Numerical study of spectral properties of ultrashort hyperbolic secant pulsed beams

The spectral properties of the ultrashort hyperbolic secant pulsed beam are studied in free space. The analytic expression of power spectrum of the ultrashort hyperbolic secant pulsed beam and some numerical calculations are given. The results show that the spectrum of the ultrashort hyperbolic secant pulsed beam appears blue shift on axis and red shift on the beam periphery. The blue shift on axis decreases down to zero quickly with the cycle number increasing. The red shift on the beam periphery increases with the diffraction angle increasing and decreases with the cycle number increasing. The beam waist also affects the red shift on the beam periphery.