Proposal of Difference-Frequency Wave Generation Induced by Dual-Wavelength Free-Electron Laser Oscillations

Optical klystrons have been developed in storage ring free-electron lasers (FELs) as insertion devices to increase the FEL gain in a straight section with limited length. By adjusting the magnetic field in the dispersion section of the optical klystron to shift the relative delay between the electron bunch and FEL pulse from an integer multiple of the FEL wavelength, FELs can oscillate at two wavelengths. The electron density of the electron bunch that interacts with the FEL pulse in a small-signal regime is modulated at the FEL wavelength period. When the FEL oscillates simultaneously at two wavelengths, the electron density of the electron bunch beats through the modulation with two periods. This beat generates long-wavelength coherent edge radiation at a bending magnet located in the straight section containing the optical klystron. Difference-frequency waves induced by dual-wavelength ultraviolet free-electron lasers generate a high-intensity mid-infrared monochromatic beam. Our findings will lay the foundation for the development of the difference-frequency waves of soft X-rays and extreme ultraviolet light using hard X-ray FELs.