1. Introduction

Topological insulators have an amazing property; in their interior they exhibit as insulators, but at their surface they possess metallic states [1]. Due to the presence of metallic surface states, the electronic energy band of a topological insulator can cross the narrow bulk bandgap, forming a single Dirac cone [2,3]. Such a band structure is very similar to that of graphene. Therefore, it can be expected that topological insulators, just like graphene, may also act as broadband saturable absorbers for passive Q-switching or for mode-locking in solid-state lasers.

Passive Q-switching of solid-state lasers with topological insulator saturable absorber (TISA) was first demonstrated in 2013 in a Nd:GdVO₄ laser operating at 1063 nm [4]. Since then, many solid-state lasers of various active ions have been reported to realize passive Q-switching with Bi₂Se₃, Bi₂Te₃, or Sb₂Te₃ TISA. These include Nd-ion lasers [5–7]; Yb-ion lasers [8–10]; Tm-ion lasers [11–15]; Er-ion lasers [14,16]; and a Pr:LiYF₄ laser [17]. Despite the much work conducted so far, the passive Q-switching performance achieved, and in particular with respect to output power or pulse duration, still remains much inferior to that attainable with other traditional saturable absorbers such as Cr⁴⁺:YAG or SESAMs. In fact, output power at the 2-W level was only produced from Tm-ion lasers operating at 2 μm, with the shortest pulse duration being about 230 ns [11,12,14]. In the more common 1-μm spectral region, the highest output power, 1.12 W, was generated from an Yb:KGW laser, but the corresponding pulse duration amounted to as long as 1.5 μs [9]; although a much shorter pulse duration of 370 ns could be achieved from an Yb:GdAl₃(BO₃)₄ laser, but the output power was limited to less than 100 mW [10].

In efforts to scale the output power of passively Q-switched solid-state lasers with topological insulators serving as saturable absorber, it is essential for the laser to be capable of operating under sufficiently high output couplings. Most 2D topological insulators suffer from low optical damage threshold or thermal instability, which proves to be the major obstacle to achieving high-power, stable Q-switched laser action. By use of high enough output couplings in the laser resonator, the intracavity circulating intensity can be greatly reduced, thus effectively diminishing the likelihood of optical damage to the internal TISA.

It is therefore crucial to properly choose the laser material for output power scaling of TISA passively Q-switched lasers. The laser medium must be able to provide high enough gain to sustain laser operation under very high output couplings. Very recently, a passively Q-switched Yb:LuPO₄/Bi₂Te₃ laser has been demonstrated, from which 4−5 W of output power could be produced under high output couplings (≥ 50%) [18]. The laser crystal used there, Yb:LuPO₄, however, cannot be grown by the conventional Czochralski method; up to now it can only be grown in high-temperature solution, showing a great difficulty in obtaining large-size crystal with high optical quality [19]. It is therefore necessary to search for other high-gain laser crystals, in the effort to scale the output power of passively Q-switched lasers with 2D TISA saturable absorbers. In the 1-μm region, Yb:YCa₄O(BO₃)₃ (Yb:YCOB) turns out to be such a laser crystal satisfying the requirement. The YCOB host crystal can accommodate Yb ions in high concentration (up to 35 at. %, usually 10−15 at. %), without causing noticeable deterioration in its optical quality. This makes it possible for an Yb:YCOB crystal to reach very high gain, allowing efficient laser action under high output couplings, despite the small stimulated emission cross-section characteristic of this laser medium [20]. In addition, Yb:YCOB also proves to be advantageous over most Yb- or Nd-ion crystals in making passively Q-switched lasers, owing to its long upper-level lifetime as well as small stimulated emission cross-section, both of which are desirable for generating high-energy laser pulses [20]. Indeed, high-power/high-energy passively Q-switched Yb:YCOB lasers have been demonstrated, with either Cr⁴⁺:YAG or GaAs serving as saturable absorber [20–22].

In this paper we report on the passive Q-switching performance of an Yb:YCOB/Bi₂Te₃ laser. We demonstrate that under high output coupling conditions, the output power achievable in stable Q-switched operation of the Yb:YCOB/Bi₂Te₃ laser could be scaled to near 4-W level; while the pulse duration could be shortened to sub-100 ns. Compared to the Yb:LuPO₄/Bi₂Te₃ laser, three times higher pulse energy was obtained with the present laser. The results achieved in our experiment reveal the great potential of these Yb-doped rare-earth calcium oxyborates crystals in the development of 1-μm solid-state lasers passively Q-switched by 2D TISAs.

2. Description of experiment

The Yb:YCOB crystal sample used was cut along its X principal axis. It was uncoated, 5 mm long, with a square aperture of 3 mm × 3 mm. The Yb-ion concentration was 15 at. %. As the TISA, a sapphire-based few-layer Bi₂Te₃ sample was utilized. It was a commercial product (Sixcarbon Tech, Shenzhen, China), and was made by using CVD technique. The number of layers of the Bi₂Te₃ sample ranged from 12 to 15. The bandgap of the Bi₂Te₃ sample was not measured in our experiment. As a typical topological insulator, Bi₂Te₃ possesses an energy band structure in which exist continuous surface-state band-threads traversing the bulk bandgap [2,3]. Previous measurement and theoretical calculation show that the bulk indirect bandgap for Bi₂Te₃ falls in a range of 0.15−0.17 eV [23,24]. The Yb:YCOB/Bi₂Te₃ laser was fabricated employing a 10 mm long plane-parallel cavity. The plane reflector was coated for high reflectance at 1020−1200 nm (> 99.8%) and for high transmittance at 976 nm (> 95%); the plane output couplers used were of transmittances (output couplings) of T = 60%, 70%, 80%. The Yb:YCOB crystal was placed close to the reflector; whereas the Bi₂Te₃ sample was inserted between the laser crystal and the output coupler. The laser crystal was cooled by cooling water which was maintained at a temperature of 5 °C. A fiber-coupled 976-nm diode laser (fiber core diameter of 105 μm and NA of 0.22) was employed to pump the laser; the pump beam was focused by a re-imaging unit and was coupled through the reflector mirror onto the Yb:YCOB crystal with a beam spot radius of approximately 70 μm.

3. Results and discussion

The absorption saturation properties in the 1-μm spectral region of the few-layer Bi₂Te₃/Sapphire sample have been studied in our recent work [18], with the modulation depth and saturation intensity determined to be ΔT = 1.1% and I_sat = 2.42 MW/cm². Employing the plane-parallel resonator described in the preceding section, we achieved efficient, stable Q-switched operation under output couplings of T = 60%, 70%, and 80%, generating linearly polarized output radiation with E//Z. The pulsed output characteristics of the laser are illustrated in Fig. 1, showing the average output power versus the incident pump power (P_in). The fraction of incident pump power absorbed by the 5 mm long Yb:YCOB crystal, was measured to be 0.96 at a very low incident pump power (less than 0.1 W); this small-signal absorption fraction was found to decrease rapidly with increasing pump power, dropping to 0.55 at P_in = 5.0 W. Due to the strong absorption saturation, it is difficult to determine the amount of absorbed pump power at a given pumping level. As a consequence, the laser performance is characterized in terms of incident pump power. The lasing threshold was reached at P_in = 1.61, 1.85, and 2.36 W for T = 60%, 70%, and 80%. One can see very similar output characteristics for T = 60% and 70%. In both cases the output power could scale with a slope efficiency of 28%, with a slightly higher output power produced under T = 60%. However, the output power attainable in this case was limited to 3.05 W, generated at P_in = 12.9 W; above this pumping level optical damage would occur to the few-layer Bi₂Te₃ sample. Under the higher output coupling of T = 70%, a maximum output power of 3.85 W could be produced at P_in = 16.7 W before the Bi₂Te₃ sample was damaged. With the output coupling increased further to T = 80%, the laser efficiency dropped severely; the output power attainable was limited to 2.16 W.

 

Fig. 1 Average output power as a function of P_in, generated from the Yb:YCOB/Bi₂Te₃ laser under output couplings of T = 60%, 70%, and 80%.

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The output beam quality was examined. At an output power of 3.0 W, the beam quality factor was measured to be 1.11 (horizontal) and 1.09 (vertical), indicating little or no components of higher-order transverse modes in the laser beam.

Figure 2(a) presents the dependence of pulse repetition rate on incident pump power measured under different output couplings. In each case, the repetition rate became increased as the pumping level was raised; at a given pump power, a smaller output coupling led to a higher repetition rate. These features are typical of passively Q-switched solid-state lasers operating under continuous-wave pumping conditions. In the case of T = 60%, the repetition rate increased from 111 kHz, measured just above threshold, to 435 kHz at P_in = 12.9 W. Under higher output couplings, the increase of repletion rate would become somewhat slower, reaching a maximum of 400 kHz (T = 70%) and 385 kHz (T = 80%).

 

Fig. 2 Pulse repetition rate (a) and pulse energy (b) versus P_in, measured (calculated) for the Yb:YCOB/Bi₂Te₃ passively Q-switched laser.

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From the measured average output power and pulse repetition rate, one can calculate the corresponding pulse energy. Figure 2(b) depicts the pulse energy versus P_in for T = 60%, 70%, and 80%. One can see that the pulse energy exhibited a similar variation behavior; it increased initially with P_in and then the energy increasing would become slower, it would eventually reach a certain magnitude that would remain roughly unchanged. Such an energy varying behavior resulted from the progressively increasing degree of the TISA bleaching. At low pumping level just above threshold, the TISA could only be bleached to a very limited degree, resulting in very moderate pulse energy; with the pump power raised continually, the TISA would become more and more bleached, hence the pulse energy was able to increase gradually; at the final stage when the pumping level was increased such that the TISA could be fully bleached, the resulting pulse energy reached a certain amount that would remain more or less fixed, independent of pump power, just as predicted for a usual passive Q-switching laser action. One notes that the largest pulse energy, 9.63 μJ, was produced in the case of T = 70%; while for T = 60% and 80%, the highest pulse energy generated was 7.01 and 5.62 μJ.

The dependence of pulse duration upon P_in is illustrated in Fig. 3(a). For each case, the pulse duration dropped very rapidly in the low pump region near the threshold; it then decreased smoothly with rising P_in, reaching at some sufficiently high pumping level a certain value that would remain roughly unchanged. The physical reason responsible for such variation of pulse duration is also attributed to the dynamic process of the TISA bleaching, just as in the situation of pulse energy. The shortest pulse duration, 96 ns, was obtained under output coupling of T = 70%; whereas in the cases of T = 60% and 80%, the minimum pulse duration was measured to be 118 and 109 ns.

 

Fig. 3 Pulse duration (a) and peak power (b) versus P_in, measured (calculated) for the Yb:YCOB/Bi₂Te₃ passively Q-switched laser.

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Given the pulse energy and duration, one can calculate the peak power. Figure 3(b) shows the calculated peak power as a function of P_in for different output couplings. Similar to the situation of pulse energy or pulse duration, the peak power would also tend to reach some fixed amount, as long as the pump power was raised to a high enough level enabling the TISA to be completely bleached. Under the output coupling of T = 70%, the peak power could reach 100.3 W; in the cases of T = 60% and 80%, the highest peak power attainable was respectively 59.4 and 51.6 W.

Figure 4 illustrates a laser pulse train recorded at the highest pump power of P_in = 16.7 W in the case of T = 70%. The amplitude fluctuations were estimated to be 2.7% (rms); while the timing jitters were 11.0% (rms). The inset gives the temporal profile of an individual laser pulse, showing an FWHM width of 96 ns.

 

Fig. 4 Pulse train recorded at P_in = 16.7 W under output coupling of T = 70%. Inset: the temporal profile of an individual laser pulse.

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The variations of pulse energy and duration with the increase of pump power, stemmed mainly from the increasing degree of bleaching in the Bi₂Te₃ absorber. By an estimation of the laser intensity reachable in the Bi₂Te₃ sample, one can understand this dynamic bleaching process. The beam radius at the position of the Bi₂Te₃ sample in the resonator, which depends on the thermal lensing of the Yb:YCOB crystal and hence on the pump power absorbed, is calculated to decrease from 0.175 mm just above threshold (assuming weak thermal lensing with a focal length of f_T = 1000 mm) to 0.081 mm at the highest pumping level (assuming a fairly strong thermal lensing, e.g., f_T = 50 mm). Let us consider the case of T = 70%. Due to the existence of cavity coupling caused by the uncoated rear surface of the sapphire substrate opposite to the plane coupler, the effective output coupling is calculated as T_eff = 49% [25,26]. So the total internal power inside the Bi₂Te₃ sample which was close to the output coupler, was roughly three times higher than the output power. Taking into account the highest peak power, 100.3 W, which was reached at the highest pumping level, one can calculate the maximum on-axis laser intensity in the Bi₂Te₃ sample to be I_max ≈3.0 MW/cm², higher than the saturation intensity I_sat = 2.42 MW/cm². One sees that the few-layer Bi₂Te₃ absorber could be fully bleached at the highest pumping level. On the other hand, just above the Q-switching threshold, e.g., at P_in = 3.5 W, at which the peak power reached 10.0 W (Fig. 3(b)), the on-axis laser intensity is estimated to be I ≈0.06 MW/cm², much lower than the saturation intensity. So the Bi₂Te₃ saturable absorber could only be bleached to a very limited degree at such low pumping levels. Clearly, with the pump power being raised, the few-layer Bi₂Te₃ absorber would become increasingly saturated.

For the Yb:YCOB/Bi₂Te₃ laser operating under high output couplings of T = 60%−80%, the emission wavelengths varied only slightly with pump power. Figure 5 shows a typical lasing spectrum for each case, measured at P_in = 9.51 W. Laser oscillation occurred over a wavelength range of 1028−1037 nm. Upon increasing the output coupling, the lasing wavelengths would shift toward short-wavelength side due to the increase of overall resonator losses.

 

Fig. 5 Lasing spectrum measured at P_in = 9.51 W under different output couplings of T = 60%, 70%, and 80%.

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In the current experiment an X-cut Yb:YCOB sample was utilized, since this crystal orientation could lead to the best passive Q-switching laser performance. With Y- or Z-cut crystal sample of the same length and the same Yb-ion concentration, the pulsed output power achievable proved to be lower, while the shortest pulse duration longer, than obtained with the X-cut crystal sample.

The passive Q-switching performance of the Yb:YCOB/Bi₂Te₃ laser could be further improved, with the maximum output power and highest energy being scaled to higher levels, and with the minimum pulse width being further shortened. The measures that can be taken include the optimization of Yb-ion concentration and of crystal length; the reduction in resonator length; the proper choice of the layer number or thickness of the Bi₂Te₃ film to optimize the modulation depth; and the improvement in optical quality of Bi₂Te₃/Sapphire sample to reduce the non-saturable losses.

It is instructive to compare the Yb:YCOB/Bi₂Te₃ and Yb:LuPO₄/Bi₂Te₃ lasers [18], both of which could be operated under high output couplings. Table 1 lists the primary parameters characterizing the passive Q-switching performance for the two lasers. The results for the Yb:YCOB/GaAs and Yb:YCOB/Cr⁴⁺:YAG lasers [20,21], are also presented in Table 1 for comparison. In the table P_max denotes the maximum output power; PRR the pulse-repetition- rate range; E_p the largest pulse energy; t_p the shortest pulse duration; P_p the highest peak power; η_s the slope efficiency; and λ the lasing wavelength. One can see that while the pulsed output powers attainable from the two lasers passively Q-switched by Bi₂Te₃ TISA were comparable, the highest repetition rate reached in the current Yb:YCOB laser proved to be 3−4 times lower than achievable in the Yb:LuPO₄ laser, leading to three times greater pulse energy, as well as higher peak power, despite the longer pulse duration. One can also notice the fairly similar performance of the current Yb:YCOB/Bi₂Te₃ and the Yb:YCOB/GaAs lasers in output power; slope efficiency; lasing wavelength; and pulse duration. On the other hand, however, the highest repetition rate reached in the Yb:YCOB/Bi₂Te₃ laser was more than two times higher than that of the Yb:YCOB/GaAs laser. In terms of pulse energy and peak power, the Yb:YCOB/Cr⁴⁺:YAG laser turns out to be much superior to all others listed in Table 1, obviously due to its much lower repetition rates. From the range of pulse repetition rates given in the table for each passively Q-switched laser, one sees that with the four pulsed lasers, a wide repetition-rate region extending from 3.0 kHz to 1.67 MHz, could be covered. It should be pointed out that the resonator lengths for these lasers were quite different, ranging from 4 mm for the Yb:LuPO₄/Bi₂Te₃ to 100 mm for the Yb:YCOB/GaAs laser [18,21]. The specific resonator length for each laser is given in the notes below Table 1, along with other resonator parameters.

Table 1. Comparison of Passive Q-switching Performance between the Current Yb:YCOB/Bi₂Te₃ Laser and the Previous Yb:LuPO₄/Bi₂Te₃, Yb:YCOB/GaAs, Yb:YCOB/Cr⁴⁺:YAG Lasers [18, 20, 21]

View Table

The purpose of the current work is to explore Yb-ion laser crystals that enable high-power efficient passively Q-switched operation with TISAs, motivated by the great potential of TISAs demonstrated in our recent work on the Yb:LuPO₄/Bi₂Te₃ laser [18]. The passive Q-switching performance of the present Yb:YCOB/Bi₂Te₃ laser proved to differ appreciably from the Yb:LuPO₄/Bi₂Te₃ laser in repetition rate, pulse energy, duration, as well as in oscillation wavelengths, due to the distinct spectroscopic properties of the two Yb-ion crystals. The significance of the present work lies in several aspects. Firstly, although the Yb:LuPO₄ exhibits very promising performance in TISA passive Q-switching, currently it cannot be grown in large size, which will greatly limit its practical applications. As a consequence, searching for more other Yb-ion crystals suitable for TISA passive Q-switching still remains essential. Secondly, despite the wide variety of Yb-ion laser crystals developed so far, not all of them are applicable in TISA passive Q-switching to generate high-power pulsed laser radiation. For instance, the Yb-ion doped orthovanadates (Yb:YVO₄, Yb:GdVO₄, Yb:LuVO₄, and their mixed ones) having exactly the same tetragonal zircon structure as for Yb:LuPO₄ (space group of I4₁/amd and point group of 4/mmm), behave poorly in TISA passive Q-switching, which have been found in our experiment. Therefore, properly choosing the most appropriate from the various Yb-ion crystals is a necessary task required for the development of TISA passively Q-switched lasers. Thirdly, Yb:YCOB turns out, among the various Yb-ion laser crystals known up to now, to be the most important to investigate in searching for laser medium for passively Q-switched lasers with TISAs, because of its unprecedented superiority in passive Q-switching with traditional saturable absorbers such as Cr⁴⁺:YAG and GaAs [20–22]. Finally, there exist a large family of Yb-ion doped rare-earth calcium oxyborates, represented by Yb:YCOB, consisting of Yb:GdCa₄O(BO₃)₃ (Yb:GdCOB), Yb:LaCa₄O(BO₃)₃ (Yb:LaCOB), Yb_t:Y_xGd_1−t−xCa₄O(BO₃)₃, Yb_t:Lu_xGd_1−t−xCa₄O(BO₃)₃, and so on, all of which are expected to exhibit similar laser properties. More importantly, due to the more substitution disorder leading to stronger inhomogeneous line broadening, some degree of modification in spectroscopic properties could be realized in mixed crystals, facilitating the optimization of passive Q-switching for some specific applications. So the promising passive Q-switching performance demonstrated in the present work with the Yb:YCOB/Bi₂Te₃ laser, provides great possibility as well as flexibility in the development of solid-state lasers operating in the 1-μm region that are passively Q-switched with TISAs.

4. Summary

In conclusion, we have demonstrated an Yb:YCa₄O(BO₃)₃ laser that could be operated under high output couplings, and could be effectively Q-switched by few-layer Bi₂Te₃ saturable absorber, producing a maximum output power of 3.85 W at a repetition rate of 400 kHz, at an incident pump power of 16.7 W with a slope efficiency of 28%. The resulting pulse energy, duration, and peak power were respectively 9.63 μJ, 96 ns, and 100.3 W. Our investigation reveals the great potential of Yb:YCa₄O(BO₃)₃ crystal and other Yb-doped rare-earth calcium oxyborates in the development of high-power, high-repetition-rate, passively Q-switched solid-state lasers in the 1-μm region with 2D topological insulator as saturable absorber.