1 Introduction

Eyesafe 2 μm solid state lasers are useful for atmospheric remote sensing, high resolution molecular spectroscopy, and nonlinear optical studies, so considerable attention has been given to the development of all solid-state 2 μm lasers. Tm and Ho codoped laser crystals can produce 2 μm wavelength lasers [1–5]. Among the laser materials used to generate 2 μm laser emission, the Tm,Ho:YLF is an excellent laser crystal due to its long pump integration time, excellent optical damage resistance, lack of thermal induced birefringence, and small upconversion loss. Diode pumped continuous wave and Q-switched Tm,Ho:YLF lasers have been widely researched [6–13].

Bistability is a phenomenon in which the system exhibits two output intensities for the same input intensity and presents various potential applications, in all-optical logic gates and optical computing, as a switch between two states of the output power, memory, converser, etc. Optical bistability has been predicted and experimentally realized in various settings, including a Fabry–Perot resonator filled with a nonlinear material [14], layered periodic structures [15], quantum cascade laser [16], two-section quantum dot laser [17], twin microdisk [18]. In solid state lasers, the optical bistability phenomenon were only observed in Tm,Ho:YLF lasers and Yb vanadate lasers. Liu et al. observed bistable continuous wave laser output in Yb:LuVO4, Yb:GdVO4, Yb:YVO4, and the mixed crystal lasers [19–22]. Moreover, in a previous study, we observed bistability output in an end-pumped Tm,Ho:YLF laser, in which the width of bistable region is about 100 mW, and the jump power is near 10 mW [23]. But the output of these bistable lasers is multimode. Some special applications such as laser communication require the bistable lasers to be single frequency output. However, till now, single frequency bistability solid state lasers have not been reported.

In this paper, we report on the first observation of single-frequency bistability in a Tm,Ho:YLF laser near room temperature. Furthermore, the width of bistable region and the jump power can be controlled by regulating the length of the laser resonator.

2 Experiment setup

The experimental setup is shown in Fig. 1. The pump laser is a fiber-coupled laser diode temperature-tuned to 792 nm emission wavelength. The diameter and numerical aperture of the fiber core are 100 μm and 0.22, respectively. The pump beam is focused by a 1:1 coupling optics system, and the pump spot diameter in the position of the Tm,Ho:YLF crystal is about 100 μm. The total transmission efficiency of the beam-reshaping system is over 90 % at 792 nm.

Fig. 1
figure 1

Experimental setup for the single frequency bistability Tm,Ho:YLF laser

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The a-cut Tm,Ho:YLF laser crystal has dopant concentrations (with respect to the Y-lattice site) of 6 % Tm, 0.4 % Ho, and a dimension of 5 mm×5 mm in cross-section and 2.5 mm in length. A plane-concave resonator is employed to make the system very simple and compact. The near hemispherical resonant is formed between the planar crystal front face and the output coupler. A dichromatic coating on the front face of the crystal is high transmitting at 792 nm, but is totally reflecting at 2 μm. The other face is only polished and uncoated at both pump and output wavelengths. To efficiently remove the heat generated with pump power from the crystal, the crystal is wrapped with indium foils and held in brass heat sink. Temperature of the heat sink is held at a constant 288 K with a thermoelectric cooler. The radius of curvature of the output coupler is 103 mm, and the transmission of the output coupler is 2 % for the best output characteristics. Two uncoated fused silica etalons which are respectively 0.1 and 1 mm thick are used to choose and tune the laser frequency by angle tuning the etalons. Only for the single longitudinal mode operation the etalons are inserted into the resonator.

3 Results and discussion

When no etalon is put into the resonator, the Tm,Ho:YLF laser oscillates in multimode. Figure 2(a) shows the multimode output power as a function of the incident pump power for a cavity length of 65 mm. When the pump power is increased from zero, the 2 μm laser dose not oscillate until a critical point of pump power, referred to as on-threshold, is reached at P in=P on=765 mW, at which the output power jumps from zero to a substantial level of 68 mW, referred to as jump power. Above this point, the output power increases nearly linearly with pump power. When the pump power is decreased starting from a level in excess of P on, the output power decreases with nearly the same slope, with the laser still oscillating for pump powers below P on. Further reduction of the pump power eventually leads to cessation of the 2 μm laser oscillation at the off-threshold P off=510 mW. Therefore, a hysteresis loop in the dependence of the output power on the pump power is present. In the pump power range defined by P off<P in<P on, the operation of the Tm,Ho:YLF laser is bistable (P on–P off is defined as the width of bistable region), and the output power at a given pump level depends on the way that this pump level is reached.

Fig. 2
figure 2

The output power of the Tm,Ho:YLF laser as a function of pump power for a cavity length of 65 mm, showing a hysteresis loop: (a) multimode and (b) single longitudinal mode

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To achieve single frequency operation and spectral tuning, we insert two uncoated solid fused silica etalons with thickness 1 mm and 100 μm into the resonator. By careful rotation of the etalons, the stable single longitudinal mode operation near 2054 nm is obtained. Figure 2(b) plots the single longitudinal mode output power as a function of the pump power. It can be noted that the single longitudinal mode laser is also bistable. The off-threshold and on-threshold is 790 and 1370 mW, respectively, and the jump power at the on-threshold is 78 mW. Compared with the multimode power shown in Fig. 2(a), the on-threshold and off-threshold of the single longitudinal mode laser increase due to the insertion loss of the etalons. The influence of the energy transfer upconvertion to the threshold pump powers become severer with the increase of loss. The higher the threshold pump power is, the larger is the influence of energy transfer upconvertion to it, which leads to the further increase of the threshold pump power [9]. So the width of bistable region is increased from 255 to 580 mW as shown in Fig. 2.

Figure 3 shows the single longitudinal mode laser spectrum from the scanning F–P interferometer with a free spectral range (FSR) of 3.75 GHz. The output laser is detected by a high speed InGaAs detector and recorded using a Tektronix TDS3032B digital oscilloscope with 300 MHz bandwidth. In Fig. 3, the upper trace is the Fabry–Perot ramp voltage and the lower trace is the voltage of the InGaAs detector measuring the Tm,Ho:YLF laser transmission through the Fabry–Perot interferometer. The transverse output beam profiles are measured with a beam analyzer (Electrophysics, MicronViewer 7290A), and shown in inset of Fig. 4. It can be seen that no higher-order transverse modes are observed and the output beam is close to fundamental transverse electromagnetic mode (TEM00). The beam radius for the single frequency Tm,Ho:YLF laser at the 2 W pump power is measured by the knife-edge method. The positive 100 mm focal length lens is located at the position approximately 400 mm from the output coupler. Measured position-dependent beam radii near the focus are shown in Fig. 4. The beam quality factor M2 of 1.2 is determined by fitting the standard Gaussian beam propagation expression to the measured data. Thus, the laser is single frequency operation. This single frequency bistability output is very interesting since it may be used to laser communication and remote sensing systems.

Fig. 3
figure 3

Fabry–Perot spectrum of the single frequency Tm,Ho:YLF laser

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Fig. 4
figure 4

Beam radius as a function of the distance from focusing lens at the pump power of 2 W, and the inset shows transverse beam profile

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Figure 5 shows the width of bistable region and the jump power at the on-threshold as a function of the cavity length, when the Tm,Ho:YLF laser is single frequency operation. As observed from Fig. 5, with the increase of the length of the laser resonator from 65 to 100 mm, the width of the bistable region decreases nearly linearly from 580 to 0 mW, and the jump power at the on-threshold also reduces from 78 to 0 mW nearly linearly. So the width of bistable region and the jump power at the on-threshold can be tuned by changing the length of the laser resonator. As shown in Fig. 6, in our experiment, the diameter of pump beam waist in the Tm,Ho:YLF laser crystal is a constant of about 100 μm, however the diameter of 2 μm laser mode in the Tm,Ho:YLF crystal is alterable by changing the length of the laser resonator. When the length of the resonator is between 65 and 100 mm, the size of laser mode, which is near constant along the optical axis in the crystal, is more than the pump beam waist. Moreover, it increases with the decrease of the resonator length. So the non-pumping region in the laser mode becomes larger when the length of the laser resonator is decreased from 100 to 65 mm. Because of the quasi-three-level characteristics of the Tm,Ho:YLF crystal near room temperature, the non-pumping region can be treated as a saturable absorber. At the same time, the pump region has a shorter upper level effective lifetime than the non-pumping region at on-threshold pump power due to the influence of energy transfer upconversion, which makes the pump region have larger saturation absorption intensity than the non-pumping region. Thus, the Tm,Ho:YLF laser satisfies the condition of optical bistability [13]. With increasing laser mode size, the effective absorbing length of the laser crystal will become longer under the same pumping conditions [22]. It means that the effective thickness of saturable absorber increases with the 2 μm laser mode, so both the on-threshold and off-threshold increase with the thickness of the saturable absorber due to the absorption losses of the saturable absorber. The increase of the on-threshold is more than that of the off-threshold, because the influences of the energy transfer upconversion and excited-state absorption become severer with the increase of pump power when the laser does not oscillate. So the width of bistable region and the jump power at on-threshold increase with the decrease of the resonator length due to the evident increase of on-threshold.

Fig. 5
figure 5

The jump power and bistable region width as a function of the cavity length

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Fig. 6
figure 6

The radii of the pump beam and laser modes for different cavity lengths as a function of position along the crystal length

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The output powers for the single frequency and multimode as a function of pump power are measured at the length of the resonator of 90 mm, and shown in Fig. 7. For the multimode output power, the achieved maximum output power is 436 mW when the pump power is 2 W, and the slope efficiency with respect to pump power is 27.4 %. The maximum single frequency output power is about 180 mW, and the slope efficiency is 11.6 % which is the maximum for different lengths of the laser resonator. Moreover, laser spectra are recorded using a monochromator associated with a TE-cooled InGaAs detector. The center wavelength of the multimode laser is 2066 nm, however, the wavelength of the single frequency laser is reduced to 2054 nm. Furthermore, for the single frequency Tm,Ho:YLF laser, the laser frequency can be continuously tuned 1.25 GHz by slightly changing the tilt angle of the 1 mm thick etalon.

Fig. 7
figure 7

Output power performance of the multimode and single frequency laser near room temperature

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4 Conclusion

In conclusion, the first all-optical single frequency bistability around 2 μm from an end-pumped Tm,Ho:YLF laser with double etalons is demonstrated experimentally. The width of the bistable region is as large as 580 mW, and the jump power is as large as 78 mW for a cavity length of 65 mm. Furthermore, the width of bistable region and the jump power at the on-threshold can be tuned by regulating the length of the laser resonator. When the cavity length is 90 mm, the maximum output power of single frequency is 180 mW at the pump power of 2 W, which corresponds to a slope efficiency of 11.6 %. The laser frequency can be continuously tuned about 1.25 GHz. The laser is very suitable to laser lidar systems and all-optical switching systems.