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Laser Modeling


German: Modellierung von Lasern

Categories: lasers, methods, physical foundations

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What a Model is


Some important aspects of models are the following:

  • Although a model should in some ways be similar to some part of reality, it is always much simpler than reality, because plenty of details have been omitted in the process of constructing the model. (This is called abstraction.) The level of detail of a model should be such that it is as simple as possible while still being useful for studying the phenomena of interest.
  • A model contains some number of variables and parameters, related to physical quantities and properties, and a number of assumptions. These assumptions should be made explicit, since they are not always very well fulfilled in reality, and this can easily be overlooked.
  • Laser models contain mathematical relations (e.g. differential equations) as essential ingredients. Such relations connect different model variables with each other. The resulting equations can sometimes be solved by analytical means, whereas in other cases numerical methods have to be used. Particularly in the latter case, some computer software is usually required (see below). Such models are often called computer models, but note that the computer and the software are only tools to solve equations and to conveniently display the results; the essence of any such model is a mental construction.


laser modeling


Uses and Benefits of Laser Models


Possible benefits of laser modeling include:

  • A quantitative understanding of the inner workings allows the optimization of laser designs concerning performance, component costs, compactness, robustness, etc.
  • In the case of problems, a model can produce essential insight to analyze the cause and to find a working solution. A model may be used, e.g., to check whether certain suspected effects can be responsible for observed misbehavior, and a simulation can show whether a conceived remedy would be sufficiently effective and which side effects it may have.
  • A laser model can save a lot of time and costly experiments by performing “numerical experiments” to find out, e.g., to what extent improvements can be expected from certain design changes, or how strong certain effects really are.
  • It also makes it possible to check certain beliefs and thus potentially to improve the level of understanding, which may also trigger useful new ideas. Therefore, laser models can be very valuable as educational tools.


Software for Laser Modeling




  • Some software programs offer forms to fill in the required data, and may present the results in the same form, in tables, or in graphical form. Input forms make it easy to get started, at least if they are accompanied by clear descriptions, consistency checks, and the like. However, such software is often not particularly flexible; for example, its forms define a fixed way of parametrizing the data, and it often does not provide convenient ways of systematically checking large numbers of input data sets. Therefore, it is often tedious to go far beyond checking a few sample cases, although the understanding of more general types of relations may actually be of interest.
  • Other software is controlled with script files, containing commands to start certain actions. Powerful script-controlled software also allows the use of mathematical expressions instead of numbers only, so that the user can use the most appropriate parametrization. Also, it is often possible on a user level to automate certain tasks, such as doing some calculation for a given range of parameters and storing the results in a user-defined format, and to reuse parts of code with “copy and paste”, rather than e.g. typing a lot of numbers into multiple forms. Such flexibility can be extremely valuable. A disadvantage is that it is usually more difficult to learn a script language, even though a good documentation, combined with a set of sample input files (demo files), can speed up this learning process considerably.


Failing Modeling Exercises


  • oversimplification, effectively excluding relevant effects from a model
  • too sophisticated approaches which may make the handling inconvenient or the computation time too long
  • lack of access to required input data
  • too large number of parameters to interpret observed results correctly (note that a match between simulated and measured results does not prove the correctness of a model!)
  • errors in mathematical equations, programming logic or in physical assumptions, which may be difficult to detect and locate, if sufficiently developed validation procedures are not available
  • a lack of experience concerning how to answer the relevant questions once the model works

A Strategy for Successful Modeling


  • It is extremely important first to collect a set of specific questions so that correct and comprehensive answers would constitute a real help, e.g. for a laser development project. Omitting this step can result in unfocused, unsystematic and consequently inefficient work.
  • Next, it must be determined whether there is a kind of model which is capable of providing the answers, based on the available data, and without excessive amounts of work. There are cases, e.g., where a certain model could in principle be used, but would require more comprehensive or more precise data than are available. This may be a case for abandoning a modeling project at this early stage.
  • If the previous steps could be carried out successfully, the model can be constructed. This typically involves decisions concerning what aspects and effects to include or exclude, putting together various equations, and often arranging their evaluation with numerical methods on a computer. Powerful modeling software, e.g. simulation software, can be very helpful.
  • Before a model can be used in practice, it needs to be validated, i.e., its correctness must be checked. This can involve the comparison of results with a set of experimental data, which is often not easy, however: a disagreement may indicate an error in the model, or the failure to take into account an important effect, but may also result from incorrect data. Another class of validity tests is based on the comparison with analytical results, which can often be obtained at least for some simplified cases and are relatively flexible and reliable.
  • Finally, the model can be used to address the originally formulated questions, to obtain a deeper understanding of the relations between various parameters and of certain limitations e.g. by doing “numerical experiments”.



The RP Photonics Buyer's Guide contains 7 suppliers for laser modeling software. Among them:



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