Experiments on Generation of Various Dark and Bright Pulses From an FM Mode-Locked Laser

Abstract

We experimentally describe the generation of various dark and bright pulses from an FM mode-locked laser with, for example, Gaussian, secant hyperbolic (sech), double-sided exponential, rectangular, parabolic, triangular, Nyquist, and even tangent hyperbolic (tanh) shapes. The experiments were carried out by constructing a 20 GHz actively FM mode-locked erbium fiber laser. Since a continuous wave (CW) offset is needed to form a dark pulse, which can be considered the sum of a negative pulse and a rectangular pulse in one time slot. Therefore, a specific filter, which is installed in the laser cavity, consists of <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">$A(\omega + n\Omega _{m})$ </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> and a sinc function spectrum that is newly introduced as a Fourier transformation of a rectangular pulse for describing the CW offset. 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 also generated a positive bright pulse that consists of a positive pulse with a positive CW offset. The generated optical pulses agreed well with the theory, where the spectral profiles even below −40 dB coincided well with the numerical profiles. We could also generate parabolic and triangular dark pulses in the intensity expression. Finally, we demonstrated tanh <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$(t/T)$ </tex-math></inline-formula> pulse generation, which is an odd function and well known as a dark soliton solution of the nonlinear Schrödinger equation. This pulse was generated by changing the odd function into an even function by cascading positive and negative tanh <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$(t/T)$ </tex-math></inline-formula> pulses at half the repetition rate.