A method of calculating the propagation of electromagnetic fields both in waveguides and in free space, using the “Fast Fourier Transform”

LURE, Bât. 209D, Université de Paris-Sud, BP 34, 91898 Orsay Cedex, France

Corresponding author: prazeres@lure.u-psud.fr

Received: 7 February 2001
Revised: 19 July 2001
Accepted: 2 August 2001
Published online: 15 December 2001

Abstract

The following calculation method permits the evaluation of the transverse distribution of the field amplitude Ψ(x,y,z) propagating in a waveguide. This method is based on a standard method for propagation in free space, which is using the Fast Fourier Transform (FFT). It is very simple in practice, and it does not require a mode decomposition for the waveguide propagation. It uses the properties of periodicity and symmetry of the FFT in the transverse plane in order to take into account the influence of the waveguide. The advantage of this calculation method is the full compatibility with the case of a guided wave (waveguide propagation), an unguided wave (free space propagation) and any intermediate regime where the guiding occurs softly or only in a limited part of the waveguide; for example when an input wave is not guided at the entrance of the waveguide, and becomes guided at the end. In practice, these conditions are observed experimentally for example in the infrared “Free Electron Lasers”, which are broadband tunable lasers, and some of them are using a waveguide, in the center of the optical cavity, coupled with free space areas. The calculation method presented here works in this special configuration. On the other hand, although not using a mode decomposition, this method allows also a rapid decomposition in eigenmodes TE_pq and TM_pq. Using only one symmetry operator and one FFT, it gives the whole set of mode amplitudes.