High-gain harmonic generation (HGHG) is effective to produce fully coherent free-electron laser (FEL) pulses for various scientific applications. Due to the limitation of seed lasers, HGHG typically operates at a low repetition rate. In this paper, a harmonic-enhanced HGHG scheme is proposed to relax the peak power requirement for the seed laser, which can therefore operate at megahertz and a higher repetition rate. Moreover, the setup of the scheme is compact and can be adopted in an existing single-stage HGHG facility to extend the shortest achievable wavelength. Simulations show that FEL emission at 13.5 nm (20th harmonic) can be obtained with a 270 nm, 1 MW (peak power) seed laser.

To generate optical vortex with multiple topological charges, a simple scheme based on the phase mask shaping technique is proposed and applied in a seeded free electron laser. With a tailored phase mask, an extreme-ultraviolet (EUV) vortex with multiple topological charges can be produced. To prove the feasibility of this method, an eight-step phase mask is designed to shape the seed laser. The simulation results demonstrate that 100-MW, fully coherent EUV vortex pulses with topological charge 2 can be generated based on the proposed technique. We have also demonstrated the possibility of generating higher topological charges by using a phase mask with more steps.