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Applied Optics

Applied Optics


  • Editor: James C. Wyant
  • Vol. 46, Iss. 5 — Feb. 10, 2007
  • pp: 774–784

Comparison of phase-aberrated laser beam quality criteria

Eugeny Perevezentsev, Anatoly Poteomkin, and Efim Khazanov  »View Author Affiliations

Applied Optics, Vol. 46, Issue 5, pp. 774-784 (2007)

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With any form of phase distortions there is the need to qualitatively characterize beam quality. Three different qualitative criteria are most commonly used for this purpose, each of them describing the beam with one ratio: the overlapping integral, the Strehl ratio, and the M 2 parameter. We have analyzed the interrelation of the above- mentioned criteria in the three most common types of beam quality degradation: thermal lens, electronic self-focusing, and spherical aberration. Approximate analytical expressions for all three criteria and three types of beam distortion are derived for Gaussian and super-Gaussian intensity profiles. The efficiency of characterizing those beams by various criteria is discussed.

© 2007 Optical Society of America

OCIS Codes
(140.6810) Lasers and laser optics : Thermal effects
(220.1000) Optical design and fabrication : Aberration compensation

ToC Category:
Lasers and Laser Optics

Original Manuscript: March 28, 2006
Revised Manuscript: September 17, 2006
Manuscript Accepted: October 2, 2006
Published: January 25, 2007

Eugeny Perevezentsev, Anatoly Poteomkin, and Efim Khazanov, "Comparison of phase-aberrated laser beam quality criteria," Appl. Opt. 46, 774-784 (2007)

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  1. E. A. Khazanov, "Characteristic features of the operation of different designs of the Faraday isolator for high average laser-radiation power," Quantum Electron. 30, 147-151 (2000). [CrossRef]
  2. G. Mueller, R. S. Amin, D. Guagliardo, D. McFeron, R. Lundock, D. H. Reitze, and D. B. Tanner, "Method for compensation of thermally induced modal distortions in the input optical components of gravitational wave interferometers," Class. Quantum Grav. 19, 1793-1801 (2002). [CrossRef]
  3. E. A. Khazanov, N. F. Andreev, A. N. Mal'shakov, O. V. Palashov, A. K. Poteomkin, A. M. Sergeev, A. A. Shaykin, V. V. Zelenogorsky, I. Ivanov, R. S. Amin, G. Mueller, D. B. Tanner, and D. H. Reitze, "Compensation of thermally induced modal distortions in Faraday isolators," IEEE J. Quantum Electron. 40, 1500-1510 (2004). [CrossRef]
  4. K. Strehl, "Uber Luftschlieren und Zonenfehler," Z. Instrumentenkd. 22, 213-217 (1902).
  5. M. Born and E. Wolf, Principles of Optics (Pergamon, 1980).
  6. V. N. Mahajan, "Strehl ratio for primary aberrations in terms of their aberration variance," J. Opt. Soc. Am. 73, 860-861 (1983). [CrossRef]
  7. V. N. Mahajan, "Strehl ratio for primary aberrations: some analytical results for circular and annular pupils," J. Opt. Soc. Am. 72, 1258-1266 (1982). [CrossRef]
  8. V. N. Mahajan, "Strehl ratio for circular and annular pupils: errata," J. Opt. Soc. Am. A 10, 2092 (1993). [CrossRef]
  9. D. D. Lowenthal, "Marechal intensity criteria modified for Gaussian beams," Appl. Opt. 13, 2126-2133 (1974). [CrossRef] [PubMed]
  10. D. D. Lowenthal, "Marechal intensity criteria modified for Gaussian beams: errata," Appl. Opt. 13, 2774 (1974). [CrossRef] [PubMed]
  11. V. N. Mahajan, "Strehl ratio of Gaussian beam," J. Opt. Soc. Am. A 22, 1824-1833 (2005). [CrossRef]
  12. R. Herloski, "Strehl ratio for untruncated Gaussian beams," J. Opt. Soc. Am. A 2, 1027-1030 (1985). [CrossRef]
  13. A. van der Bos, "Rayleigh wavefront criterion: comment," J. Opt. Soc. Am. A 16, 2307-2309 (1999). [CrossRef]
  14. A. van den Bos, "Aberration and the Strehl ratio," J. Opt. Soc. Am. A 17, 356-358 (2000). [CrossRef]
  15. Y. F. Chen, T. M. Huang, C. F. Kao, C. L. Wang, and S. C. Wang, "Optimization in scaling fiber-coupled laser-diode end-pumped lasers to higher power: influence of thermal effect," IEEE J. Quantum Electron. 33, 1424-1429 (1997). [CrossRef]
  16. P. J. Gardner, M. C. Roggemann, B. M. Welsh, R. D. Bowersox, and T. E. Luke, "Comparison of measured and computed Strehl ratios for light propagated through a channel flow of a He-N2 mixing layer at high Reynolds numbers," Appl. Opt. 36, 2559-2567 (1997). [CrossRef] [PubMed]
  17. S. Stallinga, "Strehl ratio for focusing into biaxially birefringent media," J. Opt. Soc. Am. A 21, 2406-2413 (2004). [CrossRef]
  18. A. E. Siegman, "New developments in laser resonators," in Optical Resonators, D. A. Holmes, ed., Proc. SPIE 1224, 2-14 (1990).
  19. N. Reng and B. Eppich, "Definition and measurements of high-power laser beam parameters," Opt. Quantum Electron. 24, S973-S992 (1992). [CrossRef]
  20. S. Amano and T. Mochizuki, "Propagation characteristics of a diffracted M2 beam," Appl. Opt. 41, 6325-6331 (2002). [CrossRef] [PubMed]
  21. A. Parent, M. Morin, and P. Lavigne, "Propogation of super-Gaussian field distribution," Opt. Quantum Electron. 24, S1071-S1079 (1992). [CrossRef]
  22. R. Borghi and M. Santarsiero, "M2 factor of Bessel-Gauss beams," Opt. Lett. 22, 262-264 (1997). [CrossRef] [PubMed]
  23. R. M. Herman and T. A. Wiggins, "Rayleigh range and the M2 factor for Bessel-Gauss beams," Appl. Opt. 37, 3398-3400 (1998). [CrossRef]
  24. A. K. Poteomkin and E. A. Khazanov, "Calculation of the M2 factor of the laser beam by the method of moments," Quantum Electron. 35, 1042-1044 (2005). [CrossRef]
  25. B. J. Neubert and B. Eppich, "Influences on the beam propagation ratio M2," Opt. Commun. 250, 241-251 (2005). [CrossRef]
  26. W. W. Simmons, J. T. Hunt, and W. E. Warren, "Light propagation through large laser systems," IEEE J. Quantum Electron. QE-17, 1727-1744 (1981). [CrossRef]
  27. A. K. Poteomkin, E. V. Katin, A. V. Kirsanov, G. A. Luchinin, A. N. Mal'shakov, M. A. Martyanov, A. Z. Matveev, O. V. Palashov, E. A. Khazanov, and A. A. Shaykin, "Compact 100 J/100 GW Nd:Phosphate laser for optical parametric chirped pulse amplifier pumping," Quantum Electron. 35, 302-310 (2005). [CrossRef]
  28. S. N. Vlasov, V. A. Petrishchev, and V. I. Talanov, "Averaged description of wave beams in linear and nonlinear media," Izv. Vyssh. Uchebn. Zaved. , Radiofiz 14, 1353-1363 (1971).
  29. C. Pare and P.-A. Belanger, "Beam propagation in a linear or nonlinear lens-like medium using ABCD ray matrices: the method of moments," Opt. Quantum Electron. 24, S1051-S1070 (1992). [CrossRef]
  30. M. R. Duparre, B. Luedge, and S. Schroeter, "ETALONs for pure and composite transversal modes," in Laser Beam Control and Applications, A. Gisen and D. Nickel, eds., Proc. SPIE 6101, 61011C (2006). [CrossRef]

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