A scattering matrix formulation for Gaussian beam-mode analysis

The authors have show that scattering matrix theory enables Gaussian beam mode analysis to be extended in a straightforward way to take account of multiple reflections and scattering between modes. The use of propagating modes as basis functions, unlike those of fourier optics, allows the treatment of a vastly expanded range of problems. As well as the example of the Fabry-Perot interferometer used to illustrate this technique, other applications include, for example, calculation of the reflection coefficient of a thick dielectric lens, and of the Q of a confocal resonator with finite-sized reflectors, and has an obvious application to the analysis and design of beam-waveguide feed systems for large antennas. Although they have illustrated the theory for the simplest case of cylindrical symmetry, it is equally applicable to more complicated field distributions, or indeed to problems involving polarization, just by increasing the number of basis functions used. Despite this increase in N, substantial economies of computer time may be achieved in many cases through consideration of the symmetries of the problem