This work focuses on the development of a new high power, ultrashort pulse dye laser system based on solid state Nd:YAG pump sources for a synchronously pumped dye laser and a series of dye amplifiers. This system will be applied to the study of picosecond and sub-picosecond laser-produced plasmas. For comparison, experiments are presented in which the propagation velocity of laser-produced plasmas pumped by 10 ns pulses is studied. Results of the propagation velocity as a function of ambient gas pressure and input pulse energy are given and are in good agreement with theoretical models. In order to produce ultrashort pulse pumped plasmas, it is necessary to focus the input beam to a small spot size without any temporal broadening of the pulse. A novel solution to the pulse front distortion problem using a combination of a lens and Fresnel type zone plate as a focusing device is presented.