Waves, Solitons and Turbulence in Optical Systems - Abstract
Kane, Deb
There is a large research literature on fractal dimensions of various sorts that can be used to give dimensional information about a nonlinear dynamical system. Correlation dimension (CD) is the measure most applicable to time series data such as the output power time series from a nonlinear laser system. We have been researching calculation of CD using output power time series from experimental nonlinear laser systems for about ten years. CD calculation is sensitive to noise and can fail because the signal to noise ratio of the experimental time series data is too low. Even when the signal to noise ratio is sufficiently high for a robust CD calculation to be completed there are several claims in the literature that CD only can be calculated successfully for low dimensional systems – CD less than 3. Our research is broadly in agreement with this, but we also conclude that there are useful insights about the system that can be gleaned from the details of the steps in the calculation. This will be illustrated by presenting and contrasting calculations of CD for time series from three different nonlinear laser systems; which when combined with analysis of tailored, ideal simulated time series data leads to useful meaning from CD calculations. Additionally, we also have a focus on generating CD maps for a broad range of the key variables in each of the nonlinear laser systems. The time series data for all the systems explored is available via an open science web database, so others can undertake their own studies using these high quality datasets.