Solitons in Nonlocal Media

More documents

Recommendations

Info

List of Figures 1.1 (a) In the isotropic phase the molecules are positioned without long range order. (b) In nematics the molecules have no positional order, but have an orientational order. The molecular mean axis at each point is expressed by a vectorial field ˆn called director. . . . . . . . . . . . . . . 8 1.2 Typical dimensions of a 5CB molecule (a) and chemical structure (b). . 8 1.3 Spherical reference system. Axis z is directed as the director ˆn. . . . . . 9 1.4 (a) In absence of external electric fields the director lies on the plane yz, forming an angle θ0 with ˆz. (b) When an electric field is applied parallel to ˆy, a dipole is induced in the molecules, which rotates towards the electric field in order to minimize their energy. The equilibrium angle θ is reached when the total torque acting on molecules becomes null. I note how rotations take place in a plane defined by the excitation geometry. 12 2.1 Sketch of the NLC sample: (a) side view, (b) top view, (c) front view. Voltage at 1kHz is applied along x via two transparent electrodes de- posited onto the glass slides that define the yz plane. ITO stands for Indium Tin Oxide. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 2.2 (a) Experimental set-up. (b) Input field E and its polarization in the plane xy at z = 0. i.e. at the interface between air and NLC. Sign convention is such that β shown in the figure is positive. . . . . . . . . . 17 2.3 Director ˆn and the two angles ξ and γ used to describe its orientation in space. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 vii
LIST OF FIGURES 2.4 Reorientation angle ξ [fig. 2.4(a)] and electrostatic potential V [fig. 2.4(b)] inside the cell for applied voltages ranging from 0 to 4.5V . In fig. 2.4(c) is plotted the maximum angle ξ, labeled ξmax, versus applied voltage V. From fig. 2.4(a) ξmax is always placed in x ′ = a/2, as predictable given problem symmetry. . . . . . . . . . . . . . . . . . . . . . . . . . . 20 2.5 (a) Acquired optical field distribution when input beam excites both e and o components. The Poynting vector of the ordinary wave is parallel to z, while the extraordinary one bends towards larger y due to walk- off. The power is low and the extraordinary wave does not induce any nonlinear effects. (b) Input polarization angle β versus applied voltage V. The solid (dashed) line from the model represents the optimum angle β that allows all the injected power to be transferred to an e (o) wave in bulk NLC (z > d). Such an angle remains fixed at 45 ◦ (135 ◦ ) as the bias varies. Symbols are measured data, from linear (20mW; squares) to nonlinear (3mW; stars) regimes. . . . . . . . . . . . . . . . . . . . . . 21 2.6 Ordinary propagation in the cell. . . . . . . . . . . . . . . . . . . . . . . 22 2.7 Extraordinary Poynting vector Se. . . . . . . . . . . . . . . . . . . . . . 22 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, re- spectively. (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 2.9 (a) Linear diffraction. (b) Soliton propagation. Blue arrows represent the NLC director. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 2.10 Extraordinary-wave propagation in a NLC cell for V = 0: beams are launched in x = a/2 and impinge normally to the input interface. . . . . 29 2.11 NLC E7: refractive indices n = √ ǫ (black curve) and n⊥ = √ ǫ⊥ (red curve) versus vacuum wavelength λ. Dots are experimental values, lines are interpolations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 viii
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 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

Create successful ePaper yourself

Delete template?

Save as template?