Laser Phase Relations of High-Order Harmonic Generation

Laser phase relations of high-order harmonic generation (HHG) are calculated with the saddle point theory. The results show a two-peak structure including a symmetric and an asymmetric temporal distributions of the instantaneous frequency of HHG radiation. These distributions are fitted with Gaussian and polynomial functions, respectively. Two calculation formulae are presented to analyse attosecond x-rays with specified time duration and energy bandwidth in experiments.