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Spiral patterns, spiral breakup, and zigzag spirals in an optical device
Martine Le Berre1, Elisabeth Ressayre, Andrée Tallet
1Laboratoire de Photophysique du CNRS, Bâtiment 210, Université de Paris-Sud, 91405-Orsay, Cedex, France.
Summary
This study reveals complex patterns in optical parametric oscillators. Hopf and Turing instabilities create novel spiral and turbulent structures, advancing understanding of nonlinear optics.
Area of Science:
- Nonlinear Optics
- Complex Systems Dynamics
Background:
- Degenerate optical parametric oscillators (OPOs) with saturable absorbers are complex nonlinear systems.
- Understanding pattern formation in such systems is crucial for controlling light properties.
Purpose of the Study:
- To investigate the instabilities and pattern formation in a degenerate OPO with a saturable absorber.
- To analyze the emergence of spiral and turbulent patterns above lasing thresholds.
Main Methods:
- Numerical simulations of the full OPO equations.
- Derivation of a normal form near the Hopf threshold.
- Analysis of pattern formation driven by a bi-Laplacian term in a complex Ginzburg-Landau equation.
Main Results:
- Successive Hopf and Turing instabilities observed above the lasing threshold.
- Formation of various spiral patterns and defect turbulent patterns.
- Destabilization of spirals into smaller structures and emergence of a new spiral pattern with notched arms at higher thresholds.
Conclusions:
- The interplay of Hopf and Turing instabilities leads to rich pattern dynamics in degenerate OPOs.
- A normal form analysis accurately predicts spiral formation driven by a bi-Laplacian term.
- Complex spatio-temporal patterns emerge from the nonlinear interactions within the OPO system.