**3. Mode‐locked ytterbium‐doped fiber laser with carbon nanotubes**

Single‐walled carbon nanotube is an enrolled two‐dimensional graphene honeycomb sheet with a diameter of typically 0.6–2 nm and a length distribution ranging from tens of nanome‐ ters to several micrometers. Depending on their chirality [26], single‐walled nanotubes exhibit two different electrical properties, metallic or semiconducting. Semiconducting nanotubes have an energy band gaps like those in ordinary semiconductors; thus, photons having corresponding wavelength are absorbed. Single‐walled nanotubes are a kind of promising material as saturable absorber for passive mode locking because the bandgap energy can be controlled by the tube diameter, which would be applied for different spectral ranges.

The absorption loss and modulation depth of the nanotubes‐based saturable absorber can be adjusted by changing the concentration of nanotubes, the interaction length of light with nanotubes, nonsaturable loss of fiber structure, and substrate materials. To study the effect of modulation depth on the mode locking in a larger normal dispersion cavity with high nonlinearity, the evanescent field used here is from the D‐shaped fiber that was fabricated by ablating part of the cladding of single mode fiber by the femtosecond laser‐induced water breakdown method [27]. Top‐ and side‐view microscope images of the as‐prepared D‐shaped fiber are shown in **Figure 7(a)**. Averaged distance between the core and the flat face of the fiber is about 7 μm, and the entire length of D‐shaped fiber is 900 μm. Measured insertion loss of the D‐shaped fiber is about 0.6 dB which guarantees the lower loss in the cavity. Secondly, the commercial solution of single‐walled carbon nanotubes with the purity of approximately 95% was used in the experiments. The diameter distribution of nanotubes is around 1.5 nm. The nanotube solution was further diluted to be a concentration of 0.05 wt% with a ten‐hour ultrasonically agitated process to minimize bundling of nanotubes. Finally, the well‐dis‐ persed aqueous solution was sprayed on the D‐shaped surface of the fiber. These devices were dried out in a vacuum oven at the temperature of 40 °C for 30 min carefully adjusted to reduce agglomeration and detaching of nanotubes. Simple encapsulation for these saturable absorb‐ ers was performed to avoid unexpected damage. A microscope image of the nanotube– deposited D‐shaped fiber is shown in **Figure 7(b)**. The transmission values of the saturable absorber were recorded by using the ultrashort‐pulse fiber laser with a MHz repetition rate at different average power. The results for both the D‐shaped fiber with nanotubes and with‐

out nanotubes are presented in **Figure 7(c)**. The result shows that the transmissivity can be changed with the increase of the input power indicating the existence of saturable absorp‐ tion. The power‐dependent transmissivity induced by nanotubes can be decreased to ∼28%. Nonsaturable loss induced by both D‐shaped fiber and other impurities is about 21%. The modulation depth of about 51% can be provided, which is higher and sufficient.

**Figure 7.** (a) Top‐view and side‐view microscope images of a D‐shaped zone in fiber, (b) microscope image of carbon nanotube–deposited D‐shaped fiber, and (c) transmissivity curves of saturable absorber and D‐shaped fiber versus the input power.

#### **3.1. Ultrashort‐pulse generation**

For the deliverable high energy of the pulse, the stabilization of mode locking should be ensured in a normal and large cavity dispersion accompanied with a high nonlinearity. A spectral filter, which is added in such a laser cavity, can be considered as an effective absorb‐ er in the spectral domain to cut off the temporal wings of the pulse and stable the mode locking. It is assumed that the spectral filter has a Gaussian profile, so the spectral filter is numerical‐

ing on pulse shaping could be investigated for the stabilization of the mode locking, as well

Single‐walled carbon nanotube is an enrolled two‐dimensional graphene honeycomb sheet with a diameter of typically 0.6–2 nm and a length distribution ranging from tens of nanome‐ ters to several micrometers. Depending on their chirality [26], single‐walled nanotubes exhibit two different electrical properties, metallic or semiconducting. Semiconducting nanotubes have an energy band gaps like those in ordinary semiconductors; thus, photons having corresponding wavelength are absorbed. Single‐walled nanotubes are a kind of promising material as saturable absorber for passive mode locking because the bandgap energy can be controlled by the tube diameter, which would be applied for different spectral ranges.

The absorption loss and modulation depth of the nanotubes‐based saturable absorber can be adjusted by changing the concentration of nanotubes, the interaction length of light with nanotubes, nonsaturable loss of fiber structure, and substrate materials. To study the effect of modulation depth on the mode locking in a larger normal dispersion cavity with high nonlinearity, the evanescent field used here is from the D‐shaped fiber that was fabricated by ablating part of the cladding of single mode fiber by the femtosecond laser‐induced water breakdown method [27]. Top‐ and side‐view microscope images of the as‐prepared D‐shaped fiber are shown in **Figure 7(a)**. Averaged distance between the core and the flat face of the fiber is about 7 μm, and the entire length of D‐shaped fiber is 900 μm. Measured insertion loss of the D‐shaped fiber is about 0.6 dB which guarantees the lower loss in the cavity. Secondly, the commercial solution of single‐walled carbon nanotubes with the purity of approximately 95% was used in the experiments. The diameter distribution of nanotubes is around 1.5 nm. The nanotube solution was further diluted to be a concentration of 0.05 wt% with a ten‐hour ultrasonically agitated process to minimize bundling of nanotubes. Finally, the well‐dis‐ persed aqueous solution was sprayed on the D‐shaped surface of the fiber. These devices were dried out in a vacuum oven at the temperature of 40 °C for 30 min carefully adjusted to reduce agglomeration and detaching of nanotubes. Simple encapsulation for these saturable absorb‐ ers was performed to avoid unexpected damage. A microscope image of the nanotube– deposited D‐shaped fiber is shown in **Figure 7(b)**. The transmission values of the saturable absorber were recorded by using the ultrashort‐pulse fiber laser with a MHz repetition rate at different average power. The results for both the D‐shaped fiber with nanotubes and with‐

**3. Mode‐locked ytterbium‐doped fiber laser with carbon nanotubes**

is the bandwidth of the spectral filter. The influence of the spectra filter‐

)<sup>2</sup> , where ω is the angular

ly implemented in the model by a function as: T(ω)=exp −(ω / Ω<sup>f</sup>

as the performance optimization of the pulses [25].

frequency, and Ω<sup>f</sup>

288 290High Energy and Short Pulse Lasers

The presented experimental setup is schematically shown in **Figure 8(a)**. A side‐pumping scheme of ytterbium‐doped fiber was taken as the gain fiber pumped by 915‐nm laser diode through a fiber combined with a coupling efficiency of 90%.

A lower absorption coefficient of gain fiber could suppress thermal effects to some extent, a 10‐m‐long ytterbium‐doped double‐clad fiber (Nufern SM‐YDF‐5/130) with a cladding absorption coefficient of 1.16 m-1 at 915 nm. The dispersion and nonlinear coefficients of ytterbium‐doped fiber are 0.02ps<sup>2</sup> · m−1 and 0.0048W−1 · m−1 , respectively. A 20‐m‐long single‐ mode fiber was employed to extend the cavity length, which correspondingly decreased the repetition rate. An optical coupler (OC) provided a 20% output ratio. The dispersion and nonlinear coefficients of single‐mode fiber are 0.022 ps<sup>2</sup> · m−1 and 0.0047 W−1 · m−1 , respective‐ ly. The total length of laser cavity is ∼36.5 m with the all‐normal cavity dispersion of ∼0.76 ps<sup>2</sup> .

Self‐starting mode locking has been achieved at the pump power of ∼0.6 W by appropriate‐ ly adjusting polarization controller. The self‐consistent pulse evolution and stable mode locking indicate that the saturable absorber performs a filtering‐equivalent function by the loss depending on light intensity to promote and stabilize the mode‐locking operation in all‐normal dispersion cavity as we expected. The pulse train generated has been observed by the oscilloscope trace as shown in **Figure 8(b)**. The pulse sequence was traced up to 2.5 μs by an oscilloscope connected with a high‐speed photodetector (3 GHz). The figure exhibits the round‐trip time of ∼178.7 ns corresponding to the repetition rate of 5.59 MHz, which is consistent with the cavity length.

The temporal profile and spectral of the pulse recorded at the pump power of 2 W are shown in **Figure 8(c)** and **(d)**. The spectrum was measured by a spectrometer with the resolution of 1 nm (Ocean Optics Inc., HR4000). The operation wavelength is around 1085 nm, which indicated nearly four energy‐level lasing behavior of ytterbium ions. The pulse duration is 46.6 ps, and the spectrum has an approximately M‐shaped profile on a linear scale with a bandwidth of ∼12.8 nm, which implies that the mode‐locking operation in the dissipative soliton regime. The pulse duration could be further decreased to 941 fs from the outside cavity simple compression by using a segment of single‐mode fiber with negative dispersion. The near Gaussian fitting shape of the pulse suggests that linear chirp dominates across the pulse in the cavity.

**Figure 8.** (a) Schematic diagram of mode‐locked fiber laser, (b) oscilloscope traces of pulse train, (c) pulse profile trace of the pulse, and (d) output spectrum (the inset is the spectrum in a log scale).

When the pump power was increased to 3.5 W, the corresponding pulse duration was enlarged to 62.6 ps, and the spectral width was broadened to 16.3 nm. The output power was almost linearly increased to 162 mW, and the corresponding pulse energy was raised to ∼29 nJ. The experimental results manifest that the evanescent‐field interaction scheme and large modula‐ tion depth of the saturable absorber would be preferentially chosen for the achievement of high‐energy pulses. Mode‐locked fiber lasers could be robust against optical wave breaking due to the linear chirp across the pulse, showing a stretched pulse with the duration up to a few or even several hundred picoseconds.

Unlike nonlinear polarization rotation effect, various new nanomaterials hardly generate fs‐ level ultrashort pulses directly from the laser oscillators [28]. A robust self‐starting picosec‐ onds ytterbium‐doped fiber laser is easy to be realized by using one of other 2D materials or topological insulators, at the aspect of characteristics of the pulses, those results are similar to these of carbon nanotubes yet. The pulse duration is limited by large normal dispersion, while the larger linear chirp dissipative solitons pulses are easy to be compressed. So the research interests are focused on various pulses dynamics of stable, self‐starting mode locking of the fiber lasers in all‐normal dispersion regime.

#### **3.2. Nanosecond‐level pulse generation**

The temporal profile and spectral of the pulse recorded at the pump power of 2 W are shown in **Figure 8(c)** and **(d)**. The spectrum was measured by a spectrometer with the resolution of 1 nm (Ocean Optics Inc., HR4000). The operation wavelength is around 1085 nm, which indicated nearly four energy‐level lasing behavior of ytterbium ions. The pulse duration is 46.6 ps, and the spectrum has an approximately M‐shaped profile on a linear scale with a bandwidth of ∼12.8 nm, which implies that the mode‐locking operation in the dissipative soliton regime. The pulse duration could be further decreased to 941 fs from the outside cavity simple compression by using a segment of single‐mode fiber with negative dispersion. The near Gaussian fitting shape of the pulse suggests that linear chirp dominates across the pulse

**Figure 8.** (a) Schematic diagram of mode‐locked fiber laser, (b) oscilloscope traces of pulse train, (c) pulse profile trace

When the pump power was increased to 3.5 W, the corresponding pulse duration was enlarged to 62.6 ps, and the spectral width was broadened to 16.3 nm. The output power was almost linearly increased to 162 mW, and the corresponding pulse energy was raised to ∼29 nJ. The experimental results manifest that the evanescent‐field interaction scheme and large modula‐ tion depth of the saturable absorber would be preferentially chosen for the achievement of high‐energy pulses. Mode‐locked fiber lasers could be robust against optical wave breaking due to the linear chirp across the pulse, showing a stretched pulse with the duration up to a

of the pulse, and (d) output spectrum (the inset is the spectrum in a log scale).

few or even several hundred picoseconds.

in the cavity.

290 292High Energy and Short Pulse Lasers

Carbon nanotubes have been demonstrated it suitable for stable long‐duration pulse mode locked in all‐normal dispersion regime [29]. Absence of nonlinear polarization evolution dynamics gives giant chirped pulses that can be suitable for compression. Here, an ultralong cavity ytterbium‐doped fiber laser mode locked by nanotubes‐based saturable absorber has been experimentally investigated. It is used a saturable absorber with the unsaturated loss of ∼57.8% and the modulation depth of ∼4.7%. The ring cavity was elongated by an one‐ kilometer‐long single‐mode fiber (YOFC, C1060), which results in an ultralong laser cavity with the length of 1021 m.

**Figure 9.** Characteristics of noise‐like pulses. Train trace (a), single pulse (b) and optical spectrum (c).

**Figure 10.** Characteristics of soliton rains. Train trace (a), single pulse (b), and optical spectrum (c).

Stable mode‐locked pulses were obtained by slightly adjusting PC at the pump power of 0.81 W. The amplitude of the pulse was increased with the increase of pump power until the power of 1.81 W, which changing into a state of multipulses. The pulse sequence and single pulse, which is a typical noise‐like pulse, have been measured and shown in **Figure 9(a)** and **(b)**, respectively. The repetition period of the pulse is approximately 5 μs. The pulse dura‐ tion is approximately 292.6 ns. When the pump power was 1.81 W, another stable state, that is, soliton rains, could be obtained with carefully adjusting the polarization controller. **Figure 10** shows the pulse train, single pulse, and the spectrum ofthe fiberlaser at the pumping power of 1.93 W. Within each pulse period, the pulse contains background noise, drifted pulse, and phase‐condensed soliton. The intensity of the drifted pulse is about 10% of the phase‐ condensed soliton. The pulse width of phase condensation soliton is about 102.5 ns at 3 dB, as shown in **Figure 10(b)**. The steady soliton rains cannot be maintained once the pump power is above 1.93 W. The maximum output poweris ∼40.3 mW with single pulse energy of ∼201.5  nJ. Output spectra of the noise‐like pulses and soliton rains have been measured and shown in **Figures 9(c)** and **10(c)**. It can be seen that both spectra have several central wavelengths indicating that the presence of filtering effect in the cavity could be used as a multiwave‐ length short‐pulse fiber laser.

Recently, it has been reported that the generated pulses of an ultralong cavity fiber laser can deliver microjoule‐level energy in the nanosecond range [30]. In the all‐normal dispersion fiber laser systems, the stable mode‐locking pulses exhibits that the formation of pulse shaping is the product of complicated processes of energy conversion. Various nonlinear effects such as self‐phase modulation, dispersion wave, peak clamping, which have strong influence on the stability of mode locking, and combining with high cavity dispersion can lead to complex pulsing phenomena, like wave‐breaking of the soliton pulse as noise‐like pulses in the results above. On the other hand, the Raman‐induced noise‐like pulses can be realized by the Raman effect in a fiber laser with high nonlinearity and dispersion [31].
