Introduction to Data Visualisation

As the saying goes: A picture is worth a thousand words. That is why displaying your data in graphical form is a good idea.

In general, the output of a simulator algorithm consists of numerical data. In other words, a bunch of numbers that is difficult to interpret and analyse. And here is where data visualisation comes in. There are countless ways of visualizing data using graphs, bar plots, pie chart, maps, surfaces, cross-sections, projections, images, animations, ...

2D Graphs: A lot of information can be packed into a 2D graph. In this section, we present sample plots related to the numerical simulation of semiconductor lasers and amplifiers. Fig. 1.1 shows the gain and emission spectra of a quantum dot laser during startup (more details can be found here).

Fig. 1.1: Transient gain spectrum (light blue curve) and emission spectrum (orange curve) of a QDL during startup. The gain spectrum is calculated at time intervals of 1.5ps. The emission spectrum corresponds to the Fourier transform of the complex optical fields (sampled over a period of 15ps).

To increase the impact of the figure I chose a high contrast between the colours of the curves and the background colour of the html page. The colour coded labelling of the vertical axes and the legend help the reader interpret the graph correctly.

The figure is rendered in Scalable Vector Graphics - SVG format that allows readers of electronic media to zoom in without loss of quality. Increasing the browser font will increase the figure size. Note: SVG is supported by most modern browsers. Older browsers might required a plugin that can handle SVG files. If the browser does not support SVG a fallback bitmap file is loaded instead.
Animations: Animations are ideal to display dynamic processes or a change of state. Their impact stems from the ability of our brain to detect even minute changes of an image.
Figure 1.2 shows the cavity-internal optical fields (left), the material gain (center) and the injection current density (right) of a quantum dot laser during the startup phase. More details about quantum dot lasers and the content of Fig. 1.2 can be found here.

Fig. 1.2: Animated plot showing the field intensity in the resonator cavity of a quantum dot laser with an injection stripe width of 8μm and a cavity length of 400μm (left plot). The plot in the center shows the local material gain. The plot on the right shows the local injected current density. The QDL is homogeneously broadened (broadening 25meV). Note: Snap-shots have been taken at a time interval of 1ps.

Publishing: For publishing purposes high quality figures are mandatory. If it is not feasible to produce SVG figures (e.g. due to file memory constraints) publishers usually require a resolution of at least 600 dpi for figures including graphs. It is important to keep in mind that most readers of scientific publications will print the document using a monochrome printer. In this case, the details of graphs and annotation should be readable and distinguishable if rendered in grayscale mode.
amplified optical pulse

Fig. 1.3: Amplification of an optical pulse with a duration of 500fs in a homogeneously broadened quantum dot amplifier (left) and an inhomogeneously broadened quantum dot amplifier (right).

Fig. 1.3 shows the amplification of an optical pulse with a duration of 500fs during the propagation through a quantum dot semiconductor optical amplifier (QDSOA). Details related to the modelling of QDSOAs can be accessed here.
Fig. 1.3 captures the essence of the information being presented without the use of colour. Contour plots and shades of gray are used to visualize the intensity and shape of the optical pulse.

Besides high resolution, there are other factors that contribute to the quality of a figure:
  • Readable labels and annotation.
  • Amount of information contained.
  • Suitable scaling of graph axes.
  • Contrasting colour choice.
  • Adequate figure size.
  • Descriptive caption.

Many scientist neglect the impact of a high quality figure. It is always worth spending that little extra time to improve the readability, contrast, and overall appeal of a figure included in a presentation or a publication.