  In this paper, a simple method is proposed to extend the photon energy range
of a soft x-ray self-seeding free-electron laser (FEL). A normal monochromator
is first applied to purify the FEL spectrum and provide a coherent seeding
signal. This coherent signal then interacts with the electron beam in the
following reverse tapered undulator section to generate strong coherent
microbunchings while maintain the good quality of the electron beam. After
that, the pre-bunched electron beam is sent into the third undulator section
which resonates at a target high harmonic of the seed to amplify the coherent
radiation at shorter wavelength. Three dimensional simulations have been
performed and the results demonstrate that the photon energy gap between 1.5
keV and 4.5 keV of the self-seeding scheme can be fully covered and 100
GW-level peak power can be achieved by using the proposed technique.
