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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 16, Iss. 22 — Oct. 27, 2008
  • pp: 17171–17185

Spontaneous polarization induced by natural thermalization of incoherent light

Antonio Picozzi  »View Author Affiliations

Optics Express, Vol. 16, Issue 22, pp. 17171-17185 (2008)

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We analyze theoretically the polarization properties of a partially coherent optical field that propagates in a nonlinear Kerr medium. We consider the standard model of two resonantly coupled nonlinear Schrödinger equations, which account for a wave-vector mismatch between the orthogonal polarization components. We show that such a phase-mismatch is responsible for the existence of a spontaneous repolarization process of the partially incoherent optical field during its nonlinear propagation. The repolarization process is characterized by an irreversible evolution of the unpolarized beam towards a highly polarized state, without any loss of energy. This unexpected result contrasts with the commonly accepted idea that an optical field undergoes a depolarization process under nonlinear evolution. The repolarization effect can be described in details by simple thermodynamic arguments based on the kinetic wave theory: It is shown to result from the natural tendency of the optical field to approach its thermal equilibrium state. The theory then reveals that it is thermodynamically advantageous for the optical field to evolve towards a highly polarized state, because this permits the optical field to reach the “most disordered state”, i.e., the state of maximum (nonequilibrium) entropy. The theory is in quantitative agreement with the numerical simulations, without adjustable parameters. The physics underlying the reversible property of the repolarization process is briefly discussed in analogy with the celebrated Joule’s experiment of free expansion of a gas. Besides its fundamental interest, the repolarization effect may be exploited to achieve complete polarization of unpolarized incoherent light without loss of energy.

© 2008 Optical Society of America

OCIS Codes
(030.6600) Coherence and statistical optics : Statistical optics
(190.0190) Nonlinear optics : Nonlinear optics

ToC Category:
Coherence and Statistical Optics

Original Manuscript: July 14, 2008
Revised Manuscript: August 17, 2008
Manuscript Accepted: August 25, 2008
Published: October 13, 2008

Antonio Picozzi, "Spontaneous polarization induced by natural thermalization of incoherent light," Opt. Express 16, 17171-17185 (2008)

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  1. R. W. Boyd, Nonlinear Optics (Acad. Press, Third Ed., 2008).
  2. Y. S. Kivshar and G. P. Agrawal, Optical Solitons : From Fibers to Photonic Crystals (Ac. Press, 2003).
  3. G. P. Agrawal, Nonlinear Fiber Optics (Acad. Press., New York, 2001).
  4. A. C. Newell and J. V. Moloney, Nonlinear Optics (Addison-Wesley Publ. Comp., 1992).
  5. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University Press, New York, 1995).
  6. J. W. Goodman, Statistical Optics (Wiley-Interscience Publ., New York, 1985).
  7. E. L. O�??Neill, Introduction to Statistical Optics (Dover Publ., New York, 1963).
  8. E. Wolf, Introduction to the Theory of Coherence and Polarization of Light (Cambridge Univ. Press, 2007).
  9. C. Brosseau, Fundamentals of Polarized Light: A Statistical Optics Approach (John Wiley & Sons, 1998).
  10. G. P. Agrawal and E. Wolf, "Propagation-induced polarization changes in partially coherent optical beams," J. Opt. Soc. Am. A 17, 2019 (2000). [CrossRef]
  11. W. Huang, S. A. Ponomarenko, M. Cada, and G. P. Agrawal, "Polarization changes of partially coherent pulses propagating in optical fibers," J. Opt. Soc. Am. A 24, 3063 (2007). [CrossRef]
  12. M. Mitchell, Z. Chen, Ming-feng Shih, and M. Segev, "Self-Trapping of Partially Spatially Incoherent Light," Phys. Rev. Lett. 77, 490 (1996). [CrossRef] [PubMed]
  13. M. Mitchell and M. Segev, "Self-trapping of incoherent white light," Nature (London) 387, 880 (1997). [CrossRef]
  14. M. Segev and D. N. Christodoulides, Incoherent Solitons, Eds. S. Trillo and W. Torruellas, Spatial Solitons (Springer, Berlin, 2001).
  15. D. N. Christodoulides, T. H. Coskun, M. Mitchell, and M. Segev, "Theory of Incoherent Self-Focusing in Biased Photorefractive Media," Phys. Rev. Lett. 78, 646 (1997). [CrossRef]
  16. M. Mitchell, M. Segev, T. Coskun, and D. N. Christodoulides, "Theory of Self-Trapped Spatially Incoherent Light Beams," Phys. Rev. Lett. 79, 4990 (1997). [CrossRef]
  17. D. N. Christodoulides, E. D. Eugenieva, T. H. Coskun, M. Segev, and M. Mitchell, "Equivalence of three approaches describing partially incoherent wave propagation in inertial nonlinear media," Phys. Rev. E 63, 035601 (2001). [CrossRef]
  18. B. Hall, M. Lisak, D. Anderson, R. Fedele, and V. E. Semenov, "Statistical theory for incoherent light propagation in nonlinear media," Phys. Rev. E 65, 035602 (2002). [CrossRef]
  19. S. A. Ponomarenko and G. P. Agrawal, "Asymmetric incoherent vector solitons," Phys. Rev. E 69, 036604 (2004). [CrossRef]
  20. L. Levi, T. Schwartz, O. Manela, M. Segev, and H. Buljan, "Spontaneous pattern formation upon incoherent waves: From modulation-instability to steady-state," Opt. Express 16, 7818-7831 (2008). [CrossRef] [PubMed]
  21. A. Picozzi and M. Haelterman, "Parametric Three-Wave Soliton Generated from Incoherent Light," Phys. Rev. Lett. 86, 2010-2013 (2001). [CrossRef] [PubMed]
  22. A. Picozzi, M. Haelterman, S. Pitois, and G. Millot, "Spectral incoherent solitons: a localized soliton behavior in the frequency domain," Phys. Rev. Lett. 92, 143906 (2004). [CrossRef] [PubMed]
  23. A. Sauter, S. Pitois, G. Millot, and A. Picozzi, "Incoherent modulation instability in instantaneous nonlinear Kerr media," Opt. Lett. 30, 2143-2145 (2005). [CrossRef] [PubMed]
  24. M. Wu, P. Krivosik, B. A. Kalinikos, and C. E. Patton, "Random Generation of Coherent Solitary Waves from Incoherent Waves," Phys. Rev. Lett. 96, 227202 (2006). [CrossRef] [PubMed]
  25. O. Cohen, H. Buljan, T. Schwartz, J. W. Fleischer, and M. Segev, "Incoherent solitons in instantaneous nonlocal nonlinear media," Phys. Rev. E 73, 015601 (2006). [CrossRef]
  26. C. Rotschild, T. Schwartz, O. Cohen and M. Segev, "Incoherent spatial solitons in effectively instantaneous nonlinear media," Nature Photon. 2, 371 (2008). [CrossRef]
  27. A. Picozzi, S. Pitois, and G. Millot, "Spectral incoherent solitons: a localized soliton behavior in the frequency domain," Phys. Rev. Lett 101, 093901 (2008). [CrossRef] [PubMed]
  28. A. Picozzi and M. Haelterman, "Condensation in Hamiltonian Parametric Wave Interaction," Phys. Rev. Lett. 92, 103901 (2004). [CrossRef] [PubMed]
  29. A. Picozzi, "Nonequilibrated Oscillations of Coherence in Coupled Nonlinear Wave Systems," Phys. Rev. Lett. 96, 013905 (2006). [CrossRef] [PubMed]
  30. C. Connaughton, C. Josserand, A. Picozzi, Y. Pomeau, and S. Rica, "Condensation of Classical Nonlinear Waves," Phys. Rev. Lett. 95, 263901 (2005). [CrossRef]
  31. S. Pitois, S. Lagrange, H. R. Jauslin, and A. Picozzi, "Velocity Locking of Incoherent Nonlinear Wave Packets," Phys. Rev. Lett. 97, 033902 (2006). [CrossRef] [PubMed]
  32. S. Lagrange, H. R. Jauslin, and A. Picozzi, "Thermalization of the dispersive three-wave interaction," Europhys. Lett. 79, 64001 (2007). [CrossRef]
  33. A. Picozzi, "Towards a nonequilibrium thermodynamic description of incoherent nonlinear optics," Opt. Express 15, 9063 (2007). [CrossRef] [PubMed]
  34. G. During, A. Picozzi, and S. Rica, "Breakdown of wave turbulence and nonlinear wave condensation," Physica D (to be published).
  35. B. Barviau, B. Kibler, S. Coen, and A. Picozzi, "Towards a thermodynamic description of supercontinuum generation," Opt. Lett. (to be published).
  36. A. Picozzi and S. Rica, "Coherence absorption induced by thermalization of incoherent fields" Europhys. Lett. (to be published).
  37. B. Crosignani, B. Daino, and P. Di Porto, "Depolarization of light due to the optical Kerr effect in lowbirefringence single-mode fibers," J. Opt. Soc. Am. B 3, 1120 (1986). [CrossRef]
  38. V. E. Chernov and B. A. Zon, "Depolarization of laser radiation in a nonlinear medium," J. Opt. Soc. Am. B 10, 210 (1993). [CrossRef]
  39. Yu. P. Svirko and N. I. Zheludev, Polarization of Light in Nonlinear Optics (Wiley & Sons, 2000).
  40. Yu. P. Svirko and N. I. Zheludev, "Propagation of partially polarized light," Phys. Rev. A 50, 709 (1994). [CrossRef] [PubMed]
  41. A. Picozzi, "Entropy and degree of polarization for nonlinear optical waves," Opt. Lett. 29, 1653 (2004). [CrossRef] [PubMed]
  42. H. Prakash and D. K. Singh, "Change in coherence properties and degree of polarization of light propagating in a lossless isotropic nonlinear Kerr medium," J. Phys. B: At. Mol. Opt. Phys. 41, 045401 (2008). [CrossRef]
  43. D. J. Benney and P. G. Saffman, "Nonlinear interactions of random waves in a dispersive medium," Proc. R. Soc. London Ser. A 289, 301 (1966). [CrossRef]
  44. A. C. Newell, "The closure problem in a system of random gravity waves," Rev. of Geophys. 6, 1-31 (1968). [CrossRef]
  45. V. N. Tsytovich, Nonlinear Effects in Plasma (Plenum N.Y., 1970).
  46. A. Hasegawa, Plasma Instabilities and Nonlinear Effects (Springer-Verlag, 1975). [CrossRef]
  47. R. Z. Sagdeev, D. A. Usikov, and G. M. Zaslavsky, Nonlinear Physics (Harwood Publ., 1988).
  48. V. E. Zakharov, V. S. L�??vov, and G. Falkovich, Kolmogorov Spectra of Turbulence I (Springer, Berlin, 1992).
  49. A. C. Newell, S. Nazarenko, and L. Biven, "Wave turbulence and intermittency," Physica D 152, 520 (2001). [CrossRef]
  50. V. E. Zakharov, F. Dias, and A. Pushkarev, "One-dimensional wave turbulence," Phys. Rep. 398, 1 (2004). [CrossRef]
  51. S. Dyachenko, A. C. Newell, A. Pushkarev, and V. E. Zakharov, "Optical turbulence: weak turbulence, condensates and collapsing filaments in the nonlinear Schrödinger equation," Physica D 57, 96 (1992). [CrossRef]
  52. M. Le Bellac, F. Mortessagne, and G. Batrouni, Equilibrium and Nonequilibrium Statistical Thermodynamics (Cambridge Univ. Press, 2004). [CrossRef]
  53. J. E. Heebner, R. Bennink, R. W. Boyd, and R. Fisher, "Conversion of unpolarized light to polarized light with greater than 50% efficiency by photorefractive two-beam coupling," Opt. Lett. 25, 257 (2000). [CrossRef]
  54. S. Pitois, A. Picozzi, G. Millot, H. R. Jauslin, and M. Haelterman, "Polarization and modal attractors in conservative counterpropagating four-wave interaction," Europhys. Lett. 70, 88 (2005). [CrossRef]
  55. S. Pitois, J. Fatome, and G. Millot, "Polarization attraction using counter-propagating waves in optical fiber at telecommunication wavelengths," Opt. Express 16, 6646 (2008). [CrossRef] [PubMed]
  56. D.C. Hutchings, J. S. Aitchison, and J. M. Arnold, "Nonlinear refractive coupling and vector solitons in anisotropic cubic media," J. Opt. Soc. Am. B 14, 869 (1997). [CrossRef]
  57. C. M. de Sterke and J. E. Sipe, "Polarization instability in a waveguide geometry," Opt. Lett 16, 202 (1991). [CrossRef] [PubMed]
  58. J. U. Kangand, G. I. Stegeman, J. S. Aitchison, and N. Akhmediev, "Observation of Manakov Spatial Solitons in AlGaAs Planar Waveguides," Phys. Rev. Lett 76, 3699 (1996). [CrossRef]
  59. A. Schauer, I. V. Melnikov, and J. S. Aitchison, "Collisions of orthogonally polarized spatial solitons in AlGaAs slab waveguides," J. Opt. Soc. Am. B 21, 57 (2004). [CrossRef]
  60. The elements Ji j (z) do not depend on the spatial position r because of the assumption of homogeneous statistics [5, 10, 11]. Note also that the degree of polarization do not depend on the basis of polarization in which it is calculated [9].
  61. Note that the property |E+ |/|E+>(z) = |E- |2(z) has not been observed for an intensity of the field grater than the critical intensity of polarization instability.
  62. V. E. Zakharov and S. V. Nazarenko, "Dynamics of the Bose-Einstein condensation," Physica D 201, 203-211 (2005). [CrossRef]
  63. B. Rumpf and A. C. Newell, "Coherent Structures and Entropy in Constrained, Modulationally Unstable Nonintegrable Systems," Phys. Rev. Lett. 87, 054102 (2001). [CrossRef] [PubMed]
  64. R. Jordan and C. Josserand, "Self-organization in nonlinear wave turbulence," Phys. Rev. E 61, 1527-1539 (2000). [CrossRef]
  65. Conversely, in the case of incoherently coupled NLS equations, one has to introduce two distinct Lagrange�??s multipliers μx and μy for each conserved quantity Ix and Iy, as discussed in details in Ref.[31].
  66. A. Picozzi, C. Montes, and M. Haelterman, "Coherence properties of the parametric three-wave interaction driven from an incoherent pump," Phys. Rev. E 66, 056605 (2002). [CrossRef]
  67. A. Picozzi and P. Aschieri, "Influence of dispersion on the resonant interaction between three incoherent waves," Phys. Rev. E 72, 046606 (2005). [CrossRef]
  68. P. Ohberg and S. Stenholm, "Internal Josephson effect in trapped double condensates," Phys. Rev. A 59, 3890 (1999). [CrossRef]

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