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Correlation sum scalings from mixed-mode oscillations in weakly coupled molecular lasers

Eusebius J Doedel¹, Carlos L Pando Lambruschini²

¹Department of Computer Science, Concordia University, 1455 boulevard de Maisonneuve O., Montréal, Québec H3G 1M8, Canada.

Chaos (Woodbury, N.Y.)

|September 1, 2022

Summary

Investigating coupled lasers reveals that resonance overlap explains dynamical transitions in chaotic regimes. This finding impacts understanding laser synchronization and scaling behaviors.

Area of Science:

Nonlinear dynamics
Laser physics
Chaos theory

Background:

Mixed-mode oscillations occur in uncoupled lasers.
Coupled laser systems exhibit complex dynamics.

Purpose of the Study:

To investigate a model of two symmetrically coupled lasers.
To explain dynamical transitions in the chaotic regime using resonance overlap.
To analyze the dependence of scaling regions on optical coupling strength.

Main Methods:

Analysis of time series data.
Investigation of resonance overlap phenomena (N:N+1 and N:N resonances).
Calculation of dimension correlation sums.

Main Results:

Resonance overlap explains dynamical transitions in chaotic regimes.
Two distinct scaling regions in the dimension correlation sum were identified, dependent on optical coupling strength.
For small coupling, scaling regions resemble those of uncoupled lasers.
For larger coupling (below synchronization), steeper scaling regions emerge, especially in smaller partitions.

Conclusions:

Resonance overlap is a key mechanism for understanding dynamical transitions in coupled chaotic lasers.
The optical coupling strength significantly influences the observed scaling behaviors.
This study provides insights into the route to synchronization in coupled laser systems.

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