  It is reported that [Z. Huang et al., Phys. Rev. Lett. 109, 204801 (2012)],
high-gain free-electron laser (FEL) can be generated by transverse-dispersed
electron beams from laser-plasma accelerators (LPAs) using transverse-gradient
undulator (TGU) assuming an ideal constant dispersion function without focusing
optics. The constant dispersion function keeps electrons beyond the resonant
energy bandwidth still being on resonant with the FEL radiation. Instead, in
this paper, the case with focusing optics in an LPA-driven FEL using TGU is
numerically studied, in which the dispersion function should be monotonously
decreasing along the undulator. Even though the FEL resonance is not always
satisfied for off-energy electrons in this case, through subtly optimizing the
initial dispersion and focusing parameters, it is feasible to achieve a similar
radiation power to the case assuming an ideal constant dispersion function
without focusing optics, and meanwhile, to attain a good transverse coherence.
Moreover, higher radiation power could be expected if longitudinally tapering,
transverse-gradient variation in different sections are systematically
conducted, which is demonstrated with intense global multiparameters
optimizations based on GENESIS simulation.
