1 Introduction

Passively Q-switched solid-state nanosecond lasers are attractive in terms of compactness, efficiency, simplicity and high pulse energy output [1–3]. To realize such laser sources, excellent saturable absorbers (SAs) are essential. As for the Q-switched solid-state 2 μm lasers which are commonly used in scientific and military spheres, numerous materials had been successfully applied as SAs, such as Cr:ZnS [4], Cr:ZnSe [5], Fe:ZnSe, InGaAs/GaAs [6] and PbS-doped glass [7]. Among the abovementioned SAs, Cr:ZnS, Cr:ZnSe and Fe:ZnSe faced the drawbacks of low output efficiencies as a result of the giant linear losses, while for InGaAs/GaAs and PbS-doped glass, the complex fabrication process, high risk of optical damages and exorbitant prices limited their roles. So the efforts to investigate novel SAs suitable for 2 μm lasers are still need to be paid. Recently, the allotropes of carbon, graphene and carbon nanotubes (CNTs) gained their popularity in passively Q-switched lasers at 2 μm for their diverse advantages, e.g., large optical absorption, easy fabrication, low cost, as well as broadband absorption [8, 9]. Based on these two kinds of SAs, passively Q-switched 2 μm lasers were actively investigated by several research groups [10–14]. However, most of the pulse durations obtained from graphene or CNTs Q-switched solid-state bulk 2 μm lasers were beyond 500 ns [10–13]. For CNTs, the increase in the layer numbers can enhance the mechanical strength, the thermal stability as well as the laser damage threshold, which are of great importance for short-pulse operation [15], while for graphene, the increase in the layer numbers may increase the nonsaturable loss, which would decrease the modulation depth [16]. Since the pulse width is directly interrelated to the cavity round trip time and inversely proportional to the modulation depth of the SA [17], monolayer graphene or MWCNT, as well as a compact cavity with short cavity length, is helpful for obtaining short pulses for 2 μm lasers.

Thulium (Tm)-doped crystals are usually employed as gain mediums to generate laser radiations around 2 μm, not only because the Tm3+ ions have absorption bands around 800 nm which could be directly obtained from commercial GaAs/AlGaAs laser diodes, but it also benefits from an efficiency-enhancing cross-relaxation process that can lead to two ions in the upper laser level for one pump photon [18]. As a member of Tm-doped crystals, Tm:LuAG was deemed to be a promising gain material for solid-state 2 μm lasers. The strong crystal field in Tm:LuAG crystal provides a large stark-splitting in the Tm3+ ions, which could decrease the thermally induced population in the ground-state level and subsequently lower the laser threshold [19]. Moreover, a fluorescence lifetime as high as 7.1 ms indicates a promising high energy storage capacity [19]. Besides, a large thermal conductivity of 7.9 W/mK could remove the generated heat efficiently when being pumped, which is very helpful for short-pulse operation [20]. Up to now, both the active and passive Q-switching Tm:LuAG lasers have been achieved [14, 19]. With acoustic-optical modulator (AOM) as Q-switcher, pulse with the shortest duration of 199 ns under a repetition rate of 20 Hz has been achieved, while the complex experimental facilities and low repetition rate limited its applications. In our recent work, a passively Q-switched Tm:LuAG laser with single-walled carbon nanotube (SWCNT) was successfully demonstrated which yielded a maximum output pulse energy of 40.6 μJ and a minimum pulse duration of 405 ns. The results indicated that Tm:LuAG crystal held promising prospect in achieving short-pulse operation, and thus by using monolayer graphene or MWCNT that superior to SWCNT, the passively Q-switched Tm:LuAG laser producing narrower pulses is expected. But as far as we know, no related reports on passively Q-switched Tm:LuAG lasers with monolayer graphene or MWCNT were found yet.

Based on dual-loss-modulation mechanism, the doubly passively Q-switched lasers by simultaneously using two kinds of SAs were shown to generate shorter pulses with higher peak powers in comparison with single SA Q-switching operation. By combining two kinds of SAs in the cavity simultaneously, such as Cr4+:YAG and GaAs [21], V3+:YAG and Co:LMA [22], the doubly passively Q-switched lasers at 1.06 and 1.34 μm were demonstrated. Concerning on the pulsed 2 μm lasers, the dual-loss modulation technique is also expected to improve the laser performance in further lowering the pulse duration and enhancing the pulse peak powers. However, to the best of our knowledge, there is no related report on doubly passively Q-switched laser at 2 μm up to now.

In this paper, a laser-diode-pumped doubly passively Q-switched Tm:LuAG laser at 2 μm is presented for the first time. Monolayer graphene with high modulation depth and MWCNT with good thermal conductivity as well as high laser damage threshold were employed as SAs simultaneously to compress the pulse width. In addition, a short cavity length was employed. Under the above conditions, a pulse width as short as 102 ns was obtained at the incident pump power of 5.8 W, corresponding to a pulse peak power of 171 W.

2 Experiments and discussions

The monolayer graphene and the MWCNT used in this work were the same samples as described in our previous work [23] and [24]. The single-layer graphene was grown by CVD method, which was similar to the technique demonstrated by Cho et al. [25], and then transferred onto a piece of quartz with an approximate area of 2 × 2 cm2. The nonsaturable loss and the lifetime of this graphene were 1.2 % [23] and ~200 fs [26], respectively. The employed MWCNT was grown by electric arc discharge technique, similar to that described in Ref. [27]. The diameter of the MWCNT is about 20–40 nm, and the length distribution is from 1 to 2 μm, with a nonsaturable loss of 12 % and the lifetime of 330 fs [27].

The schematic experimental setup is shown in Fig. 1. A fiber-coupled diode laser with core diameter of 100 μm and maximum output power of 50 W was used as pump resource. The emission wavelength of this pump laser was 790 nm at 15 °C, which is near the peak absorption wavelength of the Tm:LuAG crystal. A 1:1 imaging module was employed to focus the pump light into the gain material with a pump spot diameter of 100 μm. The 4 × 4 × 8 mm3 Tm:LuAG crystal was grown by the Czochralski technique with 6 at.% Tm3+ ions doped. Both surfaces of this crystal were antireflection (AR) coated from 750 to 850 nm (reflectivity < 2 %) and 1930 to 2230 nm (reflectivity < 0.8 %). The crystal was wrapped with indium foils and held in brass heat sink to efficiently remove the heat generated from the crystal under pumping, and the temperature was held at 15 °C with a water cooler. Mirror M 1 with a curvature radius of 200 cm was employed as the input mirror, which was high reflectivity (HR) coated from 1850 to 2100 nm (reflectivity > 99.9 %) and AR coated from 750 to 850 nm (reflectivity < 2 %). The plane mirror M 2 with transmission of T = 2 % from 1820 to 2100 nm was employed as output coupler (OC). A single-band bandpass filter (FF01-800/12-25), which had a high reflectivity (>99.9 %) at the center wavelength of 800 nm with a bandwidth of 12 nm, was used to remove the leaking pump light. To shorten the pulse duration, the physical length between M 1 and M 2 was designed to be as short as 3.5 cm. The laser pulse trains were recorded by a fast InGaAs photodetector (EOT, ET-5000, USA) with a rise time of 35 ps and monitored by a digital oscilloscope (1 GHZ bandwidth, Tektronix DPO 7102, USA). A laser power meter (MAX500AD, Coherent, USA) was used to measure the average output powers.

Fig. 1
figure 1

Schematic of a laser-diode-pumped dual-loss-modulated passively Q-switched Tm:LuAG laser with MWCNT and monolayer graphene SAs

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Figure 2 shows the average output powers versus the incident pump powers for single MWCNT passive Q-switching, single graphene passive Q-switching and double passive Q-switching lasers, respectively. As shown in Fig. 2, the obtained average output powers increased monotonically with the augment of incident pump powers. The dual-loss-modulated passively Q-switched laser had the highest threshold power and the lowest output power due to the dual-loss insertion. When the incident pump power reached to 5.8 W, the highest output power of 873 mW and the maximum optical conversion efficiency of 15.1 % were obtained for singly graphene Q-switched laser, higher than that of the singly MWCNT Q-switched one, which we attribute to the relatively larger nonsaturable loss of the MWCNT SA. Because the resonant absorption occurs efficiently only in semiconductor MWCNT whose diameter corresponds to a resonance at the photon energy, the large number of MWCNTs that are not in resonance with the operational wavelength merely gives rise to the high nonsaturable loss of MWCNT via scattering [28].

Fig. 2
figure 2

Average output powers versus the incident pump powers for three kinds of Q-switched lasers

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Figure 3 shows the pulse widths versus the incident pump powers for singly passively and doubly passively Q-switched lasers. As it shows, the pulse widths decreased with the incident pump powers increased from thresholds to 5.8 W, and the doubly passively Q-switched laser could generate shorter pulses than either the monolayer graphene or MWCNT Q-switched one. The shortest pulse width generated from the doubly passively Q-switched and singly passively Q-switched laser with monolayer graphene or MWCNT was 102, 235 and 284 ns at the incident pump power of 5.8 W, respectively. Figure 4 shows the temporal pulse profiles of the singly passively Q-switched and dual-loss-modulated passively Q-switched lasers at the incident pump power of 5.8 W.

Fig. 3
figure 3

Pulse widths versus the incident pump powers for singly passively Q-switched and doubly passively Q-switched lasers

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Fig. 4
figure 4

Temporal profiles of three kinds of passively Q-switched lasers at the incident pump power of 5.8 W

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We define a compression ratio t c of the pulse duration as follows:

$$t_{\text{c}} = \frac{{t_{\text{s}} }}{{t_{\text{d}} }}$$
(1)

where t s and t d were the pulse widths achieved from the singly and doubly passively Q-switched lasers, respectively. At the incident pump power of 5.8 W, the compression ratios t c of the doubly passively Q-switched lasers were 2.3 and 2.8 when compared with the singly passively Q-switched laser with monolayer graphene or MWCNT, respectively. Apart from the larger losses, the reason why dual-loss modulation could compress the pulse width may be as follows: Graphene and MWCNT have different saturation intensity Isat and lifetime. According to ref [29], for graphene, Isat is estimated to be in the range of a few tens of MW/cm2, while for MWCNT with 20–40 nm outer diameter, Isat is in the range of GW/cm2. In addition, graphene possesses shorter relaxation time than MWCNT. Different saturation intensities and lifetimes of two SAs may have different contributions to the pulse formation in the doubly passively Q-switched laser, resulting in sharper rising and falling edges of the pulse as well as shorter pulse width, as shown in Fig. 4. Due to the absence of characteristic descriptions of two SAs at 2 μm in the rate equation model until now, it is difficult to discuss the relevant mechanisms quantitatively and theoretically based on the simulation method at 1.3 μm in Ref. [30]. However, we think that the pulse compression mechanism of graphene and MWCNT at 2 μm is analogous to that in the doubly passively Q-switched laser with V3+:YAG and Co:LMA at 1.3 μm [30]. Even the doubly passively Q-switched laser with graphene and MWCNT has similar nonsaturable losses in comparison with the singly passively Q-switched laser with graphene or MWCNT, the doubly passively Q-switched laser can still compress the pulse width.

To illustrate our explanation experimentally, a MWCNT with nonsaturable loss of 15 % was employed for comparison. Despite the fact that the MWCNT possesses nonsaturable loss higher than the combination of saturable absorbers used in the double Q-switching operation, the shortest pulse width obtained by the MWCNT with nonsaturable loss of 15 % was 245 ns, while the shortest pulse width obtained by the doubly passively Q-switched laser with the nonsaturable losses of 13.2 % was 102 ns. The pulse profiles of the doubly passively Q-switched laser with nonsaturable loss of 13.2 % and the MWCNT with nonsaturable loss of 15 % Q-switched laser at the incident pump power of 5.8 W were shown in Fig. 5.

Fig. 5
figure 5

Pulse profiles of the doubly passively Q-switched laser with nonsaturable loss of 13.2 % and MWCNT with nonsaturable loss of 15 % Q-switched laser at the incident pump power of 5.8 W

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Figure 6 gives the repetition rates of three kinds of passively Q-switched lasers as functions of the incident pump powers. It can be seen that all the repetition rates increased with the pump powers, and the highest repetition rate of 72 kHz was obtained for singly monolayer graphene Q-switched laser at the incident pump power of 5.8 W, while the repetition rates of doubly passively Q-switched laser were lower than the singly passively Q-switched one, which was attributed to the higher insertion losses.

Fig. 6
figure 6

Repetition rates of three kinds of passively Q-switched lasers as functions of the incident pump powers

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According to the repetition rates, the pulse widths and the average output powers, the pulse peak powers of the Q-switched lasers were calculated and shown in Fig. 7. The doubly passively Q-switched laser could generate higher peak power than the singly passively Q-switched lasers. At the incident pump power of 5.8 W, the highest peak power obtained from the doubly Q-switched laser was 171 W, while those in the singly passively Q-switched lasers with graphene or MWCNT were 51.5, 42.8 W. An enhancement factor P i of the pulse peak power is defined as:

$$p_{\text{i}} = \frac{{p_{\text{d}} }}{{p_{\text{s}} }}$$
(2)

where P s and P d are the pulse peak powers of the singly and doubly Q-switched lasers, respectively. At the incident pump power of 5.8 W, in comparison with singly passively Q-switched laser with graphene or MWCNT, the peak power enhancement factors of the doubly passively Q-switched laser were 3.3 and 4, respectively. The experimental results show that the doubly passively Q-switched laser could improve the peak power efficiently in comparison with the singly passively Q-switched lasers.

Fig. 7
figure 7

Peak powers versus the incident pump powers for three kinds of Q-switched lasers

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3 Conclusions

In this paper, a dual-loss-modulated passively Q-switched Tm:LuAG laser with MWCNT and monolayer graphene SAs around 2 μm is demonstrated for the first time. The experimental results show that the doubly passively Q-switched laser could compress the pulse widths and improve the peak powers efficiently in comparison with the singly passively Q-switched one. The maximum pulse width compression ratio and the highest peak power enhancement factor are 2.8 and 4 times, corresponding to the shortest pulse width of 102 ns and maximum peak power of 171 W, respectively.