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Spectral principle for frequency synchronization in repulsive laser networks and beyond
Mostafa Honari-Latifpour1,2, Jiajie Ding1,2, Igor Belykh3
1Department of Physics, Queens College, City University of New York, New York, New York 11367, USA.
Chaos (Woodbury, N.Y.)
|February 3, 2025
Summary
Network topology significantly impacts laser frequency synchronization. Repulsive coupling networks show that specific topologies like bipartite networks optimize synchronization, unlike local rings or all-to-all networks.
Area of Science:
- Nonlinear dynamics
- Optical engineering
- Network science
Background:
- Laser synchronization is crucial for high-power output and optical computing.
- The influence of network topology on laser frequency synchronization is not well understood.
Purpose of the Study:
- Investigate the role of network topology in frequency synchronization for heterogeneous laser model oscillators with repulsive coupling.
- Develop a predictive principle for synchronization onset based on spectral properties.
Main Methods:
- Formulated a complex matrix combining a signless Laplacian (repulsive coupling) and intrinsic frequency detuning.
- Analyzed the spectral properties, specifically the gap between the two smallest eigenvalues, of this complex matrix.
- Compared synchronization behavior across different network topologies (local rings, all-to-all, bipartite).
Main Results:
- A general approximate principle for predicting frequency synchronization onset was discovered.
- The eigenvalue gap of the complex matrix generally dictates the coupling threshold for synchronization.
- Local rings and all-to-all networks hinder synchronization, while full bipartite networks exhibit optimal synchronization properties.
- The spectral principle was extended to repulsive Kuramoto networks.
Conclusions:
- Network topology plays a critical role in achieving frequency synchronization in repulsive coupling systems.
- Full bipartite networks are optimal for laser synchronization, offering design guidelines.
- The spectral principle provides a powerful tool for predicting and optimizing synchronization in optical oscillator networks.
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