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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 18, Iss. 26 — Dec. 20, 2010
  • pp: 27567–27581

Optics InfoBase > Optics Express > Volume 18 > Issue 26 > Page 27567

M2-factor of a stochastic electromagnetic beam in a Gaussian cavity

Shijun Zhu and Yangjian Cai  »View Author Affiliations


Optics Express, Vol. 18, Issue 26, pp. 27567-27581 (2010)
http://dx.doi.org/10.1364/OE.18.027567


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Abstract

With the help of a tensor method, an explicit expression for the M 2 -factor of a stochastic electromagnetic Gaussian Schell-model (EGSM) beam in a Gaussian cavity is derived. Evolution properties of the M2-factor of an EGSM beam in a Gaussian cavity are studied numerically in detail. It is found that the behavior of the M 2 -factor of an EGSM beam in a Gaussian cavity is determined by the statistical properties of the source beam and the parameters of the cavity. Thermal lens effect induced changes of the M2-factor of an EGSM beam in a Gaussian cavity is also investigated. Our results will be useful in many applications, such as free-space optical communications, laser radar system, optical trapping and optical imaging, where stochastic electromagnetic beams are required.

© 2010 OSA

OCIS Codes
(030.0030) Coherence and statistical optics : Coherence and statistical optics
(230.5750) Optical devices : Resonators
(260.5430) Physical optics : Polarization
(350.5500) Other areas of optics : Propagation

ToC Category:
Coherence and Statistical Optics

History
Original Manuscript: October 8, 2010
Revised Manuscript: December 4, 2010
Manuscript Accepted: December 8, 2010
Published: December 15, 2010

Citation
Shijun Zhu and Yangjian Cai, "M2-factor of a stochastic electromagnetic beam in a Gaussian cavity," Opt. Express 18, 27567-27581 (2010)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-26-27567


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References

  1. E. Wolf, “Unified theory of coherence and polarization of random electromagnetic beams,” Phys. Lett. A 312(5-6), 263–267 (2003). [CrossRef]
  2. F. Gori, M. Santarsiero, G. Piquero, R. Borghi, A. Mondello, and R. Simon, “Partially polarized Gaussian Schell-model beams,” J. Opt. A, Pure Appl. Opt. 3(1), 1–9 (2001). [CrossRef]
  3. O. Korotkova, M. Salem, and E. Wolf, “Beam conditions for radiation generated by an electromagnetic Gaussian Schell-model source,” Opt. Lett. 29(11), 1173–1175 (2004). [CrossRef] [PubMed]
  4. O. Korotkova, “Scintillation index of a stochastic electromagnetic beam propagating in random media,” Opt. Commun. 281, 2342–2348 (2008).
  5. Y. Cai, O. Korotkova, H. T. Eyyuboğlu, and Y. Baykal, “Active laser radar systems with stochastic electromagnetic beams in turbulent atmosphere,” Opt. Express 16(20), 15834–15846 (2008). [CrossRef] [PubMed]
  6. Z. Tong, Y. Cai, and O. Korotkova, “Ghost imaging with electromagnetic stochastic beams,” Opt. Commun. 283(20), 3838–3845 (2010). [CrossRef]
  7. C. Zhao, Y. Cai, and O. Korotkova, “Radiation force of scalar and electromagnetic twisted Gaussian Schell-model beams,” Opt. Express 17(24), 21472–21487 (2009). [CrossRef] [PubMed]
  8. E. Wolf, Introduction to the theory of coherence and polarization of light (Cambridge U. Press, 2007).
  9. N. Hodgson, and H. Weber, Optical resonators-Fundamentals, advanced concepts and applications (London Springer-Verlag, 1997).
  10. A. G. Fox and T. Li, “Resonate modes in a maser interferometer,” Bell Syst. Tech. J. 40, 453–488 (1961).
  11. G. D. Boyd and J. P. Gordon, “Confocal multimode resonator for millimeter through optical wavelength masers,” Bell Syst. Tech. J. 40, 489–508 (1961).
  12. H. Kogelnik and T. Li, “Laser beams and resonators,” Appl. Opt. 5(10), 1550–1567 (1966). [CrossRef] [PubMed]
  13. L. W. Casperson and S. D. Lunnam, “Gaussian modes in high loss laser resonators,” Appl. Opt. 14(5), 1193–1199 (1975). [CrossRef] [PubMed]
  14. E. Wolf, “Spatial coherence of resonant modes in a maser interferometer,” Phys. Lett. 3(4), 166–168 (1963). [CrossRef]
  15. E. Wolf and G. S. Agarwal, “Coherence theory of laser resonator modes,” J. Opt. Soc. Am. A 1(5), 541–546 (1984). [CrossRef]
  16. F. Gori, “Propagation of the mutual intensity through a periodic structure,” Atti Fond. Giorgio Ronchi 35, 434–447 (1980).
  17. G. Cincotti, P. DeSantis, G. Guattari, and C. Palma, “Propagation of partially coherent beams in a periodic sequence of lenses and Gaussian apertures,” Pure Appl. Opt. 3(4), 561–571 (1994). [CrossRef]
  18. A. Mascello, M. R. Perrone, and C. Palma, “Coherence evolution of laser beams in cavities with variable-reflectivity mirrors,” J. Opt. Soc. Am. A 14(8), 1890–1901 (1997). [CrossRef]
  19. P. De Santis, A. Mascello, C. Palma, and M. R. Perrone, “Coherence growth of laser radiation in Gaussian cavities,” IEEE J. Quantum Electron. 32(5), 802–812 (1996). [CrossRef]
  20. C. Palma, G. Cardone, and G. Cincotti, “Spectral changes in Gaussian-cavity lasers,” IEEE J. Quantum Electron. 34(7), 1082–1088 (1998). [CrossRef]
  21. E. Wolf, “Coherence and polarization properties of electromagnetic laser modes,” Opt. Commun. 265(1), 60–62 (2006). [CrossRef]
  22. T. Saastamoinen, J. Turunen, J. Tervo, T. Setälä, and A. T. Friberg, “Electromagnetic coherence theory of laser resonator modes,” J. Opt. Soc. Am. A 22(1), 103–108 (2005). [CrossRef]
  23. M. Yao, Y. Cai, H. T. Eyyuboğlu, Y. Baykal, and O. Korotkova, “Evolution of the degree of polarization of an electromagnetic Gaussian Schell-model beam in a Gaussian cavity,” Opt. Lett. 33(19), 2266–2268 (2008). [CrossRef] [PubMed]
  24. O. Korotkova, M. Yao, Y. Cai, H. T. Eyyuboğlu, and Y. Baykal, “State of polarization of a stochastic electromagnetic beam in an optical resonator,” J. Opt. Soc. Am. A 25(11), 2710–2720 (2008). [CrossRef]
  25. Z. Tong, O. Korotkova, Y. Cai, H. T. Eyyuboğlu, and Y. Baykal, “Correlation properties of random electromagnetic beams in laser resonators,” Appl. Phys. B 97(4), 849–857 (2009). [CrossRef]
  26. S. Zhu, F. Zhou, Y. Cai, and L. Zhang, “Thermal lens effect induced changes of polarization, coherence and spectrum of a stochastic electromagnetic beam in a Gaussian cavity,” Appl. Phys. B DOI: .
  27. S. Zhu, Y. Cai, and O. Korotkova, “Propagation factor of a stochastic electromagnetic Gaussian Schell-model beam,” Opt. Express 18(12), 12587–12598 (2010). [CrossRef] [PubMed]
  28. A. E. Siegman, “New developments in laser resonators,” in Optical Resonators, D. A. Holmes, ed., Proc. SPIE 1224, 2C14 (1990).
  29. A. E. Siegman and S. W. Townsend, “Output beam propagation and beam quality from a multimode stable-cavity laser,” IEEE J. Quantum Electron. 29(4), 1212–1217 (1993). [CrossRef]
  30. J. J. Chang, “Time-resolved beam-quality characterization of copper-vapor lasers with unstable resonators,” Appl. Opt. 33(12), 2255–2265 (1994). [CrossRef] [PubMed]
  31. J. Hilgevoord, “The standard deviation is not an adequate measure of quantum uncertainty,” Am. J. Phys. 70(10), 983 (2002). [CrossRef]
  32. G. N. Lawrence, “Proposed international standard for laser-beam quality falls short,” Laser Focus World 109–114 (1994).
  33. R. Martinez-Herrero and P. M. Mejias, “Second-order spatial characterization of hard-edge diffracted beams,” Opt. Lett. 18(19), 1669–1671 (1993). [CrossRef] [PubMed]
  34. R. Martínez-Herrero, P. M. Mejías, and M. Arias, “Parametric characterization of coherent, lowest-order Gaussian beams propagating through hard-edged apertures,” Opt. Lett. 20(2), 124–126 (1995). [CrossRef] [PubMed]
  35. F. Gori, M. Santarsiero, and A. Sona, “The change of width for a partially coherent beam on paraxial propagation,” Opt. Commun. 82(3-4), 197–203 (1991). [CrossRef]
  36. M. Santarsiero, F. Gori, R. Borghi, G. Cincotti, and P. Vahimaa, “Spreading properties of beams radiated by partially coherent Schell-model sources,” J. Opt. Soc. Am. A 16(1), 106–112 (1999). [CrossRef]
  37. B. Zhang, X. Chu, and Q. Li, “Generalized beam-propagation factor of partially coherent beams propagating through hard-edged apertures,” J. Opt. Soc. Am. A 19(7), 1370–1375 (2002). [CrossRef]
  38. X. Chu, B. Zhang, and Q. Wen, “Generalized M2 factor of a partially coherent beam propagating through a circular hard-edged aperture,” Appl. Opt. 42(21), 4280–4284 (2003). [CrossRef] [PubMed]
  39. P. A. Belanger, “Beam quality factor of the LP01 mode of the step-index fiber,” Opt. Eng. 32(9), 2107–2109 (1993). [CrossRef]
  40. S. Saghafi and C. J. R. Sheppard, “The beam propagation factor for higher order Gaussian beams,” Opt. Commun. 153(4-6), 207–210 (1998). [CrossRef]
  41. B. Lü, B. Zhang, and H. Ma, “Beam-propagation factor and mode-coherence coefficients of hyperbolic-cosine Gaussian beams,” Opt. Lett. 24(10), 640–642 (1999). [CrossRef]
  42. G. Zhou, “Generalized beam propagation factors of truncated partially coherent cosine-Gaussian and cosh-Gaussian beams,” Opt. Laser Technol. 42(3), 489–496 (2010). [CrossRef]
  43. D. Deng, “Generalized M2-factor of hollow Gaussian beams through a hard-edge circular aperture,” Phys. Lett. A 341(1-4), 352–356 (2005). [CrossRef]
  44. D. Deng, X. Fu, C. Wei, J. Shao, and Z. Fan, “Far-field intensity distribution and M2 factor of hollow Gaussian beams,” Appl. Opt. 44(33), 7187–7190 (2005). [CrossRef] [PubMed]
  45. S. Yin, B. Zhang, and Y. Dan, “Effects of the deformation of reflection volume Bragg gratings on the M2-factor of super-Gaussian laser beams,” Opt. Commun. 283(7), 1418–1423 (2010). [CrossRef]
  46. D. Deng, H. Guo, X. Chen, and H. Kong, “Characteristics of coherent and incoherent off-axis elegant Hermite-Gaussian beam combinations,” J. Opt. A, Pure Appl. Opt. 5(5), 489–494 (2003). [CrossRef]
  47. D. Deng, “Propagation properties of off-axis cosh Gaussian beam combinations through a first-order optical system,” Phys. Lett. A 333(5-6), 485–494 (2004). [CrossRef]
  48. Y. Dan and B. Zhang, “Beam propagation factor of partially coherent flat-topped beams in a turbulent atmosphere,” Opt. Express 16(20), 15563–15575 (2008). [CrossRef] [PubMed]
  49. Y. Yuan, Y. Cai, J. Qu, H. T. Eyyuboğlu, Y. Baykal, and O. Korotkova, “M2-factor of coherent and partially coherent dark hollow beams propagating in turbulent atmosphere,” Opt. Express 17(20), 17344–17356 (2009). [CrossRef] [PubMed]
  50. F. Wang and Y. Cai, “Second-order statistics of a twisted Gaussian Schell-model beam in turbulent atmosphere,” Opt. Express 18(24), 24661–24672 (2010). [CrossRef] [PubMed]
  51. Y. Yuan, Y. Cai, C. Zhao, H. T. Eyyuboğlu, and Y. Baykal, “Propagation factors of laser array beams in turbulent atmosphere,” J. Mod. Opt. 57(8), 621–631 (2010). [CrossRef]
  52. Q. Lin and Y. Cai, “Tensor ABCD law for partially coherent twisted anisotropic Gaussian-Schell model beams,” Opt. Lett. 27(4), 216–218 (2002). [CrossRef]
  53. L. Mandel, and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, 1995)
  54. J. F. Urchueguía, G. J. de Valcarcel, and E. Roldan, “Laser instabilities in a Gaussian cavity mode with Gaussian pump profile,” J. Opt. Soc. Am. B 15(5), 1512–1520 (1998). [CrossRef]
  55. T. Shirai, O. Korotkova, and E. Wolf, “A method of generating electromagnetic Gaussian Schell-model beams,” J. Opt. A, Pure Appl. Opt. 7(5), 232–237 (2005). [CrossRef]
  56. J. Tervo, T. Setala, and A. Friberg, “Degree of coherence for electromagnetic fields,” Opt. Express 11(10), 1137–1143 (2003). [CrossRef] [PubMed]
  57. J. P. Gordon, R. C. C. Leite, R. S. Moore, S. P. S. Porto, and J. R. Whinnery, “Long-transient effects in lasers with inserted liquid samples,” J. Appl. Phys. 36(1), 3–8 (1965). [CrossRef]
  58. S. J. Sheldon, L. V. Knight, and J. M. Thorne, “Laser-induced thermal lens effect: a new theoretical model,” Appl. Opt. 21(9), 1663–1669 (1982). [CrossRef] [PubMed]
  59. C. A. Carter and J. M. Harris, “Comparison of models describing the thermal lens effect,” Appl. Opt. 23(3), 476–481 (1984). [CrossRef] [PubMed]
  60. T. Xu and S. Wang, “Propagation of Ince-Gaussian beams in a thermal lens medium,” Opt. Commun. 265(1), 1–5 (2006). [CrossRef]
  61. R. Weber, B. Neuenschwander, and H. P. Weber, “Thermal effects in solid-state laser materials,” Opt. Mater. 11(2-3), 245–254 (1999). [CrossRef]
  62. J. R. Whinnery, “Laser measurement of optical absorption in liquids,” Acc. Chem. Res. 7(7), 225–231 (1974). [CrossRef]
  63. C. Hu and J. R. Whinnery, “New thermooptical measurement method and a comparison with other methods,” Appl. Opt. 12(1), 72–79 (1973). [CrossRef] [PubMed]
  64. S. Wang, “Matrix methods in treating decentred optical systems,” Opt. Quantum Electron. 17(1), 1–14 (1985). [CrossRef]

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