Solitons in Nonlocal Media

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2.5 Theory of Nonlinear Optical Propagation in NLC Figure 2.13: Plot of It on the plane ts for win = 3.5µm and P = 0.1 (a), 1 (b) and 3mW(c). In the first case beam linearly diffracts, whereas in the other two cases solitary propagation takes place. Wavelength is equal to 633nm. the found value into eq. (2.20) and compute the corresponding θ distribution. I iterate the procedure until self-consistency is achieved (34; 83). Higher order solitons can be found out by simply changing the initial guess. As an example, the computed u for P = 0.5mW at λ = 633nm is shown in fig. 2.15(a and c). The angle θ is sketched in fig. 2.15(b and d): profile is asymmetric due to the different boundary conditions along the two transverse dimensions, but close to the cell center, i.e. the intensity peak position, is nearly symmetric. Consequently, the beam is nearly cylindrically symmetric, perceiving the same index well in all the transverse plane. Such property will be analytically demonstrated in the next chapter. In fig. 2.16(a-d) the numerically calculated soliton profiles for four powers are compared with Gaussian best-fits: the actual solitary shapes are almost Gaussian, in agreement with the hypothesis of high nonlocality for the NLC, with slight departures only on the tails. Another consequence of the NLC high nonlocality is that the soliton existence curve on the plane waist-power goes like P ∝ waist 2 [eq. (2.17) and fig. 2.16(e)] 32
2.5 Theory of Nonlinear Optical Propagation in NLC (a) λ = 633nm. (b) λ = 1064nm. Figure 2.14: Plots of beam waist versus input waist win and propagation coordinate s at λ = 633nm (a) and λ = 1064nm (b), for four different powers. Values reported in the colorbars are in microns. 33
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 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 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
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4.4 Breathing as explained in secti
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4.4 Breathing experimental yz evolu
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5 Dissipative Self-Confined Optical
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5.2 Light Self-Confinement in Dye D
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(a) (b) 5.4 Role of Gain Saturation
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γ [m −1 ] w t [µm] 80 40 60 40
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5.4 Role of Gain Saturation having
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5.6 Co-Propagating Pump form γ =
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(a) λ = 633nm (b) λ = 532nm 5.6 C
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Appendix A Optical Properties of NL
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A.2 Derivation of the Electromagnet
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A.2 Derivation of the Electromagnet
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Appendix B Numerical Algorithm B.1
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B.1 Simulations of Nonlinear Optica
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Appendix C Analysis of the Index Pe
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Eq. (C.7) can be expressed as V υ
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C.4 Computation of V υ m C.4 Compu
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Appendix D List of Publications D.1
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D.2 Conference Papers M. Peccianti,
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REFERENCES [10] Y. Nakamura and I.
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REFERENCES [33] N. I. Nikolov, D. N
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REFERENCES [52] ——, “Spatial
Page 148 and 149:
REFERENCES [72] M. A. Karpierz, “
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REFERENCES [93] G. Assanto and G. S
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REFERENCES [111] E. Rosencher and B
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Solitons in Nonlocal Media

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