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. [ABSTRACT FROM AUTHOR]