Towards a nonequilibrium thermodynamic description of incoherent nonlinear optics
Optics Express, Vol. 15, Issue 14, pp. 9063-9083 (2007)
http://dx.doi.org/10.1364/OE.15.009063
Acrobat PDF (294 KB)
Abstract
This concise review is aimed at providing an introduction to the kinetic theory of partially coherent optical waves propagating in nonlinear media. The subject of incoherent nonlinear optics received a renewed interest since the first experimental demonstration of incoherent solitons in slowly responding photorefractive crystals. Several theories have been successfully developed to provide a detailed description of the novel dynamical features inherent to partially coherent nonlinear optical waves. However, such theories leave unanswered the following important question: Which is the long term (spatiotemporal) evolution of a partially incoherent optical field propagating in a nonlinear medium? In complete analogy with kinetic gas theory, one may expect that the incoherent field may evolve, owing to nonlinearity, towards a thermodynamic equilibrium state. Weak-turbulence theory is shown to describe the essential properties of this irreversible process of thermal wave relaxation to equilibrium. Precisely, the theory describes an irreversible evolution of the spectrum of the field towards a thermodynamic equilibrium state. The irreversible behavior is expressed through the H-theorem of entropy growth, whose origin is analogous to the celebrated Boltzmann’s H-theorem of kinetic gas theory. It is shown that thermal wave relaxation to equilibrium may be characterized by the existence of a genuine condensation process, whose thermodynamic properties are analogous to those of Bose-Einstein condensation, despite the fact that the considered optical wave is completely classical. In spite of the formal reversibility of optical wave propagation, the condensation process occurs by means of an irreversible evolution of the field towards a homogeneous plane-wave (condensate) with small-scale fluctuations superimposed (uncondensed particles), which store the information necessary for the reversible propagation. As a remarkable result, an increase of entropy (“disorder”) in the optical field requires the generation of a coherent structure (plane-wave). We show that, beyond the standard thermodynamic limit, wave condensation also occurs in two spatial dimensions. The numerical simulations are in quantitative agreement with the kinetic wave theory, without any adjustable parameter.
© 2007 Optical Society of America
1. Introduction
1. See, e.g., J. Ducuing and N. Bloembergen, “Statistical Fluctuations in Nonlinear Optical Processes,” Phys. Rev. 133, A1493 – A1502 (1964). [CrossRef]
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6. M. Soljacic, M. Segev, T. Coskun, D. N. Christodoulides, and A. Vishwanath “Modulation Instability of Incoherent Beams in Noninstantaneous Nonlinear Media,” Phys. Rev. Lett. 84, 467 (2000). [CrossRef] [PubMed]
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2. Model equation
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3. Inhomogenous statistics
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4. Homogenous statistics
4.1. Boltzmann’s like equation
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4.2. Properties of the kinetic equation
21. 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]
21. 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]
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5. Condensation of classical optical waves
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5.1. Condensation in 3D
19. C. Connaughton, C. Josserand, A. Picozzi, Y. Pomeau, and S. Rica, “Condensation of Classical Nonlinear Waves,” Phys. Rev. Lett. 95, 263901 (2005). [CrossRef]
19. C. Connaughton, C. Josserand, A. Picozzi, Y. Pomeau, and S. Rica, “Condensation of Classical Nonlinear Waves,” Phys. Rev. Lett. 95, 263901 (2005). [CrossRef]
19. C. Connaughton, C. Josserand, A. Picozzi, Y. Pomeau, and S. Rica, “Condensation of Classical Nonlinear Waves,” Phys. Rev. Lett. 95, 263901 (2005). [CrossRef]
19. C. Connaughton, C. Josserand, A. Picozzi, Y. Pomeau, and S. Rica, “Condensation of Classical Nonlinear Waves,” Phys. Rev. Lett. 95, 263901 (2005). [CrossRef]
19. C. Connaughton, C. Josserand, A. Picozzi, Y. Pomeau, and S. Rica, “Condensation of Classical Nonlinear Waves,” Phys. Rev. Lett. 95, 263901 (2005). [CrossRef]
5.2. Beyond the thermodynamic limit: Condensation in 2D
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19. C. Connaughton, C. Josserand, A. Picozzi, Y. Pomeau, and S. Rica, “Condensation of Classical Nonlinear Waves,” Phys. Rev. Lett. 95, 263901 (2005). [CrossRef]
81. R. Lacaze, P. Lallemand, Y. Pomeau, and S. Rica, “Dynamical formation of a BoseEinstein condensate,” Physica D 152–153, 779–786 (2001). [CrossRef]
82. M. J. Davis, S. A. Morgan, and K. Burnett, “Simulations of Bose Fields at Finite Temperature,” Phys. Rev. Lett. 87, 160402 (2001). [CrossRef] [PubMed]
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87. N. G. Berloff and B. V. Svistunov “Scenario of strongly nonequilibrated Bose-Einstein condensation,” Phys. Rev. A 66, 013603 (2002). [CrossRef]
88. S. Nazarenko and M. Onorato “Wave turbulence and vortices in Bose-Einstein condensation,” Physica D 219, 1 (2006). [CrossRef]
6. Perspectives and conclusion
6.1. Importance of coherent phase effects in incoherent optical interactions
89. J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78, 1135–1184 (2006). [CrossRef]
15. A. Picozzi and M. Haelterman, “Parametric Three-Wave Soliton Generated from Incoherent Light,” Phys. Rev. Lett. 86, 2010–2013 (2001). [CrossRef] [PubMed]
90. 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]
91. A. Picozzi and P. Aschieri, “Influence of dispersion on the resonant interaction between three incoherent waves,” Phys. Rev. E 72, 046606 (2005). [CrossRef]
92. C. Montes, A. Picozzi, and K. Gallo, “Ultra-coherent signal output from an incoherent cw-pumped singly resonant optical parametric oscillator,” Opt. Comm. 237, 437–449 (2004). [CrossRef]
15. A. Picozzi and M. Haelterman, “Parametric Three-Wave Soliton Generated from Incoherent Light,” Phys. Rev. Lett. 86, 2010–2013 (2001). [CrossRef] [PubMed]
16. A. Picozzi, M. Haelterman, S. Pitois, and G. Millot, “Incoherent Solitons in Instantaneous Response Nonlinear Media,” Phys. Rev. Lett. 92, 143906 (2004). [CrossRef] [PubMed]
20. A. Picozzi, “Nonequilibrated Oscillations of Coherence in Coupled Nonlinear Wave Systems,” Phys. Rev. Lett. 96, 013905 (2006). [CrossRef] [PubMed]
6.2. Thermodynamics of a pure wave system?
21. 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]
Acknowledgments
References and links
1. | See, e.g., J. Ducuing and N. Bloembergen, “Statistical Fluctuations in Nonlinear Optical Processes,” Phys. Rev. 133, A1493 – A1502 (1964). [CrossRef] |
2. | 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] |
3. | M. Mitchell and M. Segev, “Self-trapping of incoherent white light,” Nature (London) 387, 880 (1997). [CrossRef] |
4. | Y.S. Kivshar and G.P. Agrawal, “Optical Solitons : From Fibers to Photonic Crystals” (Ac. Press, 2003). |
5. | M. Segev and D. N. Christodoulides, “Incoherent Solitons,” Eds. S. Trillo and W. Torruellas, Spatial Solitons (Springer, Berlin, 2001). |
6. | M. Soljacic, M. Segev, T. Coskun, D. N. Christodoulides, and A. Vishwanath “Modulation Instability of Incoherent Beams in Noninstantaneous Nonlinear Media,” Phys. Rev. Lett. 84, 467 (2000). [CrossRef] [PubMed] |
7. | D. Kip, M. Soljacic, M. Segev, E. Eugenieva, and D. N. Christodoulides, “Modulation instability and pattern formation in spatially incoherent light beams,” Science 290, 495–498 (2000). [CrossRef] [PubMed] |
8. | C. Anastassiou, M. Soljacic, M. Segev, E. D. Eugenieva, D. N. Christodoulides, D. Kip, Z. H. Musslimani, and J. P. Torres, “Eliminating the Transverse Instabilities of Kerr Solitons,” Phys. Rev. Lett. 85, 4888 (2000). [CrossRef] [PubMed] |
9. | S. M. Sears, M. Soljacic, D. N. Christodoulides, and M. Segev, “Pattern formation via symmetry breaking in nonlinear weakly correlated systems,” Phys. Rev. E 65, 036620 (2002). [CrossRef] |
10. | D. N. Christodoulides, T. H. Coskun, M. Mitchell, Z. Chen, and M. Segev, “Theory of Incoherent Dark Solitons,” Phys. Rev. Lett. 80, 5113 (1998). [CrossRef] |
11. | Z. Chen, M. Mitchell, M. Segev, T. H. Coskun, and D. N. Christodoulides, “Self-trapping of dark incoherent light beams,” Science 280, 889 (1998). [CrossRef] [PubMed] |
12. | H. Buljan, M. Soljacic, T. Carmon, and M. Segev, “Cavity pattern formation with incoherent light,” Phys. Rev. E 68, 016616 (2003). [CrossRef] |
13. | H. Buljan, O. Cohen, J. W. Fleischer, T. Schwartz, M. Segev, Z. H. Musslimani, N. K. Efremidis, and D. N. Christodoulides “Random-Phase Solitons in Nonlinear Periodic Lattices,” Phys. Rev. Lett. 92, 223901 (2004). [CrossRef] [PubMed] |
14. | O. Cohen, G. Bartal, H. Buljan, T. Carmon, J. W. Fleischer, M. Segev, and D. N. Christodoulides, “Observation of random-phase lattice solitons,” Nature (London) 433, 500 (2005). [CrossRef] [PubMed] |
15. | A. Picozzi and M. Haelterman, “Parametric Three-Wave Soliton Generated from Incoherent Light,” Phys. Rev. Lett. 86, 2010–2013 (2001). [CrossRef] [PubMed] |
16. | A. Picozzi, M. Haelterman, S. Pitois, and G. Millot, “Incoherent Solitons in Instantaneous Response Nonlinear Media,” Phys. Rev. Lett. 92, 143906 (2004). [CrossRef] [PubMed] |
17. | A. Picozzi and M. Haelterman, “Condensation in Hamiltonian Parametric Wave Interaction,” Phys. Rev. Lett. 92, 103901 (2004). [CrossRef] [PubMed] |
18. | 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] |
19. | C. Connaughton, C. Josserand, A. Picozzi, Y. Pomeau, and S. Rica, “Condensation of Classical Nonlinear Waves,” Phys. Rev. Lett. 95, 263901 (2005). [CrossRef] |
20. | A. Picozzi, “Nonequilibrated Oscillations of Coherence in Coupled Nonlinear Wave Systems,” Phys. Rev. Lett. 96, 013905 (2006). [CrossRef] [PubMed] |
21. | 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] |
22. | 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] |
23. | G.A. Pasmanik, “Self-interaction of incoherent light beams,” Sov. Phys. JETP 39, 234 (1974). |
24. | 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] |
25. | 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] |
26. | 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] |
27. | L. Mandel and E. Wolf, “Optical Coherence and Quantum Optics” (Cambridge University Press, New York, 1995). |
28. | 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] |
29. | M. Lisak, L. Helczynski, and D. Anderson, “Relation between different formalisms describing partially incoherent wave propagation in nonlinear optical media,” Opt. Commun. 220, 321 (2003). [CrossRef] |
30. | A. W. Snyder and D. J. Mitchell, “Big incoherent solitons,” Phys. Rev. Lett. 80, 1422 (1998). [CrossRef] |
31. | A. Hasegawa, “Dynamics of an ensemble of plane waves in nonlinear dispersive media,” Phys. Fluids 18, 77–78 (1975). [CrossRef] |
32. | A. Hasegawa, “Envelope soliton of random phase waves,” Phys. Fluids 20, 2155–2156 (1977). [CrossRef] |
33. | K. Hasselmann, “On the non-linear energy transfer in a gravity-wave spectrum. Part 1. General theory,” J. Fluid Mech. 12, 481–500 (1962). [CrossRef] |
34. | K. Hasselmann, “On the non-linear energy transfer in a gravity-wave spectrum. Part 2. Conservation theorems; wave-particle analogy; irreversibility,” J. Fluid Mech. 15, 273–281 (1963). [CrossRef] |
35. | A. C. Newell, “The closure problem in a system of random gravity waves,” Rev. of Geophys. 6, 1–31 (1968). [CrossRef] |
36. | V. N. Tsytovich, “Nonlinear Effects in Plasma” (Plenum, New York, 1970). |
37. | A. Hasegawa, Plasma Instabilities and Nonlinear Effects (Springer-Verlag, New York, 1975). [CrossRef] |
38. | P. A. Robinson, “Nonlinear wave collapse and strong turbulence,” Rev. Mod. Phys. 69, 507 (1997). [CrossRef] |
39. | V. E. Zakharov, V. S. L’vov, and G. Falkovich, “Kolmogorov Spectra of Turbulence I” (Springer, Berlin, 1992). |
40. | 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] |
41. | A. C. Newell, S. Nazarenko, and L. Biven, “Wave turbulence and intermittency,” Physica D 152–153, 520–550 (2001). [CrossRef] |
42. | K. Huang, “Statistical Mechanics” (Wiley, 1963). |
43. | Y. Pomeau, “Long time behavior of solutions of nonlinear classical field equations: the example of NLS defocusing,” Physica D 61, 227 (1992). [CrossRef] |
44. | R.W. Boyd, “Nonlinear Optics” (Acad. Press, 2002). |
45. | N.N. Akhmediev and A. Ankiewicz, “Solitons - Non-linear pulses and beams” (Springer, 1997). |
46. | A. C. Newell and J. V. Moloney, “Nonlinear Optics” (Addison-Wesley Publ. Comp., 1992). |
47. | J. T. Manassah, “Self-phase modulation of incoherent light revisited,” Opt. Lett. 16, 1638 (1991). [CrossRef] [PubMed] |
48. | A. Papoulis and S.U. Pillai “Probability, Random Variables, and Stochastic Processes” (McGraw-Hill, Fourth Edition, 2002). |
49. | J. Garnier, J.-P. Ayanides, and O. Morice, “Propagation of partially coherent light with the Maxwell-Debye equation,” J. Opt. Soc. Am. B 20, 1409–1417 (2003). [CrossRef] |
50. | V. E. Zakharov, S. L. Musher, and A. M. Rubenchik, “Hamiltonian approach to the description of non-linear plasma phenomena,” Phys. Reports 129, 285–366 (1985). [CrossRef] |
51. | T. H. Coskun, D. N. Christodoulides, Z. Chen, and M. Segev “Dark incoherent soliton splitting and phase-memory effects: Theory and experiment,” Phys. Rev. E 59, R4777 (1999). [CrossRef] |
52. | C. C. Jeng, M. F. Shih, K. Motzek, and Y. Kivshar “Partially Incoherent Optical Vortices in Self-Focusing Nonlinear Media,” Phys. Rev. Lett. 92, 043904 (2004). [CrossRef] [PubMed] |
53. | K. Motzek, F. Kaiser, J. R. Salgueiro, Y. Kivshar, and C. Denz, “Incoherent vector vortex-mode solitons in self-focusing nonlinear media,” Opt. Lett. 29, 2285 (2004). [CrossRef] [PubMed] |
54. | A. Dreischuh, D. N. Neshev, D. E. Petersen, O. Bang, and W. Krolikowski, “Observation of Attraction between Dark Solitons,” Phys. Rev. Lett. 96, 043901 (2006). [CrossRef] [PubMed] |
55. | N. Akhmediev, W. Krolikowski, and A. W. Snyder, “Partially Coherent Solitons of Variable Shape,” Phys. Rev. Lett. 81, 4632 (1998). [CrossRef] |
56. | A. A. Sukhorukov and N. N. Akhmediev “Coherent and Incoherent Contributions to Multisoliton Complexes,” Phys. Rev. Lett. 83, 4736 (1999). [CrossRef] |
57. | O. Bang, D. Edmundson, and W. Krolikowski, “Collapse of Incoherent Light Beams in Inertial Bulk Kerr Media,” Phys. Rev. Lett. 83, 5479 (1999). [CrossRef] |
58. | T. H. Coskun, A. G. Grandpierre, D. N. Christodoulides, and M. Segev “Coherence enhancement of spatially incoherent light beams through soliton interactions,” Opt. Lett. 25, 826 (2000). [CrossRef] |
59. | W. Krolikowski, D. Edmundson, and O. Bang, “Unified model for partially coherent solitons in logarithmically nonlinear media,” Phys. Rev. E 61, 3122 (2000). [CrossRef] |
60. | M. Peccianti and G. Assanto “Incoherent spatial solitary waves in nematic liquid crystals,” Opt. Lett. 26, 1791–1793 (2001). [CrossRef] |
61. | S. A. Ponomarenko, N. M. Litchinitser, and G. P. Agrawal “Theory of incoherent optical solitons: Beyond the mean-field approximation,” Phys. Rev. E 70, 015603 (2004). [CrossRef] |
62. | S. A. Ponomarenko and G. P. Agrawal “Asymmetric incoherent vector solitons,” Phys. Rev. E 69, 036604 (2004). [CrossRef] |
63. | Ting-Sen Ku, Ming-Feng Shih, A. A. Sukhorukov, and Y. S. Kivshar “Coherence Controlled Soliton Interactions,” Phys. Rev. Lett. 94, 063904 (2005). [CrossRef] [PubMed] |
64. | K. G. Makris, H. Sarkissian, D. N. Christodoulides, and G. Assanto “Nonlocal incoherent spatial solitons in liquid crystals,” J. Opt. Soc. Am. B 22, 1371–1377 (2005). [CrossRef] |
65. | D. Anderson, L. Helczynski-Wolf, M. Lisak, and V. Semenov, “Features of modulational instability of partially coherent light: Importance of the incoherence spectrum,” Phys. Rev. E 69, 025601 (2004). [CrossRef] |
66. | L. Helczynski, M. Lisak, and D. Anderson “Influence of higher-order dispersion on modulational instability and pulse broadening of partially incoherent light,” Phys. Rev. E 67, 026602 (2003). [CrossRef] |
67. | S. B. Cavalcanti, G. P. Agrawal, and M. Yu, “Noise amplification in dispersive nonlinear media,” Phys. Rev. A 51, 4086 (1995). [CrossRef] [PubMed] |
68. | A. Mussot, E. Lantz, H. Maillotte, T. Sylvestre, C. Finot, and S. Pitois, “Spectral broadening of a partially coherent CW laser beam in single-mode optical fibers,” Opt. Exp. 12, 2838 (2004). [CrossRef] |
69. | R. Z. Sagdeev, D. A. Usikov, and G. M. Zaslavsky, “Nonlinear Physics” (Harwood Academic Publ., Chur, Switzerland, 1988). |
70. | S. Lagrange, H. R. Jauslin, and A. Picozzi, “Thermalization of the dispersive three-wave interaction” (submitted). |
71. | C. Conti, S. Trillo, P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, and J. Trull, “Nonlinear Electromagnetic X-Waves,” Phys. Rev. Lett. 90, 170406 (2003). [CrossRef] [PubMed] |
72. | P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, J. Trull, C. Conti, and S. Trillo, “Spontaneously Generated X-Shaped Light Bullets,” Phys. Rev. Lett. 91, 093904 (2003); [CrossRef] [PubMed] |
73. | M. Kolesik, E. M. Wright, and J. V. Moloney, “Dynamic Nonlinear X Waves for Femtosecond Pulse Propagation in Water,” Phys. Rev. Lett. 92, 253901 (2004). [CrossRef] [PubMed] |
74. | A. Picozzi and M. Haelterman “Hidden Coherence Along Space-Time Trajectories in Parametric Wave Mixing,” Phys. Rev. Lett. 88, 083901 (2002). [CrossRef] [PubMed] |
75. | O. Jedrkiewicz, A. Picozzi, M. Clerici, D. Faccio, and P. Di Trapani, “Emergence of X-Shaped Spatiotemporal Coherence in Optical Waves,” Phys. Rev. Lett. 97, 243903 (2006). [CrossRef] |
76. | V. E. Zakharov and S. V. Nazarenko, “Dynamics of the Bose-Einstein condensation,” Physica D 201, 203–211 (2005). [CrossRef] |
77. | V.E. Zakharov, A.N. Pushkarev, V.F. Shvetz, and V.V. Yan’kov, “Solitonic turbulence,” Pis’ma v Zh. Eksp. Teor. Fiz. 48, 79–81 (1988) [JETP Lett. 48, 83–85 (1988)]. |
78. | B. Rumpf and A. C. Newell, “Coherent Structures and Entropy in Constrained, Modulationally Unstable Nonintegrable Systems,” Phys. Rev. Lett. 87, 054102 (2001). [CrossRef] [PubMed] |
79. | R. Jordan and C. Josserand, “Self-organization in nonlinear wave turbulence,” Phys. Rev. E 61, 1527–1539 (2000). [CrossRef] |
80. | P. Aschieri and A. Picozzi (to be published). |
81. | R. Lacaze, P. Lallemand, Y. Pomeau, and S. Rica, “Dynamical formation of a BoseEinstein condensate,” Physica D 152–153, 779–786 (2001). [CrossRef] |
82. | M. J. Davis, S. A. Morgan, and K. Burnett, “Simulations of Bose Fields at Finite Temperature,” Phys. Rev. Lett. 87, 160402 (2001). [CrossRef] [PubMed] |
83. | M. J. Davis, S. A. Morgan, and K. Burnett, “Simulations of thermal Bose fields in the classical limit,” Phys. Rev. A 66, 053618 (2002). [CrossRef] |
84. | R. Y. Chiao and J. Boyce “Bogoliubov dispersion relation and the possibility of superfluidity for weakly interacting photons in a two-dimensional photon fluid,” Phys. Rev. A 60, 4114 (1999). [CrossRef] |
85. | R. Y. Chiao, T. H. Hansson, J. M. Leinaas, and S. Viefers, “Effective photon-photon interaction in a two-dimensional photon fluid,” Phys. Rev. A 69, 063816 (2004). [CrossRef] |
86. | T. Frisch, Y. Pomeau, and S. Rica “Transition to dissipation in a model of superflow,” Phys. Rev. Lett. 69, 1644 (1992). [CrossRef] [PubMed] |
87. | N. G. Berloff and B. V. Svistunov “Scenario of strongly nonequilibrated Bose-Einstein condensation,” Phys. Rev. A 66, 013603 (2002). [CrossRef] |
88. | S. Nazarenko and M. Onorato “Wave turbulence and vortices in Bose-Einstein condensation,” Physica D 219, 1 (2006). [CrossRef] |
89. | J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78, 1135–1184 (2006). [CrossRef] |
90. | 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] |
91. | A. Picozzi and P. Aschieri, “Influence of dispersion on the resonant interaction between three incoherent waves,” Phys. Rev. E 72, 046606 (2005). [CrossRef] |
92. | C. Montes, A. Picozzi, and K. Gallo, “Ultra-coherent signal output from an incoherent cw-pumped singly resonant optical parametric oscillator,” Opt. Comm. 237, 437–449 (2004). [CrossRef] |
OCIS Codes
(030.6600) Coherence and statistical optics : Statistical optics
(190.0190) Nonlinear optics : Nonlinear optics
(190.5530) Nonlinear optics : Pulse propagation and temporal solitons
ToC Category:
Theoretical Concepts and Methods
History
Original Manuscript: February 8, 2007
Revised Manuscript: May 9, 2007
Manuscript Accepted: May 11, 2007
Published: July 9, 2007
Virtual Issues
Focus Serial: Frontiers of Nonlinear Optics (2007) Optics Express
Citation
Antonio Picozzi, "Towards a nonequilibrium thermodynamic description of incoherent nonlinear optics," Opt. Express 15, 9063-9083 (2007)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-14-9063
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References
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- 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]
- M. Mitchell and M. Segev, "Self-trapping of incoherent white light," Nature (London) 387, 880 (1997). [CrossRef]
- Y. S. Kivshar and G. P. Agrawal, "Optical Solitons : from Fibers to Photonic Crystals" (Ac. Press, 2003).
- M. Segev and D. N. Christodoulides, "Incoherent Solitons," S. Trillo and W. Torruellas, eds., Spatial Solitons (Springer, Berlin, 2001).
- M. Soljacic, M. Segev, T. Coskun, D. N. Christodoulides, and A. Vishwanath "Modulation Instability of Incoherent Beams in Noninstantaneous Nonlinear Media," Phys. Rev. Lett. 84, 467 (2000). [CrossRef] [PubMed]
- D. Kip, M. Soljacic, M. Segev, E. Eugenieva, and D. N. Christodoulides, "Modulation instability and pattern formation in spatially incoherent light beams," Science 290, 495-498 (2000). [CrossRef] [PubMed]
- C. Anastassiou, M. Soljacic, M. Segev, E. D. Eugenieva, D. N. Christodoulides, D. Kip, Z. H. Musslimani, and J. P. Torres, "Eliminating the Transverse Instabilities of Kerr Solitons," Phys. Rev. Lett. 85, 4888 (2000). [CrossRef] [PubMed]
- S. M. Sears, M. Soljacic, D. N. Christodoulides, and M. Segev, "Pattern formation via symmetry breaking in nonlinear weakly correlated systems," Phys. Rev. E 65, 036620 (2002). [CrossRef]
- D. N. Christodoulides, T. H. Coskun, M. Mitchell, Z. Chen, and M. Segev, "Theory of Incoherent Dark Solitons," Phys. Rev. Lett. 80, 5113 (1998). [CrossRef]
- Z. Chen, M. Mitchell, M. Segev, T. H. Coskun, and D. N. Christodoulides, "Self-trapping of dark incoherent light beams," Science 280, 889 (1998). [CrossRef] [PubMed]
- H. Buljan, M. Soljacic, T. Carmon, and M. Segev, "Cavity pattern formation with incoherent light," Phys. Rev. E 68, 016616 (2003). [CrossRef]
- H. Buljan, O. Cohen, J. W. Fleischer, T. Schwartz, M. Segev, Z. H. Musslimani, N. K. Efremidis, and D. N. Christodoulides "Random-Phase Solitons in Nonlinear Periodic Lattices," Phys. Rev. Lett. 92, 223901 (2004). [CrossRef] [PubMed]
- O. Cohen, G. Bartal, H. Buljan, T. Carmon, J. W. Fleischer, M. Segev, D. N. Christodoulides, "Observation of random-phase lattice solitons," Nature (London) 433, 500 (2005). [CrossRef] [PubMed]
- A. Picozzi and M. Haelterman, "Parametric Three-Wave Soliton Generated from Incoherent Light," Phys. Rev. Lett. 86, 2010-2013 (2001). [CrossRef] [PubMed]
- A. Picozzi, M. Haelterman, S. Pitois, and G. Millot, "Incoherent Solitons in Instantaneous Response Nonlinear Media," Phys. Rev. Lett. 92, 143906 (2004). [CrossRef] [PubMed]
- A. Picozzi and M. Haelterman, "Condensation in Hamiltonian Parametric Wave Interaction," Phys. Rev. Lett. 92, 103901 (2004). [CrossRef] [PubMed]
- A. Sauter, S. Pitois, G. Millot, A. Picozzi, "Incoherent modulation instability in instantaneous nonlinear Kerr media," Opt. Lett. 30, 2143-2145 (2005). [CrossRef] [PubMed]
- C. Connaughton, C. Josserand, A. Picozzi, Y. Pomeau, and S. Rica, "Condensation of Classical Nonlinear Waves," Phys. Rev. Lett. 95, 263901 (2005). [CrossRef]
- A. Picozzi, "Nonequilibrated Oscillations of Coherence in Coupled Nonlinear Wave Systems," Phys. Rev. Lett. 96, 013905 (2006). [CrossRef] [PubMed]
- 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]
- 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]
- G.A. Pasmanik, "Self-interaction of incoherent light beams," Sov. Phys. JETP 39, 234 (1974).
- M. Mitchell, M. Segev, T. Coskun, D.N. Christodoulides, "Theory of Self-Trapped Spatially Incoherent Light Beams," Phys. Rev. Lett. 79, 4990 (1997). [CrossRef]
- D.N. Christodoulides, T.H. Coskun, M. Mitchell, M. Segev, "Theory of Incoherent Self-Focusing in Biased Photorefractive Media," Phys. Rev. Lett. 78, 646 (1997). [CrossRef]
- 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]
- L. Mandel and E. Wolf, "Optical Coherence and Quantum Optics" (Cambridge University Press, New York, 1995).
- 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]
- M. Lisak, L. Helczynski, D. Anderson, "Relation between different formalisms describing partially incoherent wave propagation in nonlinear optical media," Opt. Commun. 220, 321 (2003). [CrossRef]
- A. W. Snyder and D. J. Mitchell, "Big incoherent solitons," Phys. Rev. Lett. 80, 1422 (1998). [CrossRef]
- A. Hasegawa, "Dynamics of an ensemble of plane waves in nonlinear dispersive media," Phys. Fluids 18, 77-78 (1975). [CrossRef]
- A. Hasegawa, "Envelope soliton of random phase waves," Phys. Fluids 20, 2155-2156 (1977). [CrossRef]
- K. Hasselmann, "On the non-linear energy transfer in a gravity-wave spectrum. Part 1. General theory," J. Fluid Mech. 12, 481-500 (1962). [CrossRef]
- K. Hasselmann, "On the non-linear energy transfer in a gravity-wave spectrum. Part 2. Conservation theorems; wave-particle analogy; irreversibility," J. Fluid Mech. 15, 273-281 (1963). [CrossRef]
- A. C. Newell, "The closure problem in a system of random gravity waves," Rev. of Geophys. 6, 1-31 (1968). [CrossRef]
- V. N. Tsytovich, Nonlinear Effects in Plasma (Plenum, New York, 1970).
- A. Hasegawa, Plasma Instabilities and Nonlinear Effects (Springer-Verlag, New York, 1975). [CrossRef]
- P. A. Robinson, "Nonlinear wave collapse and strong turbulence," Rev. Mod. Phys. 69, 507 (1997). [CrossRef]
- V. E. Zakharov, V. S. L’vov and G. Falkovich, Kolmogorov Spectra of Turbulence I (Springer, Berlin, 1992).
- S. Dyachenko, A. C. Newell, A. Pushkarev, and V. E. Zakharov, "Optical turbulence: weak turbulence, condensates and collapsing filaments in the nonlinear Schr¨odinger equation," Physica D 57, 96 (1992). [CrossRef]
- A. C. Newell, S. Nazarenko and L. Biven, "Wave turbulence and intermittency," Physica D 152-153, 520-550 (2001). [CrossRef]
- K. Huang, Statistical Mechanics (Wiley, 1963).
- Y. Pomeau, "Long time behavior of solutions of nonlinear classical field equations: the example of NLS defocusing," Physica D 61, 227 (1992). [CrossRef]
- R. W. Boyd, Nonlinear Optics (Acad. Press, 2002).
- N. N. Akhmediev and A. Ankiewicz, Solitons - Non-linear pulses and beams (Springer, 1997).
- A. C. Newell and J. V. Moloney, "Nonlinear Optics (Addison-Wesley, 1992).
- J. T. Manassah, "Self-phase modulation of incoherent light revisited," Opt. Lett. 16, 1638 (1991). [CrossRef] [PubMed]
- A. Papoulis, and S. U. Pillai, Probability, Random Variables, and Stochastic Processes (McGraw-Hill, Fourth Edition, 2002).
- J. Garnier, J.-P. Ayanides, and O. Morice, "Propagation of partially coherent light with the Maxwell-Debye equation," J. Opt. Soc. Am. B 20, 1409-1417 (2003). [CrossRef]
- V. E. Zakharov, S. L. Musher and A. M. Rubenchik, "Hamiltonian approach to the description of non-linear plasma phenomena," Phys. Reports 129, 285-366 (1985). [CrossRef]
- T. H. Coskun, D. N. Christodoulides, Z. Chen, and M. Segev "Dark incoherent soliton splitting and phasememory effects: Theory and experiment," Phys. Rev. E 59, R4777 (1999). [CrossRef]
- C. C. Jeng, M. F. Shih, K. Motzek, and Y. Kivshar "Partially Incoherent Optical Vortices in Self-Focusing Nonlinear Media," Phys. Rev. Lett. 92, 043904 (2004). [CrossRef] [PubMed]
- K. Motzek, F. Kaiser, J. R. Salgueiro, Y. Kivshar, and C. Denz, "Incoherent vector vortex-mode solitons in selffocusing nonlinear media," Opt. Lett. 29, 2285 (2004). [CrossRef] [PubMed]
- A. Dreischuh, D. N. Neshev, D. E. Petersen, O. Bang, and W. Krolikowski, "Observation of attraction between Dark Solitons," Phys. Rev. Lett. 96, 043901 (2006). [CrossRef] [PubMed]
- N. Akhmediev, W. Krolikowski, and A. W. Snyder, "Partially Coherent Solitons of Variable Shape," Phys. Rev. Lett. 81, 4632 (1998). [CrossRef]
- A. A. Sukhorukov and N. N. Akhmediev "Coherent and Incoherent Contributions to Multisoliton Complexes," Phys. Rev. Lett. 83, 4736 (1999). [CrossRef]
- O. Bang, D. Edmundson, andW. Krolikowski, "Collapse of Incoherent Light Beams in Inertial Bulk Kerr Media," Phys. Rev. Lett. 83, 5479 (1999). [CrossRef]
- T. H. Coskun, A. G. Grandpierre, D. N. Christodoulides, and M. Segev "Coherence enhancement of spatially incoherent light beams through soliton interactions," Opt. Lett. 25, 826 (2000). [CrossRef]
- W. Krolikowski, D. Edmundson, and O. Bang, "Unified model for partially coherent solitons in logarithmically nonlinear media," Phys. Rev. E 61, 3122 (2000). [CrossRef]
- M. Peccianti and G. Assanto "Incoherent spatial solitary waves in nematic liquid crystals," Opt. Lett. 26, 1791- 1793 (2001). [CrossRef]
- S. A. Ponomarenko, N. M. Litchinitser, and G. P. Agrawal "Theory of incoherent optical solitons: Beyond the mean-field approximation," Phys. Rev. E 70, 015603 (2004). [CrossRef]
- S. A. Ponomarenko and G. P. Agrawal "Asymmetric incoherent vector solitons," Phys. Rev. E 69, 036604 (2004). [CrossRef]
- Ting-Sen Ku, Ming-Feng Shih, A. A. Sukhorukov, and Y. S. Kivshar "Coherence controlled soliton interactions,"Phys. Rev. Lett. 94, 063904 (2005). [CrossRef] [PubMed]
- K. G. Makris, H. Sarkissian, D. N. Christodoulides, and G. Assanto "Nonlocal incoherent spatial solitons in liquid crystals," J. Opt. Soc. Am. B 22, 1371-1377 (2005). [CrossRef]
- D. Anderson, L. Helczynski-Wolf, M. Lisak, and V. Semenov, "Features of modulational instability of partially coherent light: Importance of the incoherence spectrum," Phys. Rev. E 69, 025601 (2004). [CrossRef]
- L. Helczynski, M. Lisak, and D. Anderson "Influence of higher-order dispersion on modulational instability and pulse broadening of partially incoherent light," Phys. Rev. E 67, 026602 (2003). [CrossRef]
- S. B. Cavalcanti, G. P. Agrawal, and M. Yu, "Noise amplification in dispersive nonlinear media," Phys. Rev. A 51, 4086 (1995). [CrossRef] [PubMed]
- A. Mussot, E. Lantz, H. Maillotte, T. Sylvestre, C. Finot, and S. Pitois, "Spectral broadening of a partially coherent CW laser beam in single-mode optical fibers," Opt. Exp. 12, 2838 (2004). [CrossRef]
- R. Z. Sagdeev, D. A. Usikov, and G. M. Zaslavsky, "Nonlinear Physics" (Harwood Academic Publ., Chur, Switzerland, 1988).
- S. Lagrange, H. R. Jauslin, and A. Picozzi, "Thermalization of the dispersive three-wave interaction" (submitted).
- C. Conti, S. Trillo, P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, and J. Trull, "Nonlinear Electromagnetic X-Waves," Phys. Rev. Lett. 90, 170406 (2003). [CrossRef] [PubMed]
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