1. INTRODUCTION

Lasers, since first demonstrated by a ruby crystal in 1960 [1], have shown tremendous progress so far. On account of the advantages of large pulse energy, short pulse duration, and high peak power, pulse lasers, including mode-locking and $Q$-switching, receive more widespread attention [2,3]. Pulsed lasers with the pulse width from nanosecond to subpicosecond scales play a key role in the industrial machining, remote sensing, and military defense areas [4]. Ultrashort femtosecond lasers have significant applications in the fields of the in-situ detection, complex reaction dynamics, medical survey, and telecommunication [3]. Passive pulse modulation could be operated with compact and cost-effective structures, such that it has become an influential research direction in the laser field. Taking advantage of saturable absorption of saturable absorbers, that is part of the third-order nonlinear properties, passive pulse modulation in the $Q$-switched or mode-locking lasers could be easily implemented. Traditional saturable absorbers, such as ion-doped crystals (Cr:YAG, Cr:ZnSe, V:YAG, and so on) [5 –7], GaAs [8], and color-center crystals (for example ${\mathrm{F}}_2\text{:}\mathrm{LiF}$) [9], are wavelength-sensitive and are only applied in their respective corresponding wavelength bands. Although the commercial semiconductor saturable absorber mirrors (SESAMs) could be fabricated for the specific wavelength from 0.4 to 2.5 μm by using different semiconductor material systems [2,10], the relatively complex structural design may increase the product cost and the difficulty of preparation. In addition, the quasi-phase-matching technique in optical superlattice, which is feasible for a wide wavelength range as long as it is in the transparent spectral region of the optical superlattice material, is also a promising method to obtain passive mode-locking lasers [11 –13]. Nevertheless, this technique requires the high-efficiency generation of second-harmonic generation and elaborate design of the resonant cavity and the second-harmonic crystal. Therefore, the development of low-cost and robust broadband saturable absorbers is still an intense focus of research nowadays [2].

Graphene, as the representative of the two-dimensional (2D) materials, since found by K. Geim and K. S. Novoselov, has profoundly promoted and broadened the research areas of 2D materials in the fields of electronics and optoelectronics due to an abundance of fantastic physics [14 –23]. With in-depth studies, many other novel 2D materials are discovered and are brought into people’s horizons, such as transition metal dichalcogenides (TMDCs) (typically ${\mathrm{MoS}}_2$, ${\mathrm{MoSe}}_2$, ${\mathrm{WS}}_2$, and so on) [16,17,19,24,25], transition metal oxides (for instance ${\mathrm{MoO}}_3$ and ${\mathrm{TiO}}_2$) [17,24,26], topological insulators (${\mathrm{Bi}}_2{\mathrm{Se}}_3$, ${\mathrm{Bi}}_2{\mathrm{Te}}_3$, and ${\mathrm{Sb}}_2{\mathrm{Te}}_3$) [16,17,24,27], as well as silicone [28], germanane [16,28], black phosphorus [29,30], and other graphene analogues (typically $h$-BN) [19,24]. For the major 2D materials, the layered structure results in the strong in-plane coupling and the weak van der Waals coupling between layers. Therefore monolayer or few-layer 2D perfect samples could be easily fabricated by mechanical exfoliation or chemical exfoliation [18,31]. In addition, aiming at the growth habits and atomic arrangements for different 2D materials, many more efforts are made to explore the economical and practical growth methods, such as chemical vapor deposition, and epitaxial growth on adaptive substrates [21,25]. The layered 2D materials exhibit numerous exotic physical, chemical, and mechanical properties such that they are rapidly developed. Many potential functional applications in terms of 2D materials in some aspects will be realized in the near future, including optical modulators, photodetectors, logic transistors, high-frequency transistors, energy storage, and sensor devices [16 –18,24,31].

Most 2D semiconductor materials show a simple two energy band structure of the conduction band and the valence band. Light that is of higher energy than the gap energy can excite carriers from the valance band to the conduction band. If the excitation has stronger intensity, all possible initial states are depleted and the final states are partially occupied in accordance with the Pauli blocking effect such that the absorption will be saturated [2]. Thus the 2D semiconductor materials give some opportunities for the fabrication of cost-effective and flexible broadband saturable absorbers, and some 2D materials have realized this goal [4,32 –34]. Saturable absorption is the modulation of nonlinear absorption. However, the bandgap of a semiconductor determines the responding wavelength and every semiconductor has its specialized bandgap. Based on the photoelectric effect, the semiconductors materials with a narrow bandgap have broad responding wavelength bands. Therefore, besides the narrow bandgap, for 2D materials such as graphene, the modulation of the bandgap should be important, especially for the materials with large bandgaps such as ${\mathrm{MoS}}_2$ [13,35]. In this review, what is discussed will mainly concentrate on the state-of-the-art research exploration and development about the saturable absorbers for several 2D materials. The content consists of the band-gap modification by impurity of ${\mathrm{MoS}}_2$, band-gap modulation by phase transition of ${\mathrm{VO}}_2$, and broadband modulation by inherent bandgaps for graphene and ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ topological insulator. This work can show some guiding designing functions for the investigation of other 2D layered optoelectronic materials.

2. BAND-GAP ENGINEERING FOR ${\mathrm{MoS}}_2$

Layered ${\mathrm{MoS}}_2$, a typical representative of the layered TMDCs family, is composed of the sandwiches combined by van der Waals interactions, and each sandwich consists of covalently bound S–Mo–S trilayers with two hexagonal layers of S atoms and an intermediate hexagonal plane of Mo atoms [17,25,36 –38]. The monolayer ${\mathrm{MoS}}_2$ has a direct band-gap at the $K$ point of the Brillouin zone with a gap of 1.8 eV (0.7 μm), and the bulk ${\mathrm{MoS}}_2$ is of an indirect band-gap between the $\mathrm{\Gamma }$ point (valence band) and $K$ point (conduction band) of the Brillouin zone with a gap of ranging from 0.86 eV (1.4 μm) to 1.29 eV (1.0 μm) [39 –44]. Besides the change of thickness, the bandgap of ${\mathrm{MoS}}_2$ was also modified by the other engineering technologies, such as the external electric field and the external strain [45 –48]. Atomic-layered ${\mathrm{MoS}}_2$ exhibits intriguing physical properties distinct from its bulk state, for example, the dramatical increasing of luminescence quantum efficiency for ${\mathrm{MoS}}_2$ from the bulk state to single layer. Therefore, layered ${\mathrm{MoS}}_2$ attracts more interest in the fabrication of ultrathin and flexible nanoelectronic devices [16,25], and was brought into various research fields, such as lubrication, hydrodesulfurization catalysis, supercapacitors, and field-effect transistors [36 –38,49].

Monolayer ${\mathrm{MoS}}_2$ has been proven with strong optical response, such as enhanced photon absorption and large photocurrent caused by van Hove singularities or band nesting [50,51]. In 2012, using the spatially and temporally resolved pump-probe technique with a 390 nm pump source and a 660 nm probe source, R. Wang et al. measured and discussed the ultrafast carrier dynamics of atomically thin ${\mathrm{MoS}}_2$ [52]. One year later, more nonlinear investigations were carried out [53 –55], and it is significant that ultrafast saturable absorption of ${\mathrm{MoS}}_2$ nanosheets was demonstrated around 800 nm by K. P. Wang et al. [56].

Most of the studies were in pursuit of the high-quality layered ${\mathrm{MoS}}_2$ samples in order to obtain remarkable electronic and optical properties [37 –39]; however, the generation of defects, which deviate from a perfect crystal structure, was inevitable in the preparation of ${\mathrm{MoS}}_2$ samples. The probable defects could localize electronic states and change the energy level, leading to some fantastic physical phenomena, such as the Mott transition and Anderson localization [57].

Recently, S. X. Wang et al. systematically analyzed the band-gap change of multilayer ${\mathrm{MoS}}_2$ in a theoretical analysis with the ratio $(R)$ between Mo and S atoms slightly deviating from 1:2 [34]. The first-principle theoretical calculations were performed by using the plane-wave basis Vienna ab initio simulation package [58,59], and the atomic arrangement of ${\mathrm{MoS}}_2$ was the universal AB stacking $(2\mathrm{H}-{\mathrm{MoS}}_2)$. As shown in Fig. 1, the bandgap is about 1.08 eV (1.2 μm) for multilayered ${\mathrm{MoS}}_2$ with the stoichiometric ratio, which corresponds well to the previous calculated value for bulk ${\mathrm{MoS}}_2$ [40]. The other results with different $R$ values are displayed in Fig. 2. When $R$ is larger than 2.09, ${\mathrm{MoS}}_2$ exhibits metallic character, and the generation of saturable absorption requiring suitable patterns or distances between the metal units becomes difficult. When the $R$ is located in the range 1.89–2 and 2–2.09, few-layered ${\mathrm{MoS}}_2$ showed an indirect semiconductor property and its energy gap is 0.08 eV (15.5 μm), 0.23 eV (5.4 μm), 0.48 eV (2.6 μm), 0.63 eV (2.0 μm), and 0.26 eV (4.7 μm) for the $R$ with a value of 2.09, 2.04, 1.97, 1.94, and 1.89, respectively. Thus, it can be concluded that the band-gap of ${\mathrm{MoS}}_2$ would be reduced by the introduction of some Mo or S defects in a suitable range. The smaller band-gap means the broadband saturable absorption of defective ${\mathrm{MoS}}_2$ becomes possible.

 

Fig. 1. Brillouin zone (left) and calculated band structure (blue lines, right) of bulk ${\mathrm{MoS}}_2$ with stoichiometric ratio. Selected from Ref. [34].

Download Full Size | PDF

 

Fig. 2. Theoretical band gap of ${\mathrm{MoS}}_2$ samples; (a) AB stacked ${\mathrm{MoS}}_2$ observed from the top (left) and side (right); (b) calculated band structure of bulk ${\mathrm{MoS}}_2$ with $R=1:2.12$; (c) calculated band structure of bulk ${\mathrm{MoS}}_2$ with $R=1:2.09$; (d) calculated band structure of bulk ${\mathrm{MoS}}_2$ with $R=1:2.04$; (e) calculated band structure of bulk ${\mathrm{MoS}}_2$ with $R=1:1.97$; (f) calculated band structure of bulk ${\mathrm{MoS}}_2$ with $R=1:1.94$; (g) calculated band structure of bulk ${\mathrm{MoS}}_2$ with $R=1:1.89$. Selected from Ref. [34].

Download Full Size | PDF

Then the ${\mathrm{MoS}}_2$ samples were fabricated by the pulse laser deposition (PLD) method, which is an efficient technique to produce the S imperfections for ${\mathrm{MoS}}_2$ samples, since low-mass S is evaporated more easily than high-mass Mo [60]. The $R$ lies in the range 1.89–1.97 moving from the center to the edge of the sample surveyed by X-ray photoelectron spectrometry. As demonstrated in Fig. 3, the measured absorbance of the ${\mathrm{MoS}}_2$ sample decreases with an increase of wavelength [34]. For the $R$ with the value of 1.89, the energy gap for ${\mathrm{MoS}}_2$ samples is only 0.26 eV, corresponding to a wavelength of 4.7 μm. In contrast to the absorption range of standard stoichiometric ${\mathrm{MoS}}_2$, the prepared ${\mathrm{MoS}}_2$ samples are more likely to have broadband saturable absorption.

 

Fig. 3. Measured absorption spectrum of ${\mathrm{MoS}}_2$ sample. Selected from Ref. [34].

Download Full Size | PDF

Saturable absorption of ${\mathrm{MoS}}_2$ was investigated employing the two-level saturable absorber model widely used for 2D quantum wells [61,62]

Saturable absorption of the as-grown ${\mathrm{MoS}}_2$ sample was measured with a picosecond pulse laser with a pulse width of 40 ps at 1.06 μm, and the data was analyzed with Eq. (4). The saturation intensity of ${\mathrm{MoS}}_2$ was calculated with $2.45\mathrm{GW}/{\mathrm{cm}}^2$, a value larger than that of graphene $(0.61–0.71\mathrm{MW}/{\mathrm{cm}}^2)$ and comparable to that of ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ $(4.3\mathrm{GW}/{\mathrm{cm}}^2)$. The saturable carrier density $N_s$ is about $1.4\times {10}^{17}{\mathrm{cm}}^{-2}$, a magnitude 2–3 orders larger than graphene ($5.84\times {10}^{13}$ to $8.16\times {10}^{14}{\mathrm{cm}}^{-2}$) [32,34,63].

Using the ${\mathrm{MoS}}_2$ samples as saturable absorbers, passively $Q$-switched lasers at wavelengths of 1.06, 1.42, and 2.1 μm were successfully operated with $\mathrm{Nd}\text{:}{\mathrm{GdVO}}_4$, $\mathrm{Nd}\text{:}{\mathrm{Y}}_3{\mathrm{Ga}}_5{\mathrm{O}}_{12}$ (Nd:YGG), and $\mathrm{Tm}\text{:}\mathrm{Ho}\text{:}{\mathrm{Y}}_3{\mathrm{Ga}}_5{\mathrm{O}}_{12}$ (Tm:Ho:YGG) crystals, respectively, as gain materials. The average output power and the repetition rate with the increase of pump power are demonstrated in Fig. 4, and the typical pulses at the wavelengths of 1.06, 1.42, and 2.1 μm are shown in Fig. 5. $Q$-switched lasers for the broadband ${\mathrm{MoS}}_2$ saturable absorber, ranging from 1.06 to 2.1 μm were obtained in this experiment with sub-microsecond temporal widths and maximum output powers of up to a few hundred milliwatts.

 

Fig. 4. Average output power and repetition rate of passively $Q$-switched laser; (a) passively $Q$-switched $\mathrm{Nd}\text{:}{\mathrm{GdVO}}_4$ laser performance at 1.06 μm; (b) passively $Q$-switched Nd:YGG laser performance at 1.42 μm; (c) passively $Q$-switched Tm:Ho:YGG laser performance at 2.1 μm; (d) relation between the carrier density ($N$) and pulse repetition rate at the laser wavelength of 1.42 μm. Selected from Ref. [34].

Download Full Size | PDF

 

Fig. 5. Passively $Q$-switched laser spectra and pulses; (a) passively $Q$-switched $\mathrm{Nd}\text{:}{\mathrm{GdVO}}_4$, Nd:YGG, and Tm:Ho:YGG laser spectra of at center wavelengths of 1.06, 1.42, and 2.1 μm, respectively; (b) passively $Q$-switched $\mathrm{Nd}\text{:}{\mathrm{GdVO}}_4$, Nd:YGG, and Tm:Ho:YGG laser spectra with the pulse width of 970, 729, and 410 ns, respectively. Selected from Ref. [34].

Download Full Size | PDF

Many research results about the pulse modulation with ${\mathrm{MoS}}_2$ saturable absorbers have been demonstrated so far. It has shown remarkable mode-locking or $Q$-switched performance in the different gain materials, such as Yb-doped fibers (around 1 μm) [65,66], Er-doped fibers (1.5 to 1.6 μm) [67 –70], Tm-doped fiber (around 2 μm) [71], $\mathrm{Nd}\text{:}{\mathrm{GdVO}}_4$ [34], Nd:YGG [34], and Tm:Ho:YGG [34]. For the perfectly single-layered ${\mathrm{MoS}}_2$, saturable absorption is hardly acquired when the wavelength is above 0.7 μm due to the large band-gap (1.8 eV). Even if ${\mathrm{MoS}}_2$ is in the bulk state (1.08 eV), the modulation wavelength would still be not longer than 1.2 μm [34]. Employing band-gap engineering, which is similar to the fabrication of SESAMs [13], broadband pulse modulation for few-layer ${\mathrm{MoS}}_2$ was successfully obtained with a range 1.06–2.1 μm. This approach may benefit the exploitation and development of new 2D optoelectronic devices for some 2D materials with a large inherent band-gap.

3. PHASE-TRANSITION MODULATION FOR ${\mathrm{VO}}_2$

Phase transitions are ubiquitous in nature, such as superconductive phase transitions [72], ferroelectric and antiferroelectric phase transitions [73], and insulator–metal transitions (IMTs) [74 –81]. The complex physical science contained in the transition process is intriguing with respect to the study of phase-transition kinetics in an attempt to well-understand the changes of energy structure, electron correlation, electron-lattice coupling, and so on [79]. ${\mathrm{VO}}_2$, an archetypal IMT, exhibits a reversible IMT at about 340 K accompanied by a transition from a low-temperature insulating phase with a monoclinic space group of $P{2}_1/c$ to a high-temperature rutile metallic phase with a tetragonal space group of $P{4}_2/mnm$ [75,77,79]. Therefore, it worth noting that the IMT phase transition of ${\mathrm{VO}}_2$ could change the bandgap and broaden the responding wavelength band with the increase of the temperature.

The IMT of ${\mathrm{VO}}_2$ could be considered as the Coulomb interactions between $3d$ electrons of ${\mathrm{V}}^{4+}$ ions and the degeneracy of their energy levels. For the rutile metallic phase of ${\mathrm{VO}}_2$, each ${\mathrm{V}}^{4+}$ ion is located at the octahedral site surrounded by six ${\mathrm{O}}^{2-}$ ions. Based on the Goodenough’s model [82], the $d$ levels of the ${\mathrm{V}}^{4+}$ ions are first split into low-energy triply degenerate $t_{2g}$ states and high-energy doubly degenerate $e_g^{\sigma }$ states. The $e_g^{\sigma }$ states lie 3.5 eV above the Fermi level and are empty bands [75,83]. The $t_{2g}$ multiplet then are separated into an $a_{1g}$ singlet ($d_{\Vert }$ state) and an $e_g^{\pi }$ doublet ($\pi$ state and ${\pi }^{*}$ state). The $a_{1g}(d_{\Vert })$ orbitals are parallel to the $c$-axis with $\sigma$ bonding of V–V pairs, and the $e_g^{\pi }$ doublet ($\pi$ and ${\pi }^{*}$) are strongly hybridized with the O $2p$ orbitals. The $d_{\parallel }$ orbitals and ${\pi }^{*}$ orbitals partly overlap and both of them partially occupy the Fermi level. The monoclinic insulating phase is identified as a Peierls–Mott insulator, and in that phase, the dimerization and tilting of the V–V pairs could lead to the $d_{\parallel }$ band along the $c$-axis is split into a lower-energy bonding combination and a higher-energy anti-bonding one $(d_{\parallel }^{*})$ [83 –85]. Moreover, the $e_g^{\pi }$ states (${\pi }^{*}$ state) are shifted to the upper position because of the increase of hybridization between the $e_g^{\pi }$ doublet with O $2p$ orbitals. Ultimately, for the monoclinic phase, the bonding $d_{\parallel }$ orbitals are completely occupied, but the anti-bonding $d_{\parallel }(d_{\parallel }^{*})$ and ${\pi }^{*}$ orbitals are empty due to both states being above the Fermi level [78 –80,83 –85].

IMT of ${\mathrm{VO}}_2$ could be triggered with different stimuli, such as temperature, light, electric field, mechanical strain, and magnetic field [76 –78,86 –88]. In terms of linear optical response, ${\mathrm{VO}}_2$ undergoes a large and rapid change, so it has potential use in ultrafast switching and sensing [89]. However the nonlinear optical response of ${\mathrm{VO}}_2$ with respect to pulse modulation in the IMT process, which is vital in terms of photonic and optoelectronic applications, has not reported up to now.

Using the first-principle theoretical calculations and the atomic structural parameters previously reported [58,59,80], the density of states (DOSs) for ${\mathrm{VO}}_2$ in the different states were calculated, consisting of the insulating phase, phases near the IMT point, and metallic phase [90]. As presented in Fig. 6, the room-temperature monoclinic phase behaves as an insulator with a band-gap of 0.68 eV, coinciding well with the result measured by photoemission spectroscopy [83]. In addition, accompanied by the IMT being in progress, the ${\mathrm{VO}}_2$ band-gap decreases and its phase enters a tetragonal metallic state from the monoclinic insulating state. The calculation of DOS for two phases at the IMT temperature point indicates that ${\mathrm{VO}}_2$ has an optical response to light with a wavelength shorter than 1.85 μm (0.68 eV), corresponding to the band-gap of the pure insulating phase.

 

Fig. 6. Theoretical DOS for ${\mathrm{VO}}_2$ in different phases; (a) DOS in the monoclinic phase at room temperature with a band-gap of 0.68 eV; (b) DOS in the monoclinic phase near the IMT point with a band-gap of 0.36 eV; (c) DOS in the tetragonal phase near the IMT point; (d) DOS in the tetragonal phase and final metallic states. Selected from Ref. [90].

Download Full Size | PDF

As displayed in Fig. 7, the linear optical response of the ${\mathrm{VO}}_2$ sample fabricated by the PLD method was investigated at 1.06 μm under different temperatures. It is seen that both the transmission and reflection decrease and the absorption coefficient increases with increasing temperature. When the temperature decreases, all the linear optical properties show hysteresis because of the hysteretic twisting of V–V pairs in ${\mathrm{VO}}_2$. The experimental results show good agreement with the previous literature [74].

 

Fig. 7. Linear optical response of ${\mathrm{VO}}_2$ layer; (a) reflection and transmission of ${\mathrm{VO}}_2$ at different temperatures and light wavelength of 1.06 μm measured by increasing (↑) and decreasing (↓) the temperature; (b) linear absorption coefficient of ${\mathrm{VO}}_2$ at different temperatures and light wavelength of 1.06 μm measured by increasing (↑) and decreasing (↓) the temperature. Selected from Ref. [90].

Download Full Size | PDF

Since light is capable of inducing the IMT process, investigating the nonlinear response of ${\mathrm{VO}}_2$ is difficult for the traditional $Z$-scan technique by using picosecond or femtosecond pulses. Therefore, the ${\mathrm{VO}}_2$ sample was employed as a saturable modulator to generate pulse lasers, and the kinetic process of the nonlinear response for ${\mathrm{VO}}_2$ during IMT was analyzed from the pulsed laser performance. The passively $Q$-switched laser at a wavelength of 1.06 μm was demonstrated with a $\mathrm{Nd}\text{:}{\mathrm{GdVO}}_4$ crystal as the gain medium and the ${\mathrm{VO}}_2$ sample as the saturable absorber. On the basis of the analysis of Fig. 8(a), it is worth mentioning that the output power during an increasing and a decreasing of the pump power also shows hysteresis. The IMT of ${\mathrm{VO}}_2$ occurs in the pump range from 2.6 to 5.4 W, corresponding to the temperatures 310 and 360 K, respectively. When the pump power is below 2.6 W, ${\mathrm{VO}}_2$ is a pure insulator, and the pulse modulation is generated on account of the small band-gap (0.68 eV). When the pump power is above 5.4 W, ${\mathrm{VO}}_2$ fully becomes a metal material, and the pulse modulation is caused by the saturable properties of the surface plasmon resonance absorption [91 –94].

 

Fig. 8. Laser performance with ${\mathrm{VO}}_2$ as an optical switch; (a) average output power and central temperature of the laser beam in ${\mathrm{VO}}_2$ sample recorded during increasing (↑) and decreasing (↓) pump power. Inset: laser patterns achieved with CCD; (b) repetition rate and pulse width during increase (↑) and decrease (↓) of pump power; (c) peak power during increase (↑) and decrease (↓) of pump power; (d) modulation depth with increase (↑) and decrease (↓) of central temperature generated by the pump power. Selected from Ref. [90].

Download Full Size | PDF

As displayed in Fig. 8(b), it is surprising that a minimum pulse width of 43 ns is obtained at a pump power of 4.4 W, where a break point appeared in the repetition rate, corresponding to a central temperature of 347 K. The result is much better than those of the topological insulator (pulse width of 660 ns) and ${\mathrm{MoS}}_2$ (pulse width of 970 ns) in the same experimental setup [34,63]. As demonstrated in Fig. 8(d), the modulation depth $\mathrm{\Delta }T$ could be theoretically calculated by [95]

 

Fig. 9. Nonlinear optical response of ${\mathrm{VO}}_2$ layer; (a) saturation intensity with increase (↑) and decrease (↓) of central temperature induced by pump power in the IMT process; (b) nonlinear absorption coefficient with increase (↑) and decrease (↓) of central temperature induced by pump power in the IMT process. Selected from Ref. [90].

Download Full Size | PDF

In recent years, ${\mathrm{VO}}_2$ has received more attention in some areas, including electronics, ultrafast techniques, energy technology, optical storage, and ionic gating [74 –76,89 –92,96]. By studying the kinetics of the third-order optical nonlinearity during the IMT of ${\mathrm{VO}}_2$, it is worth noting that ${\mathrm{VO}}_2$ is of a broad response band (below 1.85 μm) and has fantastic saturable absorption properties in the IMT process. The remarkable $Q$-switched laser with a minimum pulse width of 43 ns and the sensitive nonlinear optical responses all show the utility of phase-transition materials in the development of potential optoelectronic devices.

4. BROADBAND MODULATION BY INHERENT BAND-GAPS

A. Graphene

Graphene is of a very stable honeycomb hexagonal structure assembled by $s{p}^2$-hybridized carbon atoms [18,21]. Notwithstanding the significant template for fabricating other allotropes of carbon, such as fullerenes, carbon nanotubes, and graphite, graphene was not discovered until 2004 [97], and ironically, the date is later than all these allotropes [22]. For the $s{p}^2$ hybridization of graphene, the $\sigma$ bond is formed by one $s$ orbital and two $p$ orbital ($p_x$ and $p_y$) electrons between two carbon atoms in the planar structure. The $\pi$ electron that is the electron in the unaffected $p$ orbital $(p_z)$ is perpendicular to the 2D honeycomb plane. The inter-couplings between the electron wave functions of each two nearest $\pi$ electrons can lead to the formation of a half-filled $\pi$ band or a half-filled ${\pi }^{*}$ band, corresponding to the valence band and conduction band, respectively [15,22,23].

Zero band-gap of graphene possesses linear dispersion near the Dirac point. Furthermore, this material is insensitive to wavelength, and shows relatively large absorption of visible-to-infrared light (about 2.3% for a monolayer), which all were beneficial for the acquisition of broadband optical response [98 –100], As for the carrier dynamics of graphene, the intraband carrier relaxation time and the interband relaxation time are about 10–150 fs and 0.4–1.7 ps, respectively [101 –103]. The longer interband relaxation can act as the modulation switching by changing the intrinsic electron and hole carrier densities of graphene. In addition, graphene is also of superior thermal conductivity (5300 W/m/K for a monolayer) [104], large electron mobility of ${10}^5{\mathrm{cm}}^2/\mathrm{V}/\mathrm{s}$ [18,105], and remarkable elastic properties (a Young’s modulus of 1.0 TPa) [106]. As a consequence, graphene is a candidate broadband saturable absorber for the generation of mode-locking or $Q$-switched pulses.

In 2009, 5 years after the discovery of graphene, the saturable absorption of graphene was first investigated by Q. L. Bao et al. [32]. The saturation intensity $I_S$ ranges from 0.61 to $0.71\mathrm{MW}/{\mathrm{cm}}^2$ for different layers of graphene, corresponding to the saturation density ranging from $8.16\times {10}^{13}$ to $5.84\times {10}^{13}$ [32,107]. This research group also demonstrated the first saturable modulation of graphene in the Er-doped fiber mode-locking laser. The laser oscillation wavelength is about 1.57 μm and the minimum pulse width is about 756 fs. In 2010, the first graphene-based $Q$-switched laser was presented by Z. Q. Luo et al. in the Er-doped fiber with a pulse width of 3.7 μs [108]. Employing a Nd:YAG ceramic medium and a graphene modulator in 2010, W. D. Tan et al. reported the first diode-pumped solid-state bulk mode-locking laser with the obtained pulse width of 4 ps at 1.06 μm [64]. Since then, graphene has set off a new wave of research in the mode-locking and $Q$-switched pulse laser fields. The preparing method causes the prepared graphene saturable absorber to have a low damage threshold and consequently cannot be used in the $Q$-switching lasers with larger pulse energy than mode-locking lasers.

In the same year of 2010, by means of using graphene epitaxially grown on SiC with high refractive index as the saturable absorber and as the output coupler [109], we obtained the stable passively $Q$-switched laser for Nd:YAG at 1.06 μm, and it is the first time that the graphene saturable absorber was applied in the $Q$-switched solid-state pulse laser field. The pulse profiles under different pump power are demonstrated in Fig. 10 and the minimum pulse width is 161 ns. A similar experiment was implemented in the $\mathrm{Nd}\text{:}{\mathrm{LuVO}}_4$ gain crystal at 1.06 μm, and as shown in Fig. 11, the minimum pulse width is about 56.2 ns [110].

 

Fig. 10. (a) Display of the cw laser recorded by a digital oscilloscope; (b) $Q$-switched pulse profile under the pump power of 11.2 W; (c) $Q$-switched pulse profile under the pump power of 12.9 W; (d) $Q$-switched pulse profile under the pump power of 14.6 W; (e) $Q$-switched pulse profile under the pump power of 16.5 W. Selected from Ref. [109].

Download Full Size | PDF

 

Fig. 11. Pulse profile with the width of 56.2 ns. Selected from Ref. [110].

Download Full Size | PDF

In addition, recently, graphene was used as a pulse modulator for the generation of a pulsed optical vortex at a wavelength of 1.36 μm in the gain medium of Nd:LYSO [111]. In that experiment, the thermal effect in the Nd:LYSO crystal caused by the large quantum defect of 40.5% is used to do mode-matching selection among different Laguerre–Gaussian (${\mathrm{LG}}_{p,l}$) modes. As exhibited in Fig. 12, the different ${\mathrm{LG}}_{p,l}$ with corresponding topological charge of $1\hslash$ ($l=0$, 1, and 2) are directly obtained by controlling the pump power. Corresponding Hermite–Gaussian (${\mathrm{HG}}_{m,n}$) modes are easily transformed with using two identical cylindrical lenses. Importantly, no topological charge is lost in the whole process suggesting that there is no angular momentum transfer between graphene and vortex pulses such that graphene shows the potential application of generating pulse optical vortices.

 

Fig. 12. (a) Continuous wave and pulsed output power of ${\mathrm{LG}}_{p,l}$ modes versus the absorbed pump power; (b) transverse pattern of the laser beam. Top row, achieved ${\mathrm{LG}}_{p,l}$ modes. Bottom row, the converted ${\mathrm{HG}}_{m,n}$ modes corresponding the ${\mathrm{LG}}_{p,l}$ modes. Selected from Ref. [111].

Download Full Size | PDF

B. ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ Topological Insulator

In recent years, topological insulators (${\mathrm{Bi}}_2{\mathrm{Se}}_3$, ${\mathrm{Bi}}_2{\mathrm{Te}}_3$, and ${\mathrm{Sb}}_2{\mathrm{Te}}_3$) has drawn great attention in the frontier of science research, due to the exotic physical properties [27,112 –118]. Topological insulators show a rhombohedral crystal structure and belong to the space group of ${\mathit{D}}_{3d}^5(R\overline{3}m)$. Each layer for this kind of materials is of a quintuple-layered sandwich structure along the direction of the 3-fold rotation axis of symmetry; for instance, the layered configuration of ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ is Se1–Bi1–Se2–Bi1’–Se1’. The coupling between two atomic layers of one quintuple layer is stronger than that between two quintuple layers held together predominantly by the van der Waals forces [113,114].

Two energy states simultaneously exist in topological insulators, and they are the bulk state and the metallic surface state, respectively. ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ topological insulators have the largest energy gap of the bulk state with a value of about 0.3 eV, and no impurity states exist in the gap [113,115]. The metallic surface state is topological protection with the combination of spin–orbit coupling and time-reversal symmetry against probable scattering [27,116,118]. Similar to graphene, the surface state consists of massless Dirac fermions with a linear energy–momentum relationship. Graphene has two spin-degenerate Dirac cones located at the $K$ and $K^{\prime }$ points, respectively. Nevertheless, for the ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ class of topological insulators materials, there is only a single surface Dirac cone around the $\mathrm{\Gamma }$ point with no spin degeneracy [113 –115]. Some splendid physical properties were discovered with the gradually in-depth investigations of topological insulators, such as the electromagnetic effect, superconductivity, and quantum anomalous Hall effect [112 –115,119,120].

Along with the active research of electronic and magnetic phenomena of topological insulators, its optical characteristic also aroused research interest. Considering the small energy gap of the bulk state for topological insulators, the saturable absorption was expected to generate under strong excitation with the wavelength not longer than 4.13 μm [114,115]. In 2012, F. Bernard et al. discovered that the ${\mathrm{Bi}}_2{\mathrm{Te}}_3$ topological insulator has saturable absorption at a wavelength of 1.55 μm [121], and then, using the saturable absorber fabricated by ${\mathrm{Bi}}_2{\mathrm{Te}}_3$ topological insulator and the gain medium of Er-doped fiber, C. J. Zhao et al. first obtained the mode-locking lasers with a pulse width of 1.2 ps at 1.56 μm [33].

In 2013, our group demonstrated the stable passively $Q$-switched laser for $\mathrm{Nd}\text{:}{\mathrm{GdVO}}_4$ at 1.06 μm with the ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ topological insulator as the pulse modulator [63]. On the strength of a $Z$-scan technique, saturable absorption of ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ saturable modulator was measured and was fitted with Eq. (4). The saturation intensity was determined to be $4.3\mathrm{GW}/{\mathrm{cm}}^2$, a value that is much larger than that of graphene $(0.61–0.71\mathrm{MW}/{\mathrm{cm}}^2)$ [32,63]. The output power and pulse profiles under different pump power are demonstrated in Fig. 13, and the minimum pulse width is about 666 ns. Employing the same ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ saturable absorber, a dual-wavelength simultaneously $Q$-switched $\mathrm{Nd}\text{:}{\mathrm{Lu}}_2{\mathrm{O}}_3$ laser was also achieved [122]. As shown in Fig. 14, the shortest pulse width is about 720 ns and the laser wavelengths are 1077 and 1081 nm, respectively.

 

Fig. 13. (a) Average output power and pulse energy vs. increasing incident pump power; (b) pulse width and repetition rate vs. incident pump power; (c) display recorded by digital oscilloscope for lasers. One through 6 are pulse profiles of cw $\mathrm{Nd}\text{:}{\mathrm{GdVO}}_4$ laser, and pulsed lasers under pump power of 1.19, 1.27, 1.46, 1.67, and 1.85 W, respectively. Selected from Ref. [63].

Download Full Size | PDF

 

Fig. 14. (a) Single-pulse profile with duration of 720 ns. Inset, corresponding pulse train with the repetition rate of 94.7 kHz; (b) laser spectrum of the dual-wavelength laser at 1077 and 1081 nm. Selected from Ref. [122].

Download Full Size | PDF

At the beginning of pulse modulation for topological insulators (${\mathrm{Bi}}_2{\mathrm{Se}}_3$, ${\mathrm{Bi}}_2{\mathrm{Te}}_3$, and ${\mathrm{Sb}}_2{\mathrm{Te}}_3$), the $Q$-switched or mode-locking lasers are concentrated on the wavelengths from 1 to 1.6 μm in the gain media such as $\mathrm{Nd}\text{:}{\mathrm{GdVO}}_4$ [63], Yb-doped fibers [123], Er-doped fibers [33,124 –126], and Er:YAG ceramic [127]. In 2014, M. W. Jung reported the mode-locked femtosecond pulse laser at 1935 nm with ${\mathrm{Bi}}_2{\mathrm{Te}}_3$ topological insulator as the saturable absorber and the Tm/Ho co-doped fiber as the gain medium [128]. Soon after, Z. Q. Luo et al. demonstrated a $Q$-switched double-clad single-mode ${\mathrm{Tm}}^{3+}$-doped fiber laser at 2 μm wavelength with ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ topological insulator as the saturable modulator [129]. These two experiments confirm the broadband saturable modulation of topological insulators with the applicable wavelength expanded to 2 μm or longer wavelengths.

5. CONCLUSIONS

In this paper, on the basis of the band-gap modulation, some latest research results about 2D broadband saturable absorbers, including ${\mathrm{MoS}}_2$ and ${\mathrm{VO}}_2$, graphene, and ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ topological insulator were systematically elucidated and reviewed. For the few-layer ${\mathrm{MoS}}_2$, the broadband pulse modulation was achieved from 1.06 to 2.1 μm by introducing appropriate S defects to reduce the intrinsic band-gap. For the ${\mathrm{VO}}_2$ IMT, the transition process from the insulator phase to metal phase resulted in some fantastic results in terms of pulse modulation, such as small pulse widths and sensitive nonlinear optical responses. In addition, with respect to graphene and ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ topological insulator, the small inherent bandgaps leaded to the success of broadband saturated absorption. As a consequence, this work shows the excellent performance of band-gap engineering for exploring 2D broadband saturable materials, and importantly, it opens up an available application opportunity for 2D materials in photonics and optoelectronics.