Introduction

The first laser was demonstrated in 1960. It was hailed as a high-brightness, directed beam of light – the “solution without a problem”. It was pulsed – bursts of light of a short duration, spaced equally in time. A continuous wave (cw) laser, being one in which a constant amount of laser light is emitted over time, was demonstrated before the close of 1960. Today’s laser pointer is an example of such a laser. Since that time, research has delivered a plethora of laser systems which show diversity in (i) spectral content (colours), (ii) spatial distribution of the light (as is seen with the laser beam on a wall at appropriate scale), and (iii) the pattern of the output power in time. The latter, when measured at equal time intervals, is called an output power time series. These output power time series are central to our research. Diverse, but characteristic, patterns are achieved in the time series using a selection of different laser systems.  It is the diversity in the output characteristics of laser light sources that has led to their ubiquitous uptake in communications, industry, science, medicine and the home. The prospect of new applications and better serving existing ones continues to drive laser research.

Different laser systems are diverse in their outputs and uses
Laser output power time series are central to this research

Our expertise is in nonlinear laser systems.  A nonlinearity is any physical mechanism that leads to a relationship between the level of the cause (such as the electrical current in a semiconductor laser) not being a simple multiple of the effect (the output power of the semiconductor laser). Fig. 1 shows this in the form of effect versus cause.

Fig. 1 Comparison of linear and nonlinear cause and effect relationships.
Fig. 1 Comparison of linear and nonlinear cause and effect relationships.

Nonlinearities we explore include delayed optical feedback, optical injection, and modulation.  The form of the output from a single type of nonlinear laser system varies with a change in driving parameters for the system, such as the pump level or the level of the nonlinearity inducing parameter. As a function of such parameters, regions of system operation with qualitatively different patterns in the output power time series can be categorised. A dynamics map of the output is generated.  An example is shown in Fig. 2.

Fig. 2 Dynamic map from a semiconductor with delayed optical feedback laser system and associated timeseries and frequency spectrum for the points at the arrow tips.
Fig. 2 Dynamic map from a semiconductor with delayed optical feedback laser system and associated timeseries and frequency spectrum for the points at the arrow tips.

The different nonlinear laser systems use different laser gain media (such as solid state crystals or semiconductor devices) and/or different nonlinearity inducing approaches to provide a large pool of output types. These are then categorised and used in applications.

A single type of nonlinear laser system can generate several types of output
Different nonlinear laser systems increase the pool of types of output

We have mentioned pulsed and cw output from lasers. Commonly the pattern in the output power time series from a nonlinear laser system is chaotic. Visual inspection of a chaotic time series may not distinguish it from noise. Fig. 3 shows typical cw, pulsed, and chaotic output power patterns. A noise trace is also included.

Fig. 3 Different types of output: pulsed, cw, chaos and noise.
Fig. 3 Different types of output: pulsed, cw, chaos and noise.

All chaos is not the same – some chaos is more complex, and therefore closer to noise, than other types. The Nonlinear Laser Systems team at Macquarie University undertakes world leading research in mapping complexity and related measures using experimental data from nonlinear laser systems. This data is our own and that from the systems of other leading research groups around the world. We have a focus on systems which are of strong scientific interest in their own right and which generate nonlinear outputs required for applications. We are extending chaos and complexity analysis to bigger, higher resolution datasets that support discovering all the features of a particular system at a fine grain. Our approach is one that can transform tens to hundreds of thousands of data sets, or more, into forms that the human brain can evaluate and comprehend. From this, science knowledge is grown. We are also selecting systems to generate a range of high quality experimental data tailored to support the development of knowledge discovery using machine learning strategies. Collecting and using bigger data sets is an important enabler of learning more science from these systems.

The types of output include the complex and chaotic
Being able to quantify the complexity matters
Bigger data does lead to better science

Understanding complexity and chaos in a broad range of nonlinear systems is also a major field of research and knowledge. Important nonlinear systems include those in acoustics, economics, finance, ecology, lasers, electronics, mechanics, physiology, etc. The nonlinear laser systems represent ones in which high quality, measured output power data from a range of different laser systems become a tool for researching and testing machine learning strategies. These data for a range of different physical parameters show differentiated levels of intrinsic complexity both within a single system and between different systems. Also, extending the nonlinear laser systems to ones that produce interdependent spatial and time dependent data streams will further support this research strategy.

Nonlinear systems occur in many contexts
Nonlinear laser systems data is of high quality
What is learnt in one context is relevant to others

Our current SIEF project is exploring whether the time-to-new-science in nonlinear laser systems research can be reduced by implementing machine learning strategies. Data-driven modeling is part of this. Most of the nonlinear laser systems have a reasonably accurate and quantitative theoretical model that can be used to generate noiseless simulated data. Thus, machine learning outcomes from the systems can be checked against mathematics-based models. This will augment testing experimental results against theoretical predictions. Thus, a pathway exists to develop improved theoretical models led by experiment. Fundamental and technical noise is present in all experimental data. Its impact on quantifying complexity in nonlinear systems is detrimental and poorly understood. This impact will be tested by generating experimental data sets with systematically varied levels of signal-to-noise to use in the studies.  With the library of data from the nonlinear laser system time series being established by Sirca, the data will be available for use by other researchers in nonlinear science and machine learning. It will be an important research tool across a range of disciplines.

High quality data can be degraded to simulate low quality data
The impact of data degradation is being researched
The impact of known levels of noise on complexity analysis is being measured