OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Editor: Franco Gori
  • Vol. 31, Iss. 2 — Feb. 1, 2014
  • pp: 238–245

Second-order moments of an electromagnetic Gaussian Schell-model beam in a uniaxial crystal

Yan Shen, Lin Liu, Chengliang Zhao, Yangsheng Yuan, and Yangjian Cai  »View Author Affiliations


JOSA A, Vol. 31, Issue 2, pp. 238-245 (2014)
http://dx.doi.org/10.1364/JOSAA.31.000238


View Full Text Article

Enhanced HTML    Acrobat PDF (583 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

We derive the analytical expressions for the second-order moments of an electromagnetic Gaussian Schell-model (EGSM) beam propagating in a uniaxial crystal. With the help of the derived formulas, we study the evolution properties of the propagation factor, the effective radius of curvature and the Rayleigh range of an EGSM beam in a uniaxial crystal. It is found that the evolution properties of an EGSM beam in a uniaxial crystal are much different from its evolution properties in free space and are closely determined by the initial beam parameters and the parameters of the uniaxial crystal. The uniaxial crystal provides one way for modulating the properties of an EGSM beam.

© 2014 Optical Society of America

OCIS Codes
(030.1640) Coherence and statistical optics : Coherence
(260.1180) Physical optics : Crystal optics
(260.5430) Physical optics : Polarization
(350.5500) Other areas of optics : Propagation

ToC Category:
Coherence and Statistical Optics

History
Original Manuscript: October 11, 2013
Revised Manuscript: December 4, 2013
Manuscript Accepted: December 8, 2013
Published: January 9, 2014

Citation
Yan Shen, Lin Liu, Chengliang Zhao, Yangsheng Yuan, and Yangjian Cai, "Second-order moments of an electromagnetic Gaussian Schell-model beam in a uniaxial crystal," J. Opt. Soc. Am. A 31, 238-245 (2014)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-31-2-238


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 1995).
  2. C. Brosseau, Fundamentals of Polarized Light: A Statistical Approach (Wiley, 1998).
  3. D. F. V. James, “Change of polarization of light beams on propagation in free space,” J. Opt. Soc. Am. A 11, 1641–1643 (1994). [CrossRef]
  4. F. Gori, “Matrix treatment for partially polarized, partially coherent beams,” Opt. Lett. 23, 241–243 (1998). [CrossRef]
  5. G. P. Agrawal and E. Wolf, “Propagation-induced polarization changes in partially coherent optical beams,” J. Opt. Soc. Am. A 17, 2019–2023 (2000). [CrossRef]
  6. F. Gori, M. Santarsiero, R. Borghi, and G. Piquero, “Use of the van Cittert–Zernike theorem for partially polarized sources,” Opt. Lett. 25, 1291–1293 (2000). [CrossRef]
  7. E. Wolf, “Unified theory of coherence and polarization of random electromagnetic beams,” Phys. Lett. A 312, 263–267 (2003). [CrossRef]
  8. F. Gori, M. Santarsiero, G. Piquero, R. Borghi, A. Mondello, and R. Simon, “Partially polarized Gaussian Schell-model beams,” J. Opt. A 3, 1–9 (2001). [CrossRef]
  9. O. Korotkova, M. Salem, and E. Wolf, “Beam conditions for radiation generated by an electromagnetic Gaussian Schell-model source,” Opt. Lett. 29, 1173–1175 (2004). [CrossRef]
  10. E. Wolf, Introduction to the Theory of Coherence and Polarization of Light (Cambridge University, 2007).
  11. H. Roychowdhury and O. Korotkova, “Realizability conditions for electromagnetic Gaussian Schell-model sources,” Opt. Commun. 249, 379–385 (2005). [CrossRef]
  12. F. Gori, M. Santarsiero, R. Borghi, and V. Ramírez-Sánchez, “Realizability condition for electromagnetic Schell-model sources,” J. Opt. Soc. Am. A 25, 1016–1021 (2008). [CrossRef]
  13. G. Piquero, F. Gori, P. Romanini, M. Santarsiero, R. Borghi, and A. Mondello, “Synthesis of partially polarized Gaussian Schell-model sources,” Opt. Commun. 208, 9–16 (2002). [CrossRef]
  14. T. Shirai, O. Korotkova, and E. Wolf, “A method of generating electromagnetic Gaussian Schell-model beams,” J. Opt. A 7, 232–237 (2005). [CrossRef]
  15. J. Ellis, A. Dogariu, S. Ponomarenko, and E. Wolf, “Degree of polarization of statistically stationary electromagnetic fields,” Opt. Commun. 248, 333–337 (2005). [CrossRef]
  16. T. Setälä, A. Shevchenko, M. Kaivola, and A. Friberg, “Degree of polarization for optical near fields,” Phys. Rev. E 66, 016615 (2002). [CrossRef]
  17. Y. Cai, D. Ge, and Q. Lin, “Fractional Fourier transform for partially coherent and partially polarized Gaussian–Schell-model beams,” J. Opt. A 5, 453–459 (2003). [CrossRef]
  18. O. Korotkova and E. Wolf, “Changes in the state of polarization of a random electromagnetic beam on propagation,” Opt. Commun. 246, 35–43 (2005). [CrossRef]
  19. S. Zhu, L. Liu, Y. Chen, and Y. Cai, “State of polarization and propagation factor of a stochastic electromagnetic beam in a gradient-index fiber,” J. Opt. Soc. Am. A 30, 2306–2313 (2013). [CrossRef]
  20. O. Korotkova and E. Wolf, “Generalized Stokes parameters of random electromagnetic beams,” Opt. Lett. 30, 198–200 (2005). [CrossRef]
  21. O. Korotkova, M. Salem, and E. Wolf, “The far-zone behavior of the degree of polarization of electromagnetic beams propagating through atmospheric turbulence,” Opt. Commun. 233, 225–230 (2004). [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, 103–108 (2005). [CrossRef]
  23. E. Wolf, “Coherence and polarization properties of electromagnetic laser modes,” Opt. Commun. 265, 60–62 (2006). [CrossRef]
  24. 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, 2266–2268 (2008). [CrossRef]
  25. 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, 2710–2720 (2008). [CrossRef]
  26. Y. Cai and O. Korotkova, “Twist phase-induced polarization changes in electromagnetic Gaussian Schell-model beams,” Appl. Phys. B 96, 499–507 (2009). [CrossRef]
  27. E. Wolf, “Polarization invariance in beam propagation,” Opt. Lett. 32, 3400–3401 (2007). [CrossRef]
  28. M. Salem and E. Wolf, “Coherence-induced polarization changes in light beams,” Opt. Lett. 33, 1180–1182 (2008). [CrossRef]
  29. S. Zhu, Y. Cai, and O. Korotkova, “Propagation factor of a stochastic electromagnetic Gaussian Schell-model beam,” Opt. Express 18, 12587–12598 (2010). [CrossRef]
  30. S. Zhu and Y. Cai, “M2-factor of a stochastic electromagnetic beam in a Gaussian cavity,” Opt. Express 18, 27567–27581 (2010). [CrossRef]
  31. O. Korotkova, “Scintillation index of a stochastic electromagnetic beam propagating in random media,” Opt. Commun. 281, 2342–2348 (2008). [CrossRef]
  32. O. Korotkova, Y. Cai, and E. Watson, “Stochastic electromagnetic beams for LIDAR systems operating through turbulent atmosphere,” Appl. Phys. B 94, 681–690 (2009). [CrossRef]
  33. Y. Cai, O. Korotkova, H. T. Eyyuboğlu, and Y. Baykal, “Active laser radar systems with stochastic electromagnetic beams in turbulent atmosphere,” Opt. Express 16, 15834–15846 (2008). [CrossRef]
  34. C. Zhao, Y. Cai, and O. Korotkova, “Radiation force of scalar and electromagnetic twisted Gaussian Schell-model beams,” Opt. Express 17, 21472–21487 (2009). [CrossRef]
  35. Z. Tong, Y. Cai, and O. Korotkova, “Ghost imaging with electromagnetic stochastic beams,” Opt. Commun. 283, 3838–3845 (2010). [CrossRef]
  36. L. Zhang, F. Wang, Y. Cai, and O. Korotkova, “Degree of paraxiality of a stochastic electromagnetic Gaussian Schell-model beam,” Opt. Commun. 284, 1111–1117 (2011). [CrossRef]
  37. M. Yao, Y. Cai, O. Korotkova, Q. Lin, and Z. Wang, “Spatio-temporal coupling of random electromagnetic pulses interacting with reflecting gratings,” Opt. Express 18, 22503–22514 (2010). [CrossRef]
  38. G. Wu and Y. Cai, “Modulation of spectral intensity, polarization and coherence of a stochastic electromagnetic beam,” Opt. Express 19, 8700–8714 (2011). [CrossRef]
  39. F. Wang, G. Wu, X. Liu, S. Zhu, and Y. Cai, “Experimental measurement of the beam parameters of an electromagnetic Gaussian Schell-model source,” Opt. Lett. 36, 2722–2724 (2011). [CrossRef]
  40. C. Zhao, Y. Dong, G. Wu, F. Wang, Y. Cai, and O. Korotkova, “Experimental demonstration of coupling of an electromagnetic Gaussian Schell-model beam into a single-mode optical fiber,” Appl. Phys. B 108, 891–895 (2012). [CrossRef]
  41. M. Salem and G. P. Agrawal, “Coupling of stochastic electromagnetic beams into optical fibers,” Opt. Lett. 34, 2829–2831 (2009). [CrossRef]
  42. M. Salem and G. P. Agrawal, “Effects of coherence and polarization on the coupling of stochastic electromagnetic beams into optical fibers,” J. Opt. Soc. Am. A 26, 2452–2458 (2009). [CrossRef]
  43. M. Salem and G. P. Agrawal, “Effects of coherence and polarization on the coupling of stochastic electromagnetic beams into optical fibers: errata,” J. Opt. Soc. Am. A 28, 307 (2011). [CrossRef]
  44. J. J. Stamnes and V. Dhayalan, “Transmission of a two-dimensional Gaussian beam into a uniaxial crystal,” J. Opt. Soc. Am. A 18, 1662–1669 (2001). [CrossRef]
  45. A. Ciattoni and C. Palma, “Optical propagation in uniaxial crystals orthogonal to the optical axis: paraxial theory and beyond,” J. Opt. Soc. Am. A 20, 2163–2171 (2003). [CrossRef]
  46. A. Ciattoni and C. Palma, “Anisotropic beam spreading in uniaxial crystals,” Opt. Commun. 231, 79–92 (2004). [CrossRef]
  47. B. Tang, “Hermite–cosine–Gaussian beams propagating in uniaxial crystals orthogonal to the optical axis,” J. Opt. Soc. Am. A 26, 2480–2487 (2009). [CrossRef]
  48. A. Ciattoni, G. Cincotti, and C. Palma, “Propagation of cylindrically symmetric fields in uniaxial crystals,” J. Opt. Soc. Am. A 19, 792–796 (2002). [CrossRef]
  49. L. Zhang and Y. Cai, “Statistical properties of a nonparaxial Gaussian Schell-model beam in a uniaxial crystal,” Opt. Express 19, 13312–13325 (2011). [CrossRef]
  50. L. Zhang and Y. Cai, “Evolution properties of a twisted Gaussian Schell-model beam in a uniaxial crystal,” J. Mod. Opt. 58, 1224–1232 (2011). [CrossRef]
  51. G. Zhou, R. Chen, and X. Chu, “Propagation of Airy beams in uniaxial crystals orthogonal to the optical axis,” Opt. Express 20, 2196–2205 (2012). [CrossRef]
  52. C. Zhao and Y. Cai, “Paraxial propagation of Lorentz and Lorentz–Gauss beams in uniaxial crystals orthogonal to the optical axis,” J. Mod. Opt. 57, 375–384 (2010). [CrossRef]
  53. D. Deng, C. Chen, X. Zhao, and H. Li, “Propagation of an Airy vortex beam in uniaxial crystals,” Appl. Phys. B 110, 433–436 (2013). [CrossRef]
  54. D. Liu and Z. Zhou, “Propagation of partially polarized, partially coherent beams in uniaxially crystals orthogonal to the optical axis,” Eur. Phys. J. D 54, 95–101 (2009). [CrossRef]
  55. D. Liu and Z. Zhou, “Generalized Stokes parameters of stochastic electromagnetic beams propagating through uniaxial crystals orthogonal to the optical axis,” J. Opt. A 11, 065710 (2009). [CrossRef]
  56. X. Du and D. Zhao, “Propagation of uniformly polarized stochastic electromagnetic beams in uniaxial crystals,” J. Electromagn. Waves Appl. 24, 971–981 (2010). [CrossRef]
  57. 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, 17344–17356 (2009). [CrossRef]
  58. F. Wang and Y. Cai, “Second-order statistics of a twisted Gaussian Schell-model beam in turbulent atmosphere,” Opt. Express 18, 24661–24672 (2010). [CrossRef]
  59. H. Weber, “Propagation of higher-order intensity moments in quadratic-index media,” Opt. Quantum Electron. 24, S1027–S1049 (1992). [CrossRef]
  60. R. Martinez-Herrero and P. M. Mejias, “Second-order spatial characterization of hard-edge diffracted beams,” Opt. Lett. 18, 1669–1671 (1993). [CrossRef]
  61. R. Martinez-Herrero, P. M. Mejias, and M. Arias, “Parametric characterization of coherent, lowest-order Gaussian beams propagating through hard-edged apertures,” Opt. Lett. 20, 124–126 (1995). [CrossRef]
  62. A. E. Siegman, “New developments in laser resonators,” Proc. SPIE 1224, 2–14 (1990).
  63. F. Gori, M. Santarsiero, and A. Sona, “The change of width for a partially coherent beam on paraxial propagation,” Opt. Commun. 82, 197–203 (1991). [CrossRef]
  64. 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, 106–112 (1999). [CrossRef]
  65. X. Ji, H. T. Eyyuboğlu, and Y. Baykal, “Influence of turbulence on the effective radius of curvature of radial Gaussian array beams,” Opt. Express 18, 6922–6928 (2010). [CrossRef]
  66. H. T. Eyyuboğlu, Y. Baykal, and X. Ji, “Radius of curvature variations for annular, dark hollow and flat topped beams in turbulence,” Appl. Phys. B 99, 801–807 (2010). [CrossRef]
  67. S. Du, Y. Yuan, C. Liang, and Y. Cai, “Second-order moments of a multi-Gaussian Schell-model beam in a turbulent atmosphere,” Opt. Laser Technol. 50, 14–19 (2013). [CrossRef]
  68. G. Gbur and E. Wolf, “The Rayleigh range of Gaussian Schell-model beams,” J. Mod. Opt. 48, 1735–1741 (2011).

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