**4.1. Topological insulators**

fs) [63]. In 2014, Tarka et al. [89] reported generation of 168 fs pulses. Both lasers (from [89] and [63]) were characterized by similar cavity design and similar saturable absorber (graphene obtained via LPE), with quite low modulation depth (2.6 and 2.0%). In both cases the pulse duration was also comparable (168 and 174 fs). The significant improvement in terms of pulse duration was possible not only by proper dispersion management, but mainly by increasing of the SA modulation depth to 11% [88]. The parameters of the three lasers with shortest

> **Cavity net dispersion**

(~-0.0015 ps2

168 fs 15.2 nm Anomalous LPE graphene in

ps2 )

Thulium-doped fiber lasers operating in the 1.9–2.0 μm are currently considered as one of the most important branches of laser technology [90, 91]. The number of applications of such lasers

Pulsed Tm-doped fiber lasers are suitable for use in many surgical and dermatological procedures. Due to strong absorption of the 1.9–2.0 μm radiation in water, heating of only small areas of human tissues is achieved. The light penetration into the tissue is at the level of microns, which allows precise cutting. In addition, bleeding is suppressed by coagulation [92].

The second application, where Tm-doped fiber lasers might be used is laser spectroscopy, e.g., remote detection of air pollutants. The 1.9–2.0 μm spectral region contains multiple absorption lines of several molecules, especially two harmful greenhouse gases: carbon dioxide (CO2) and nitrous oxide (N2O). Carbon dioxide is the primary greenhouse gas that is contributing to recent climate change. It is absorbed and emitted naturally as part of the carbon cycle (e.g., animal and plant respiration, volcanic eruptions, ocean-atmosphere exchange), but also human activities strongly contribute to the global emission of CO2 (e.g., burning of fossil fuels) [93]. Nitrous oxide is also a major greenhouse gas and air pollutant. The N2O molecules stay in the atmosphere for an average of 120 years before being removed by a sink or destroyed through chemical reactions. Globally, about 40% of total N2O emissions come from human activities [94]. Nitrous oxide is emitted from agriculture (when nitrogen is added to the soil

)

**Saturable absorber**

Multilayer CVDgraphene/PMMA

LPE graphene in Polivinyl alcohol **SA mod. depth**

11% [88]

2.6% [89]

2% [63]

**Ref.**

**type**

chitosan

(PVA)

reported pulses are summarized in **Table 2**.

**duration**

138 Two-dimensional Materials - Synthesis, Characterization and Potential Applications

**FWHM bandwidth**

88 fs 48 nm Balanced

174 fs 15.6 nm Balanced (~-0.05

**Table 2.** Summarized parameters of three graphene-based lasers emitting the shortest pulses.

**Author/Group Pulse**

1J. Sotor et al. / Wroclaw Univ. of Technology

2J. Tarka et al. / Wroclaw Univ. of Technology

Univ.

3D. Popa et al. / Cambridge

rapidly grows.

*3.5.4. Thulium-doped fiber lasers*

Among all the identified topological insulators, three have found very much attention by the photonics community: bismuth telluride (Bi2Te3), bismuth selenide (Bi2Se3) and antimony telluride (Sb2Te3). Carrier recombination mechanism in those materials was already investi‐ gated using time-resolved and angle-resolved photoelectron spectroscopy (tr-ARPES) [101– 104], confirming the presence of surface metallic states.

The first mode-locked fiber laser incorporating a TI-based saturable absorber was proposed by Zhao et al. [22]. The oscillator emitted 1.21 ps pulses at 1558 nm with the use of Bi2Te3 TI. Further studies on the third-order nonlinear properties of Bi2Te3 performed by the same group revealed that the material might exhibit modulation depth up to 61.2% and possesses a very high third-order nonlinear refractive index, at the level of 10−14 m2 /W [105]. The most prominent and important research results on TI-based lasers include: the first demonstration of a Bi2Se3 based fiber laser [106], the first demonstration of harmonic mode locking with Bi2Te3 [107], first demonstration of the usage of Sb2Te3 topological insulator for mode locking [32], harmonic mode locking with Sb2Te3 [108], or development of TI-polymer composites [33]. The shortest pulse generated with a TI-based saturable absorber was reported in 2016 by Liu et al. [47]. The oscillator incorporated Sb2Te3 TI deposited on a tapered fiber and delivered 70 fs pulses at 1542 nm wavelength, whose 3 dB spectral width is 63 nm with a repetition rate of 95.4 MHz. However, the mode locking was not truly SA based—the cavity contained an additional polarizer and wave-plates. Thus, the mode locking was a result of a hybrid combination of saturable absorption and NPR. The shortest pulses achieved directly from an oscillator modelocked only by a TI-based SA were 128 fs [48].
