Solitons in Nonlocal Media

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4.4 Breathing as explained in section 4.4.1, and the propagation is investigated by acquiring the scattered light through the cell top by means of a microscope and a CCD camera. The light behavior at both wavelengths is monitored but, in order to prevent chromatic distortions due to the microscope, the infrared component is filtered out; for this reason I present only images of the visible component at 633nm. Additional optics are arranged such that both beams have equal Rayleigh lengths of 60µm, so that diffraction lengths are similar. The corresponding minimum waists are 2.8 and 3.7µm for red and IR, respectively. The soliton propagation distance is nearly twenty times the diffraction length. Firstly, the linear behavior is investigated, i.e., when each beam diffracts either in the absence of the second one or in the presence of negligible XPM; then both components are launched to exploit XPM and generate a VS thanks to the combined effect. I report the experimental photographs in fig. 4.6 in the plane ts. In the first plot of fig. 4.6 a 1.2 mW IR beam is launched , together with a low-power red beam (a power of 0.1mW, i.e. a negligible contribution to reorientation dynamics) is used as a probe to scan the index well induced by the IR 1 . The IR beam is unable to self-localize, as the red probe diffracts. The second panel of fig. 4.6 displays the case of a 0.4mW red beam launched alone: self-focusing does not occur and beam diffracts. Instead, when 1.2mW IR and 0.4mW red beams are injected together, as in the last panel of fig. 4.6, the nonlinear response is enhanced through incoherent XPM and supports a self-localized wave, i.e., a two-color vector soliton. The white contour lines in fig. 4.6 are the simulation results. Owing to the actual experimental limitations (that include the use of a non-achromatic lens, wavelength dependent Fresnel reflections and scattering, the presence of a inhomogeneous NLC transition layer in 0 < z < 100µm), in the simulations I implement a phase-front curvature for the input beams and assume unequal coupling coefficient at the two wavelengths. To investigate the breathing of these multicomponent beams, both red and IR input powers Pred and PIR are varied, respectively, while keeping the launch conditions (Rayleigh length, tilt, polarization) fixed. Figure 4.7 (left column) shows the 1 I remind that shorter wavelengths are better confined than longer ones: this means that, assuming that both beams undergo the same index profile, red diffraction implies IR diffraction as well. In fact, given the better coupling with NLC molecules, the red index well is even deeper than the IR one for a given director distribution. 84
4.4 Breathing Figure 4.6: Color-coded acquired intensity profiles for red light in the plane ts (i.e. after a rotation by δ). Contour maps of the calculated intensity distributions are superimposed (white lines) to the experimental data. (a) A weak 0.1mW red beam is co-launched with a 1.2mW IR beam; (b) a 0.4mW red beam is injected in the absence of IR; (c) 0.4mW red and 1.2mW IR beams are co-launched and generate a vector soliton. The simulations were carried out taking effective input coupling efficiency of 40% and 50% for red and IR and initial beam curvatures of radius -130 m (waist in z = −40µm), respectively. 85
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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
Page 44 and 45:
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 52 and 53:
Page 54 and 55: 2.5 Theory of Nonlinear Optical Pro
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 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 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
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