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Computationally determined existence and stability of transverse structures. I. Periodic optical patterns
G K Harkness1, W J Firth, G-L Oppo
1Department of Physics, University of Strathclyde, 107 Rottenrow, Glasgow G4 ONG, Scotland.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|November 22, 2002
Summary
We developed a computer-assisted Fourier-transform technique to find stationary solutions in optical cavities. This method identifies stable patterns and their instability mechanisms, useful for understanding complex optical phenomena.
Area of Science:
- Nonlinear optics
- Pattern formation in optical systems
Background:
- Saturable absorbers in driven optical cavities exhibit complex spatio-temporal dynamics.
- Understanding stationary solutions and their stability is crucial for controlling optical patterns.
Purpose of the Study:
- To present a novel Fourier-transform based, computer-assisted technique for analyzing stationary solutions in driven optical cavities.
- To illustrate the method's capability in identifying and characterizing pattern solutions, including hexagonal and roll patterns.
Main Methods:
- Utilizing a Fourier-transform based numerical approach.
- Analyzing solutions as a function of wave number and input pump.
- Determining the domain of stability (Busse balloon) for identified patterns.
Main Results:
- Successfully found essentially exact hexagonal and roll stationary solutions.
- Demonstrated the method's applicability across varying wave numbers and input pump levels.
- Observed pattern phenomena such as cracking and shrinking patches in specific parameter regions.
Conclusions:
- The presented computer-assisted technique is widely applicable for finding and analyzing stationary solutions in optical systems.
- The method provides insights into pattern stability and the underlying mechanisms of instability.
- This approach aids in understanding and potentially controlling complex optical pattern formation.