Ultrashort Gaussian pulse-width expansion and shape deformation induced by group velocity dispersion

Pulse-width expansion and pulse shape deformation of an ultra-short Gaussian pulse induced by both low and high order group velocity dispersion was theoretically analyzed in terms of energy conservation and coupled equations for three wave radiations. As an example, the optical parametric interaction processes in a negative uniaxial crystal $\mathrm{CsLiB_6O_{10}}$ with 50 fs of ultra-short Gaussian pulse were simulated. The results indicate that the degree of the pulse expansion induced by low and high order group velocity dispersion is determined by both the wavelength of the incident wave and crystal length. A pulse could be expanded to 1.41 times than its initial value as a crystal length equals to the dispersion length, and further heavily expanded with decreasing wavelength and increasing crystal length. The pulse expansion induced by high order group velocity dispersion using incident wavelength 213 nm is 1.6 times than that using 532 nm in 50 fs pulse width without chirp modulation, and the symmetry deformation and the frequency pushing phenomena of ultra-short pulse shape is also found.