Introduction Self-Organization in Nonlinear Optics — Kaleidoscope of Patterns

Vorontsov, Mikhail A.; Miller, Walter B.

doi:10.1007/978-3-642-60315-0_1

Cited by 2 publications

(1 citation statement)

References 48 publications

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“…This topic has already been reviewed in a number of works [2][3][4][5][6][7][8][9][10]. We treat the problem here by means of a description of the optical resonators by order parameter equations, reflecting the universal properties of optical pattern formation.…”

Section: Introductionmentioning

confidence: 99%

Transverse Patterns in Nonlinear Optical Resonators

Staliūnas

Sánchez‐Morcillo

2003

Springer Tracts in Modern Physics

175

156

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This book is devoted to the formation and dynamics of localized structures (vortices, solitons) and of extended patterns (stripes, hexagons, tilted waves) in nonlinear optical resonators such as lasers, optical parametric oscillators, and photorefractive oscillators. Theoretical analysis is performed by deriving order parameter equations, and also through numerical integration of microscopic models of the systems under investigation. Experimental observations, and possible technological implementations of transverse optical patterns are also discussed. A comparison with patterns found in other nonlinear systems, i.e. chemical, biological, and hydrodynamical systems, is given.

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Section: Introductionmentioning

confidence: 99%

Transverse Patterns in Nonlinear Optical Resonators

Staliūnas

Sánchez‐Morcillo

2003

Springer Tracts in Modern Physics

175

156

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Pulsating and Rotating Spirals in a Delayed Feedback Diffractive Nonlinear Optical System

Budzinskiy

Razgulin

2021

Int. J. Bifurcation Chaos

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We study spiral waves in a mathematical model of a nonlinear optical system with a feedback loop. Starting from a delayed scalar diffusion equation in a thin annulus with oblique derivative boundary conditions, we shrink the annulus and derive the limiting equation on a circle. Based on the explicitly constructed normal form of the Hopf bifurcation for the one-dimensional delayed scalar diffusion equation, we make predictions about the existence and stability of two-dimensional spirals that we verify in direct numerical simulations, observing pulsating and rotating spiral waves.

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Introduction Self-Organization in Nonlinear Optics — Kaleidoscope of Patterns

Cited by 2 publications

References 48 publications

Transverse Patterns in Nonlinear Optical Resonators

Transverse Patterns in Nonlinear Optical Resonators

Pulsating and Rotating Spirals in a Delayed Feedback Diffractive Nonlinear Optical System

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