Properties of the third harmonic of the radiation from self-amplified spontaneous emission free electron laser

Recent theoretical and experimental studies have shown that the 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 a detailed study of the nonlinear harmonic generation in the SASE FEL obtained with a 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 formulas for radiation power of the odd harmonics at saturation. It was also found that coherence time at saturation falls inversely proportional to the harmonic number, and relative spectrum bandwidth remains constant with the harmonic number.