Vol. 21

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2010-05-06

Degree of Polarization of a Twisted Electromagnetic Gaussian Schell-Model Beam in a Gaussian Cavity Filled with Gain Media

By Shijun Zhu and Yangjian Cai
Progress In Electromagnetics Research B, Vol. 21, 171-187, 2010
doi:10.2528/PIERB10041105

Abstract

Analytical formula for the cross-spectral density matrix of a twisted electromagnetic Gaussian Schell-model (TEGSM) beam propagating through an astigmatic ABCD optical system in gain or absorbing media is derived based on the unified theory of coherence and polarization. Generalized tensor ABCD law in media is derived. As an application example, the evolution properties of the degree of polarization of a TEGSM beam in a Gaussian cavity filled with gain media are studied numerically in detail. It is shown that the behavior of the degree of polarization depends on the parameters of the gain media and the TEGSM beam. Our results will be useful for the spatial modulation of polarization properties of stochastic electromagnetic beam.

Citation


Shijun Zhu and Yangjian Cai, "Degree of Polarization of a Twisted Electromagnetic Gaussian Schell-Model Beam in a Gaussian Cavity Filled with Gain Media," Progress In Electromagnetics Research B, Vol. 21, 171-187, 2010.
doi:10.2528/PIERB10041105
http://test.jpier.org/PIERB/pier.php?paper=10041105

References


    1. Mandel, L. and E. Wolf, Optical Coherence and Quantum Optics, Cambridge U. Press, 1995.

    2. Kato, Y., K. Mima, N. Miyanaga, S. Arinaga, Y. Kitagawa, M. Nakatsuka, and C. Yamanaka, "Random phasing of high-power lasers for uniform target acceleration and plasma-instability suppression ," Phys. Rev. Lett., Vol. 53, No. 11, 1057-1060, 1984.
    doi:10.1103/PhysRevLett.53.1057

    3. Paganin, D. and K. A. Nugent, "Noninterferometric phase imaging with partially coherent light," Phys. Rev. Lett., Vol. 80, No. 12, 2586-2589, 1998.
    doi:10.1103/PhysRevLett.80.2586

    4. Wang, F., Y. Cai, H. T. Eyyuboglu, and Y. K. Baykal, "Average intensity and spreading of partially coherent standard and elegant Laguerre-Gaussian beams in turbulent atmosphere," Progress In Electromagnetics Research, Vol. 103, 33-56, 2010.

    5. Cai, Y. and S. Zhu, "Ghost imaging with incoherent and partially coherent light radiation," Phys. Rev. E, Vol. 71, No. 5, 056607, 2005.
    doi:10.1103/PhysRevE.71.056607

    6. Cai, Y. and S. Zhu, "Ghost interference with partially coherent radiation," Opt. Lett., Vol. 229, No. 23, 2716-2718, 2004.
    doi:10.1364/OL.29.002716

    7. Cai, Y. and S. He, "Propagation of a partially coherent twisted anisotropic Gaussian Schell-model beam in a turbulent atmosphere," Appl. Phys. Lett., Vol. 89, No. 4, 041117, 2006.
    doi:10.1063/1.2236463

    8. Cai, Y. and U. Peschel, "Second-harmonic generation by an astigmatic partially coherent beam," Opt. Express, Vol. 15, No. 23, 15480-15492, 2007.
    doi:10.1364/OE.15.015480

    9. Zhao, C., Y. Cai, X. Lu, and H. T. Eyyuboglu, "Radiation force of coherent and partially coherent flat-topped beams on a Rayleigh particle," Opt. Express, Vol. 17, No. 3, 1753-1765, 2009.
    doi:10.1364/OE.17.001753

    10. Gori, F., "Collet-wolf sources and multimode lasers," Opt. Commun., Vol. 34, No. 3, 301-305, 1980.
    doi:10.1016/0030-4018(80)90382-X

    11. Friberg, A. T. and R. J. Sudol, "Propagation parameters of Gaussian Schell-model beams," Opt. Commun., Vol. 41, No. 6, 383-387, 1982.
    doi:10.1016/0030-4018(82)90161-4

    12. Wang, F. and Y. Cai, "Experimental observation of fractional Fourier transform for a partially coherent optical beam with Gaussian statistics ," J. Opt. Soc. Am. A, Vol. 24, No. 7, 1937-1944, 2007.
    doi:10.1364/JOSAA.24.001937

    13. Simon, R., E. C. G. Sudarshan, and N. Mukunda, "Anisotropic Gaussian Schell-model beams: Passage through optical systems and associated invariants," Phys. Rev. A, Vol. 31, No. 4, 2419-2434, 1985.
    doi:10.1103/PhysRevA.31.2419

    14. Simon, R. and N. Mukunda, "Twisted Gaussian Schell-model beams," J. Opt. Soc. Am. A, Vol. 10, No. 1, 95-109, 1993.
    doi:10.1364/JOSAA.10.000095

    15. Ambrosini, D., V. Bagini, F. Gori, and M. Santarsiero, "Twisted Gaussian Schell-model beams: A superposition model," J. Mod. Opt., Vol. 41, No. 7, 1391-1399, 1994.
    doi:10.1080/09500349414551331

    16. A. T., E. Tervonen, J. Turunen, "Interpretation and experimental demonstration of twisted Gaussian Schell-model beams," J. Opt. Soc. Am. A, Vol. 11, No. 6, 1818-1826, 1994.
    doi:10.1364/JOSAA.11.001818

    17. Simon, R. and N. Mukunda, "Gaussian Schell-model beams and general shape invariance," J. Opt. Soc. Am. A, Vol. 16, No. 10, 2465-2475, 1999.
    doi:10.1364/JOSAA.16.002465

    18. Lin, Q. and Y. Cai, "Tensor ABCD law for partially coherent twisted anisotropic Gaussian-Schell model beams," Opt. Lett., Vol. 27, No. 4, 216-218, 2002.
    doi:10.1364/OL.27.000216

    19. Lin, Q. and Y. Cai, "Fractional fourier transform for partially coherent Gaussian-Schell model beams," Opt. Lett., Vol. 27, No. 19, 1672-1674, 2002.
    doi:10.1364/OL.27.001672

    20. Ponomarenko, S. A., "Twisted Gaussian Schell-mode solitons," Phys. Rev. E, Vol. 64, No. 3, 036618, 2001.
    doi:10.1103/PhysRevE.64.036618

    21. Cai, Y. and Q. Lin, "Spectral shift of partially coherent twisted anisotropic Gaussian Schell-model beams in free space," Opt. Commun., Vol. 204, No. 1-6, 17-23, 2002.

    22. Cai, Y., Q. Lin, and D. Ge, "Propagation of partially coherent twisted anisotropic Gaussian Schell-model beams in dispersive and absorbing media," J. Opt. Soc. Am. A, Vol. 19, No. 10, 2036-2042, 2002.
    doi:10.1364/JOSAA.19.002036

    23. Cai, Y. and Q. Lin, "Propagation of partially coherent twisted anisotropic Gaussian Schell-model beams through misaligned optical systems," Opt. Commun., Vol. 211, No. 1-6, 1-8, 2002.
    doi:10.1016/S0030-4018(02)01829-1

    24. Cai, Y. and L. Hu, "Propagation of partially coherent twisted anisotropic Gaussian Schell-model beams through an apertured astigmatic optical system," Opt. Lett., Vol. 131, No. 6, 685-687, 2006.
    doi:10.1364/OL.31.000685

    25. Cai, Y., Q. Lin, and O. Korotkova, "Ghost imaging with twisted Gaussian Schell-model beam," Opt. Express, Vol. 17, No. 4, 2450-2464, 2009.

    26. Serna, J. and J. M. Movilla, "Orbital angular momentum of partially coherent beams," Opt. Lett., Vol. 26, No. 7, 405-406, 2001.
    doi:10.1364/OL.26.000405

    27. Gori, F., "Matrix treatment for partially polarized partially coherent beams," Opt. Lett., Vol. 23, No. 4, 241-243, 1998.
    doi:10.1364/OL.23.000241

    28. Wolf, E., "Unified theory of coherence and polarization of random electromagnetic beams," Phys. Lett. A, Vol. 312, No. 5-6, 263-267, 2003.
    doi:10.1016/S0375-9601(03)00684-4

    29. Wolf, E., Introduction to the Theory of Coherence and Polarization of Light, Cambridge U. Press, 2007.

    30. Gori, F., M. Santarsiero, G. Piquero, R. Borghi, A. Mondello, and R. Simon, "Partially polarized Gaussian schell-model beams," J. Opt. A: Pure Appl. Opt., Vol. 3, No. 1, 1-9, 2001.
    doi:10.1088/1464-4258/3/1/301

    31. Korotkova, O., M. Salem, and E. Wolf, "Beam conditions for radiation generated by an electromagnetic Gaussian Schell-model source," Opt. Lett., Vol. 29, No. 11, 1173-1175, 2004.
    doi:10.1364/OL.29.001173

    32. Korotkova, O., "Scintillation index of a stochastic electromagnetic beam propagating in random media," Opt. Commun., Vol. 281, No. 9, 2342-2348, 2008.

    33. Cai, Y., O. Korotkova, H. T. Eyyuboglu, and Y. Baykal, "Active laser radar systems with stochastic electromagnetic beams in turbulent atmosphere," Opt. Express, Vol. 16, No. 20, 15835-15846, 2008.
    doi:10.1364/OE.16.015834

    34. Korotkova, O., Y. Cai, and E. Watson, "Stochastic electromagnetic beams for LIDAR systems operating through turbulent at mosphere," Appl. Phys. B, Vol. 94, No. 4, 681-690, 2009.
    doi:10.1007/s00340-009-3404-4

    35. Korotkova, O., M. Salem, and E. Wolf, "The far-zone behavior of the degree of polarization of electromagnetic beams propagating through atmospheric turbulence," Opt. Commun., Vol. 233, No. 4-6, 225-230, 2004.
    doi:10.1016/j.optcom.2004.01.005

    36. Shirai, T., O. Korotkova, and E. Wolf, "A method of generating electromagnetic Gaussian Schell-model beams," J. Opt. A: Pure Appl. Opt., Vol. 7, No. 5, 232-237, 2005.
    doi:10.1088/1464-4258/7/5/004

    37. Gori, F., M. Santarsiero, R. Borghi, and V. Ramrez-Sanchez, "Realizability condition for electromagnetic Schell-model sources," J. Opt. Soc. Am. A, Vol. 25, No. 5, 1016-1021, 2008.
    doi:10.1364/JOSAA.25.001016

    38. Kanseri, B. and H. C. Kandpal, "Experimental determination of electric cross-spectral density matrix and generalized Stokes parameters for a laser beam," Opt. Lett., Vol. 33, No. 20, 2410-2412, 2008.
    doi:10.1364/OL.33.002410

    39. Yao, M., Y. Cai, H. T. Eyyuboglu, Y. Baykal, and O. Korotkova, "The evolution of the degree of polarization of an electromagnetic Gaussian Schell-model beam in a Gaussian cavity," Opt. Lett., Vol. 33, No. 19, 2266-2268, 2008.
    doi:10.1364/OL.33.002266

    40. Korotkova, O., M. Yao, Y. Cai, H. T. Eyyubogu, and Y. Baykal, "The state of polarization of a stochastic electromagnetic beam in an optical resonator," J. Opt. Soc. Am. A, Vol. 25, No. 11, 2710-2720, 2008.
    doi:10.1364/JOSAA.25.002710

    41. Cai, Y. and O. Korotkova, "Twist phase-induced polarization changes in electromagnetic Gaussian Schell-model beams," Appl. Phys. B, Vol. 96, No. 2-3, 499-507, 2009.
    doi:10.1007/s00340-009-3469-0

    42. Zhao, C., Y. Cai, and O. Korotkova, "Radiation force of scalar and electromagnetic twisted Gaussian Schell-model beams," Opt. Express, Vol. 17, No. 24, 21472-21487, 2009.
    doi:10.1364/OE.17.021472

    43. Zhu, S. and Y. Cai, "Spectral shift of a twisted electromagnetic Gaussian Schell-model beam focused by a thin lens," Appl. Phys. B, Vol. 99, No. 1-2, 317-323, 2010.
    doi:10.1007/s00340-010-3906-0

    44. Youngworth, K. S. and T. G. Brown, "Focusing of high numerical aperture cylindrical-vector beams," Opt. Express, Vol. 7, No. 2, 77-87, 2000.
    doi:10.1364/OE.7.000077

    45. Zhan, Q., "Trapping metallic Rayleigh particles with radial polarization," Opt. Express, Vol. 12, No. 15, 3377-3382, 2004.
    doi:10.1364/OPEX.12.003377

    46. Sick, B., B. Hecht, and L. Novotny, "Orientational imaging of single molecules by annular illumination," Phys. Rev. Lett., Vol. 85, No. 21, 4482-4485, 2000.
    doi:10.1103/PhysRevLett.85.4482

    47. Novotny, L., M. R. Beversluis, K. S. Youngworth, and T. G. Brown, "Longitudinal field modes probed by single molecules," Phys. Rev. Lett., Vol. 86, No. 23, 5251-5254, 2001.
    doi:10.1103/PhysRevLett.86.5251

    48. Oron, R., S. Blit, N. Davidson, and A. A. Friesem, "The formation of laser beams with pure azimuthal or radial polarization," Appl. Phys. Lett., Vol. 77, No. 21, 3322-3324, 2000.
    doi:10.1063/1.1327271

    49. Li, J., K. I. Ueda, M. Musha, A. Shirakawa, and L. X. Zhong, "Generation of radially polarized mode in Yb fiber laser by using a dual conical prism," Opt. Lett., Vol. 31, No. 20, 2969-2971, 2006.
    doi:10.1364/OL.31.002969

    50. Bomzon, Z., V. Kleiner, and E. Hasman, "Formation of radially and azimuthally polarized light using space-variant subwavelength metal stripe gratings ," Appl. Phys. Lett., Vol. 79, No. 11, 1587-1589, 2001.
    doi:10.1063/1.1401091

    51. Fox, A. G. and T. Li, "Resonate modes in a maser interferometer," Bell Syst. Tech. J., Vol. 40, No. 3, 453-488, 1961.

    52. Wolf, E., "Spatial coherence of resonant modes in a maser interferometer," Phys. Lett., Vol. 3, No. 1, 166-168, 1963.

    53. Wolf, E. and G. S. Agarwal, "Coherence theory of laser resonator modes," J. Opt. Soc. Am. A, Vol. 1, No. 5, 541-546, 1984.
    doi:10.1364/JOSAA.1.000541

    54. Gori, F., "Propagation of the mutual intensity through a periodic structure," Atti Fond. Giorgio Ronchi, Vol. 35, No. 4, 434-447, 1980.

    55. DeSantis, P., A. Mascello, C. Palma, and M. R. Perrone, "Coherence growth of laser radiation in Gaussian cavities," IEEE J. Quantum Electron., Vol. 32, No. 5, 802-812, 1996.
    doi:10.1109/3.493004

    56. Palma, C., G. Cardone, and G. Cincotti, "Spectral changes in Gaussian-cavity lasers," IEEE J. Quantum Electron., Vol. 34, No. 7, 1082-1088, 1998.
    doi:10.1109/3.687848

    57. Wolf, E., "Coherence and polarization properties of electromagnetic laser modes," Opt. Commun., Vol. 265, No. 1, 60-62, 2006.
    doi:10.1016/j.optcom.2006.02.053

    58. Saastamoinen, T., J. Turunen, J. Tervo, T. Setala, and A. T. Friberg, "Electromagnetic coherence theory of laser resonator modes," J. Opt. Soc. Am. A, Vol. 22, No. 1, 103-108, 2005.
    doi:10.1364/JOSAA.22.000103

    59. Tong, Z., O. Korotkova, Y. Cai, H. T. Eyyuboglu, and Y. Baykal, "Correlation properties of random electromagnetic beams in laser resonators ," Appl. Phys. B, Vol. 97, No. 4, 849-857, 2009.
    doi:10.1007/s00340-009-3629-2

    60. Tong, Z. and O. Korotkova, "Stochastic electromagnetic beams in positive-and negative-phase materials," Opt. Lett., Vol. 35, No. 2, 175-177, 2010.
    doi:10.1364/OL.35.000175

    61. Collins, S. A., "Lens-system diffraction integral written in terms of matrix optics ," J. Opt. Soc. Am., Vol. 60, No. 9, 1168-1177, 1970.
    doi:10.1364/JOSA.60.001168

    62. Luneburg, R. K., Mathematical Theory of Optics, Chap. 4, U. California Press, Berkeley, Calif., 1964.