Solitons in Nonlocal Media

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1.5 Spatial Solitons in Nematic Liquid Crystals field: its purpose was to set an initial angle between the director and the beam wavevec- tor 1 (73), helping soliton formation. They demonstrated nonlocal interactions between solitons (74) and the propagation of incoherent solitons (75) (see section 1.4.4). More- over, they utilized soliton-soliton interactions to demonstrate all-optical logic gates (76). Theoretically, they developed a general model for spatial solitons in liquid crys- talline media (30), demonstrating how nonlocality in NLC can be changed by altering some experimental parameter [see also (73; 77)], and proving, both experimentally and theoretically, the existence of accessible solitons (51). Finally, the steering of spatial solitons was demonstrated by changing the applied voltage in NLC cells where the walk-off is directly observable (47). Such configuration can be used in optical demultiplexers driven by voltage, e.g. reconfigurable all-optical networks. This geometry will be analyzed in more details in the next chapter, as some of its features was studied as part of this thesis. 1 Nonlinearity maximization corresponds to choose an initial angle equal to π/4. 14
2 Scalar Solitons in Nematic Liquid Crystals 2.1 Cell Geometry Let me consider the NLC planar cell shown in fig. 2.1. Two glass slides, defining the plane yz, are separated by a = 100µm by means of mylar spacers, and confine the liquid crystal E7 for capillarity. The internal interfaces are treated to force planar anchoring of the molecules in the yz plane, with a pre-tilt of 2 ◦ along x to give a preferential orientation to the NLC molecules, and avoid bulk disclinations (58). To control the director distribution at the discontinuity air-NLC 1 an input interface composed by a third slide was placed parallel to the plane xy, and suitably rubbed. The planar anchoring at the input interface is such that the director ˆn belongs to the plane xy and, furthermore, determines the molecular alignment at π/4 with respect to both x and y. A low-frequency bias V, 2 applied via two transparent Indium Tin Oxide electrodes (fig. 2.1), is used to change the director distribution in the absence of optical excitation, hence varying the medium properties. In the absence of an external bias (V = 0), the NLC director ˆn in bulk lies in the plane yz (neglecting the pre-tilt angle which is small) at π/4 with respect to ˆz, with ˆn · ˆy > 0 and ˆn · ˆz > 0. As discussed in detail below, such configuration allows the direct observation of walk-off, at variance with the geometry previously used (see section 1.5). 1.4.4). 1 Without the interface there would be a meniscus. 2 Frequency is chosen so that the NLC molecules respond only to temporally averaged voltages (see 15
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 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
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(a) Equivalent potential Veq(〈ξ
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W NL 0 = ǫak0 2ne cos δ cos[2(θ0
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3.4 Soliton Oscillations in a Finit
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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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