Spectrum and width of mode-locked laser pulses

An analytical theory is given of the spectrum of the pulses generated by a ring laser that is mode locked by a synchronously modulated absorber. A steady-state solution is defined by requiring that, in a round trip, the joint effect of the active medium and the modulated absorber leave the pulses unchanged. The resulting integral equation is solved approximately, and the frequency spectrum of the pulses is obtained in closed form. Although the spectrum cannot be transformed analytically to obtain the pulse shape, the second moment of the shape, which gives a measure of the width, is found. The spectrum and width are found to depend on the curvature of the modulator waveform, near its maximum transmission, and on the gain and bandwidth of the active medium, which is assumed to have a Lorentzian line shape.