10. A Ti:Sapphire laser resonator has an optical path length of 1 meter. The gain bandwidth of the laser gain medium is 30 nm when center wavelength is 790 nm. (a) Estimate the number of longitudinal modes in the bandwidth. (b) What is the shortest pulse width of a mode-locked laser pulse that can be achieved with this laser system? A transform limited sech pulse has a pulse width-bandwidth product of 0.315. [10 points]