We demonstrate that an asymmetrical π phase-shifted fiber Bragg grating operated in reflection can provide the required spectral response for implementing an all-optical fractional differentiator. There are different (but equivalent) ways to design it, e.g., by using different gratings lengths and keeping the same index modulation depth at both sides of the π phase shift, or vice versa. Analytical expressions were found relating the fractional differentiator order with the grating parameters. The device shows a good accuracy calculating the fractional time derivatives of the complex field of an arbitrary input optical waveform. The introduced concept is supported by numerical simulations.

Simultaneous and independent active Q switching and active mode locking of an erbium-doped fiber laser is demonstrated using all-fiber modulation techniques. A magnetostrictive rod attached to the output fiber Bragg grating modulates the Q factor of the Fabry–Perot cavity, whereas active mode locking is achieved by amplitude modulation with a Bragg-grating-based acousto-optic device. Fully modulated Q-switched mode-locked trains of optical pulses were obtained for a wide range of pump powers and repetition rates. For a Q-switched repetition rate of $500\mathrm{Hz}$ and a pump power of $100\mathrm{mW}$, the laser generates trains of 12–14 mode-locked pulses of about $1\mathrm{ns}$ each, within an envelope of $550\mathrm{ns}$, an overall energy of $0.65\mu \mathrm{J}$, and a peak power higher than $250\mathrm{W}$ for the central pulses of the train.

We investigated the dissipative solitons resonance in an ytterbium-doped fiber ring laser in which all the elements are polarization maintaining (PM). A semiconductor saturable absorber mirror was used as a mode-locker. The cavity included a normal dispersion single-mode fiber (SMF) and an anomalous dispersion photonic crystal fiber. The change of the length of the PM SMF allows the variation of the net-normal dispersion of the cavity in the range from 0.022 ps² to 0.262 ps². As the absolute value of the net-normal dispersion increases from 0.022 ps² to 0.21 ps², a square-shaped single pulse transformed to a single right-angle trapezoid-shaped pulse, and, at the dispersion of 0.262 ps², to multiple right-angle trapezoid-shaped pulses, per round-trip.

Active mode locking of an erbium-doped all-fiber laser with a Bragg-grating-based acousto-optic modulator is demonstrated. The fiber Bragg grating was acoustically modulated by a standing longitudinal elastic wave, which periodically modulates the sidebands at twice the acoustic frequency. The laser has a Fabry–Perot configuration in which cavity loss modulation is achieved by tuning the output fiber Bragg grating to one of the acoustically induced sidebands. Optical pulses at $9\mathrm{MHz}$ repetition rate, $120\mathrm{mW}$ peak power, and $780\mathrm{ps}$ temporal width were obtained. The output results to be stable and has a timing jitter below $40\mathrm{ps}$. The measured linewidth, $2.8\mathrm{pm}$, demonstrates that these pulses are transform limited.

We propose a simple and fast procedure to retrieve the phase profile of arbitrary light pulses. It combines a first experimental stage, followed by a one-step numerical stage. To this end, it is necessary to perform a Fresnel transform, which is obtained just by propagating the light pulses through an optical fiber. We experimentally test this proposal recovering the phase profile in the light pulses provided by a passively mode-locked laser. The proposal is then compared with a temporal variation of the Gerchberg–Saxton recursive algorithm, which is specially modified for this purpose.