1. Introduction

Diode-pumped solid states lasers (DPSSL) have attracted scientific interest due to their huge potential in various applications such as manufacturing, defense, laser ignition, metrology, medicine and remote sensing [1–5]. Because of the simple energy level structure of Yb ions with only two manifolds relating to the lasing process, Yb-doped materials have the advantages of low quantum defects and the absence of excited state absorption. Thus, Yb-doped materials become one of the most popular laser media for DPSSL [6].

However, at room temperature (RT), the Yb-doped materials operate as a quasi-three-level laser resulting from a finite population in the lower laser level, which causes a decrease of the laser inversion population and an increase of the reabsorption loss at the laser wavelength [7]. Consequently, the thermal issues need to be particularly concerned to develop efficient lasers based on Yb-doped materials. However, the output power and the beam quality of the lasers are limited by thermally induced effects such as thermal distortion, birefringence, or stress fracture in the solid-state laser media [8].

Cryogenic technique has been used to solve the thermal issues to improve performance of the lasers. The significant improvements of the thermal properties and spectroscopic properties of Yb-doped materials at cryogenic temperature (CT) has been demonstrated in Ref. [9,10] and four-level laser operation is achieved because of the lower laser level becomes thermally depopulated [11], leading to improved efficiency and lower threshold operation for Yb-doped lasers.

Several works have shown that cryogenic cooling for the gain medium can effectively enhance the output performance of the lasers [12–18]. For instance, a cryogenic Yb:YAG laser pumped by VBG stabilized narrow band 968.7 nm laser diode (LD) achieved a maximum output power of 6.54 W at 140 K, while less than 0.2 W output at 300 K [14]. A continuous-wave (CW) Yb:YAG laser obtained a maximum output power of 5.1 W at 60 K pumped by 940 nm LD, and a ∼0.25 W output power was obtained by same setup at 200 K [7]. Particularly, in a CW cryogenic Nd:YAP laser operation based on zero thermal expansion, a wavefront peak-to-valley values (PV) improved from 6.79 µm to 2.55 µm as temperature decreased from 290 to 180 K [19]. It is evident that cryogenic cooling can significantly improve the output power and beam quality of laser. However, most of researches to cryogenic Yb:YAG lasers aimed to output power properties. As we known, however, no one has reported the improvements to wavefront PV and thermal lens effect of Yb:YAG at CT.

Here in this work, wavelength-switching performance and thermal lens effect of Yb:YAG lasers pumped by 940 nm laser diode in CW regime from RT to CT are experimentally investigated. A maximum output power of 13.16 W and an optic-optic efficiency of 25.6% are achieved with an incident pump power of 60 W at 80 K. The wavelength-switching performance is observed and explained by laser threshold behavior as temperature. Furthermore, the thermal lens effect is evaluated by wavefront PV measurements with Shack-Hartmann wavefront sensor (SH-WFS) manufactured by Imagine Optics. The wavefront PV improves from 1.375 µm (about 1.33$\lambda $) at 300 K to 0.338 µm (about 0.33$\lambda $) at 80 K. Correspondingly, the thermal lens dioptric power (inversion of thermal lens focal length) is 1.71 m^-1 at 300 K and 0.15 m^-1 at 80 K. The tenfold slighter thermal lens effect at CT compared to RT and the brilliant beam quality factor M² of about 1.10 at both x and y direction display the ability to achieve high power lasers with high beam quality.

2. Experimental setup

The experimental configuration of the cryogenic Yb:YAG laser is exhibited in Fig. 1. The LD pump source is a CW fiber-coupled laser diode delivering a maximum output power of 60 W. The LD central wavelength is fixed at 940 nm with a spectral bandwidth of ∼3 nm. The pump beam is imaged onto the Yb:YAG crystal in 1:3 ratio using a pair of focusing lens, which are antireflection (AR) coated for the pump wavelength. The core diameter of the fiber is 200 µm with a numerical aperture of 0.22. The 2.0 at. % Yb:YAG rod with a length of 10 mm and a diameter of 3 mm is used as the gain medium with AR coating at 940 nm and 1030 nm for the end facets. The rod laser crystal is wrapped with indium foil and mounts in a copper heat sink to improve the heat dissipation efficiency. The copper heat sink is attached to the cold finger of the temperature-controlled cryostat and placed in a vacuum chamber. Tow plane-parallel optical windows coated with 99.8% transmittance at a wavelength range of 800 nm-1100 nm are equipped at the vacuum chamber. Two plat mirrors, M1 and M2, are outside the vacuum chamber to adjust the resonator cavity and prevent the miss-alignment of the cavity at low temperatures. The rear M1 is coated with high reflection (HR) at 1030 nm and AR coated at 940 nm. The output coupler M2 is coated with partial reflection at 1030 nm (R = 97%) and AR coated at 940 nm.

 

Fig. 1. Experimental setup for the cryogenic Yb:YAG laser.

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3. Results and discussion

Figure 2 shows the output powers of the Yb:YAG laser as a function of the absorbed pump power at different temperatures of 300, 250, 200, 150, 80 K. It can be observed that the laser power increases linearly with the absorbed pump power. A maximum output power of 13.16 W is achieved at 80 K under an absorbed pump power of 51.5 W, corresponding to an optic-optic efficiency of 25.6%. At 300 K, the output power is only 3.59 W with an optic-optic efficiency of 8.0%. These results confirm that the output power and optic-optic efficiency are significant improvements at 80 K, more than 3 times higher than that at RT. Besides, the decrease of threshold absorbed pump power ${P_{th}}$ with a decrease in temperature is displayed in Fig. 3, which is coincide with results in [7]. As seen in Fig. 3, the minimum ${P_{th}}$ is 1.10 W at 80 K.

 

Fig. 2. Output power versus the absorbed pump power at different temperatures of 300, 250, 200, 150, 80 K.

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Fig. 3. Experimental and calculated threshold absorbed pump power versus temperature.

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The spectra of Yb:YAG laser with a fixed incident pump power of 60 W for the temperature 300, 250, 200, 150, 80 K are measured in Fig. 4. Note that the central wavelength shifts from 1049.7 nm to 1049.4 nm when the crystal is cooled down from 300 K to 250 K. As the temperature continually decreases to 200 K, the wavelength-switching effect is found. The laser oscillation near 1049.0 nm disappears, and the laser oscillation near 1030.0 nm is dominant. As the temperature further decreases from 200 K to 80 K, the central wavelength shifts from 1030.8 nm to 1029.5 nm. These results are consistent with [20].

 

Fig. 4. The spectra of Yb:YAG laser with a fixed incident pump power of 60 W for the temperature 300, 250, 200, 150, 80 K.

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To explain the wavelength-switching performance, the ${P_{th}}$ calculation of 1030 nm and 1049 nm were given based on rate equations [21,22]

Table 1. Parameters for Yb:YAG lasers used in the ${{\boldsymbol P}_{{\boldsymbol th}}}$ calculation

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The calculation values of ${P_{th}}$ as a function of temperature are also shown in Fig. 3. At temperature above ∼230 K, the ${P_{th}}$ at 1049 nm is lower than the ${P_{th}}$ at 1030 nm. But, the ${P_{th}}$ at 1049 nm increases more rapidly than the ${P_{th}}$ at 1030 nm as temperature drops. Furthermore, at temperature below ∼230 K, the ${P_{th}}$ at 1049 nm is higher than the ${P_{th}}$ at 1030 nm, thus the mode at 1049 nm can be suppressed and the 1030 nm mode can operate at temperature below ∼230 K. Therefore, the ${P_{th}}$ is a combining effect of mode competition between two wavelength of 1030 nm and 1049 nm.

To give a further explanation of the wavelength-switching performance, the small gain coefficients are calculated. The calculated small gain coefficients are shown in Fig. 5. The gain at line 1050 nm and 1030 nm increase with different rates as temperature drops. At temperature below ∼230 K, the gain at line 1050 nm is smaller than the gain at 1030 nm, leading to the appearance of 1030 nm and the disappearance of 1050 nm. This is consistent with the calculated ${P_{th}}$.

 

Fig. 5. Calculated small gain coefficient versus temperature.

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Similarly, the wavelength-switching performance can be observed for the output coupler reflectivity higher than ∼88% at RT [23]. As the gain at 1049 nm and 1030 nm are influenced by output coupler reflectivity and the temperature, it can be expected to achieve dual-wavelength cryogenic Yb:YAG laser by adopting the optimum temperature and the best reflectivity of output coupler. It is of great benefit to develop a high power and high efficiency dual-wavelength Yb:YAG laser.

A direct wavefront measurement is performed using an SH-WFS with similar measurement setup to [24], providing an accurate wavefront PV and a direct full 2-D wavefront mapping to display the wavefront distortions and thermal lens effect as a function of temperature. Figure 6 (a) shows the 2-D wavefront mapping with a fixed incident pump power of 60 W for different temperature 80, 150, 200, 250 and 300 K. It also can be inferred from the 2-D wavefront mapping that the defocus resulting from the thermal lens effect is the main optic aberration, which is further proved by the 2-D wavefront mapping after defocus correction with the software supported by Imagine Optics as shown in Fig. 6 (b). The PV of the beam wavefront improves from 1.375 µm (about 1.33$\lambda $) to 0.338 µm (about 0.33$\lambda $) as the temperature decreases from 300 K to 80 K as shown in Fig. 6, indicating a better beam quality is achieved at CT. The wavefront PV after defocus correction is nearly 0.2 µm (about 0.15$\lambda $) at all temperature from 300 K to 80 K, which can be considered as aberration-free wavefront. Thus, the defocus PV is obtained by difference between wavefront PV before and after defocus correction, so that the thermal lens dioptric power is achieved [25]. It means the thermal lens effect as a function of temperature can be specifically investigated.

 

Fig. 6. The 2-D wavefront mapping (a) before and (b) after defocus correction with a fixed incident pump power of 60 W for different temperature 80, 150, 200, 250 and 300 K.

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Based on the optic aberration theory, the thermal lens dioptric power is determined by the defocus wave aberration shown as below [26,27]

 

Fig. 7. The wavefront PV and thermal lens dioptric power versus temperature.

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The experimental beam quality factor M² at 80 K is also completed as shown in Fig. 8. It is measured to be 1.11 along x direction and 1.10 along y direction, corresponding to an average M² value of 1.10. Therefore, the compensation of thermal lens effects by cryogenic cooling is of great benefit for achieving high beam quality laser as well as high output power.

 

Fig. 8. Experimental beam quality factor M² at 80 K

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4. Conclusion

In conclusion, wavelength-switching performance and thermal lens effect of cryogenic Yb:YAG laser are experimentally investigated. The maximum output power of 13.16 W, corresponding to an optic-optic efficiency of 25.6%, is achieved at 80 K with an absorbed pump power of 51.5 W. The wavelength-switching performance explained by laser threshold behavior versus temperature is observed. Particularly, the thermal lens effects of Yb:YAG are directly charactered by wavefront measurement using SH-WFS. The best wavefront PV is 0.338 µm (about 0.33$\lambda $) at 80 K. The thermal lens dioptric power determined by defocus PV decreases from 1.71 m^-1 (300 K) to 0.15 m^-1 (80 K), indicating both thermal lensing and wavefront distortion effects are significantly mitigated without the need of any additional correction system. Both the beam quality factor of M² is quite good at the x and y direction. Thus, high power lasers with high beam quality achieved by cryogenic cooling can be anticipated.