Solitons in Nonlocal Media

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REFERENCES [10] Y. Nakamura and I. Tsukabayashi, “Observation of modified korteweg-de vries solitons in a multicomponent plasma with negative ions,” Phys. Rev. Lett., vol. 52, no. 26, pp. 2356–2359, Jun 1984. 2 [11] L. Khaykovich, F. Schreck, G. Ferrari, T. Bourdel, J. Cubizolles, L. D. Carr, Y. Castin, and C. Salomon, “Formation of a Matter-Wave Bright Soliton,” Science, vol. 296, no. 5571, pp. 1290–1293, 2002. [Online]. Available: http://www.sciencemag.org/cgi/content/abstract/296/5571/1290 2 [12] A. J. Heeger, S. Kivelson, J. R. Schrieffer, and W. P. Su, “Solitons in conducting polymers,” Rev. Mod. Phys., vol. 60, no. 3, pp. 781–850, Jul 1988. 2 [13] V. Belinski and E. Verdaguer, Gravitational solitons. Cambridge: Cambridge University Press, 2001. 2 [14] D. S. Ricketts, X. Li, and D. Ham, “A self-sustained electrical soliton oscillator,” IEEE Trans. Microwave Theor. Tech., vol. 54, pp. 373–382, 2006. 2 [15] R. W. Boyd, Nonlinear Optics. Boston: Academic Press, 1992. 2, 4, 13 [16] T. H. Maiman, “Stimulated optical radiation in ruby,” Nature, vol. 187, pp. 493– 494, 1960. 2 [17] P. A. Franken, A. E. Hill, C. W. Peters, and G. Weinreich, “Generation of optical harmonics,” Phys. Rev. Lett., vol. 7, no. 4, pp. 118–119, Aug 1961. 2 [18] R. Y. Chiao, E. Garmire, and C. H. Townes, “Self-trapping of optical beams,” Phys. Rev. Lett., vol. 13, no. 15, pp. 479–482, Oct 1964. 2, 13 [19] P. L. Kelley, “Self-focusing of optical beams,” Phys. Rev. Lett., vol. 15, no. 26, pp. 1005–1008, Dec 1965. 2 [20] A. Yariv, Ed., Optical Electronics in Modern Communications. Oxford: Oxford University Press, 1997. 2 [21] Y. S. Kivshar and B. Luther-Davies, “Dark optical solitons: physics and applications,” Physics Reports, vol. 298, pp. 81–197, 1998. 3 122
REFERENCES [22] H. A. Haus and W. S. Wong, “Solitons in optical communications,” Rev. Mod. Phys., vol. 68, no. 2, pp. 423–444, Apr 1996. 3 [23] G. I. Stegeman and M. Segev, “Optical Spatial Solitons and Their Interactions: Universality and Diversity,” Science, vol. 286, no. 5444, pp. 1518–1523, 1999. [Online]. Available: http://www.sciencemag.org/cgi/content/abstract/286/5444/1518 3 [24] G. Stegeman, D. Christodoulides, and M. Segev, “Optical spatial solitons: his- torical perspectives,” Selected Topics in Quantum Electronics, IEEE Journal of, vol. 6, no. 6, pp. 1419–1427, Nov/Dec 2000. 3 [25] H. L. Pecseli and J. J. Rasmussen, “Nonlinear electron waves in strongly magne- tized plasma,” Plasma Phys., vol. 22, p. 421, 1980. 4 [26] A. Parola, L. Salasnich, and L. Reatto, “Structure and stability of bosonic clouds: Alkali-metal atoms with negative scattering length,” Phys. Rev. A, vol. 57, no. 5, pp. R3180–R3183, May 1998. 4 [27] P. Pedri and L. Santos, “Two-dimensional bright solitons in dipolar bose-einstein condensates,” Phys. Rev. Lett., vol. 95, p. 200404, 2005. 4 [28] P. Van and T. Fulop, “Weakly nonlocal fluid mechanics - the schrodinger equation,” LONDON A, vol. 462, p. 541, 2006. [Online]. Available: http://www.citebase.org/abstract?id=oai:arXiv.org:quant-ph/0304062 4 [29] C. Conti and G. Assanto, Encyclopedia of Modern Optics. Oxford: Elsevier, 2004, vol. 5, ch. Nonlinear optics applications: Bright spatial solitons, pp. 43–55. 4 [30] C. Conti, M. Peccianti, and G. Assanto, “Route to nonlocality and observation of accessible solitons,” Phys. Rev. Lett., vol. 91, p. 073901, 2003. 4, 6, 14, 37, 47 [31] A. W. Snyder and D. J. Mitchell, “Accessible solitons,” Science, vol. 276, p. 1538, 1997. 4, 5, 6, 27, 28, 29, 34, 58, 89, 91, 98 [32] W. Krolikowski and O. Bang, “Solitons in nonlocal nonlinear media: exact solu- tions,” Phys. Rev. E, vol. 63, p. 016610, 2000. 4, 5, 7, 37 123
Page 1:
Solitons in Nonlocal Media Alessand
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To everybody who has supported me a
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Contents List of Figures vii 1 Intr
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CONTENTS 4.3.3 Soliton Trajectory .
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List of Figures 1.1 (a) In the isot
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LIST OF FIGURES 2.12 Numerical resu
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LIST OF FIGURES 3.7 As in fig. 3.6,
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LIST OF FIGURES 3.14 (a) 3D sketch
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LIST OF FIGURES 4.7 Left column: ac
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LIST OF FIGURES C.1 Plot of V υ m(
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1.2 Optical Solitons cialized liter
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1.3 Nonlocality width 1 . Nonlocali
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1.3 Nonlocality ∆n(x) = I(x ′
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(a) Isotropic phase (b) Nematic pha
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1.4 Liquid Crystals interaction ene
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(a) E = 0 (b) E = 0 1.4 Liquid Crys
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1.5 Spatial Solitons in Nematic Liq
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2.2 Set-Up Figure 2.1: Sketch of th
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Φ = ⎛ ⎜ ⎝ Ex Hy Ey −Hx ⎞
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(a) Reorientation angle versus x
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2.4 Soliton Observation to the Free
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2.5 Theory of Nonlinear Optical Pro
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Page 48 and 49:
shape Ee ∝ exp − (x−a/2)2 +t
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Page 56 and 57:
3 Nonlocality and Soliton Propagati
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3.1 Definition 2 √ ln2w x/t; more
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3.2 Role of the Boundary Conditions
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3.3 Soliton Trajectory 3.3.1 Genera
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x = 〈x〉, 3.3 Soliton Trajectory
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3.3.3 Highly Nonlocal Case 3.4 Soli
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3.4 Soliton Oscillations in a Finit
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(a) Equivalent potential Veq(〈ξ
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W NL 0 = ǫak0 2ne cos δ cos[2(θ0
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3.4 Soliton Oscillations in a Finit
Page 92 and 93: 4 Vector Solitons in Nematic Liquid
Page 94 and 95: 4.2 Cell Geometry and Basic Equatio
Page 96 and 97: 4.3 Highly Nonlocal Limit about 2mW
Page 98 and 99: 4.3 Highly Nonlocal Limit (a) Initi
Page 100 and 101: 4.3 Highly Nonlocal Limit Figure 4.
Page 102 and 103: (a) Oscillation amplitude for beam
Page 104 and 105: 4.4 Breathing as explained in secti
Page 106 and 107: 4.4 Breathing experimental yz evolu
Page 108 and 109: 5 Dissipative Self-Confined Optical
Page 110 and 111: 5.2 Light Self-Confinement in Dye D
Page 112 and 113: (a) (b) 5.4 Role of Gain Saturation
Page 114 and 115: γ [m −1 ] w t [µm] 80 40 60 40
Page 116 and 117: 5.4 Role of Gain Saturation having
Page 118 and 119: 5.6 Co-Propagating Pump form γ =
Page 120 and 121: (a) λ = 633nm (b) λ = 532nm 5.6 C
Page 122 and 123: Appendix A Optical Properties of NL
Page 124 and 125: A.2 Derivation of the Electromagnet
Page 126 and 127: A.2 Derivation of the Electromagnet
Page 128 and 129: Appendix B Numerical Algorithm B.1
Page 130 and 131: B.1 Simulations of Nonlinear Optica
Page 132 and 133: Appendix C Analysis of the Index Pe
Page 134 and 135: Eq. (C.7) can be expressed as V υ
Page 136 and 137: C.4 Computation of V υ m C.4 Compu
Page 138 and 139: Appendix D List of Publications D.1
Page 140 and 141: D.2 Conference Papers M. Peccianti,
Page 144 and 145: REFERENCES [33] N. I. Nikolov, D. N
Page 146 and 147: REFERENCES [52] ——, “Spatial
Page 148 and 149: REFERENCES [72] M. A. Karpierz, “
Page 150 and 151: REFERENCES [93] G. Assanto and G. S
Page 152: REFERENCES [111] E. Rosencher and B
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