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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.

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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.