Publication:
Parametric characterization of the spatial structure of non-uniformly polarized laser beams

Loading...
Thumbnail Image
Full text at PDC
Publication Date
2002
Authors
Mejías López, Jesús Ángel
Martínez Herrero, Rosario
Movilla Serrano, Jesús María
Advisors (or tutors)
Editors
Journal Title
Journal ISSN
Volume Title
Publisher
Pergamon-Elsevier Sciance Ltd
Citations
Google Scholar
Research Projects
Organizational Units
Journal Issue
Abstract
We present an approach for describing the spatial structure of partially polarized light fields. Unlike the treatments usually encountered in the literature, in which the polarization state is represented by position-dependent functions, the formalism shown here characterizes the polarization by means of a family of measurable overall parameters averaged over the transverse spatial region where the beam intensity reaches significant values. Generalized degrees of polarization are introduced to evaluate the uniformity of the spatial distribution of the polarization state of the beam-like field. The possibility of improvement and optimization of the quality of a polarized laser beam (understood as the general usefulness of such field for collimation and focussing) is analyzed by employing first-order optical systems. Finally, attention is briefly devoted to non-paraxial electromagnetic vector beams, whose Parametric description of their polarization properties constitutes, at present, a challenge for theoreticians.
Description
© 2002 Elsevier Science Ltd. The research work leading to this paper was supported by the Ministerio de Educación y Cultura of Spain, Projects PB97-0295 and BFM 2001–1356, within the framework of EUREKA projects EU-1269 and EU-2359. The curves plotted in Figs. 26 and 27 were numerically computed by Drs. S. Bosch and A. Carnicer. We would also like to thank Prof. H. Weber, Mr. A. Vázquez and Mr. G. Mann from the Optisches Institut at the Technische Universität in Berlin for their continuous interest and support all along the experimental work described in Section 5.4. We are also grateful to Dr. J. Serna for helpful discussions and for his assistance in the preparation of this manuscript. One of the authors (G.P.) wishes to thank Prof. F. Gori, Dr. M. Santarsiero and Dr. R. Borghi for helpful discussions concerning PGSM sources.
Keywords
Citation
[1] L. Mandel, E. Wolf, Optical Coherence and Quantum Optics, Cambridge University Press,Cambridge, 1995. [2] A. Aspect, J. Dalibard, G. Roger, Experimental test of Bell’s inequalities using time-varying analyzers, Physical Review Letters 49 (25) (1982) 1804–1807. [3] S.F. Mason, Molecular Optical Activity and the Chiral Discrimination, Cambridge University Press, Cambridge, 1982. [4] M.V. Berry, Quantal phase factors accompanying adiabatic changes, Proceedings of the Royal Society of London A 392 (1984) 45–57. [5] H. Schmitzer, Nonlinearity of Pancharatnam’s Topological phase, S. Klein, W. Dultz, Physical Review Letters 71 (10) (1993) 1530–1533. [6] W.A. Shurcliff, Polarized Light, Harvard University Press, Cambridge, MA, 1962. [7] W.G. Egan, Photometry and Polarization in Remote Sensing, Elsevier, New York, 1985. [8] G.P. Konnen, Polarized Light in Nature, Cambridge University, Cambridge, 1985. [9] R.M.A. Azzam, N.M. Bashara, Ellipsometry and Polarized Light, North-Holland, Amsterdam, 1987. [10] K.L. Coulson, Polarization and Intensity Light in the Atmosphere, A. Deepak, Hampton, VA, 1988. [11] D.S. Kliger, J.W. Lewis, C.E. Randall, Polarized Light in Optics and Spectroscopy, Academic Press, Boston, 1990. [12] E. Collett, Polarized Light, Marcel Dekker Inc, New York, 1992. [13] W. Boerner, H. Motts (Eds.), Radar Polarimetry, Proceedings SPIE, 1747, The International Society for Optical Engineering, Bellingham, 1992. [14] M. Bass (Ed.), Handbook on Optics, Vols. I and II, McGraw-Hill, New York, 1994. [15] C. Brosseau, Fundamentals of Polarized Light, Wiley, New York, 1998. [16] D. Fink, Polarization effects of axicons, Applied Optics 18 (5) (1979) 581–582. [17] B.J. Feldman, S.J. Gitomer, Anular lens soft aperture for high power laser systems, Applied Optics 15 (6) (1976) 1379–1380. [18] G. Giuliani, Y.K. Park, R.L. Byer, Radial birefringent element and its applications to laser resonator design, Optical Letters 5 (11) (1980) 491–493. [19] J.M. Eggleston, G. Giuliani, R.L. Byer, Radial intensity filters using radial birefringent elements, Journal of the Optical Society of America 71 (10) (1981) 1264–1272. [20] S.C. Tidwell, D.H. Ford, W.D. Kimura, Generating radially polarized beams interferometrically, Applied Optics 29 (15) (1990) 2334–2339. [21] T. Erdogan, D.G. Hall, Circularly symmetric distributed feedback semiconductor laser: an analysis, Journal of Applied Physics 68 (4) (1990) 1435–1444. [22] T. Erdogan, O. King, G.W. Wicks, D.G. Hall, E. Anderson, M.J. Rooks, Circularly symmetric operation of a concentric-circle-grating surface emitting AlGaAs/GaAs quantum well semiconductor laser, Applied Physics Letters 60 (16) (1992) 1921–1923. [23] S.C. Tidwell, G.H. Kim, W.D. Kimura, Efficient radially polarized laser beam generation with a double interferometer, Applied Optics 32 (27) (1993) 5222–5227. [24] P.L. Greene, D.G. Hall, Diffraction characteristics of the azimuthal Bessel–Gauss beam, Journal of the Optical Society of America A 13 (9) (1996) 962–966. [25] S. Sato, K. Takahashi, B. Mehmetli, Polarization effects of a high-power CO/sub2/laser beam on aluminum alloy weldability, Journal of Applied Physics 79 (12) (1996) 8917–8919. [26] B. L. u, Y. Ye, Z. Sui, B. Cai, Analysis of a radially varying transmission system used for spatial beam shaping, Optik 101 (3) (1996) 97–100. [27] I. Freund, Polarization flowers, Optics Communications 199 (1–4) (2001) 47–63. [28] R.A. Chipman, Polarimetry, Hanbook on Optics, Vol. II, McGraw-Hill, New York, 1994 (Chapter 22). [29] D.F.V. James, Change of polarization of light beams on propagation in free space, Journal of the Optical Society of America A 11 (5) (1994) 1641–1643. [30] A.A. Tovar, Production and propagation of cylindrically polarized Laguerre–Gaussian Laser beams, Journal of the Optical Society of America 15 (10) (1998) 2705–2711. [31] F. Gori, M. Santarsiero, R. Borghi, G. Piquero, Use of the van Cittert–Zernike theorem for partially polarized sources, Optical Letters 25 (17) (2000) 1291–1293. [32] G.P. Agrawal, E. Wolf, Propagation-induced polarization changes in partially coherent optical beams, Journal of the Optical Society of America A 17 (11) (2000) 2019–2023. [33] F. Gori, M. Santarsiero, G. Piquero, R. Borghi, A. Mondello, R. Simon, Partially polarized Gaussian Schell-model beams, Journal of Optics A 3 (1) (2001) 1–9. [34] G. Piquero, R. Borghi, M. Santarsiero, Gaussian Schell-model beams propagating through polarization gratings, Journal of the Optical Society of America A 18 (6) (2001) 1399–1405. [35] G. Piquero, R. Borghi, A. Mondello, M. Santarsiero, Far field of beams generated by quasihomogeneous sources passing through polarization gratings, Optics Communications 195 (5–6) (2001) 339–350. [36] Y. Fainman, J. Shamir, Polarization of nonplanar wave fronts, Applied Optics 23 (18) (1984) 3188–3195. [37] R. Simon, E.C.G. Sudarshan, N. Mukunda, Gaussian–Maxwell beams, Journal of the Optical Society of America A 3 (4) (1986) 536–540. [38] R. Simon, E.C.G. Sudarshan, N. Mukunda, Cross polarization in laser beams, Applied Optics 26 (9) (1987) 1589–1593. [39] K.E. Oughstun, Polarization properties of the freely propagating electromagnetic field of arbitrary spatial and temporal form, Journal of the Optical Society of America A 9 (4) (1992) 578–584. [40] J.F. Nye, J.V. Hajnat, The wave structure of monochromatic electromagnetic radiation, Proceedings of the Royal Society of London 409 (1987) 21–36. [41] D.G. Hall, Vector-beam solutions of Maxwell’s waves equation, Optical Letters 21 (1) (1996) 9–11. [42] P. Varga, P. Török, Exact and approximate solutions of Maxwell’s equation and the validity of the scalar wave approximation, Optical Letters 21 (1) (1996) 1523–1525. [43] S.R. Seshadri, Electromagnetic Gaussian beam, Journal of the Optical Society of America A 15 (10) (1998) 2712–2719. [44] P. Varga, P. Török, The Gaussian wave solution of Maxwell’s equations and the validity of the scalar wave approximation, Optics Communications 152 (1–3) (1998) 108–118. [45] S.R. Seshadri, Partially coherent Gaussian Schell-model electromagnetic beam, Journal of the Optical Society of America A 16 (6) (1999) 1373–1380. [46] C.J.R. Sheppard, S. Saghafi, Electromagnetic Gaussian beams beyond the paraxial approximation, Journal of the Optical Society of America A 16 (6) (1999) 1381–1386. [47] M.V. Berry, M.R. Dennis, Polarization singularities in isotropic random vector waves, Proceedings of the Royal Society of London 457 (2000) 141–155. [48] S.R. Seshadri, Average characteristics of partially coherent electromagnetic beams, Journal of the Optical Society of America A 17 (4) (2000) 780–789. [49] C.J.R. Sheppard, Polarization of almost-planes waves, Journal of the Optical Society of America A 17 (2) (2000) 335–341. [50] R. Martínez-Herrero, P.M. Mejías, S. Bosch, A. Carnicer, Vectorial structure of nonparaxial electromagnetic beams, Journal of the Optical Society of America A 18 (7) (2001) 1678–1680. [51] E. Wolf, Coherence properties of partially polarized electromagnetic radiation, Il Nuovo Cimento 13 (6) (1959) 1165–1181. [52] F. Gori, Matrix treatment for partially polarized, partially coherent beams, Optical Letters 23 (4) (1998) 241–243. [53] F. Gori, M. Santarsiero, S. Vicalvi, R. Borghi, G. Guattari, Beam coherence-polarization matrix, Journal of the European Optical Society A 7 (5) (1998) 941–951. [54] E.L. O’Neill, Introduction to Statistical Optics, Addison-Wesley Publ. Co, Reading, MA, 1963. [55] C. Whitney, Pauli-algebraic operators in polarization optics, Journal of the Optical Society of America 61 (9) (1971) 1207–1213. [56] R. Martínez-Herrero, J.M. Movilla, P.M. Mejías, Beam propagation through uniaxial anisotropic media: global changes in the spatial profile, Journal of the Optical Society of America A 18 (8) (2001) 2009–2014. [57] A.E. Siegman, Lasers, Oxford University Press, Oxford, 1986. [58] J.W. Goodman, Introduction to Fourier Optics, McGraw-Hill, New York, 1968. [59] J. Perina, Coherence of Light, Van Nostrand Reinhold Company, London, 1971. [60] M.J. Beran, G.B. Parrent, Theory of Partial Coherence, Prentice-Hall, Englewood Cliffs, NJ, 1967. [61] M. Born, E. Wolf, Principles of Optics, 7th Edition, Cambridge University Press, Cambridge, 1999. [62] J.M. Jauch, F. Rohrlich, The Theory of Photons and Electrons, Addison-Wesley Publ. Co, Cambridge, MA, 1955. [63] R. Barakat, The statistical properties of partially polarized light, Optica Acta 32 (3) (1985) 295–312. [64] C. Brosseau, R. Barakat, E. Rockower, Statistics of the Stokes parameters for Gaussian distributed fields, Optics Communications 82 (3–4) (1991) 204–208. [65] C. Brosseau, Statistics of the normalized Stokes parameters for a Gaussian stochastic plane wave field, Applied Optics 34 (22) (1995) 4788–4793. [66] C. Brosseau, D. Bicout, Entropy production in multiple scattering of light by a spatially random medium, Physical Review E 50 (6) (1994) 4997–5005. [67] F. Le Roy-Brehonnet, B. Le Jeune, Utilization of Mueller matrix formalism to obtain targets depolarization and depolarization properties, Progress in Quantum Electronics 21 (2) (1997) 109–151. [68] R. Simon, The connection between the Jones and Mueller matrices, Optics Communications 42 (5) (1982) 293–297. [69] J.J. Gil, Characteristic properties of Mueller matrices, Journal of the Optical Society of America A 17 (2) (2000) 328–334. [70] ISO/DIS 12005, Optics and optical instruments—lasers and laser related equipment—test methods for laser beam parameters: polarization (International Organization for Standardization, Geneva, Switzerland). [71] A. Walther, Radiometry and coherence, Journal of the Optical Society of America 58 (9) (1968) 1256–1259. [72] A. Walther, Reply to Marchand and Wolf, Journal of the Optical Society of America 64 (9)(1974) 1275. [73] E.W. Marchand, E. Wolf, Walther’s definitions of generalized radiance, Journal of the Optical Society of America 64 (9) (1974) 1273–1274. [74] R. Martínez-Herrero, P.M. Mejías, On the spatial parametric characterization of general light beams, in: J. Dainty (Ed.), Current Trends in Optics, Vol. II, Academic Press, New York, 1994. [75] P.M. Mejías, H. Weber, R. Martínez-Herrero, A. González-Ureña (Eds.), Proceedings of the First Workshop on Laser Beam Characterization, SEDO, Madrid, 1993. [76] H. Weber, N. Reng, J. Lüdtke, P.M. Mejías (Eds.), Proceedings of the Second Workshopon Laser Beam Characterization II, FLI, Berlín, 1994. [77] M. Morin, A. Giesen (Eds.), Third International Workshopon Laser Beam and Optics Characterization, Proceedings SPIE 2870, The International Society for Optical Engineering, Bellingham, 1996. [78] A. Giesen, M. Morin (Eds.), Fourth International Workshopon Laser Beam and Optics Characterization, VDI-TechnologieZentrum, Munich, 1998. [79] H. Laabs, H. Weber (Eds.), Proceedings of the Fifth International Workshopon Laser Beam and Optics Characterization, VDI-TechnologieZentrum, Erice, 2000. [80] Proceedings of the Sixth International Workshopon Laser Beam and Optics Characterization, Munich, 2001, in press. [81] J. Serna, P.M. Mejías, R. Martínez-Herrero, Rotation of partially coherent beams propagating through free space, Optical Quantum Electronics 24 (9) (1992) S873–S880. [82] J. Serna, J.M. Movilla, Orbital angular momentum of partially coherent beams, Optical Letters 26 (7) (2001) 405–407. [83] G. Piquero, P.M. Mejías, R. Martínez-Herrero, Sharpness changes of Gaussian beams induced by spherically aberrated lenses, Optics Communications 107 (3–4) (1994) 179–183. [84] R. Martínez-Herrero, G. Piquero, P.M. Mejías, On the propagation of the kurtosis parameter of general beams, Optics Communications 115 (3) (1995) 225–232. [85] M. Scholl, G. Herziger, Kurtosis as a tool parameter for laser welding, Proceedings of the SPIE 2375 (1995) 130–141. [86] S.A. Amarande, Beam propagation factor and the kurtosis parameter of flattened Gaussian beams, Optics Communications 129 (5–6) (1996) 311–317. [87] P. Loosen, K. Du, C. Maier, O. M.arten, M. Scholl, Laser beam characterization and measurement techniques, in: P.M. Mejías, H. Weber, R. Martínez-Herrero, A. González-Ureña (Eds.), Proceedings of Laser Beam Characterization, SEDO, Madrid, 1993. [88] J. Serna, R. Martínez-Herrero, P.M. Mejías, Parametric characterization of general partially coherent beams propagating through ABCD optical systems, Journal of the Optical Society of America A 8 (7) (1991) 1094–1098. [89] R. Martínez-Herrero, P.M. Mejías, M. Sánchez, J.L.H. Neira, Third- and fourth-order parametric characterization of partially coherent beams propagating through ABCD optical systems, Optical Quantum Electronics 24 (9) (1992) 1021–1026. [90] R. Martínez-Herrero, P.M. Mejías, C. Martínez, Parametric characterization of the phase at the far field, Optical Letters 20 (7) (1995) 651–653. [91] R. Martínez-Herrero, P.M. Mejías, On the fourth-order spatial characterization of laser beams: new invariant, Optics Communications 140 (1–3) (1997) 57–60. [92] S. Lavi, R. Prochaska, E. Keren, Generalized beam parameters and transformation law for partially coherent light, Applied Optics 27 (17) (1988) 3696–3703. [93] R. Simon, N. Mukunda, E.C.G. Sudarshan, Partially coherent beams and a generalized ABCD-law, Optics Communications 65 (5) (1988) 322–328. [94] A.E. Siegman, New developments in laser resonators, in D.A. Holmes (Ed.), Optical Resonators, Proceedings SPIE 1224, The International Society for Optical Engineering, Bellingham, 1990, pp. 2–14. [95] H. Weber, Propagation of higher-order intensity moments in quadratic-index media, Optical Quantum Electronics 24 (9) (1992) 1027–1049. [96] C. Martínez, Spatial and time characterization of continuous and pulsed light beams, Ph.D. Dissertation, Universidad Complutense, 1998. [97] G. Nemes, A.E. Siegman, Measurement of all ten second-order moments of an astigmatic beam by the use of rotating simple astigmatic (anamorphic) optics, Journal of the Optical Society of America A 11 (8) (1994) 2257–2264. [98] J. Serna, F. Encinas-Sanz, G. Nemes, Complete spatial characterization of a pulsed doughnut-type beam by use of spherical optics and a cylindrical lens, Journal of the Optical Society of America A 18 (7) (2001) 1726–1733. [99] R. Martínez-Herrero, P.M. Mejías, J.M. Movilla, Spatial characterization of partially polarized beams, Optical Letters 22 (4) (1997) 206–208. [100] S.A. Collins Jr., Lens-system Diffraction Integral written in terms of matrix optics, Journal of the Optical Society of America 60 (9) (1970) 1168–1177. [101] J.M. Movilla, Spatial parametrization of light beams: some aspects concerning polarization. Ph.D. Dissertation, Universidad Complutense, 2000. [102] J.M. Movilla, G. Piquero, R. Martínez-Herrero, P.M. Mejías, Parametric characterization of nonuniformly polarized beams, Optics Communications 149 (4–6) (1998) 230–234. [103] J.M. Movilla, G. Piquero, R. Martínez-Herrero, P.M. Mejías, On the measurement of the generalized degree of polarization, Optical Quantum Electronics 32 (12) (2000) 1333–1342. [104] Q. L. u, S. Dong, H. Weber, Analysis of TEM00 laser beam quality degradation caused by a birefringent Nd:YAG rod, Optical Quantum Electronics 27 (9) (1995) 777–783. [105] N. Kugler, S. Dong, Q. L. u, H. Weber, Investigation of the misalignment sensitivity of a birefringence compensated two-rod Nd:YAG laser system, Applied Optics 36 (36) (1997) 9359–9366. [106] G. Piquero, J.M. Movilla, P.M. Mejías, R. Martínez-Herrero, Degree of polarization of nonuniformly partially polarized beams: a proposal, Optical Quantum Electronics 31 (3) (1999) 223–225. [107] A.T. Friberg (Ed.), Selected Papers on Coherence and Radiometry, SPIE Milestone Series, MS 69, The International Society for Optical Engineering, Bellingham, 1993. [108] F. Gori, Mode propagation of the field generated by Collett–Wolf sources, Optics Communications 46 (3–4) (1983) 149–154. [109] G. Piquero, F. Gori, P. Romanini, M. Santarsiero, R. Borghi, A. Mondello, Synthesis and characterization of partially polarized Gaussian Schell-model sources, Proceedings of the Sixth International Workshop on Laser Beam and Optics Characterization, Munich, June 2001, in press. [110] ISO/DIS 11146, Optics and optical instruments—lasers and laser related equipment- test methods for laser beam parameters: beam widths, divergence angle and beam propagation factor (International Organization for Standardization, Geneva, Switzerland) 1999. [111] R. Martínez-Herrero, P.M. Mejías, G. Piquero, Quality improvement of partially coherent symmetric-intensity beams caused by quartic phase distorsions, Optical Letters 17 (23) (1992) 1650–1651. [112] J. Serna, P.M. Mejías, R. Martínez-Herrero, Beam quality changes of Gaussian Schell-model fields propagating through Gaussian apertures, Applied Optics 31 (22) (1992) 4330–4331. [113] R. Martínez-Herrero, P. M. Mejías, Quality improvement of symmetric-intensity beams propagating through pure phase plates, Optics Communications 95 (1–3) (1993) 18–20. [114] A.E. Siegman, Analysis of laser beam quality degradation caused by spherical aberration, Applied Optics 32 (30) (1993) 5893–5901. [115] A.E. Siegman, Binary phase plates cannot improve laser beam quality, Optical Letters 18 (9) (1993) 675–677. [116] J.A. Ruff, A.E. Siegman, Measurement of beam quality degradation due to spherical aberration in a simple lens, Optical Quantum Electronics 26 (6) (1994) 629–632. [117] L.W. Casperson, Phase plates transform laser beam, Laser Focus World 30 (5) (1994) 223–228. [118] J.M.Movilla, R. Martínez-Herrero, P.M. Mejías, Quality improvement of partially polarized beams, Applied Optics 40 (33) (2001) 6098–6101. [119] G. Piquero, J.M. Movilla, R. Martínez-Herrero, P.M. Mejías, Beam quality of partially polarized beams propagating through lens-like birefringent elements, Journal of the Optical Society of America A 16 (11) (1999) 2666–2668.
Collections