Theory of the synchronously pumped picosecond dye laser

The circulation of a synchronously mode locked dye laser pulse in a linear cavity configuration containing a dye cell as an active medium and a bandwidth-limiting element is treated. The condition that the pulse shape reproduces after each cavity round-trip provides a nonlinear integro-differential equation for the steady-state pulse shape. For the solution of this equation an approximate method, not limited to small pulse energies, is given and the pulse duration, intensity, energy, asymmetry of the pulse shape, stable regions and other interesting parameters are discussed.