What is the value of numerical simulation?
I just came across an editorial in the new issue of Nature Photonics (link) which points out the importance of theoretical papers that present new ideas and concepts. In general, I very much support his views, however, the editor also characterizes numerical simulation as less valuable, because it “only solves known equations numerically.” You can imagine that I did not quite like this comment, especially since “numerical simulation” contributes the first three letters to our NUSOD conference and to the title of this blog.
This editorial got me thinking about the true value of numerical simulation in optoelectronics. On one hand, simulation helps to explain experimental results that would otherwise be hard to understand. In most cases, only numerical simulation is able to quantitatively reproduce measurements by combining all relevant physical processes self-consistently and by considering the actual microstructure of optoelectronic devices. It gives deep insight into internal processes and properties, such as the pictured electron density distribution inside quantum wells.
On the other hand, numerical simulation enables the practical test of new theoretical ideas by embedding them into a realistic environment. New theories are often developed in the form of differential equations, and their quantitative evaluation typically requires numerical methods. I already realized early on as a physics student that analytical solutions of real-world problems can only be found under extremely restricted and idealized conditions, if at all.
In other words, numerical simulation enables us to connect theory and practice in a realistic way. Even more, it enables quantitative predictions on how specific (new) physical mechanisms or structures influence the practical performance of novel devices. In my view, this is the core value of numerical simulation and it is also the main reason companies shell out more than $100k for some of the commercial software in optoelectronics. However, performance predictions remain the “holy grail” of numerical simulation as their reliability very much depends on the accuracy of models and input data, just like the weather forecast.