Experiments on an AM Mode-Locked Laser as an Arbitrary Optical Function Generator

Abstract

We show experimentally that various optical pulses can be generated from an AM mode-locked laser by employing a 10 GHz harmonically and regeneratively mode-locked erbium fiber laser. A software-controlled liquid crystal on silicon (LCoS) optical filter device, which can control the amplitude and phase of the input signal as a function of optical frequency, was employed to implement a specific filter function. The filter was characterized by the Fourier transformed spectral profile <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$A(\omega )$ </tex-math></inline-formula> of the output pulse <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$a(t)$ </tex-math></inline-formula> , <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$A(\omega +\Omega _{m}), $ </tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$A(\omega -\Omega _{m})$ </tex-math></inline-formula> . Here, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\Omega _{m}$ </tex-math></inline-formula> is the AM modulation angular frequency. The filter resolution was set at 10 GHz. By installing a specific filter in the laser cavity, we succeeded in generating various pulses such as Gaussian, secant hyperbolic (sech), double-sided and single-sided exponential, parabolic, triangular, and Nyquist pulses with an arbitrary roll-off factor as with an optical function generator. It is interesting to note that we could experimentally generate very precise transform-limited (TL) optical pulses, which were originally designed by calculating the filter function. The generated spectral profile agreed well with the numerical results even below −40 dB, which also agreed with the theory. As we have shown theoretically, we could generate sech and parabolic pulses without fiber nonlinearity. An asymmetric single-sided pulse can also be generated by incorporating a complex filter function with phase information, where a small amount of phase rotation of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\sim \pi $ </tex-math></inline-formula> /60 in each round trip played an important role in generating the asymmetric pulse. Without the phase change, the pulse became symmetric and was no longer the designed pulse. A clean triangular pulse was difficult to generate since parabolic pulse shaping on the top of a sinusoidal intensity modulation is ineffective in creating a sharp peak.