Insights on correlation dimension from dynamics mapping of three experimental nonlinear laser systems

Area of Science:

• Nonlinear Dynamics
• Laser Physics
• Data Analysis

Background:

• Analyzed large datasets from three distinct laser systems (photonic integrated chip semiconductor laser, external cavity semiconductor laser, solid-state laser).
• Investigated laser outputs including constant, periodic, pulsed, and chaotic behaviors under varying parameters.
• Systems represent general experimental nonlinear systems with systematically varying complexity.

Purpose of the Study:

• Introduce a novel semi-automatic procedure for calculating correlation dimension (CD) from experimental laser time series.
• Develop the 'minimum gradient detection algorithm' for interrogating nonlinear system dynamics.
• Enhance the analysis of complex dynamical systems using large datasets.

Main Methods:

• Implemented the 'minimum gradient detection algorithm' based on the Grassberger-Proccacia algorithm.
• Applied the procedure to tens of thousands of time series from three laser systems.
• Mapped CD results across extended parameter spaces to classify dynamical outputs.

Main Results:

• Achieved robust correlation dimension measurements for numerous laser time series.
• Confidently identified regions of low CD (< 3) across all three laser systems.
• Successfully differentiated high-complexity chaos and dynamic noise from technical noise in laser outputs, a first for CD analysis.

Conclusions:

• Interrogating systems in a mapping context provides more CD information than isolated time series analysis.
• The CD/minimum gradient algorithm is valuable for analyzing large datasets in nonlinear science.
• This approach complements other complexity measures like permutation entropy and conventional physical measurements.