Chapter 1 BASIC THEORY

1.1 The paraxial wave equation

1.2 Susceptibilities in atomic vapors

REFERENCES

Chapter 2 SPATIAL LIGHT CONTROL

2.1 Photonic topological insulators in atomic ensembles

2.1.1 Theoretical model

2.1.2 Refractive index change

2.1.3 Topology of the photonic band gap structure

2.1.4 Photonic Floquet topological insulator

2.1.5 Discussion

2.1.6 Summary

Appendix Ⅰ:Band structure of a honeycomb lattice-the tight-binding method

AⅠ.1 Full band structure

AⅠ.2 Strained band structure

Appendix Ⅱ:Band structure of a honeycomb lattice-the plane-wave expansion method

2.2 Talbot effect of multi-wave mixings

2.2.1 Theoretical model and analysis

2.2.2 Suppression and enhancement conditions

2.2.3 Talbot effect of multi-wave mixing signals

2.2.4 Summary

2.3 Nonlinear Talbot effect from rogue waves

2.3.1 Basic rogue wave solutions

2.3.2 One-dimensional case

2.3.3 Two-dimensional case-linear Talbot effect

2.3.4 Two-dimensional case-nonlinear Talbot effect

2.3.5 Summary

2.4 Beam splitter and combiner based on Bloch oscillations

2.4.1 Waveguide array with m≤0 members modulated

2.4.2 Beam splitter based on the V-type modulated waveguide array

2.4.3 Beam combiner based on the ？-type modulated waveguide array

2.4.4 Summary

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Chapter 3 NONLINEARITY-INDUCED SPATIAL MODULATION

3.1 Introduction

3.2 Optical vortices induced in atomic vapors

3.2.1 Theoretical model

3.2.2 Simple vortex and necklace incidence

3.2.3 Azimuthon incidence

3.2.4 The enhancement region

3.2.5 The liquid-like behavior of light and potential experiment

3.2.6 Summary

3.3 Interactions between incoherent solitons

3.3.1 Theoretical model

3.3.2 Numerical simulations and discussions

3.3.3 Summary

3.4 Azimuthons in weakly nonlinear waveguides

3.4.1 Theoretical model

3.4.2 Rotating localized dipoles

3.4.3 Rotating higher order localized modes

3.4.4 Summary

REFERENCES

Chapter 4 SPATIAL CONTROL OF NOVEL LIGHT BEAMS

4.1 Introduction

4.2 Interactions between Airy beams

4.2.1 Theoretical model

4.2.2 Interactions of Airy beams

4.2.3 Interactions of nonlinear accelerating beams

4.2.4 Interactions of different accelerating beams

4.2.5 Summary

4.3 Airy beams with initial velocity

4.3.1 One-dimensional case

4.3.2 Two-dimensional case

4.3.3 A little discussion

4.3.4 Summary

4.4 Dual accelerating Airy-Talbot recurrence effect

4.4.1 Theoretical model

4.4.2 Numerical simulations

4.4.3 Superposition of finite-energy Airy beams

4.4.4 Summary

4.5 Nonparaxial self-accelerating beams

4.5.1 Theoretical model

4.5.2 Mathieu beams

4.5.3 Weber beams

4.5.4 Fresnel integrals

4.5.5 Summary

4.6 Fresnel diffraction patterns as self-accelerating beams

4.6.1 One-dimensional case

4.6.2 Two-dimensional case

4.6.3 Summary

4.7 Spatial control of light due to harmonic potential

4.7.1 Theoretical model

4.7.2 Solutions and numerical simulations

4.7.3 Chirped finite energy Airy beams

4.7.4 Two-dimensional Airy beams

4.7.5 Two-dimensional case-the rotating light

4.7.6 Summary

4.8 Self-Fourier beams

4.8.1 Theoretical model

4.8.2 Discussion

4.8.3 Analytical solutions

4.8.4 Self-Fourier beams

4.8.5 Summary

4.9 Spatial control in a fractional Schr？dinger equation

4.9.1 Theoretical model

4.9.2 One-dimensional case

4.9.3 Two-dimensional case

4.9.4 Summary

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Chapter 5 CONCLUSION AND OUTLOOK

5.1 Summary

5.2 Outlook

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