Theory of AM Mode-Locking of a Laser as an Arbitrary Optical Function Generator

We present theoretically an AM mode-locked laser that can generate various kinds of optical pulses. By employing a non-perturbative master equation in the frequency domain, we show that we can design an arbitrary output pulse waveform, a(t) , output from a laser with a specific optical filter, F {A}(\omega) , characterized by a Fourier transformed spectral profile A(\omega) of a(t) , A(\omega +\Omega {m}) , and A(\omega -\Omega {m}). Here, \Omega {m} is the AM modulation frequency. Although the optical filter F{A}(\omega) generally has a complex frequency response, most F{A}(\omega) filters are characterized by real values as long as the mode-locked pulse waveform is symmetric in the time domain. However, F{A}(\omega) becomes spectrally complex when our aim is to generate an asymmetrically mode-locked waveform, for example a single-sided exponential pulse. The actual F{A}(\omega) can be designed by using, for example, a liquid crystal on silicon (LCoS) optical filter, which can simultaneously control the amplitude and the phase of the input signal. A sech pulse (soliton) has already been generated based on the nonlinear Schrödinger equation by using Kerr nonlinearity in a fiber, but we show in this paper that the pulse can be generated very precisely even without nonlinearity. Since the present method enables us to generate triangular, double-sided exponential pulses as well as Gaussian, sech, parabolic, and even Nyquist pulses in the amplitude expression, we may be able to use AM mode-locked lasers as optical function generators.