Solitons in Nonlocal Media

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To everybody who has supported me all along this adventure.
Acknowledgements First, I would like to thank Prof. Gaetano Assanto who gave me the pos- sibility to join into his research group Nooel (Nonlinear Optics and Op- toElectronics Lab), a unique opportunity in Italy. He taught (and keeps teaching) me how to make good research and supervised all my work during my PhD course, guiding me towards important goals and providing me with a lot of precious advices. I would like to thank Dr. Marco Peccianti: we closely collaborated during the three years of my PhD; he performed the experiments I address in this thesis in chapters 3 and 4. He taught me experimental techniques and several aspects of liquid crystals, making himself always available for fruitful discussions. Special thanks to Claudio Conti, Andrea Fratalocchi, Alessia Pasquazi and Armando Piccardi, who helped me in various stages in the study of liquid crystals. I would like to thank Dr. Malgosia Kaczmarek and Dr. Andriy Dyadusha from the School of Physics and Astronomy in Southampton and Prof. Cesare Umeton, An- tonio De Luca and Giuseppe Coschigano from University of Calabria for providing samples of high quality, essential to carry out good experiments. I also thank the other people who worked in the Nooel throughout the years, both for their friendship and their scientific support; in rigorous al- phabetic order Emiliano Alberici, Armando Altieri, Michele Balbi, Mattia Cichocki, Stefano Cozza, Lorenzo Colace, Andrea Del Monte, Andrea Di Falco, Pasquale Ferrara, Giuseppe Leo, GianLorenzo Masini, Valeria Maz- zoni, Andrea Natale, Francesco Petullà, Marco Ravaro, Alessio Rocchetti, Usman Sapaev, Vito Sorianello and Salvatore Stivala. I would like to thank all my (other) friends: without their help and support reaching this goal would have been much hard. Thanks to all of you guys. Last, but not least, I would like to thank my family, who provided me all the assistance I needed to complete this important stage of my education.
Page 1: Solitons in Nonlocal Media Alessand
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 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 62 and 63:
Page 64 and 65:
Page 66 and 67:
Page 68 and 69:
Page 70 and 71:
Page 72 and 73:
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3.3 Soliton Trajectory 3.3.1 Genera
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x = 〈x〉, 3.3 Soliton Trajectory
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3.3.3 Highly Nonlocal Case 3.4 Soli
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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
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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Solitons in Nonlocal Media

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