Difference frequency generation in free electron lasers

We propose a simple scheme for difference frequency generation in free electron lasers (FELs), in which the electron beam interacts with a dual-frequency laser and emits intense coherent radiation at the difference frequency. We analytically show that the microbunch formation in the electron beam, which is the most important process in FELs, is dominated by nonlinear wave mixing in the proposed scheme. Numerical examples of applying the proposed scheme to generating terahertz radiation are presented as one of the most important applications.