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.