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Dynamics of hexagonal patterns in a self-focusing Kerr cavity
1Instituto de Física Interdisciplinar y Systemas Complejos (IFISC, CSIC-UIB), Campus Universitat Illes Balears, E-07122 Palma de Mallorca, Spain. damia@imedea.uib.es
Summary
This study analyzes secondary bifurcations in nonlinear optics hexagonal patterns. We identify various instabilities and bifurcations based on wave number, revealing typical scenarios in self-focusing systems.
Area of Science:
- Nonlinear Optics
- Pattern Formation
- Mathematical Physics
Background:
- Hexagonal patterns are common in nonlinear optical systems.
- Understanding pattern stability is crucial for controlling optical phenomena.
- Secondary bifurcations can lead to complex dynamic behaviors.
Purpose of the Study:
- To analyze secondary bifurcations of stationary hexagonal patterns.
- To investigate the linear stability of these patterns across different wave numbers.
- To characterize the types of instabilities and bifurcations that occur.
Main Methods:
- Numerical computation of hexagonal pattern solutions.
- Linear stability analysis using Bloch analysis.
- Investigation of patterns with all allowed wave numbers.
Main Results:
- Computed hexagonal pattern solutions for all allowed wave numbers.
- Identified phase instabilities.
- Observed stationary and oscillatory amplitude instabilities.
- Detected oscillatory finite wavelength bifurcations.
- Demonstrated a typical bifurcation scenario in self-focusing systems.
Conclusions:
- Secondary bifurcations lead to diverse instabilities in hexagonal patterns.
- The wave number of the pattern dictates the type of instability observed.
- Results provide insights into pattern dynamics in nonlinear optical systems.
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