Calculation of intracavity laser modes in the case of a partial waveguiding in the vacuum chamber of the “CLIO” FEL

A new method to calculate the propagation of the laser field in a waveguide is presented here. This method uses the “Fast Fourier Transform”, without mode decomposition, and it is compatible with the propagation both in a waveguide and in the free space. This is interesting in the case of the FEL, when the optical cavity is not completely guided, and when the guiding occurs softly or only in a limited part of the waveguide; for example, when the input wave is not guided at the entrance and becomes guided at the end. A numerical code, using this method for the wave propagation, is described here. It gives the total losses of the optical cavity, and the transverse profile of the laser at any point of the cavity. This code allowed us to calculate the best parameters of the “CLIO” infrared FEL, corresponding to the minimum of losses.