Solitons in Nonlocal Media

More documents

Recommendations

Info

D.2 Conference Papers M. Peccianti, A. Alberucci, and G. Assanto; Nonlinear bouncing of nematicons at the boundaries; LEOS Winter Top. 2008 Nonlinear Photonics, Sorrento (Italy), Jan. 14-16, 2008 120
References [1] E. Fermi, J. Pasta, and S. Ulam, “Studies of non linear problems,” Los Alamos National Laboratory, Technical Report, 1955. 1 [2] E. Segré, Collected Papers of Enrico Fermi. Chicago: University of Chicago Press, 1965. 1 [3] E. N. Lorenz, “Deterministic nonperiodic flow,” J. Atmos. Sci., vol. 20, pp. 130– 141, 1963. 1 [4] C. S. Gardner, J. M. Greene, M. D. Kruskal, and R. M. Miura, “Method for solving the korteweg-devries equation,” Phys. Rev. Lett., vol. 19, no. 19, pp. 1095–1097, Nov 1967. 1 [5] S. Trillo and W. E. Torruellas, Spatial Solitons. Berlin: Springer-Verlag, 2001. 2, 3 [6] Y. S. Kivshar and G. P. Agrawal, Optical Solitons. San Diego, CA: Academic, 2003. 2, 3, 5, 72 [7] J. S. Russell, “Report on waves,” in Report of the fourteenth meeting of the British Association for the Advancement of Science, York, September 1844 (Lon- don 1845), 1844, pp. 311–390. 2 [8] D. J. Korteweg and F. D. Vries, “On the change of form of long waves advancing in a rectangular canal, and on a new type of long stationary waves,” Philosophical Magazine, vol. 39, pp. 422–443, 1895. 2 [9] N. J. Zabusky and M. D. Kruskal, “Interaction of ”solitons” in a collisionless plasma and the recurrence of initial states,” Phys. Rev. Lett., vol. 15, no. 6, pp. 240–243, Aug 1965. 2 121
Page 1:
Solitons in Nonlocal Media Alessand
Page 4 and 5:
To everybody who has supported me a
Page 6 and 7:
Contents List of Figures vii 1 Intr
Page 8 and 9:
CONTENTS 4.3.3 Soliton Trajectory .
Page 10 and 11:
List of Figures 1.1 (a) In the isot
Page 12 and 13:
LIST OF FIGURES 2.12 Numerical resu
Page 14 and 15:
LIST OF FIGURES 3.7 As in fig. 3.6,
Page 16 and 17:
LIST OF FIGURES 3.14 (a) 3D sketch
Page 18 and 19:
LIST OF FIGURES 4.7 Left column: ac
Page 20 and 21:
LIST OF FIGURES C.1 Plot of V υ m(
Page 22 and 23:
1.2 Optical Solitons cialized liter
Page 24 and 25:
1.3 Nonlocality width 1 . Nonlocali
Page 26 and 27:
1.3 Nonlocality ∆n(x) = I(x ′
Page 28 and 29:
(a) Isotropic phase (b) Nematic pha
Page 30 and 31:
1.4 Liquid Crystals interaction ene
Page 32 and 33:
(a) E = 0 (b) E = 0 1.4 Liquid Crys
Page 34 and 35:
1.5 Spatial Solitons in Nematic Liq
Page 36 and 37:
2.2 Set-Up Figure 2.1: Sketch of th
Page 38 and 39:
Φ = ⎛ ⎜ ⎝ Ex Hy Ey −Hx ⎞
Page 40 and 41:
(a) Reorientation angle versus x
Page 42 and 43:
2.4 Soliton Observation to the Free
Page 44 and 45:
2.5 Theory of Nonlinear Optical Pro
Page 46 and 47:
Page 48 and 49:
shape Ee ∝ exp − (x−a/2)2 +t
Page 50 and 51:
Page 52 and 53:
Page 54 and 55:
Page 56 and 57:
3 Nonlocality and Soliton Propagati
Page 58 and 59:
3.1 Definition 2 √ ln2w x/t; more
Page 60 and 61:
3.2 Role of the Boundary Conditions
Page 62 and 63:
Page 64 and 65:
Page 66 and 67:
Page 68 and 69:
Page 70 and 71:
Page 72 and 73:
Page 74 and 75:
Page 76 and 77:
Page 78 and 79:
3.3 Soliton Trajectory 3.3.1 Genera
Page 80 and 81:
x = 〈x〉, 3.3 Soliton Trajectory
Page 82 and 83:
3.3.3 Highly Nonlocal Case 3.4 Soli
Page 84 and 85:
3.4 Soliton Oscillations in a Finit
Page 86 and 87:
(a) Equivalent potential Veq(〈ξ
Page 88 and 89:
W NL 0 = ǫak0 2ne cos δ cos[2(θ0
Page 90 and 91: 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 142 and 143: REFERENCES [10] Y. Nakamura and I.
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
show all

Solitons in Nonlocal Media

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?