Mathematical description of light beams and optical components

The following sections provide information about how the various aspects of an interferometer simulation are coded within the Finesse source code. The analysis of optical systems described here is based on the principle of superposition of light fields: a laser beam can be described as the sum of different light fields. The possible degrees of freedom are:

  • frequency,

  • geometrical shape and position,

  • polarisation.

In the analysis of interferometric gravitational wave detectors, the amplitudes and frequencies of light fields are of principal interest. The polarisation is neglected in the analysis given here, but the formalism can in principle be easily extended to include polarisation also.

This chapter describes the mathematical formalism based on plane waves only. In Chapter 4 the formalism with respect to Hermite-Gauss modes will be given; it is a straightforward extension of the plane wave analysis and makes use of the methods described