We show that the mode-locking region of the family of quasi-periodically forced Arnold circle maps with a topologically generic forcing function is dense. This gives a rigorous verification of certain numerical observations in [M. Ding, C. Grebogi and E. Ott. Evolution of attractors in quasiperiodically forced systems: from quasiperiodic to strange nonchaotic to chaotic. Phys. Rev. A 39(5) (1989), 2593–2598] for such forcing functions. More generally, under some general conditions on the base map, we show the density of the mode-locking property among dynamically forced maps (defined in [Z. Zhang. On topological genericity of the mode-locking phenomenon. Math. Ann. 376 (2020), 707–72]) equipped with a topology that is much stronger than the $C^0$ topology, compatible with smooth fiber maps. For quasi-periodic base maps, our result generalizes the main results in [A. Avila, J. Bochi and D. Damanik. Cantor spectrum for Schrödinger operators with potentials arising from generalized skew-shifts. Duke Math. J. 146 (2009), 253–280], [J. Wang, Q. Zhou and T. Jäger. Genericity of mode-locking for quasiperiodically forced circle maps. Adv. Math. 348 (2019), 353–377] and Zhang (2020).

We propose a 2.1 μm high-energy dissipative soliton resonant (DSR) fiber laser system based on a mode-locked seed laser and dual-stage amplifiers. In the seed laser, the nonlinear amplifying loop mirror technique is employed to realize mode-locking. The utilization of an in-band pump scheme and long gain fiber enables effectively exciting 2.1 μm pulses. A section of ultra-high numerical aperture fiber (UHNAF) with normal dispersion and high nonlinearity and an output coupler with a large coupling ratio are used to achieve a high-energy DSR system. By optimizing the UHNAF length to 55 m, a 2103.7 nm, 88.1 nJ DSR laser with a 3-dB spectral bandwidth of 0.48 nm and a pulse width of 17.1 ns is obtained under a proper intracavity polarization state and pump power. The output power and conversion efficiency are 0.233 W and 4.57%, respectively, both an order of magnitude higher than those of previously reported holmium-doped DSR seed lasers. Thanks to the high output power and nanosecond pulse width of the seed laser, the average power of the DSR laser is linearly scaled up to 50.4 W via a dual-stage master oscillator power amplifier system. The 3-dB spectral bandwidth broadens slightly to 0.52 nm, and no distortion occurs in the amplified pulse waveform. The corresponding pulse energy reaches 19.1 μJ, which is the highest pulse energy in a holmium-doped mode-locked fiber laser system to the best of our knowledge. Such a 2.1 μm, high-energy DSR laser with relatively wide pulse width has prospective applications in mid-infrared nonlinear frequency conversion.

We report on a compact and robust self-referenced optical frequency comb with a tunable repetition rate, generated by an all-polarization-maintaining (PM) mode-locked Er-doped fiber laser. The spacing between comb teeth can be tuned above 300 kHz at a repetition rate of 101 MHz. The repetition rate and the carrier–envelope offset of the laser are stabilized separately, and the relative residual phase noises are determined to be $336~\unicode[STIX]{x03BC}\text{rad}$ and 713 mrad (1 Hz–1 MHz). The accurate frequency characteristics and the stable structure show great potential for the use of such a comb in applications of precision measurements.

We report on mode-locked thulium-doped fiber lasers with high-energy nanosecond pulses, relying on the transmission in a semiconductor saturable absorber (SESA) and a carbon nanotube (CNTs-PVA) film separately. A section of an SMF–MMF–SMF structure multimode interferometer with a transmission peak wavelength of ∼2003 nm was used as a wavelength selector to fix the laser wavelength. When the SESA acted as a saturable absorber (SA), the mode-locked fiber laser had a maximum output power of ∼461 mW with a pulse energy of ∼0.14 μJ and a pulse duration of ∼9.14 ns. In a CNT-film-based mode-locked fiber laser, stable mode-locked pulses with the maximum output power of ∼46 mW, pulse energy of ∼26.8 nJ and pulse duration of ∼9.3 ns were obtained. To the best of our knowledge, our experiments demonstrated the first 2 μm region ‘real’ SA-based dissipative soliton resonance with the highest mode-locked pulse energy from a ‘real’ SA-based all-fiberized resonator.