**2. Saturable absorbers**

#### **2.1. Saturable absorption effect**

Saturable absorption (SA) is a nonparametric nonlinear optical process, which occurs in many materials under excitation with high-power light beam. In general, the optical transmittance of a saturable absorber is power dependent in a way that it introduces larger losses for lowintensity light. After illumination with high-intensity light, the absorption saturates and the SA becomes more transparent. A saturable absorber is characterized by three main parameters: its modulation depth (*α*0), saturation intensity or saturation fluence (*I*sat/*F*sat), and nonsaturable losses (*α*NS). All those parameters are bound with a simple formula, which describes the powerdependent absorption *α*(*I*) of a two-level saturable absorber [11]:

$$\alpha\left(I\right) = \frac{\alpha\_0}{1 + \frac{I}{I\_{\rm sat}}} + \alpha\_{\rm NS} \tag{1}$$

**Figure 1.** Theoretical saturable absorption curve calculated from formula (1) with indicated three main parameters of a saturable absorber.

The modulation depth can be understood as the contrast ratio between the "on" and "off" states of the SA, i.e., the difference between the minimum and maximum transmission. The nonsaturable loss is a constant linear loss level, which cannot be saturated. The saturation fluence (or saturation intensity) is usually defined as the incident fluence (or intensity) needed to achieve half of the modulation depth. A typical saturable absorption curve calculated with the use of formula (1) is plotted in **Figure 1** together with indicated parameters (note that the *X*-axis is in the logarithmic scale). Alternatively, the *Y*-axis might be scaled in the transmittance value.

#### **2.2. Mode locking of lasers using saturable absorbers**

success, the scientists around the world extensively investigate other thin layered materials, such as topological insulators (TIs),transition metal dichalcogenides (TMDCs), black phospho‐

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

The popularity of 2D materials among researchers is mainly driven by their unique electrical properties and their potential applications in new-generation electronic devices. However, those materials are also characterized by multiple unique optical properties, such as broadband and almost wavelength-independent absorption or optical bistability (saturable absorption with ultrashort recovery time and high modulation depth). Those properties make 2D materials useful in laser technology, e.g., as saturable absorbers for lasers emitting ultrashort optical pulses. The so-called mode-locked lasers, emitting ultrashort pulses in the infrared range, are currently on demand of many industrial, military, and medical applications. They might be used in many various fields, e.g., in medicine and surgery [2], materials processing [3], laser spectroscopy [4, 5], and fundamental science (generation of terahertz waves [6], multiphoton systems for optical imaging [7], or supercontinuum generation [8]). Ultrafast lasers are also main building blocks of optical frequency combs, which are currently used in, e.g., spectrograph calibration enabling detection of extrasolar planets [9] or optical-atomic clocks [10]. The research on novel 2D materials strongly contributes to the development of novel laser sources, enabling generation of shorter pulses and broader bandwidths at new wavelength regions, previously uncovered by any other coherent light source. This chapter explains the fundamentals of ultrashort pulse generation and reviews and summarizes the most important recent achievements in the field of ultrafast lasers incorporating 2D materials.

Saturable absorption (SA) is a nonparametric nonlinear optical process, which occurs in many materials under excitation with high-power light beam. In general, the optical transmittance of a saturable absorber is power dependent in a way that it introduces larger losses for lowintensity light. After illumination with high-intensity light, the absorption saturates and the SA becomes more transparent. A saturable absorber is characterized by three main parameters: its modulation depth (*α*0), saturation intensity or saturation fluence (*I*sat/*F*sat), and nonsaturable losses (*α*NS). All those parameters are bound with a simple formula, which describes the power-

*NS*

+ (1)

 a

dependent absorption *α*(*I*) of a two-level saturable absorber [11]:

a

( ) <sup>0</sup> 1

*<sup>I</sup> <sup>I</sup>*

*sat*

*I*

a

= +

rus (BP), and many others.

**2. Saturable absorbers**

**2.1. Saturable absorption effect**

Thanks to its "bistable" nature, a saturable absorber might act as a very fast optical switch when inserted into a laser cavity. A simplified schematic of a laser resonator incorporating a saturable absorber is depicted in **Figure 2(a)**. After turning on the laser (i.e., pumping the gain medium), the saturable absorber is in its "off" state, introducing quite high losses, which predominate the laser gain (see **Figure 2(b)**). After a short period of time (e.g., few hundreds of cavity roundtrips), an optical pulse will spontaneously arise from the continuous wave (CW) noise. If the intensity of the pulse will be high enough, it will pass through the SA with smaller losses than the CW noise. In consequence, a short pulse might be emitted from such laser [12]. An ultrashort pulse is always an effect of constructive interference between a certain number of longitudinal modes in the cavity. In order to achieve this interference, the consequent modes need to have fixed phase relationship with each other. In other words, the phase of the modes

**Figure 2.** Illustration of a laser cavity with inserted saturable absorber (a) and pulse train formed in the cavity as a result of resonator loss modulation (b).

needs to be locked ("mode locking"). If the modes would oscillate randomly (without phase coherence), the output radiation would be multimode, continuous wave (CW). When the phases of the modes are locked, the laser will generate optical pulses according to the rule: more synchronized modes—shorter pulses.

There are several types of saturable absorbers currently used in laser technology. They can be generally classified into two categories: artificial and real SAs (see **Figure 3**). The term "artificial SA" refers to a mode-locking technique, where a nonlinear optical effect (which is power dependent) acts as a saturable absorber. Among those techniques, the most important include nonlinear polarization rotation (NPR), nonlinear loop mirrors (NOLM) or nonlinear amplify‐ ing loop mirror (NALM), and Kerr-lens mode locking (KLM).

Among real saturable absorbers we can distinguish two groups: semiconductors (so-called semiconductor saturable absorber mirrors, SESAMs) and nanomaterials. The SESAMs are currently one of the most widely used saturable absorbers in solid-state and fiber lasers, also in commercially available industrial systems. They are based on a well-established technology developed for more than 20 years [13]. However, SESAMs have some limitations. The technology is based on semiconductors (e.g., InGaAs/GaAs quantum wells), which are characterized by an energy band gap. Consequently, this results in a limited wavelength operation range. Thus, each SESAM needs to be designed strictly for a specific laser (operating at a certain wavelength). Fabrication of the SESAM also involves expensive and complicated molecular beam epitaxy (MBE) technology [14]. All those limitations have driven the laser community to seek for alternative, new saturable absorber materials. The field of nanomaterialbased SAs emerged in recent years to one of the most important branches of ultrafast laser technology. This new era started in 2003 as Set et al. [15] demonstrated the first CNT modelocked fiber laser. Few years later, in 2009, the first lasers utilizing graphene were reported [16, 17]. Starting from this date, the number of papers and reports on fiber lasers mode-locked with graphene and other 2D materials: topological insulators, transition metal dichalcogenides, and recently black phosphorus, grow rapidly.

**Figure 3.** Types of saturable absorbers for ultrafast lasers.

needs to be locked ("mode locking"). If the modes would oscillate randomly (without phase coherence), the output radiation would be multimode, continuous wave (CW). When the phases of the modes are locked, the laser will generate optical pulses according to the rule:

**Figure 2.** Illustration of a laser cavity with inserted saturable absorber (a) and pulse train formed in the cavity as a

There are several types of saturable absorbers currently used in laser technology. They can be generally classified into two categories: artificial and real SAs (see **Figure 3**). The term "artificial SA" refers to a mode-locking technique, where a nonlinear optical effect (which is power dependent) acts as a saturable absorber. Among those techniques, the most important include nonlinear polarization rotation (NPR), nonlinear loop mirrors (NOLM) or nonlinear amplify‐

Among real saturable absorbers we can distinguish two groups: semiconductors (so-called semiconductor saturable absorber mirrors, SESAMs) and nanomaterials. The SESAMs are currently one of the most widely used saturable absorbers in solid-state and fiber lasers, also in commercially available industrial systems. They are based on a well-established technology developed for more than 20 years [13]. However, SESAMs have some limitations. The technology is based on semiconductors (e.g., InGaAs/GaAs quantum wells), which are characterized by an energy band gap. Consequently, this results in a limited wavelength operation range. Thus, each SESAM needs to be designed strictly for a specific laser (operating at a certain wavelength). Fabrication of the SESAM also involves expensive and complicated molecular beam epitaxy (MBE) technology [14]. All those limitations have driven the laser community to seek for alternative, new saturable absorber materials. The field of nanomaterialbased SAs emerged in recent years to one of the most important branches of ultrafast laser technology. This new era started in 2003 as Set et al. [15] demonstrated the first CNT modelocked fiber laser. Few years later, in 2009, the first lasers utilizing graphene were reported [16, 17]. Starting from this date, the number of papers and reports on fiber lasers mode-locked with graphene and other 2D materials: topological insulators, transition metal dichalcogenides, and

more synchronized modes—shorter pulses.

result of resonator loss modulation (b).

recently black phosphorus, grow rapidly.

ing loop mirror (NALM), and Kerr-lens mode locking (KLM).

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

There are several techniques of fabricating saturable absorber devices using 2D materials and make them suitable for use in a mode-locked laser, which might be either a solid-state or a fiber-based laser. The most popular approaches are illustrated in **Figure 4**.

The material might be deposited on a glass plate (plano window or a wedge) and inserted into the cavity as a free-space transmission saturable absorber (**Figure 4a**). This approach is most suitable for solid-state lasers [18–20]. For example, in the work of Ugolotti et al., a graphene monolayer grown via chemical vapor deposition (CVD) was transferred from a copper substrate on to a 1 mm thick quartz plate, with the use of poly(methylmethacrylate) (PMMA) polymer. Such SA exhibited 0.75% of modulation depth at 1 μm wavelength and supported mode locking with around 32 μm spot size on the graphene surface. Glass windows with deposited SA material might also be used in fiber lasers (e.g., with graphene [21]), but this approach seems not to be as efficient as the other methods. The world's first TI-based fiber laser used a Bi2Te3 layer deposited on a quartz plate and inserted into the cavity between two collimators [22].

**Figure 4.** Common techniques of depositing SA material on optical substrates: on glass plates (a), mirrors (b), and fiber connectors (c).

The SA material might also be deposited on a mirror (**Figure 4b**) and inserted into a linear laser cavity (both fiber based or free space). In the case of a fiber ring-shaped resonator, one can use a circulator to couple the mirror with the cavity. This approach was used, e.g., by Xu et al. [23, 24] for the generation of femtosecond pulses from Er-doped fiber lasers. Graphene-coated mirrors might also serve as saturable absorbers in linear laser cavities as demonstrated by Cunning et al. [25]. However, usually graphene-coated mirrors serve as saturable absorbers for solid-state lasers [26–29]. The most impressive results were obtained by Ma et al. [29]. The SA was based on high-quality, CVD-grown monolayer graphene transferred onto a highly reflecting dielectric mirror. The spot size on the SA was about 60 μm. The laser was capable of generating 30 fs pulses at 50 nm bandwidth centered at 1070 nm [29].

The probably most popular and common technique of fabricating saturable absorbers with 2D materials is based on fiber connectors (as shown in **Figure 4c**). This approach was already demonstrated with graphene [30, 31], TIs [32, 33], TMDCs [34, 35], and BP [36, 37]. It is a very convenient method since it is alignment free and very robust. It allows to keep the cavity fully fiberized, which is very advantageous—the lasers are more compact, stable, and invulnerable to external disturbances.

The newest technique of SA fabrication is based on the evanescent field interaction effect. For this purpose, tapered fibers (microfibers) or side-polished (D-shaped) fibers might be used (**Figure 5**). The saturable absorption is based on the interaction between the evanescent field propagating in the cladding of the fiber and the deposited material. Such saturable absorbers were first used in combination with carbon nanotubes [38]. In 2010, Song et al. [39] demon‐ strated the usage of a graphene-coated D-shaped fiber as a saturable absorber. The laser was capable of generating pulses at 1561 nm with 2 nm of full width at half maximum (FWHM) bandwidth. Afterward, the deposition of TIs and TMDCs on such fibers was demonstrated [40, 41]. The alternative approach, using tapered fibers, is also commonly used and was demon‐ strated by several authors [42–46].

**Figure 5.** Saturable absorbers with evanescent field interaction: a fiber taper (a) and side-polished (D-shaped) fiber (b).

The performance of fiber lasers with evanescent field interaction is indisputable: 70 fs pulses were generated with a TI deposited on a tapered fiber [47], whereas Sb2Te2 deposited on a sidepolished fiber allowed to achieve 128 fs pulses [48]. However, both techniques have some serious drawbacks. A saturable absorber based on a D-shaped fiber, due to its asymmetry, is always characterized by a polarization-dependent loss (PDL), which mostly depends on the material type (its refractive index), interaction length, and the distance between the polished region and the fiber core. In some reports, the PDL was kept at quite low levels (e.g., 1 dB in [49] with 6 μm distance between the material and the core), but sometimes it exceeds several dB [50]. In this situation, it is difficult to distinguish whether the mode locking originates from nonlinear polarization rotation or from the saturable absorption in the 2D material. In 2015, Bogusławski et al. [51] performed an experiment, which has unambiguously proven that mode locking in such oscillators is a combination of both effects. The study revealed that the hybrid mode-locking mechanism (combined NPR with saturable absorption of Sb2Te3 topological insulator) allows to achieve the best performance (in terms of bandwidth and pulse duration), when compared with a truly NPR or a TI-SA mode-locked laser. In the case of taper-based SAs, it is worth mentioning that in order to achieve sufficient interaction the fiber diameter needs to be reduced to less than 7 μm [42–45], which makes the taper quite long (from 5 to 18 cm waist length [44, 52]), and obviously much more fragile than a normal optical fiber. On the other hand, many authors who investigated evanescent field interaction claim higher optical power-induced damage threshold for such SA in comparison to connector end-face deposition due to better thermal management [39].

### **2.3. Nonlinear absorption measurements**

**Figure 4.** Common techniques of depositing SA material on optical substrates: on glass plates (a), mirrors (b), and fiber

The SA material might also be deposited on a mirror (**Figure 4b**) and inserted into a linear laser cavity (both fiber based or free space). In the case of a fiber ring-shaped resonator, one can use a circulator to couple the mirror with the cavity. This approach was used, e.g., by Xu et al. [23, 24] for the generation of femtosecond pulses from Er-doped fiber lasers. Graphene-coated mirrors might also serve as saturable absorbers in linear laser cavities as demonstrated by Cunning et al. [25]. However, usually graphene-coated mirrors serve as saturable absorbers for solid-state lasers [26–29]. The most impressive results were obtained by Ma et al. [29]. The SA was based on high-quality, CVD-grown monolayer graphene transferred onto a highly reflecting dielectric mirror. The spot size on the SA was about 60 μm. The laser was capable

The probably most popular and common technique of fabricating saturable absorbers with 2D materials is based on fiber connectors (as shown in **Figure 4c**). This approach was already demonstrated with graphene [30, 31], TIs [32, 33], TMDCs [34, 35], and BP [36, 37]. It is a very convenient method since it is alignment free and very robust. It allows to keep the cavity fully fiberized, which is very advantageous—the lasers are more compact, stable, and invulnerable

The newest technique of SA fabrication is based on the evanescent field interaction effect. For this purpose, tapered fibers (microfibers) or side-polished (D-shaped) fibers might be used (**Figure 5**). The saturable absorption is based on the interaction between the evanescent field propagating in the cladding of the fiber and the deposited material. Such saturable absorbers were first used in combination with carbon nanotubes [38]. In 2010, Song et al. [39] demon‐ strated the usage of a graphene-coated D-shaped fiber as a saturable absorber. The laser was capable of generating pulses at 1561 nm with 2 nm of full width at half maximum (FWHM) bandwidth. Afterward, the deposition of TIs and TMDCs on such fibers was demonstrated [40, 41]. The alternative approach, using tapered fibers, is also commonly used and was demon‐

of generating 30 fs pulses at 50 nm bandwidth centered at 1070 nm [29].

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

connectors (c).

to external disturbances.

strated by several authors [42–46].

The three basic nonlinear parameters of a saturable absorber (modulation depth, saturation fluence, and nonsaturable loss) might be measured in the so-called power-dependent trans‐ mission setup, which is depicted in **Figure 6**.

As a pumping source, an amplified pulsed laser (e.g., femtosecond or picosecond) is used in order to provide intensity high enough to saturate the saturable absorber. The beam from the laser is divided into two parts. The first beam acts as a reference channel and is directed to the power meter, whereas the second beam is focused by a lens and directed to the saturable absorber (e.g., 2D material deposited on a quartz plate). The sample is scanned along the waist of the beam (in the *z*-axis) in order to change the field intensity on the surface of the material. The power in both arms is measured by a dual-channel power meter and afterward compared in order to calculate the saturable absorption curve.

**Figure 6.** Power-dependent transmission measurement of a saturable absorber in free-space configuration.

In the case of fiber-based saturable absorbers (e.g., 2D material deposited on connectors or tapered fibers/D-shaped fibers), a modified version of the setup needs to be used. The schematic of an all-fiber power-dependent transmission experiment is depicted in **Figure 7**. Here, the power incident on the sample might tune with the use of a variable optical attenuator (VOA). The beam from the pump laser is also divided into two parts, but this time using a fiber coupler with defined coupling ratio, e.g., 50%/50%. Again, after passing through the absorber, the power is measured and compared with the reference channel.

**Figure 7.** Power-dependent transmission measurement of a saturable absorber in all-fiber configuration.

### **3. Mode locking of lasers using graphene**

#### **3.1. Graphene**

Graphene, one of the allotropes of carbon, is commonly described as a "wonderful material", thanks to its unique electronic properties and a great number of possible applications. Besides the application in pulsed lasers, graphene was successfully used in many optoelectronic devices, such as photodetectors [53], modulators [54], polarizers [55], sensors [56], and solar

cells [57]. The lack of the band gap in pristine graphene [58] might generally be unwanted in some electronic applications, but makes it extremely useful in photonics. Thanks to this unique property, graphene is characterized by a constant absorption coefficient in a wide spectral range. In consequence, it might act as a saturable absorber in lasers operating at different wavelengths. The historically first lasers mode-locked with graphene were developed in 2009 independently by the groups from Singapore and United Kingdom [16, 17]. Shortly after those reports, a number of papers appeared, demonstrating novel concepts of ultrafast lasers utilizing various forms of graphene. In this section, the unique optical properties of graphene will be discussed. The recent experimental results reported in the literature are described and compared.
