  Recent theoretical and experimental studies have shown that Self-Amplified
Spontaneous Emission Free Electron Laser (SASE FEL) with a planar undulator
holds a potential for generation of relatively strong coherent radiation at the
third harmonic of the fundamental frequency. Here we present detailed study of
the nonlinear harmonic generation in the SASE FEL obtained with time-dependent
FEL simulation code. Using similarity techniques we present universal
dependencies for temporal, spectral, and statistical properties of the odd
harmonics of the radiation from SASE FEL. In particular, we derived universal
formulae for radiation power of the odd harmonics at saturation. It was also
found that coherence time at saturation falls inversely proportional to
harmonic number, and relative spectrum bandwidth remains constant with harmonic
number.
