Solitons in Nonlocal Media

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2.4 Soliton Observation to the Freedericksz transition, nonlinearity does not take place at the mW excitations normally employed for solitons. An example is shown in fig. 2.6. Figure 2.6: Ordinary propagation in the cell. Instead, when the extraordinary polarization is excited, the Poynting vector Se is in general not parallel to z. To a first approximation, in order to find Se, I can treat the beam as a plane wave 1 , which propagates in a homogeneous uniaxial medium with the optical axis given by director in x = a/2. Thus, I consider a director as in fig. 2.3, but with ξ = ξmax (which depends on the applied bias, see section 2.3). The vector Se, in general, does not lie on plane yz, as in fig. 2.7. Since in the experiments I observe the beam projection on the plane yz, I introduce α as the angle between the axis z and the projection of Se on the plane yz (fig. 2.7); I call it apparent walk- off (47), given by (79) α = arctan(tanδ cos ϕ), where ϕ = arctan is the angle between ˆy and the tan ξmax cos γ projection of ˆn on the plane xy (see fig. 2.3) and δ is the walk-off defined in section 1.4.3: in this case θ = arctan . The relation between V and α 1 cos ϕ tan γ (the information obtained from experiments) is shown in fig. 2.8(b). The acquired trajectories of e-beam in the plane yz are almost straight lines. Straight lines interpolations of the acquired trajectories in the Figure 2.7: Extraordinary Poynting vector Se. observation plane yz are shown in fig. 2.8(a). Note how the beam slightly oscillates around the straight lines, this effect being stronger for intermediate V: this is due to 1 The validity of such approach for small perturbations is discussed in section 2.5. 22
(a) Soliton trajectories in the plane yz for var- ious V. 2.4 Soliton Observation (b) Apparent walk-off angle α versus V. (c) Acquired solitons for V = 0V and V = 2V , respectively. Figure 2.8: (a) Soliton trajectories in the plane yz: dashed and solid lines are interpolating straight lines and actual beam trajectories in the plane yz, respectively. (b) Apparent walk-off α versus applied bias V: error bars are experimental data (from the slopes of the interpolating lines), whereas the solid line is the theoretical prediction. (c) Experimental images of solitons for V = 0V and V = 2V . The soliton width is narrower in the first case due to the stronger nonlinearity. 23
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 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
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4.2 Cell Geometry and Basic Equatio
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4.3 Highly Nonlocal Limit about 2mW
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4.3 Highly Nonlocal Limit (a) Initi
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4.3 Highly Nonlocal Limit Figure 4.
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(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
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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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