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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 15, Iss. 6 — Mar. 19, 2007
  • pp: 2837–2846

Simulation of vector fields with arbitrary second-order correlations

Brynmor J. Davis  »View Author Affiliations

Optics Express, Vol. 15, Issue 6, pp. 2837-2846 (2007)

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Temporally-stationary electromagnetic fields with arbitrary second-order coherence functions are simulated using standard statistical tools. In cases where the coherence function takes a commonly-used separable form, a computationally-efficient variation of the approach can be applied. This work provides a generalization of previous spatio-temporal simulators which model only scalar fields and require either restrictions on the coherence function or consider only two points in space. The simulation of a partially-polarized Gaussian Schell-model beam and a partially-radially-polarized beam are demonstrated.

© 2007 Optical Society of America

OCIS Codes
(000.5490) General : Probability theory, stochastic processes, and statistics
(030.0030) Coherence and statistical optics : Coherence and statistical optics
(260.5430) Physical optics : Polarization

ToC Category:
Coherence and Statistical Optics

Original Manuscript: January 31, 2007
Manuscript Accepted: March 4, 2007
Published: March 19, 2007

Brynmor J. Davis, "Simulation of vector fields with arbitrary second-order correlations," Opt. Express 15, 2837-2846 (2007)

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  1. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University Press, 1995).
  2. J. W. Goodman, Statistical Optics (Wiley-Interscience, 1985).
  3. G. Gbur, "Simulating fields of arbitrary spatial and temporal coherence," Opt. Express 14, 7567-7578 (2006), http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-17-7567. [CrossRef] [PubMed]
  4. E. Wolf, "Correlation-induced changes in the degree of polarization, the degree of coherence, and the spectrum of random electromagnetic beams on propagation," Opt. Lett. 28, 1078-1080 (2003). [CrossRef] [PubMed]
  5. P. Vahimaa and J. Turunen, "Finite-elementary-source model for partially coherent radiation," Opt. Express 14, 1376-1381 (2006), http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-4-1376. [CrossRef] [PubMed]
  6. A. M. Zysk, P. S. Carney, and J. C. Schotland, "Eikonal method for calculation of coherence functions," Phys. Rev. Lett. 95, 043904 (2005). [CrossRef] [PubMed]
  7. E. Wolf, "Invariance of the spectrum of light on propagation," Phys. Rev. Lett. 56, 1370-1372 (1986). [CrossRef] [PubMed]
  8. G. Magyar and L. Mandel, "Interference fringes produced by superposition of two independent Maser light beams," Nature 198, 255-256 (1963). [CrossRef]
  9. B. Davis, E. Kim, and J. R. Piepmeier, "Stochastic modeling and generation of partially polarized or partially coherent electromagnetic waves," Radio Sci. 39, RS1001 (2004).
  10. R. Simon and N. Makunda, "Twisted Gaussian Schell-model beams," J. Opt. Soc. Am. A 10, 95-109 (1993). [CrossRef]
  11. E. Wolf and G. S. Agarwal, "Coherence theory of laser resonator modes," J. Opt. Soc. Am. A 1, 541-546 (1984). [CrossRef]
  12. Y. Cai and S. He, "Propagation of a partially coherent twisted anisotropic Gaussian Schell-model beam in a turbulent atmosphere," Appl. Phys. Lett. 89, 041117 (2006). [CrossRef]
  13. E. Tervonen, J. Turunen, and A. T. Friberg, "Transverse Laser-mode structure determination from spatial coherence measurements: experimental results," Appl, Phys. B 49, 409-414 (1989). [CrossRef]
  14. L. D. A. Lundeberg, G. P. Lousberg, D. L. Boiko, and E. Kapon, "Spatial coherence measurements in arrays of coupled vertical cavity surface emitting lasers," Appl. Phys. Lett. 90, 121103 (2007). [CrossRef]
  15. 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]
  16. 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]
  17. G. H. Golub and C. F. Van Loan, Matrix Computations (Johns Hopkins University Press, 1996).
  18. J. H. Michels, P. K. Varshney, and D. D. Weiner, "Synthesis of correlated multichannel random processes," IEEE Trans. Signal Process. 42, 367-375 (1994). [CrossRef]
  19. A. Papoulis and S. U. Pillai, Probability, Random Variables and Stochastic Processes (McGraw-Hill, 2002).
  20. W. H. Carter and E. Wolf, "Coherence and radiometry with quasihomogeneous planar sources," J. Opt. Soc. Am. 67, 785-796 (1977). [CrossRef]
  21. R. Loudon, The Quantum Theory of Light (Oxford University Press, 2000).
  22. F. Gori, M. Santarsiero, G. Piquero, R. Borghi, A. Mondello, and R. Simon, "Partially polarized Gaussian Schellmodel beams," J. Opt. A 3, 1-9 (2001). [CrossRef]
  23. N. Hodgson and H. Weber, Laser Resonators and Beam Propagation: Fundamentals, Advanced Concepts and Applications (Springer, 2005).
  24. K. C. Toussaint, Jr., S. Park, J. E. Jureller, and N. F. Scherer, "Generation of optical vector beams with a diffractive optical element interferometer," Opt. Lett. 30, 2846-2848 (2005). [CrossRef]
  25. S. Quabis, R. Dorn, and G. Leuchs, "Generation of a radially polarized doughnut mode of high quality," Appl. Phys. B 81, 597-600 (2005). [CrossRef]
  26. P. M. Lurie and M. S. Goldberg, "An approximate method for sampling correlated random variables from partially-specified distributions," Manage. Sci. 44, 203-218 (1998). [CrossRef]

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