**3.2. Saturable absorption of graphene**

The power in both arms is measured by a dual-channel power meter and afterward compared

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

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

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

the power is measured and compared with the reference channel.

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

**3.1. Graphene**

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,

in order to calculate the saturable absorption curve.

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

The process of saturable absorption in a graphene was extensively studied by researchers in the recent years [59–61]. The process is schematically explained in **Figure 8**. A single graphene layer absorbs approximately a 2.3% fraction of the incident light [62]. The illumination causes excitation of the electrons from the valence band to the conduction band. After a very short relaxation time, these electrons cool down to a Fermi–Dirac distribution (step 2). After further illumination with high intensity light, the energy states in both bands fill, which blocks further absorption (Pauli blocking), and the saturable absorber bleaches [16, 61]. Graphene is charac‐ terized by a fast 70 – 150 fs relaxation transient, followed by a slower relaxation process in the 0.5 – 2.0 ps range, which was confirmed by pump-probe measurements [59, 60].

**Figure 8.** Saturable absorption in graphene [16, 59–61]. Light absorption and excitation of carriers (1), electrons cool down to a Fermi–Dirac distribution (2), and Pauli blocking (3).

As mentioned previously, a single layer of graphene absorbs approximately 2.3% of incident low intensity light. This absorption coefficient remains constant over a broad bandwidth, ranging from the visible to the mid-infrared [63]. However, the saturable absorption (i.e., the modulation depth) is slightly wavelength dependent. **Table 1** summarizes the experimentally obtained values of modulation depth, nonsaturable loss, and saturation fluence of monolayer graphene measured at four different wavelengths. It can be seen that the modulation depth is the highest at shortest wavelength (800 nm) and drops quite rapidly with increased pump wavelength (0.5% at 1500 nm).


**Table 1.** Summary of the experimentally obtained modulation depth value of monolayer graphene at different wavelengths.

An exemplary measurement of the nonlinear transmission through a CVD-grown monolayer of graphene deposited on a glass window is plotted in **Figure 9**. The curve was obtained using an experimental setup as depicted in **Figure 6**, with a 80-fs fiber laser operating at 1560 nm as an excitation source.

**Figure 9.** Measurement of saturable absorption in monolayer graphene.

Since graphene is considered as a fast saturable absorber (which is determined by its short relaxation time), its nonlinear transmission is described by different, more complex formula than the presented previously (Eq. (1)), valid for fast SAs [65, 66]:

$$T\left(F\right) = \frac{\Delta T}{\sqrt{F\_{\text{sat}} + \left(\frac{F}{F\_{\text{sat}}}\right)^2}} \operatorname{atanh}\left(\sqrt{\frac{F}{F\_{\text{sat}} + F}}\right) + \left(1 - \alpha\_{\text{NS}}\right) \tag{2}$$

where Δ*T* denotes the modulation depth. The theoretical fit (solid red line in **Figure 9**) was calculated using the following parameters: *F*sat = 105 μJ/cm2 , *α*NS = 1.1%, and Δ*T* = 1.24%. The theoretical curve fits very well the experimental data; however, it can be seen that the sample was not fully saturated due to insufficient pump power.

#### **3.3. Controlling the modulation depth of graphene-based saturable absorbers**

the highest at shortest wavelength (800 nm) and drops quite rapidly with increased pump

 1.8 < 0.9 66.5 [20] 0.75 1.59 50 [18] 0.54 1.61 14.5 [64] 0.5 1.9 14 [19]

**Table 1.** Summary of the experimentally obtained modulation depth value of monolayer graphene at different

An exemplary measurement of the nonlinear transmission through a CVD-grown monolayer of graphene deposited on a glass window is plotted in **Figure 9**. The curve was obtained using an experimental setup as depicted in **Figure 6**, with a 80-fs fiber laser operating at 1560 nm as

Since graphene is considered as a fast saturable absorber (which is determined by its short relaxation time), its nonlinear transmission is described by different, more complex formula

( ) ( ) <sup>2</sup>

æ ö <sup>=</sup> ç ÷ + - <sup>+</sup> æ ö è ø

*F F F F*

<sup>Δ</sup> <sup>1</sup> *NS sat*

a

(2)

**] Ref.**

wavelength (0.5% at 1500 nm).

wavelengths.

an excitation source.

**λ[nm] ΔT [%] αNS [%] Fsat [μJ/cm<sup>2</sup>**

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

**Figure 9.** Measurement of saturable absorption in monolayer graphene.

than the presented previously (Eq. (1)), valid for fast SAs [65, 66]:

*sat sat*

*F F*

*T F T F atanh*

+ ç ÷ è ø As shown in the previous section, the modulation depth of a single graphene layer at the two most popular fiber laser wavelengths (1 and 1.55 μm) is quite small, at the level of 1%. Typically, in the case of fiber lasers, such modulation depth is insufficient to initiate stable mode locking and generate ultrashort optical pulses. It is therefore necessary to increase the modulation depth of a graphene-based saturable absorber. This might be done by scaling the number of graphene layers in the SA device. What is also important, the modulation depth is a critical parameter which determines the behavior of a laser. The influence of the modulation depth of the saturable absorber on the performance of mode-locked lasers was already extensively investigated numerically and experimentally. As an example, the study of Sobon et al. [67] has revealed that large numbers of graphene layers are required to achieve optimal performance for subpicosecond mode-locked operation of an Er- and Tm-doped laser. Unfortunately, increasing the number of layers does not only change the modulation depth, but causes also an increase of nonsaturable losses, which are usually unwanted in fiber lasers.

The optical transmittance of multilayer graphene was investigated by Zhu et al. They have derived a simplified formula, which describes the transmittance as a function of number of layers [68]:

$$T\left(N\right) = \left(1 + \frac{1.13 \cdot \pi aN}{2}\right)^{-2} \tag{3}$$

where *N* denotes the number of layers and *α* is the fine-structure constant revealed by Nair et al. [62] (≈1/137). However, this formula is valid only for multilayer graphene with defined stacking sequence (e.g., ABA or ABC). Such ordered structure might be achieved, e.g., in a CVD growth process on nickel (Ni) substrate [68]. This formula takes into account the interactions between the adjacent layers, which are present only when the graphene layers are properly stacked.

In the case of undetermined stacking, when, e.g., the graphene layers were grown separately and afterward stacked together, and there are no inter-layer interactions, a different formula needs to be used to calculate the transmittance:

$$T\left(N\right) = \left(1 - \pi\alpha\right)^{N}\tag{4}$$

The passage of a laser beam through such a multilayer graphene stack is illustrated in **Figure 10**. The transmittance vs. number of layers curve calculated using both formulas is plotted in **Figure 11**, together with experimental data obtained in [67].

**Figure 10.** Light absorption in multilayer graphene without any interaction between the layers.

**Figure 11.** Optical transmittance of multilayer graphene: calculated from formula (1) (red line, no interaction between layers), calculated from formula (2) (blue line, including layer interactions), and measured using multilayer graphene (dotted line) [67].

As mentioned before, the modulation depth of graphene strongly depends on the number of layers. This allows to fabricate a proper saturable absorber to fulfill the requirements of a designed mode-locked laser. For example, dispersion-managed lasers (e.g., dissipative soliton lasers or stretched-pulse lasers) require much higher modulation depths than soliton lasers [69]. **Figure 12** shows the examples of nonlinear transmission curves of saturable absorbers containing 9, 12, 24, and 37 graphene layers [67]. It can be easily seen that the modulation depth increases with the growing number of layers. It starts from 3% for 9 layers, up to 7.5% for 37 layers.

**Figure 12.** Nonlinear transmission curves of saturable absorbers containing 9, 12, 24, and 37 graphene layers.

#### **3.4. Pulsed fiber lasers with graphene**

The passage of a laser beam through such a multilayer graphene stack is illustrated in **Figure 10**. The transmittance vs. number of layers curve calculated using both formulas is plotted in

**Figure 11.** Optical transmittance of multilayer graphene: calculated from formula (1) (red line, no interaction between layers), calculated from formula (2) (blue line, including layer interactions), and measured using multilayer graphene

As mentioned before, the modulation depth of graphene strongly depends on the number of layers. This allows to fabricate a proper saturable absorber to fulfill the requirements of a designed mode-locked laser. For example, dispersion-managed lasers (e.g., dissipative soliton lasers or stretched-pulse lasers) require much higher modulation depths than soliton lasers [69]. **Figure 12** shows the examples of nonlinear transmission curves of saturable absorbers containing 9, 12, 24, and 37 graphene layers [67]. It can be easily seen that the modulation depth increases with the growing number of layers. It starts from 3% for 9 layers, up to 7.5% for 37

(dotted line) [67].

layers.

**Figure 11**, together with experimental data obtained in [67].

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

**Figure 10.** Light absorption in multilayer graphene without any interaction between the layers.

The broadband saturable absorption of graphene makes this material an universal SA for different types of lasers. It has been already shown that the same graphene SA can provide mode locking in Yb-, Er-, and Tm-doped lasers [70], or can also synchronize and phase-lock two lasers simultaneously [71, 72].

**Figure 13** shows the examples of three fiber lasers: Yb- (a), Er- (b) and Tm-doped (c) modelocked with multilayer graphene composite. In the figure, each laser setup is depicted with its corresponding optical spectrum (e–g). All lasers were based on fully fiberized ring resonators and they utilized CVD-grown multilayer graphene immersed in a PMMA polymer support [73]. The Yb-doped oscillator consists of a segment of active fiber, an isolator, an output coupler (with 40/60% coupling ratio), a band-pass filter (BPF) with 2 nm FWHM, a polarization controller (PC), a 976 nm/1064 nm wavelength division multiplexer (WDM) and the saturable absorber. The laser was pumped by a 976 nm laser diode. Due to the normal dispersion of all fibers used in the cavity, a BPF is necessary to obtain dissipative soliton operation [74]. With the use of 48 layers of graphene in the SA, the laser generated pulses centered at 1059 nm and around 1.5 nm bandwidth and 17.1 MHz repetition frequency.

The Er-doped fiber laser shown in **Figure 13(b)** was realized in a simplified configuration, with the use of a hybrid component comprising an 10% output coupler (OC), a WDM and an isolator (ISO) in one integrated device. All fibers and components were polarization maintaining (PM), so there was no need to use a PC to initiate the mode locking. The optical spectrum generated with the use of 32 layers of graphene is depicted in **Figure 13(e)**. It is centered at 1561 nm and has an FWHM of 20 nm, whereas the repetition rate was 100 MHz. The Tm-doped fiber laser was designed analogously to the Er-doped laser, but in this case the cavity was not all-PM, so the laser needs polarization alignment to initiate the mode locking. The oscillator is pumped at 1566 nm wavelength using a laser diode, beforehand amplified in an Erbium-doped fiber amplifier (EDFA). In this case, 12 layers of graphene were sufficient to support stable mode locking at 1968 nm with 10 nm of bandwidth (**Figure 13f**) and 100.25 MHz repetition frequency.

**Figure 13.** Fiber lasers operating at 1 μm (a), 1.55 μm (b), and 1.97 μm (c), and the corresponding optical spectra gener‐ ated by those lasers (d, e, f).

#### **3.5. Graphene-based ultrafast lasers – literature examples**

#### *3.5.1. Solid-state lasers*

Efficient mode locking of solid-state lasers (SSLs) with the use of real saturable absorbers is quite challenging. The gain of an active medium (bulk crystal) is not as large as in fiber lasers, and in addition, the free-space resonator needs to be carefully aligned. Also the losses introduced by the SA should be possibly small. This is why most of the graphene-based SSLs utilize monolayer or bi-layer graphene. Up till now, mode locking of SSLs ranging from 532 to 2500 nm has been demonstrated [75, 76].

As an example, Baek et al. [20] demonstrated a Ti:Sapphire laser mode-locked with monolayer graphene. The laser generated 63 fs pulses at 800 nm central wavelength. There were also several reports on lasers operating around 1 μm wavelength [27–29]. The most prominent result was obtained by Ma et al. [29]. The authors have demonstrated stable 30 fs pulses centered at 1068 nm from diode pumped Yb:CaYAlO4 laser by using high-quality CVD monolayer graphene as saturable absorber. These are the shortest pulses ever reported from graphene mode-locked lasers.

Broadband saturable absorption of graphene enables to achieve ultrashort pulse generation also in the mid infrared region. For example, Ma et al. [77] demonstrated a SSL based on a Tmdoped calcium lithium niobium gallium garnet (Tm:CLNGG) crystal, generating 729 fs pulses at 2018 nm. The SA was formed by transferring CVD-grown, high-quality, and large-area graphene on a highly reflective plane mirror. Later, Cizmeciyan et al. [76] further extended the spectral coverage of graphene-based lasers by using a Cr:ZnSe crystal. High-quality monolayer graphene transferred on a CaF2 windows enabled generation of 232 fs pulses at 2500 nm wavelength.
