Theory of Generation of Various Dark and Negative Pulses From an FM Mode-Locked Laser

We show theoretically that various kinds of dark pulses and negative pulses can be generated from an FM mode-locked laser. First, we classify optical pulses into two groups, namely a positive pulse group, which has an electric field with a positive amplitude, and a negative pulse group, which has an electric field with a negative amplitude. We classify them into two further groups; one has a positive offset with a CW electric field and the other has a negative offset. Therefore, we have a total of four kinds of pulses, which we denote as positive bright, positive dark, negative bright, and negative dark pulses. We show that these pulses can be successfully generated by employing FM mode-locking with specific optical filters that we newly propose here. We generate various dark pulses including Gaussian, sech, double-sided exponential, rectangular, triangular, parabolic, and even dark Nyquist pulses, where we can precisely control their width, depth, and repetition rate. We also describe dark triangular and dark parabolic pulses with an intensity expression. Finally, we generate a tanh(
$t/T$
) pulse, which is an odd function and a dark soliton solution of the nonlinear Schrödinger equation. Since this pulse has different amplitudes with ± signs on the wings, conversion from an odd function to an even function plays an important role in achieving FM mode-locking.