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What Makes a Good Physics Model

Dr. Rüdiger Paschotta

Modeling of devices such as lasers and amplifiers can be a very useful thing to do, but it can also be a waste of time. One of the aspects determining in which category a model falls he's how well the model is made. However, it is not always obvious what makes a good model.

I always warmly recommend thinking about the model's application first. Before investing any time into setting up a model, one should always think about what kind of questions should be answered. After all, it is hard to efficiently produce answers if there are no good questions to begin with. A good model is then one which is most suitable for answering the questions of interest. Some examples of such questions are:

  • What performance can I expect from a certain laser design?
  • How to optimize the design?
  • What are the limiting factors?
  • Will certain known detrimental effects be critical, or can I safely ignore them?

Note that a good model will not only be able to answer your question, but it will also do that efficiently. This implies that the model is not more complex than necessary for the task. For example, if you already know that gain guiding effects are weak in a certain laser, it is not advisable to use a full-blown beam propagation model because it is much more efficient to work with a simplified model where fixed beam profiles, for example determined by the resonator modes, are assumed. On the other hand, if you are not sure about how important gain guiding is, only the beam propagation model can tell you. Ideally, you would use a software like RP Fiber Power with which you can implement both types of models. That software has been designed for fiber lasers and amplifiers, but it's beam propagation features can be most useful in bulk lasers.

Physics Knowledge and Experience; Software and Support

Obviously, a good understanding of the underlying physics as well as practical experience with modeling is highly useful. Otherwise, you might not be aware of certain aspects to be consider and may either get inaccurate results due to neglected effects or do an overkill by considering effects which are not really relevant.

Even the best modeling software cannot replace physics knowledge and experience. However, competent technical support, which often comes with a software license, can help you very much in these respects. Ideally, you get supported by a highly qualified person who has all that knowledge and experience and is prepared to tell you not only how to handle the software, but also to give you detailed advice on related scientific and technical aspects. This is exactly what you can get from RP Photonics. Remember that RP Photonics was founded as a technical consulting company; it was thus quite natural to offer comprehensive technical advice and not only some hints concerning how to handle the software. And of course we still offer to do the whole modeling for you.

Always keep in mind: a model is not a piece of software. It is rather a mental construction made to resemble some aspects of reality, and software can just be a tool for implementing a model. Constructing a model should begin with thinking, not with typing. You know, the principle “think first” is generally quite useful …

Other Aspects

Numerical efficiency is vital in some cases. According to my experience, however, computation speed is rarely is a crucial factor; I typically spend much more time thinking about results than waiting for the computer. In other cases, it can be a good idea to check again whether the model is more complicated than necessary. Of course, the quality of the numerical implementation can also be a vital factor; here, the user is dependent on the developer of the software.

The user interface of modeling software is quite important. The crucial aspect is of course not whether the user interface looks nice, but rather whether it is sufficiently flexible e.g. for generating the kinds of diagrams you need and for varying and optimizing the relevant input parameters.

Documentation is another very important aspect. That applies to modeling software, but also to the models made with it. Note that a model will be most useful if after some time you can easily take it out again and do more calculations. This is more likely if you have properly documented what has been assumed, what aspects have been considered and which ones have been neglected, etc.

In our software, non-trivial models are defined by scripts. If you read such a script later on, you will soon find out what you have done. Of course, a few comments are likely to be helpful.

By the way, another way to waste time is to produce useful insight with a model but then not to document that properly. The valuable results will then soon be forgotten. Assuming that the getting results and not having a model is what you finally want, that would be quite sad … but it appears to happen quite often.

Where is Modeling Useful?

It is essential for success in R & D or scientific research to identify those cases where modeling is of high value. According to my experience, many laser companies fail to recognize such opportunities, maybe simply due to a lack of know-how. They then engage in time-consuming and expensive trial-and-error procedures, where one could find the best way forward much more quickly and efficiently with a computer model.

Of course, it is often not trivial to see where modeling is vital. Two conditions must be met:

  • It must be possible to calculate or simulate certain aspects of reality.
  • That exercise must provide valuable insight which you could not get more easily or quickly by just trying out in the lab.

On the first point, one might fail for example if essential input data for model are not available. For example, if you buy poorly characterized optical fibers, no software can help you to accurately predict their performance. Less frequently, something is just too difficult to calculate for making the effort worthwhile.

Concerning the second aspect, people often underestimate the difficulties of clarifying something with a quick experiment. A computer model is “transparent”, as I like to express it: if something surprising happens, you can always look into the inner workings. (For example, you can find out about the powers or intensities at any location or time.) An experiment, however, may give you strange results without any hints concerning how to explain them.

This article is a posting of the RP Photonics Software News, authored by Dr. Rüdiger Paschotta. You may link to this page, because its location is permanent.

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