Transverse Patterns in Nonlinear Optical Resonators

1. Front Matter

   Pages I-XIV

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2. Introduction

   Pages 1-31

3. Order Parameter Equations for Lasers

   Pages 33-49

4. Order Parameter Equations for Other Nonlinear Resonators

   Pages 51-64

5. Zero Detuning: Laser Hydrodynamics and Optical Vortices

   Pages 65-79

6. Finite Detuning: Vortex Sheets and Vortex Lattices

   Pages 81-90

7. Resonators with Curved Mirrors

   Pages 91-102

8. The Restless Vortex

   Pages 103-115

9. Domains and Spatial Solitons

   Pages 117-124

10. Subcritical Solitons I: Saturable Absorber

    Pages 125-138

11. Subcritical Solitons II: Nonlinear Resonance

    Pages 139-146

12. Phase Domains and Phase Solitons

    Pages 147-167

13. Turing Patterns in Nonlinear Optics

    Pages 169-192

14. Three-Dimensional Patterns

    Pages 193-203

15. Patterns and Noise

    Pages 205-224

16. Back Matter

    Pages 225-226

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The growth of regularity from disorder, the evolution from the simple towards the complex, and the spontaneous formation of spatio temporal patterns in general are questions which intrigue everybody. This has been one of the hasic philosophical topics from ancient to modern times. Is nature able to create something fundamentally new by itself? If yes, how does this creation occurs? Or does nature only reproduce something which was already encoded in it, from the very beginning? This remained a topic exclusively for philoso phers until very recently, and it was only a few decades a. go that physicists started to convert this seemingly purely philosophical subject into a scientific discipline: a scientific discipline like other scientific disciplines, where one re lies on formulas and equations, on nunlerical simulations, and on laboratory experiments. This book is not about general questions related to pattern formation and self organization in nature. It is about spontaneous patterns in just one part of nature in nonlinear optical systems, and, more precisely, in nonlinear optical resonators. Nonlinear optical systems represent a small part of nature, hut a very representative part: one can observe here nearly all the known symmetries of patterns, one can generate nearly all known types of localized strlictlires and one can realize nearly all known spatial instabilities and spatial bifurcations.

• Nonlinear optics
• Optical vortices
• Pattern formation
• Spatial solitons
• laser
• optics

• Physikalisch-Technische Bundesanstalt Braunschweig, Braunschweig, Germany

  Kçstutis Staliūnas

• Department of Applied Physics Escuela Politécnica Superior de Gandía, Universidad Politécnica de Valencia, Grao de Gandía, Spain

  Victor J. Sánchez-Morcillo

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