Identifying and Anticipating the Threshold Bifurcation of a Complex Laser with Permutation Entropy

Area of Science:

• Nonlinear dynamics
• Optical engineering
• Statistical physics

Background:

• Permutation entropy (PE) is a measure of signal complexity.
• Complex lasers exhibit mode competition near the lasing threshold.
• Identifying bifurcation points is crucial for understanding system dynamics.

Purpose of the Study:

• To investigate the efficacy of permutation entropy (PE) in identifying and anticipating the threshold bifurcation of a complex laser.
• To compare PE's performance with standard quantifiers like lag-1 autocorrelation.

Main Methods:

• Utilizing an experimental setup with a long cavity round-trip time relative to detection system resolution.
• High statistical sampling of laser intensity dynamics per round trip.
• Calculating permutation entropy (PE) and lag-1 autocorrelation for signals below and at the threshold.

Main Results:

• Permutation entropy (PE) shows a distinct decrease significantly below the lasing threshold.
• PE reaches a sharp minimum precisely at the threshold bifurcation point.
• This minimum in PE corresponds to an abrupt increase in temporal correlations.
• Compared to lag-1 autocorrelation, which gradually increases, PE exhibits a steeper decrease, highlighting nonlinear correlations.

Conclusions:

• Permutation entropy (PE) is a sensitive indicator for detecting threshold bifurcations in complex laser systems.
• The sharp decrease in PE effectively captures the emergence of nonlinear correlations at the bifurcation point.
• PE provides a clearer and more sensitive method for identifying the lasing threshold compared to traditional methods.