  Laser seeding technique have been envisioned to produce nearly
transform-limited pulses at soft X-ray FELs. Echo-Enabled Harmonic Generation
(EEHG) is a promising, recent technique for harmonic generation with an
excellent up-conversion to very high harmonics, from the standpoint of electron
beam physics. This paper explores the constraints on seed laser performance for
reaching wavelengths of 1 nm. We show that the main challenge in implementing
the EEHG scheme at extreme harmonic factors is the requirement for accurate
control of temporal and spatial quality of the seed laser pulse. For example,
if the phase of the laser pulse is chirped before conversion to an UV seed
pulse, the chirp in the electron beam microbunch turns out to be roughly
multiplied by the harmonic factor. In the case of a Ti:Sa seed laser, such
factor is about 800. For such large harmonic numbers, generation of nearly
transform-limited soft X-ray pulses results in challenging constraints on the
Ti:Sa laser. In fact, the relative discrepancy of the time-bandwidth product of
the seed-laser pulse from the ideal transform-limited performance should be no
more than one in a million. The generated electron beam microbunching is also
very sensitive to distortions of the seed laser wavefront, which are also
multiplied by the harmonic factor. In order to have minimal reduction of the
FEL input coupling factor, it is desirable that the size-angular bandwidth
product of the UV seed laser beam be very close to the ideal i.e.
diffraction-limited performance in the waist plane at the middle of the
modulator undulator.
