Solitons in Nonlocal Media

More documents

Recommendations

Info

CONTENTS 4.3.3 Soliton Trajectory . . . . . . . . . . . . . . . . . . . . . . . . . . 77 4.3.4 Solution for Initially Overlapping Beams . . . . . . . . . . . . . . 79 4.4 Breathing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 4.4.1 Coupling Geometry . . . . . . . . . . . . . . . . . . . . . . . . . 83 4.4.2 Comparison Between Numerical Simulations and Experimental Observations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 5 Dissipative Self-Confined Optical Beams in Doped Nematic Liquid Crystals 88 5.1 Gain and Solitary Waves Propagation . . . . . . . . . . . . . . . . . . . 88 5.2 Light Self-Confinement in Dye Doped Nematic Liquid Crystals: Model . 89 5.3 Constant Optical Amplification . . . . . . . . . . . . . . . . . . . . . . . 91 5.4 Role of Gain Saturation . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 5.4.1 Mechanism for Dye Luminescence: a Simple Model . . . . . . . . 92 5.4.2 Gain Saturation: Numerical Analysis . . . . . . . . . . . . . . . . 97 5.5 Role of the Pump Profile . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 5.6 Co-Propagating Pump . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 6 Conclusions 101 A Optical Properties of NLC 102 A.1 Scattering in a NLC Cell . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 A.2 Derivation of the Electromagnetic Ruling Equation in NLC . . . . . . . 104 B Numerical Algorithm 108 B.1 Simulations of Nonlinear Optical Propagation in NLC . . . . . . . . . . 108 B.1.1 Optical Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 B.1.2 Reorientational Equation . . . . . . . . . . . . . . . . . . . . . . 110 C Analysis of the Index Perturbation Profile 112 C.1 FWHM Computation for the Nonlinear Index Perturbation . . . . . . . 112 C.2 Computation of V υ m(υ) in the Gaussian Case . . . . . . . . . . . . . . . . 113 C.3 Computation of V ξ m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114 C.4 Computation of V υ m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116 C.5 Force in the Poisson 2D for Small Displacements . . . . . . . . . . . . . 117 v
CONTENTS D List of Publications 118 D.1 Journal Papers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118 D.2 Conference Papers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 References 121 vi
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 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 48 and 49: shape Ee ∝ exp − (x−a/2)2 +t
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 140 and 141:
D.2 Conference Papers M. Peccianti,
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?