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Second-Order Overall Characterization of Non-uniformly Polarized Light Beams

  • Rosario Martínez-HerreroEmail author
  • Pedro M. Mejías
  • Gemma Piquero
Chapter
Part of the Springer Series in Optical Sciences book series (SSOS, volume 147)

In the previous chapter, the light fields were represented in the space-time domain by means of the BCP matrix (or through the mutual coherence function in the scalar case). For convenience, we will now prefer to work in the space-frequency regime.

Keywords

Beam Quality Free Propagation Generalize Degree Wigner Distribution Function Wigner Matrix 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. Abramochkin, E., Losevsky, N., Volostnikov, V. (1997): Generation of spiral-type laser beams, Opt. Commun. 141, 59–64.ADSCrossRefGoogle Scholar
  2. Alda, J., Alonso, J., Bernabeu, E. (1997): Characterization of aberrated laser beams, J. Opt. Soc. Am. A 14, 2737–2747.ADSCrossRefGoogle Scholar
  3. Alieva, T., Bastiaans, M. J. (2004): Evolution of the vortex and the asymmetrical parts of orbital angular momentum in separable first-order optical systems, Opt. Lett. 29, 1587–1589.Google Scholar
  4. Allen, L., Padgett, M. J., Babiker, M. (1999): The orbital angular momentum of light, Prog. Opt. 39, 291-372.Google Scholar
  5. Amarande, S. A. (1996): Beam propagation factor and the kurtosis parameter of flattened Gaussian beams, Opt. Commun. 129, 311–317.ADSGoogle Scholar
  6. Bastiaans, M. J. (1989): Propagation laws for the second-order moments of the Wigner distribution function in first-order optical systems, Optik 82, 173–181.Google Scholar
  7. Bekshaev, A. Y., Soskin, M. S., Vasnetsov, M. V. (2003): Optical vortex symmetry breakdown and decomposition of the orbital angular momentum of light beams, J. Opt. Soc. Am. A 20, 1635–1643.Google Scholar
  8. Born, M., Wolf, E. (1999): Principles of Optics, 7th ed. (Cambridge University Press, Cambridge).Google Scholar
  9. Deng, D. M. (2006): Nonparaxial propagation of radially polarized light beams, J. Opt. Soc. Am. B 23, 1228–1234.ADSCrossRefGoogle Scholar
  10. Encinas-Sanz, F., Serna, J., Martínez, C. Martínez-Herrero, R., Mejías, P. (1998): Time-varying beam quality factor and mode evolution TEA CO2 laser pulses, IEEE J. Quantum Electron., 34, 1835–1838.ADSCrossRefGoogle Scholar
  11. Friberg, A. T. (1993): ed., Selected Papers on Coherence and Radiometry (SPIE Milestone Series, MS 69).Google Scholar
  12. Giesen, A., Morin, M. (1998): eds., Proceedings of the 4th International Workshop on Laser Beam and Optics Characterization (LBOC4) (VDI-TechnologieZentrum, Munich).Google Scholar
  13. Giesen, A., Weber, H. (2002): eds., Proceedings of the 7th International Workshop on Laser Beam and Optics Characterization (LBOC7) (Proc. SPIE 4932, Boulder, Colorado).Google Scholar
  14. Gori, F., Bagini, V., Santarsiero, M., Frezza, F., Schettini, G., Schirripa Spagnolo, G. (1994): Coherent and partially coherent twisting beams, Opt. Rev. 1, 143–145.Google Scholar
  15. Gori, F., Santarsiero, M., Piquero, G., Borghi, R., Mondello, A., Simon, R. (2001): Partially polarized Gaussian Schell-model beams, J. Opt. A Pure Appl. Opt. 3, 1–9.ADSCrossRefGoogle Scholar
  16. Gori, F., Santarsiero, M., Borghi, R., Ramírez-Sánchez, V. (2008): Realizability condition for electromagnetic Schell-model sources, J. Opt. Soc. Am. A 25, 1016–1021.ADSCrossRefGoogle Scholar
  17. Hodgson, H., Weber, H. (1993): Influence of spherical aberration of the active medium on the performance of Nd:YAG lasers, IEEE J. Quantum Electron. 29, 2497–2507.ADSCrossRefGoogle Scholar
  18. ISO Standard 11146 (1999): Lasers and laser related equipment test methods for laser beams parameters: Beam widths, divergence angle and beam propagation factor.Google Scholar
  19. ISO/DIS 12005 (2003): Optics and optical instruments-Lasers and laser related equipment-test methods for laser beam parameters: Polarization.Google Scholar
  20. ISO 11146 (2005): Laser and laser related equipment-test methods for laser beam widths, divergence angles and beam propagation ratios, Parts 1, 2 and 3. International Organization for Standardization, Geneva, Switzerland.Google Scholar
  21. Kudryashov, A. V., Paxton, A. H., Ilchenko, V. S., Giesen, A., Nickel, D., Davis, S. J., Heaven, M. C., Schriempf, J. T. (2006): eds., Proceedings of the 8th International Workshop on Laser Beam and Optics Characterization (LBOC8) (Proc. SPIE 6110, San Jose, CA).Google Scholar
  22. Kuga, T., Torii, Y., Shiokawa, N., Hirano, T., Shimizu, Y., Sasada, H. (1997): Novel optical trap of atoms with a doughnut beam, Phys. Rew. Lett. 78, 4713–4716.ADSCrossRefGoogle Scholar
  23. Kugler, N., Dong, N., Lü, Q., Weber, H. (1997): Investigation of the misalignment sensitivity of a birefringence: compensated two-rod Nd:YAG laser system, Appl. Opt. 36, 9359–9366.ADSCrossRefGoogle Scholar
  24. Laabs, H., Weber, H. (2000): eds., Proceedings of the 5th International Workshop on Laser Beam and Optics Characterization (LBOC5) (VDI-TechnologieZentrum, Erice).Google Scholar
  25. Lavi, S., Prochaska, R., Keren, E. (1988): Generalized beam parameters and transformation law for partially coherent light, Appl. Opt. 27, 3696–3703.ADSCrossRefGoogle Scholar
  26. Lü, Q., Dong, S., Weber, H. (1995): Analysis of TEM00 laser beam quality degradation caused by a birefringent Nd:YAG rod, Opt. Quantum Electron. 27, 777–783.CrossRefGoogle Scholar
  27. Luo, S., Lu, B. (2003): M2 factor and kurtosis parameter of super-Gaussian beams passing through an axicon, Optik 114, 193–8.ADSCrossRefGoogle Scholar
  28. Machavariani, G., Lumer, Y., Moshe, I., Jackel, S. (2007): Effect of the spiral phase element on the radial-polarization (0,1) * LG beam, Opt. Commun. 271, 190–196.ADSCrossRefGoogle Scholar
  29. Mandel, L., Wolf, E. (1995): Optical Coherence and Quantum Optics (Cambridge University Press, Cambridge).Google Scholar
  30. Marchand, E. W., Wolf, E. (1974): Walther's definitions of generalized radiance, J. Opt. Soc. Am. 64(9), 1273–1274.CrossRefGoogle Scholar
  31. Martínez-Herrero, R., Mejías, P. M., Sánchez, M., Neira, J. L. H. (1992a): Third-and fourth-order parametric characterization of partially coherent beams propagating through ABCD optical systems, Opt. Quantum Electron. 24, 1021–1026.CrossRefGoogle Scholar
  32. Martínez-Herrero, R., Mejías, P. M., Piquero, G. (1992b): Quality improvement of partially coherent symmetric-intensity beams caused by quartic phase distorsions, Opt. Lett. 17, 1650–1651.ADSCrossRefGoogle Scholar
  33. Martínez-Herrero, R., Mejías, P. M. (1993a): Quality improvement of symmetric-intensity beams propagating through pure phase plates, Opt. Commun. 95, 18–20.ADSCrossRefGoogle Scholar
  34. Martínez-Herrero, R., Mejías, P. M. (1993b): Second-order spatial characterization of hard-edge diffracted beams, Opt. Lett. 18, 1669–1671.ADSCrossRefGoogle Scholar
  35. Martínez-Herrero, R., Mejías, P. M. (1994): On the spatial parametric characterization of general light beams, Current Trends in Optics, Dainty, J. ed., Vol II (Academic Press, London, 105).Google Scholar
  36. Martínez-Herrero, R., Piquero, G., Mejías, P. M. (1995a): On the propagation of the kurtosis parameter of general beams, Opt. Commun. 115, 225–232.ADSCrossRefGoogle Scholar
  37. Martínez-Herrero, R., Mejías, P. M., Hodgson, N., Weber, H. (1995b): Beam-quality changes generated by thermally-induced spherical aberration in laser cavities, IEEE J. Quantum Electron. 31, 2173–2176.ADSCrossRefGoogle Scholar
  38. Martínez-Herrero, R., Mejías, P. M., Arias, M. (1995c): Parametric characterization of coherent, lowest-order Gaussian beams propagating through hard-edge apertures, Opt. Lett. 20, 124–126.ADSCrossRefGoogle Scholar
  39. Martínez-Herrero, R., Mejías, P. M. (1997a): On the fourth-order spatial characterization of laser beams: new invariant, Opt. Commun. 140, 57–60.ADSCrossRefGoogle Scholar
  40. Martínez-Herrero, R., Mejías, P. M., Movilla, J. M. (1997b): Spatial characterization of partially polarized beams, Opt. Lett. 22, 206–208.ADSCrossRefGoogle Scholar
  41. Martínez-Herrero, R., Mejías, P. M., Piquero, G. (2003a): Anisotropic pure-phase plates for quality improvement of partially coherent, partially polarized beams, J. Opt. Soc. Am. A 20, 577–581.ADSCrossRefGoogle Scholar
  42. Martínez-Herrero, R., Mejías, P. M., Bosch, S., Carnicer, A. (2003b): Spatial width and power-content ratio of hard-edge diffracted beams, J. Opt. Soc. Am. A 20, 388–391.Google Scholar
  43. Martínez-Herrero, R., Piquero, G., Mejías, P. M. (2004): Parametric characterization of the spatial structure of partially coherent and partially polarized beams, J. Opt. A: Pure Appl. Opt. 6, S67–S71.ADSCrossRefGoogle Scholar
  44. Martínez-Herrero, R., Mejías, P. M., Movilla, J. M. (2005): Beam-quality optimization of partially polarized fields, J. Opt. Soc. Am. A 22, 1442–1446.ADSCrossRefGoogle Scholar
  45. Martínez-Herrero, R., Mejías, P. M. (2006a): On the control of the spatial orientation of the transverse profile of a light beam, Opt. Express 14, 1086–1093.ADSCrossRefGoogle Scholar
  46. Martínez-Herrero, R., Mejías, P. M. (2006b): On the spatial orientation of the transverse irradiance profile of partially coherent beams, Opt. Express 14, 3294–3303.ADSCrossRefGoogle Scholar
  47. Martínez-Herrero, R., Mejías, P. M. (2007): Invariant parameters for characterizing nonuniformly partially polarized beams, Opt. Spectrosc. 103, 886–889.CrossRefGoogle Scholar
  48. Martínez-Herrero, R., Mejías, P. M., Piquero, G. (2008): Beam quality changes of radially and azimuthally polarized fields propagating through quartic phase, Opt. Commun. 281, 756–759.ADSCrossRefGoogle Scholar
  49. Martínez-Herrero, R., Manjavacas, A. (2009): Overall second-order parametric characterization of light beams propagating through spiral phase elements, Opt. Commun. 282, 473–477.ADSCrossRefGoogle Scholar
  50. McCelland, J. J., Scheinfein, M. R. J. (1991): Laser focusing of atoms: a particle-optics approach, J. Opt. Soc. Am. B 8, 1974–1986.ADSCrossRefGoogle Scholar
  51. Mejías, P. M., Weber, H., Martínez-Herrero, R. (1993): González-Ureña, A., eds. Proceedings of the 1st Workshop on Laser Beam Characterization (LBOC1) (SEDO, Madrid).Google Scholar
  52. Mejías, P. M., Martínez-Herrero, R. (1995): Time-resolved spatial parametric characterization of pulsed light beams, Opt. Lett. 20, 660–662.ADSCrossRefGoogle Scholar
  53. Mejías, P. M., Martínez-Herrero, R., Piquero, G., Movilla, J. M. (2002): Parametric characterization of the spatial structure of non-uniformly polarizad laser beams, Prog. Quantum Electron. 26, 65–130.ADSCrossRefGoogle Scholar
  54. Molina-Terriza, G., Rebane, L., Torres, J. P., Torner, L., Carrasco, S. (2007): Probing canonical geometrical objects by digital spiral Imaging, J. Eur. Opt. Soc. Rap. Public 2, 07014–07019.CrossRefGoogle Scholar
  55. Montmerle, B. A., Gilbert, M., Thro, P. Y., Weulersse, J. M. (2006): Thermal lensing and spherical aberration in high-power transversally pumped laser rods, Opt. Commun. 259, 223–235.ADSCrossRefGoogle Scholar
  56. Morin, M., Giesen, A. (1996): eds., Proceedings of the 3th International Workshop on Laser Beam Characterization (LBOC3) (Proc. SPIE 2870, Quebec).Google Scholar
  57. Movilla, J. M., Piquero, G., Martínez-Herrero, R., Mejías, P. M. (1998): Parametric characterization of non-uniformly polarized beams, Opt. Commun. 149, 230–234.ADSCrossRefGoogle Scholar
  58. Movilla, J. M., Piquero, G., Martínez-Herrero, R., Mejías, P. M. (2000): On the measurement of the generalized degree of polarization, Opt. Quantum Electron. 32, 1333–1342.CrossRefGoogle Scholar
  59. Movilla, J. M., Martínez-Herrero, R., Mejías, P. M. (2001): Quality improvement of partially polarized beams, Appl. Opt. 40, 6098–6101.ADSCrossRefGoogle Scholar
  60. Nemes, G., Siegman, A. E. (1994): Measurement of all ten second-order moments of an astigmatic beam by the use of rotating simple astigmatic (anamorphic) optics, J. Opt. Soc. Am. A 11, 2257–2264.ADSCrossRefGoogle Scholar
  61. Niv, A., Biener, G., Kleiner, V., Hasman, E. (2005): Spiral phase elements obtained by use of discrete space-variant subwavelength gratings, Opt.Commun. 251, 306–314.ADSCrossRefGoogle Scholar
  62. Oemrawsingh, S. S. R.; van Houwelingen, J. A. W.; Eliel, E. R., Woerdman, J. P., Verstegen, E. J. K., Kloosterboer, J. G., Hooft, G. W. (2004): Production and characterization of spiral phase plates for optical wavelengths, Appl. Opt. 43, 688–694.ADSCrossRefGoogle Scholar
  63. Oron, R., Davidson, N., Friesem, A. A., Hasman, E. (2002): Continuous-phase elements can improve laser beam quality, Opt. Lett. 25, 939–941.ADSCrossRefGoogle Scholar
  64. Pepper, D. M. (1985): Nonlinear optical phase conjugation, Laser Handbook, M. L. Stitch, M. L., and M. Bass, M., eds., Vol 4 (North-Holland, Amsterdam, 433–485).Google Scholar
  65. Perina, J. (1971): Coherence of Light (Van Nostrand Reinhold Company, London).Google Scholar
  66. Piquero, G., Mejías, P. M., Martínez-Herrero, R. (1994): Sharpness changes of Gaussian beams induced by spherically aberrated lenses, Opt. Commun. 107, 179–183.ADSCrossRefGoogle Scholar
  67. Piquero, G., Gori, F., Romanini, P., Santarsiero, M., Borghi, R., Mondello, A. (2002): Synthesis of partially polarized Gaussian Schell-model sources, Opt. Commun. 208, 9–16.ADSCrossRefGoogle Scholar
  68. Ramírez-Sánchez, V., Piquero, G. (2006): Global beam shaping with non-uniformly polarized beams: a proposal, Appl. Opt. 45, 8902–8906.ADSCrossRefGoogle Scholar
  69. Sato, S., Harada, Y., Waseda, Y. (1994): Optical trapping of microscopic metal particles, Opt. Lett. 19, 1807–1809.ADSCrossRefGoogle Scholar
  70. Serna, J., Martínez-Herrero, R., Mejías, P. M. (1991): Parametric characterization of general partially coherent beams propagating through ABCD optical systems, J. Opt. Soc. Am. A 8, 1094–1098.ADSCrossRefGoogle Scholar
  71. Serna, J., Mejías, P. M., Martínez-Herrero, R. (1992a): Rotation of partially coherent beams propagating through free space, Opt. Quantum Electron. 24, S873–S880.CrossRefGoogle Scholar
  72. Serna, J., Mejías, P. M., Martínez-Herrero, R. (1992b): Beam quality changes of Gaussian Schell-model fields propagating through Gaussian apertures, Appl. Opt. 31, 4330–4331.ADSCrossRefGoogle Scholar
  73. Siegman, A. E. (1986): Lasers, (University Science Books, California).Google Scholar
  74. Siegman, A. E. (1990): New developments in laser resonators, Optical Resonators, Holmes, D. A., ed., Proc. SPIE, Vol1224, 2–14.Google Scholar
  75. Siegman, A. E. (1993a): Analysis of laser beam quality degradation caused by spherical aberration, Appl. Opt. 32, 5893–5901.ADSCrossRefGoogle Scholar
  76. Siegman, A. E. (1993b): Binary phase plates cannot improve laser beam quality, Opt. Lett. 18, 675–677.ADSCrossRefGoogle Scholar
  77. Simon, R, Mukunda, N., Sudarshan, E. C. G. (1988): Partially coherent beams and a generalized ABCD-law, Opt. Commun. 65, 322–328.ADSCrossRefGoogle Scholar
  78. Simon, R., Mukunda, N. (1993): Twisted Gaussian-Schell-model beams, J. Opt. Soc. Am. A 10, 95–109.Google Scholar
  79. Torner, L., Torres, J., Carrasco, S. (2005): Digital spiral imaging, Opt. Express 13, 873–881.ADSCrossRefGoogle Scholar
  80. Vasnetsov, M. V., Torres, J. P., Petrov, D. V., Torner, L. (2003): Observation of the orbital angular momentum spectrum of a light beam, Opt. Lett. 28, 2285–2287.Google Scholar
  81. Walther, A. (1968): Radiometry and coherence, J. Opt. Soc. Am. 58, 1256–1259.ADSCrossRefGoogle Scholar
  82. Weber, H. (1992): Propagation of higher-order intensity moments in quadratic-index media, Opt. Quantum Electron. 24, 1027–1049.CrossRefGoogle Scholar
  83. Weber, H., Reng, N., Lüdtke, J., Mejías, P. M. (1994): eds., Proceedings of the 2nd Workshop on Laser Beam Characterization (LBOC2) (FLI, Berlín).Google Scholar
  84. WLT (2001): eds., Proceedings of the 6th International Workshop on Laser Beam and Optics Characterization (LBOC6) (WLT, Munich).Google Scholar
  85. Wolf, E. (2007): Introduction to the Theory of Coherence and Polarization of Light (Cambridge University Press, Cambridge).zbMATHGoogle Scholar
  86. Xie, Q., Zhao, D. (2008): Optical vortices generated by multi-level achromatic spiral phase plates for broadband beams, Opt. Commun. 281, 7–11.ADSCrossRefGoogle Scholar
  87. Zhou, G. Q. (2006): Analytical vectorial structure of Laguerre-Gaussian beam in the far field, Opt. Lett. 31, 2616–2618.ADSCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Rosario Martínez-Herrero
    • 1
    Email author
  • Pedro M. Mejías
    • 1
  • Gemma Piquero
    • 1
  1. 1.Optics DepartmentUniversidad Complutense de MadridMadridSpain

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