The above misconfigurations can be used in the context of simple beam segments. We consider the case in which the beam parameter for the input light is specified. Ideally, the ABCD matrices then allow one to trace a beam through the optical system by computing the proper beam parameter for each beam segment. In this case, the basis system of Hermite–Gauss modes is transformed in the same way as the beam, so that the modes are not coupled.
For example, an input beam described by the beam parameter is passed through several optical components, and at each component the beam parameter is transformed according to the respective ABCD matrix. Thus, the electric field in each beam segment is described by Hermite–Gauss modes based on different beam parameters, but the relative power between the Hermite–Gauss modes with different mode numbers remains constant, i.e., a beam in a mode is described as a pure mode throughout the entire system.
In practice, it is usually impossible to compute proper beam parameter for each beam segment as suggested above, especially when the beam passes a certain segment more than once. A simple case that illustrates this point is reflection at a spherical mirror. Let the input beam be described by . From Figure 49 we know that the proper beam parameter of the reflected beam is
This work is licensed under a Creative Commons License.