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

Abstract

We describe experimentally that an FM mode-locked laser can generate various optical pulses such as Gaussian, secant hyperbolic (sech), double-sided exponential, rectangular, parabolic, triangular, and Nyquist pulses like an optical function generator. The experiments were carried out by employing a 10 GHz actively FM mode-locked erbium fiber laser, where a specific filter was installed in the laser cavity. The specific filter was characterized by the Fourier transformed spectrum <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 an 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> 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 $ </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">$n\Omega _{m})$ </tex-math></inline-formula> with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$n=- \infty \sim + \infty $ </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 angular modulation frequency. We employed a software-controlled liquid crystal on silicon (LCoS) optical filter, which can control the amplitude and the phase of the input signal as a function of optical frequency. Therefore, we were able to generate various optical pulses by simply changing the filter shape using the software. The filter resolution was 10 GHz. The generated optical pulses agreed well with the theory, where the spectral profile even below −40 dB coincided well with the theoretical profile. We proved experimentally from the product of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\Delta \nu \Delta \tau $ </tex-math></inline-formula> at −3 dB that the output pulses have none of the frequency chirp that would inevitably occur with conventional FM mode-locking. It was not possible to generate an asymmetric single-sided pulse as we pointed out theoretically. We were also able to generate parabolic and triangular intensity pulses as we predicted in a previous paper. Finally, we compared the possibilities of generating various pulses with AM and FM mode-locking techniques.