Efficient FFT Computation of Plano-plano Interferometer Modes for a Wide Range of Fresnel Numbers

A comparison is made of several iterative techniques including Huygens' integral and Fourier transform methods for computing the dominant modes of a Fabry-Perot interferometer (FPI), and the factors which limit the range of application of each method are described. It is shown that when applied to Huygens' integral method, the Fresnel approximation imposes an upper bound on the range of usuable Fresnel numbers. The Fourier expansion method used in this paper also employs the Fresnel approximation, but is valid over a different and much larger range of Fresnel numbers. The results of some numerical calculations for the normal modes of FPIs are presented to verify that the Fourier expansion method together with the fast Fourier transform (FFT) is well suited for efficient computation of FPI modes within a wide range of Fresnel numbers.