953 (2011)

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  1. R. Simon, E. C. G. Sudarshan, and N. Mukunda, “Anisotropic Gaussian Schell-model beams: passage through optical system and associated invariants,” Phys. Rev. A 31, 2419–2434 (1985). [CrossRef] [PubMed]
  2. P. A. Bélanger, “Beam propagation and the ABCD ray matrices,” Opt. Lett. 16, 196–198 (1991). [CrossRef] [PubMed]
  3. A. E. Siegman, Lasers, (University Science Books, 1986), Chaps. 15–21.
  4. B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics, (John Wiley, 1991), Chaps. 1–4,7–9,14. [CrossRef]
  5. H. Kogelnik, “Imaging of Optical Modes -Resonators and Internal Lenses”, Bell Syst. Opt. Tech. J. 44, 455–494 (1965).
  6. P. Vaveliuk, B. Ruiz, and A. Lencina, “Limits of the paraxial aproximation in laser beams,” Opt. Lett. 32, 927–929 (2007). [CrossRef] [PubMed]
  7. P. Vaveliuk, “Comment on degree of paraxiality for monochromatic light beams,” Opt. Lett. 33, 3004–3005 (2008). [CrossRef] [PubMed]
  8. P. Vaveliuk, G. F. Zebende, M. A. Moret, and B. Ruiz, “Propagating free-space nonparaxial beams,” J. Opt. Soc. Am. A 24, 3297–3302 (2007). [CrossRef]
  9. M. A. Bandres and M. Guizar-Sicairos, “Paraxial group,” Opt. Lett. 34, 13–15 (2009). [CrossRef]
  10. S. R. Seshadri, “Quality of paraxial electromagnetic beams,” Appl. Opt. 45, 5335–5345 (2006). [CrossRef] [PubMed]
  11. P. Vaveliuk, “Quantifying the paraxiality for laser beams from the M2-factor,” Opt. Lett. 34, 340–342 (2009). [CrossRef] [PubMed]
  12. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1968).
  13. K. Sundar, N. Mukunda, and R. Simon, “Coherent-mode decomposition of general anisotropic Gaussian Schell-model beams,” J. Opt. Soc. Am. A 12, 560–569 (1995). [CrossRef]
  14. G. Nemes and A. E. Siegmam, “Measurement of all ten second-order moments of an astigmatic beam by the use of rotating simple astigmatic (anamorphic) optics,” J. Opt. Soc. Am. A 11, 2257–2264 (1994). [CrossRef]
  15. A. E. Siegman, G. Nemes, and J. Serna, in Proceedings of DPSS (Diode Pumped Solid State) Lasers: Applications and Issues, Vol. 17 of OSA Trends in Optics and Photonics (Optical Society of America, 1998), paper MQ1.
  16. S. Ramee and R. Simon, “Effect of holes and vortices on beam quality,” J. Opt. Soc. Am. A 17, 84–94 (2000). [CrossRef]
  17. M. Nazarathy and J. Shamir, “First-order optics–a canonical operator representation lossless systems,” J. Opt. Soc. Am. 72, 356–364 (1982). [CrossRef]
  18. E. C. G. Sudarshan, N. Mukunda, and R. Simon, “Realization of first-order optical systems using thin lenses,” Opt. Acta 32, 855–872 (1985). [CrossRef]
  19. H. T. Yura and S. G. Hanson, “Optical beam wave propagation through complex optical systems,” J. Opt. Soc. Am. A 4, 1931–1948 (1987). [CrossRef]
  20. H. T. Yura, B. Rose, and S. G. Hanson, “Dynamic laser speckle in complex ABCD optical systems” J. Opt. Soc. Am. A 15, 1160–1166 (1998). [CrossRef]

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