Green function approach to the problem of electromagnetic field excitation in THz free electron lasers

The problem of stimulated spontaneous emission in a free electron laser oscillator with planar waveguide and cylindrical mirrors is under consideration. An efficient computational scheme for calculation of the electromagnetic radiation driven by short electron bunches is proposed. Using expansion of the electromagnetic field in a planar waveguide over optical-waveguide modes the inhomogeneous Klein-Gordon equation governing the mode amplitude has been derived. The reflected from mirrors electromagnetic radiation is described in the framework of initial-boundary problem for the homogeneous 1D Klein-Gordon equation. The Green function approach to the Klein-Gordon equation allowed us to obtain an unconditionally stable and computationally efficient numerical scheme describing the self-consistent evolution of electron bunches and electromagnetic fields.