Resonantly pumped high efficiency Ho:GdTaO $_{4}$ laser
共振泵浦高效 Ho:GdTaO $_{4}$ 激光器

Xiaoming Duan, $^{1, 5}$ Guangpeng Chen, $^{1}$ Chuanpeng Qian, $^{1}$ Yingule Shen, $^{2}$ Renqin Dou, $^{3}$ Qingli Zhang, $^{3, 6}$ Linjun LI, $^{4, 7}$ and Tongyu Dai $^{1}$
段晓明、 $^{1, 5}$ 陈光鹏、 $^{1}$ 钱传鹏、 $^{1}$ 沈颖乐、 $^{2}$ 窦仁勤、 $^{3}$ 张庆利、 $^{3, 6}$ 李林军、 $^{4, 7}$ 和戴彤宇 $^{1}$ 。 $^{I}$ National Key Laboratory of Tunable Laser Technology, Harbin Institute of Technology, Harbin 150001, China
$^{I}$ 可调谐激光技术国家重点实验室，哈尔滨工业大学，中国哈尔滨 150001 $^{2}$ School of Opto-Electronic Information Science and Technology, Yantai University, Yantai 264005, China
$^{2}$ 烟台大学光电信息科学与技术学院，中国烟台 264005 $^{3}$ The Key Laboratory of Photonic Devices and Materials, Anhui Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Hefei 230031, China
$^{3}$ 中国科学院安徽光学精密机械研究所光子器件与材料重点实验室，合肥 230031 $^{4}$ The Higher Educational Key Laboratory for Measuring & Control Technology and Instrumentations of Heilongjiang Province, Harbin University of Science and Technology, Harbin 150080, China
$^{4}$ 黑龙江省高等学校测控技术与仪器重点实验室，哈尔滨理工大学，哈尔滨，150080 $^{5} x m d u a n @ h i t . e d u . c n$ 6zql@aiofm.ac.cn7ilj2019@126.com

Abstract 摘要

We demonstrate a continuous-wave $2.1 - μ m$ laser with a new $Ho : {GdTaO}_{4}$ crystal pumped by a $1940.3 - nm$ Tm fiber laser at room temperature. The maximum output power of 11.2 W at 2068.39 nm was achieved, corresponding to a slope efficiency of $72.9 %$ . Moreover, the beam quality factor was measured to be about 1.4 at the maximum output level.
我们展示了一种连续波 $2.1 - μ m$ 激光器，该激光器采用新型 $Ho : {GdTaO}_{4}$ 晶体，在室温下由 $1940.3 - nm$ Tm 光纤激光器泵浦。在 2068.39 nm 波长处，实现了 11.2 W 的最大输出功率，斜率效率为 $72.9 %$ 。此外，在最大输出水平时，光束质量因数测量值约为 1.4。

1. Introduction 1.导言

The

2.1 - μ m

holmium (Ho) lasers based on the

^{5} I_{7} \to^{5} I_{8}

transition are valuable for many technical applications such as range finder, medical surgery, water vapor profiling, wind monitoring and spectroscopy. Moreover, it is an excellent pump source of the middle infrared nonlinear optical frequency conversions (optical parametric oscillator and optical parametric amplifier etc.). Resonantly pumping technology provides weak thermal load and upconversion loss in Ho-doped materials. As results, the resonantly pumped Ho laser can be achieved with high efficiency and high output power at room temperature [1]. In the past twenty years, many oxide and fluoride materials were successfully applied to dope the Ho ions in order to obtain

2.1 - μ m

laser radiations [2-11]. Among traditional

{Ho}^{3 +}

singly doped crystals, Ho:YAG attracts most of the attention and is widely used to obtain high output power. However, they show strong pump wavelength sensitivity due to its narrow absorption bandwidth at around

1.9 μ m

. Moreover, thermally induced birefringence of Ho:YAG crystal significantly affects the its lasing performance under high power pumping conditions. Therefore, there are many efforts to search new laser materials.
基于

^{5} I_{7} \to^{5} I_{8}

跃迁的

2.1 - μ m

钬（Ho）激光器在测距仪、医疗手术、水蒸气分析、风力监测和光谱学等许多技术应用中都具有重要价值。此外，它还是中红外非线性光学频率转换（光参量振荡器和光参量放大器等）的优秀泵浦源。共振泵浦技术可减小掺杂 Ho 的材料的热负荷和上转换损耗。因此，共振泵浦 Ho 激光器可在室温下实现高效率和高输出功率 [1]。在过去的二十年中，许多氧化物和氟化物材料被成功地用于掺杂 Ho 离子，以获得

2.1 - μ m

激光辐射 [2-11]。在传统的

{Ho}^{3 +}

单掺杂晶体中，Ho:YAG 最受关注，被广泛用于获得高输出功率。然而，由于其在

1.9 μ m

附近的吸收带宽较窄，它们显示出很强的泵浦波长敏感性。此外，在高功率泵浦条件下，Ho:YAG 晶体的热致双折射会严重影响其激光性能。因此，人们一直在努力寻找新的激光材料。

Recently, gadolinium tantalite

{GdTaO}_{4}

(GTO) crystal was used as promising host for doping of rare earth. The GTO crystal has low symmetry and strong symmetrical crystal field, which is beneficial for obtaining polarized laser output and enhancing the photoluminescence efficiency. Compared with Ho:YAG, the GTO crystal has low sensitivity for thermal-optical effect. Owing to this advantage, the Nd:GTO crystal becomes a high-performance

1 - μ m

laser material in the past few years. In 2015, the spectral properties and continuous wave (CW) 1066-nm laser performance of Nd:GTO crystal have been demonstrated [12]. At the same year, the passively mode-locked Nd:GTO laser was reported with pulse duration of 750 ps at 1066 nm [13]. In 2018, the CW and actively Q-switched Nd:GTO laser was presented with maximum CW output power of 1.93 W at 1066 nm and shortest pulse duration of 28 ns at pulse repletion rate of 10 kHz [14]. However, there is less work on the

2 - μ m

laser action of
最近，钆钽铁矿

{GdTaO}_{4}

（GTO）晶体被用作掺杂稀土的理想宿主。GTO 晶体具有低对称性和强对称晶场，有利于获得偏振激光输出和提高光致发光效率。与 Ho:YAG 相比，GTO 晶体对热光效应的敏感度较低。由于这一优点，Nd:GTO 晶体在过去几年中成为一种高性能的

1 - μ m

激光材料。2015 年，Nd:GTO 晶体的光谱特性和连续波（CW）1066 纳米激光性能得到了证实[12]。同年，被动模式锁定的 Nd:GTO 激光器在 1066 nm 波段的脉冲持续时间为 750 ps [13]。2018 年，主动 Q 开关 Nd:GTO 激光器问世，其在 1066 nm 波长的最大 CW 输出功率为 1.93 W，在 10 kHz 脉冲补给率下的最短脉冲持续时间为 28 ns [14]。然而，关于

2 - μ m

激光作用的研究较少。

RE-doped tantalite materials up to the present [15]. In 2018, a 0.33 W diode-pumped

Tm, Ho : {GdYTaO}_{4}

laser with dual-wavelength of 1949.677 nm and 2070 nm was reported.
RE掺杂的钽铁矿材料[15]。2018 年，报道了一种 0.33 W 的二极管泵浦

Tm, Ho : {GdYTaO}_{4}

激光器，具有 1949.677 nm 和 2070 nm 双波长。

In this paper, to the best of our knowledge, we demonstrate the

2.1 - μ m

lasing performance of Ho-singly-doped GTO crystal for the first time. A Ho:GTO crystal with dopant concentration of

1.0 at . %

was used as the gain medium. Using a FBG-locked 1940.3nm Tm fiber laser as the pump source, the maximum output power of 11.2 W at 2068.39 nm and the slope efficiency of

72.9 %

were reached in end-pumped Ho:GTO laser at heatsink temperature of

15^{\circ} C

. Moreover, the beam quality factor

(M^{2})

was estimated to be 1.4 at maximum output level.
据我们所知，本文首次证明了掺杂 Ho-singly 的 GTO 晶体的

2.1 - μ m

激光性能。我们使用掺杂浓度为

1.0 at . %

的 Ho:GTO 晶体作为增益介质。使用 FBG 锁定的 1940.3nm Tm 光纤激光器作为泵浦源，在散热片温度为

15^{\circ} C

时，端泵浦 Ho:GTO 激光器在 2068.39 nm 波长处的最大输出功率达到 11.2 W，斜率效率达到

72.9 %

。此外，在最大输出水平时，光束质量因数

(M^{2})

估计为 1.4。

2. Spectral properties 2.光谱特性

The M-type Ho:GTO crystal (space group I2/a, site symmetry

C_{2}

) with dopant concentration of

1.0 at . %

was grown along the

c

-axis by the Czochralski method at the Anhui Institute of Optics and Fine Mechanics, Chinese Academy of Sciences. Ho:GTO chips for spectral measurements with thickness of 2 mm were cut along

a

b

- and

c

-axis. Their end faces were optically polished. The spectral measurements were all performed at 300 K . The polarized absorption spectra in the range from 1800 nm to 2200 nm were recorded by the UV-VIS-NIR spectrophotometer (Shimadzu SolidSpec-3700, as shown in Fig. 1(a). It can be seen that there are six absorption peaks of

1874 nm, 1905 nm, 1914 nm, 1921 nm, 1932 nm

and 1947 nm , indicating that the pump wavelength has great flexibility for selection of Tm-doped bulk or fiber lasers. A fluorescence spectrometer (Horiba iHR550) was employed to measure the fluorescence spectra under 1920-nm Tm:YLF laser exciting. Figure 1(b) shows the normalized emission spectra of Ho:GTO crystal in the range from 1800 nm to 2200 nm . The strongest emission peak was located at 2070 nm for three polarized spectra. Moreover, there are two weaker emission peaks of 2056 nm and 2083 nm . With an OPO (Opolette 355I) laser exciting, the decay curve of

^{5} I_{7}

level of Ho ions was measured by a fluorescence spectrometer (Edinburgh FLSP920), as shown in Fig. 2. It has single-exponential characteristic, and the lifetime was fitted to be 6.54 ms .
中国科学院安徽光学精密机械研究所采用 Czochralski 法沿

c

轴生长出掺杂浓度为

1.0 at . %

的 M 型 Ho:GTO 晶体（空间群 I2/a，场对称性

C_{2}

）。用于光谱测量的 Ho:GTO 芯片沿

a

-、

b

- 和

c

-轴切割，厚度为 2 毫米。其端面经过光学抛光。光谱测量均在 300 K 条件下进行。UV-VIS-NIR 分光光度计（Shimadzu SolidSpec-3700，如图 1(a)所示）记录了 1800 nm 至 2200 nm 范围内的偏振吸收光谱。从图中可以看出，在

1874 nm, 1905 nm, 1914 nm, 1921 nm, 1932 nm

和 1947 nm 之间有六个吸收峰，这表明泵浦波长在掺 Tm 的体激光器或光纤激光器的选择上具有很大的灵活性。使用荧光光谱仪（Horiba iHR550）测量了 1920 nm Tm:YLF 激光激发下的荧光光谱。图 1(b) 显示了 Ho:GTO 晶体在 1800 nm 至 2200 nm 范围内的归一化发射光谱。在三个偏振光谱中，最强的发射峰位于 2070 nm 处。此外，还有两个较弱的发射峰，分别位于 2056 nm 和 2083 nm。在 OPO（Opolette 355I）激光的激励下，用荧光光谱仪（爱丁堡 FLSP920）测量了 Ho 离子

^{5} I_{7}

级的衰变曲线，如图 2 所示。它具有单指数特性，寿命拟合为 6.54 ms。

Fig. 1. The polarized absorption spectra (a) and emission spectra (b) of Ho:GTO crystal at 300 K.
图 1.300 K 时 Ho:GTO 晶体的偏振吸收光谱（a）和发射光谱（b）。

Fig. 2. The fluorescence decay curve of

^{5} I_{7}

level of Ho:GTO crystal at 300 K .
图 2.300 K 时 Ho:GTO 晶体

^{5} I_{7}

电平的荧光衰减曲线。
The dopant of Ho ions in GTO crystal was calculated to be

1.28 \times 10^{20} {cm}^{- 3}

. Thus the absorption cross sections of Ho:GTO crystal can be calculated by Eq. (1) [16].
计算得出 GTO 晶体中 Ho 离子的掺杂量为

1.28 \times 10^{20} {cm}^{- 3}

。因此，Ho:GTO 晶体的吸收截面可由式（1）计算得出[16]。

σ_{a b s} (λ) = \frac{α (λ)}{N}

Where

σ_{a b s}

is the absorption cross section,

α (λ)

is the absorption coefficient, and

N

is the unit volume concentration of Ho ions. Figure 3(a) shows the polarized absorption cross sections of Ho:GTO crystal. It can be seen that the strongest absorption peaks are located at 1932 nm , 1947 nm and 1921 nm for

E / / a, E / / b

and

E / / c

, respectively, corresponding to the cross sections of

0.84 \times 10^{- 20} {cm}^{2}, 0.62 \times 10^{- 20} {cm}^{2}

and

0.68 \times 10^{- 20} {cm}^{2}

. These absorption peaks are beneficial to high power Tm-laser pumping.
其中，

σ_{a b s}

为吸收截面，

α (λ)

为吸收系数，

N

为 Ho 离子的单位体积浓度。图 3(a) 显示了 Ho:GTO 晶体的偏振吸收截面。可以看出，

E / / a, E / / b

和

E / / c

的最强吸收峰分别位于 1932 nm、1947 nm 和 1921 nm 处，与

0.84 \times 10^{- 20} {cm}^{2}, 0.62 \times 10^{- 20} {cm}^{2}

和

0.68 \times 10^{- 20} {cm}^{2}

的截面相对应。这些吸收峰有利于高功率 Tm 激光泵浦。

The stimulated emission cross section can be calculated according to the FuchtbauerLadenburg Eq. (2) [17].
受激发射截面可根据 FuchtbauerLadenburg 公式 (2) [17] 计算得出。

σ_{e m} (λ) = \frac{λ^{5}}{8 π n^{2} c τ} \cdot \frac{I (λ)}{\int λ I (λ) d λ}

Where

σ_{e m}

is the emission cross section,

λ

is the wavelength,

I (λ)

is the intensity of the emission spectrum,

c

is the speed of light in vacuum,

n

is the refractive index of the crystals, and

τ

is the lifetime of

^{5} I_{7}

level. The refractive indices were 1.99, 2.02 and 2.11 for

a

b

- and

c

-axis, respectively, which were calculated by the Sellmeier equations of

{GdTaO}_{4}

crystal [18]. With Eq. (2), the polarized emission cross sections of Ho:GTO crystal were calculated and shown in Fig. 3(b). As a result, the maximum emission peak is located 2070 nm with cross sections of

1.01 \times 10^{- 20} {cm}^{2}, 1.03 \times 10^{- 20} {cm}^{2}

and

0.78 \times 10^{- 20} {cm}^{2}

for

E / / a, E / / b

and

E / / c

, respectively, compared with that of

1.16 \times 10^{- 20} {cm}^{2}

at 2090 nm in Ho:YAG crystal [19] and

1.50 \times 10^{- 20} {cm}^{2}

at 2050 nm in Ho:YLF crystal [20].
其中，

σ_{e m}

为发射截面，

λ

为波长，

I (λ)

为发射光谱强度，

c

为真空中的光速，

n

为晶体的折射率，

τ

为

^{5} I_{7}

级的寿命。根据

{GdTaO}_{4}

晶体的 Sellmeier 方程 [18]，

a

-、

b

- 和

c

轴的折射率分别为 1.99、2.02 和 2.11。根据公式 (2)，计算出了 Ho:GTO 晶体的偏振发射截面，如图 3(b) 所示。结果表明，最大发射峰位于 2070 nm，

E / / a, E / / b

和

E / / c

的横截面分别为

1.01 \times 10^{- 20} {cm}^{2}, 1.03 \times 10^{- 20} {cm}^{2}

和

0.78 \times 10^{- 20} {cm}^{2}

，而 Ho:YAG 晶体的横截面

1.16 \times 10^{- 20} {cm}^{2}

位于 2090 nm [19]，Ho:YLF 晶体的横截面

1.50 \times 10^{- 20} {cm}^{2}

位于 2050 nm [20]。

Fig. 3. The polarized absorption (a) and emission cross sections (b) of Ho:GTO crystal at 300 K.
图 3.300 K 时 Ho:GTO 晶体的偏振吸收截面（a）和发射截面（b）。

3. Experimental setup 3.实验装置

Figure 4 schematically illustrates the experimental setup of resonantly-pumped Ho:GTO laser. A 30 W FBG-locked Tm fiber laser was employed as the pump source, which has central wavelength of 1940.3 nm and

M^{2}

factor of 1.3 . Two lenses (

f 1 = 8 mm, f 2 = 75 mm

) were employed to collimate and focus the pump light into the Ho:GTO crystal. The

1 / e^{2} pump

radius was approximately 0.17 mm . The pump Rayleigh length

z r (z r = π ω_{p}^{2} n / λ_{p} M_{p}^{2})

was calculated to be about 75.9 mm inside the Ho:GTO crystal with refraction index of 2.11 . The

c

-cut Ho:GTO crystal was used as the gain medium, which has dimensions of

4 \times 4 {mm}^{2}

(in cross section) and 24 mm (in length). The actual single-pass pump absorption was measured to be

83.7 %

under no-lasing conditions. Both end-faces of crystal were polished and antireflection coated for pump and resonant wavelength. The Ho:GTO crystal was wrapped with 0.1 -mm-thickness indium foils and mounted in a cooper heatsink. The heatsink temperature was controlled by the thermoelectric cooler. A two-mirrors linear cavity was employed to investigate the output performance of Ho:GTO laser. The input mirror M1 was a plat mirror with high transmission (

\sim 94 %

) for pump wavelength and high reflective (

\sim 99.8 %

) for resonant wavelength. The output coupler M2 was a plano-concave mirror with radius of curvature of 100 mm . The flat mirror M with high transmission for pump light and high reflective for resonant wavelength was used as the

45^{\circ}

dichroic mirror.
图 4 是谐振泵浦 Ho:GTO 激光器的实验装置示意图。泵浦光源采用了 30 W FBG 锁定 Tm 光纤激光器，其中心波长为 1940.3 nm，

M^{2}

系数为 1.3。使用两个透镜（

f 1 = 8 mm, f 2 = 75 mm

）将泵浦光准直并聚焦到 Ho:GTO 晶体。

1 / e^{2} pump

半径约为 0.17 毫米。经计算，在折射率为 2.11 的 Ho:GTO 晶体内，泵浦瑞利长度

z r (z r = π ω_{p}^{2} n / λ_{p} M_{p}^{2})

约为 75.9 mm。

c

切割的 Ho:GTO 晶体用作增益介质，其尺寸为

4 \times 4 {mm}^{2}

（横截面）和 24 mm（长度）。在无衰减条件下，测量到的实际单通泵吸收率为

83.7 %

。晶体的两个端面都经过抛光和抗反射涂层处理，用于泵浦和谐振波长。Ho:GTO 晶体用 0.1 毫米厚的铟箔包裹，并安装在一个铜质散热器中。散热器的温度由热电冷却器控制。为了研究 Ho:GTO 激光器的输出性能，采用了双镜线性腔。输入镜 M1 是平面镜，对泵浦波长具有高透射率（

\sim 94 %

），对谐振波长具有高反射率（

\sim 99.8 %

）。输出耦合器 M2 是一个曲率半径为 100 毫米的平面凹面镜。平面镜 M 对泵浦光具有高透射率，对谐振波长具有高反射率，被用作

45^{\circ}

二向色镜。

Fig. 4. The experimental setup of resonantly-pumped Ho:GTO laser.
图 4.共振泵浦 Ho:GTO 激光器的实验装置。

4. Experimental results 4.实验结果

In this experiment we use the Coherent PM30 power meter to record the output powers. Firstly, at heatsink temperature of

15^{\circ} C

and physical cavity length of 33 mm , with output transmittances of

7.6 %, 11.4 %, 17 %, 30 %

and

50 %

, we have investigated the output
在本实验中，我们使用 Coherent PM30 功率计记录输出功率。首先，在散热器温度为

15^{\circ} C

和物理空腔长度为 33 毫米、输出透射率为

7.6 %, 11.4 %, 17 %, 30 %

和

50 %

的条件下，我们研究了输出功率。
performance of CW Ho:GTO laser, as shown in Fig. 5. The pump thresholds were 2.02 W , 2.13 W, 2.32 W, 2.79 W and 3.83 W for above five output transmittances. In the case of output transmittance of

7.6 %

, the Ho:GTO laser yielded the 7.1 W output power with absorbed pump power of 18.3 W , corresponding to a slope efficiency of

43.5 %

respect to the absorbed pump power. When output transmittance increased to

11.4 %

and

17 %

, the output power increased to 8.6 W and 9.7 W , corresponding to a slope efficiency of

55.1 %

and

61.9 %

, respectively. With output transmittance of

30 %

, the Ho:GTO laser delivered 11.2 W maximum output power and

72.9 %

slope efficiency. In addition,

1.8 %

power stability was measured over a period of one hour. With the absorbed pump power of 18.3 W , the output power slowly fluctuated between 11.1 W and 11.3 W . At output transmittance of

50 %

, output power of 8.2 W and slope efficiency of

53.0 %

was achieved. A Glan-Taylor prism was employed to measure the polarization of output beam. The Ho:GTO laser has linearlypolarized output, which was verified by a contrast ratio of approximately 20 dB . Limited by pump power, we cannot demonstrate more output power in Ho:GTO laser. But we believe that the Ho:GTO laser can produce more output power because there are no power saturation phenomenon in our experiment.
图 5 显示了 CW Ho:GTO 激光器的性能。上述五个输出透射率的泵浦阈值分别为 2.02 W、2.13 W、2.32 W、2.79 W 和 3.83 W。在输出透射率为

7.6 %

的情况下，Ho:GTO 激光器的输出功率为 7.1 W，吸收的泵浦功率为 18.3 W，相对于吸收的泵浦功率的斜率效率为

43.5 %

。当输出透射率增加到

11.4 %

和

17 %

时，输出功率分别增加到 8.6 W 和 9.7 W，对应的斜率效率分别为

55.1 %

和

61.9 %

。当输出透射率为

30 %

时，Ho:GTO 激光器的最大输出功率为 11.2 W，斜率效率为

72.9 %

。此外，还测量了一小时内

1.8 %

功率的稳定性。当吸收的泵功率为 18.3 W 时，输出功率在 11.1 W 和 11.3 W 之间缓慢波动。当输出透射率为

50 %

时，输出功率为 8.2 W，斜率效率为

53.0 %

。使用 Glan-Taylor 棱镜测量了输出光束的偏振。Ho:GTO 激光器具有线性偏振输出，其对比度约为 20 dB。受泵浦功率的限制，我们无法证明 Ho:GTO 激光器具有更大的输出功率。但我们相信，Ho:GTO 激光器可以产生更大的输出功率，因为在我们的实验中没有出现功率饱和现象。

Fig. 5. The output powers of CW Ho:GTO laser with different output transmittances.
图 5.不同输出透过率的 CW Ho:GTO 激光器的输出功率。
The passive loss of Ho:GTO crystal can be estimated by Eq. (3) [21].
Ho:GTO 晶体的无源损耗可通过公式（3）估算 [21]。

P_{t h} = k (δ_{0} - \frac{\ln R_{1} R_{2}}{2 L})

Where

P_{t h}

is the threshold power,

δ_{0}

is the passive loss of the laser crystal,

R_{1}

and

R_{2}

are the reflectivity of the input and output mirror, and

L

is the length of the laser crystal. Figure 6 depicts the threshold power depended on the

\ln R_{1} R_{2}

, the passive loss of Ho:GTO crystal was calculated to be about

0.12 {cm}^{- 1}

.
其中，

P_{t h}

为阈值功率，

δ_{0}

为激光晶体的无源损耗，

R_{1}

和

R_{2}

为输入镜和输出镜的反射率，

L

为激光晶体的长度。图 6 描述了阈值功率与

\ln R_{1} R_{2}

的关系，计算得出 Ho:GTO 晶体的无源损耗约为

0.12 {cm}^{- 1}

。

Fig. 6. Threshold power versus

\ln R_{1} R_{2}

.
图 6.阈值功率与

\ln R_{1} R_{2}

的关系。

Fig. 7. The output powers of Ho:GTO laser depended on the heatsink temperatures.
图 7.Ho:GTO 激光器的输出功率取决于散热器的温度。
Next, by using best output transmittance of

30 %

, the output characteristics of Ho:GTO laser were investigated under different heatsink temperatures. Due to quasi-three level properties, the output power of Ho laser is influenced by operating temperature. We have recorded the output powers of Ho:GTO laser under different heatsink temperatures, as shown in Fig. 7. With cavity length of 33 mm and absorbed pump power of 10.1 W , the output power of Ho:GTO laser was changed from 5.78 W to 5.19 W when the heatsink temperature increased from

11^{\circ} C

25^{\circ} C

. The slope was linear fitted to be

46 mW /^{\circ} C

, which indicates that the Ho:GTO laser has good temperature stability.
接着，利用

30 %

的最佳输出透射率，研究了 Ho:GTO 激光器在不同散热器温度下的输出特性。由于准三级特性，Ho 激光器的输出功率会受到工作温度的影响。我们记录了不同散热片温度下 Ho:GTO 激光器的输出功率，如图 7 所示。在腔长为 33 mm、吸收泵浦功率为 10.1 W 的情况下，当散热器温度从

11^{\circ} C

上升到

25^{\circ} C

时，Ho:GTO 激光器的输出功率从 5.78 W 变为 5.19 W。斜率线性拟合为

46 mW /^{\circ} C

，这表明 Ho:GTO 激光器具有良好的温度稳定性。

Fig. 8. The output spectra of CW Ho:GTO laser with different output transmittances.
图 8.不同输出透过率的 CW Ho:GTO 激光器的输出光谱。
Thirdly, the output spectra of CW Ho:GTO laser were recorded by an optical spectrum analyzer (Bristol 721A). Figure 8 gives the output spectra with output transmittances of

7.6 %

11.4 %, 17 %, 30 %

and

50 %

. The single emission peak was observed for five transmittances in this experiment. With output transmittance of

7.6 %

, the output central wavelength of 2081.68 nm with FWHM linewidth of 1.33 nm was observed. For output transmittances of

11.4 %

and

17 %

, the output central wavelength was 2081.26 nm and 2081.25 nm , respectively. The linewidth was like

7.6 %

output transmittance conditions. With increasing of transmittance to

30 %

, the output central wavelength blue shifts to 2068.39 nm with linewidth of 1.24 nm . When the output transmittance was

50 %

, the central wavelength of 2067.56 nm and linewdith of 1.16 nm was recorded. With increasing of transmittance, the output central wavelength blue shifts from 2081.26 nm to 2067.56 nm . This change may can be explained by the gain cross sections of Ho:GTO crystal at room temperature. The gain cross sections can be calculated by Eq. (4) [22].
第三，用光学光谱分析仪（Bristol 721A）记录了 CW Ho:GTO 激光器的输出光谱。图 8 给出了输出透射率为

7.6 %

、

11.4 %, 17 %, 30 %

和

50 %

时的输出光谱。在该实验中，五个透射率都观测到了单个发射峰。当输出透射率为

7.6 %

时，观察到输出中心波长为 2081.68 nm，FWHM 线宽为 1.33 nm。当输出透射率为

11.4 %

和

17 %

时，输出中心波长分别为 2081.26 nm 和 2081.25 nm。线宽与

7.6 %

输出透射率条件相同。当透射率增加到

30 %

时，输出中心波长蓝移到 2068.39 nm，线宽为 1.24 nm。当输出透射率为

50 %

时，中心波长为 2067.56 nm，线宽为 1.16 nm。随着透射率的增加，输出中心波长从 2081.26 nm 蓝移到 2067.56 nm。这一变化可以用 Ho:GTO 晶体在室温下的增益截面来解释。增益截面可通过公式（4）计算得出[22]。

σ_{gain} (λ) = β σ_{e m} (λ) - (1 - β) σ_{a b s} (λ)

where

σ_{gain} (λ)

is gain cross section,

σ_{e m} (λ)

is the emission cross section,

σ_{a b s} (λ)

is the absorption cross section,

β

is the population inversion parameter defined as the ratio of the number of active ions in the excited state to the total number of active ions [23]. With different value of

β

, the gain cross sections of Ho:GTO crystal were calculated for

E / / a, E / / b

and

E / / c

, as shown in Fig. 9. In can be seen that the preferred lasing wavelength of Ho:GTO crystal is fixted at around 2070 nm for

E / / c

, but they are varying for

E / / a

and

E / / b

. With

β

of 0.3, the preferred lasing wavelength of Ho:GTO crystal is located at around 2086nm and 2083 nm for

E / / a

and

E / / b

, respectively. In the case of

β

of 0.5 , the preferred lasing wavelength slightly shifts to 2083 nm for

E / / a

, but it decreases to 2070 nm for

E / / b

. When the

β

is 0.7 , the preferred lasing wavelength shifts to 2071 nm and 2070 nm for

E / / a

and

E / / b

, respectively. Theoretically, the value of

β

increases with increasing of output transmittance [7]. Therefore, in this work the output wavelength of about 2081 nm was achieved with lower output transmittances. With increasing of output transmittance, the output wavelength jumped to be about 2068 nm .
其中，

σ_{gain} (λ)

为增益截面，

σ_{e m} (λ)

为发射截面，

σ_{a b s} (λ)

为吸收截面，

β

为种群反转参数，定义为处于激发态的活性离子数与活性离子总数之比[23]。随着

β

值的不同，计算了

E / / a, E / / b

和

E / / c

时 Ho:GTO 晶体的增益截面，如图 9 所示。可以看出，对于

E / / c

，Ho:GTO 晶体的首选激光波长固定在 2070 nm 左右，但对于

E / / a

和

E / / b

，它们的波长是变化的。当

β

为 0.3 时，对于

E / / a

和

E / / b

而言，Ho:GTO 晶体的首选激光波长分别位于 2086 纳米和 2083 纳米左右。当

β

为 0.5 时，

E / / a

的首选激光波长略微移动到 2083 nm，但

E / / b

的首选激光波长则下降到 2070 nm。当

β

为 0.7 时，

E / / a

和

E / / b

的首选激光波长分别移至 2071 nm 和 2070 nm。理论上，

β

的值会随着输出透射率的增加而增加 [7]。因此，在这项工作中，输出波长约为 2081 nm，输出透射率较低。随着输出透射率的增加，输出波长跃升至约 2068 nm。

Fig. 9. The gain cross sections of Ho:GTO crystal at 300 K .
图 9.300 K 时 Ho:GTO 晶体的增益截面。

Fig. 10. The

M^{2}

measurement of Ho:GTO laser. Insert, the far-field 2D beam profile.
图 10.Ho:GTO 激光器的

M^{2}

测量。插图，远场二维光束剖面图。
Finally, the

M^{2}

factors of CW Ho:GTO laser with output transmittance of

30 %

were measured at output power of

2 W, 5 W

and 11 W . A lens with focal length of 150 mm was used to transform the Ho laser beam. The distance between lens and output coupler M2 was 250 mm . We use

90 / 10

knife-edge to measure the beam radii at different positions, as shown in Fig. 10. The

M^{2}

factors of Ho:GTO laser were calculated to be 1.1, 1.2 and 1.4 for output power of

2 W, 5 W

and 11 W , respectively. In addition, we used a camera (Cinogy CR 200 HP ) to take the far-field beam profile at output power of 11 W , which was shown as the inset of Fig. 10, indicating

{TEM}_{00}

beam propagation.
最后，在输出功率为

2 W, 5 W

和 11 W 时，测量了输出透射率为

30 %

的 CW Ho:GTO 激光器的

M^{2}

因子。使用焦距为 150 mm 的透镜来转换 Ho 激光光束。透镜和输出耦合器 M2 之间的距离为 250 毫米。我们使用

90 / 10

刀刃测量不同位置的光束半径，如图 10 所示。经计算，当输出功率为

2 W, 5 W

和 11 W 时，Ho:GTO 激光器的

M^{2}

因子分别为 1.1、1.2 和 1.4。此外，我们还使用照相机（Cinogy CR 200 HP）拍摄了输出功率为 11 W 时的远场光束轮廓，如图 10 的插图所示，显示了

{TEM}_{00}

光束的传播情况。

5. Summary 5.总结

In summary, the polarized absorption and emission cross sections of Ho:GTO crystal were investigated at room temperature. A Ho:GTO crystal with dopant concentration of

1.0 at . %

was employed to discover its laser performance. Under 1940.3-nm Tm fiber pumping, the maximum output power of 11.2 W at 2068.39 nm and the slope efficiency of

72.9 %

was
总之，我们研究了室温下 Ho:GTO 晶体的偏振吸收和发射截面。采用掺杂浓度为

1.0 at . %

的 Ho:GTO 晶体研究了其激光性能。在 1940.3 nm Tm 光纤泵浦下，2068.39 nm 波长处的最大输出功率为 11.2 W，斜率效率为

72.9 %

。
achieved in the Ho:GTO laser. These results indicate that the Ho:GTO laser is a promising candidate for highly efficient

2.1 - μ m

lasers.
在 Ho:GTO 激光器中实现。这些结果表明，Ho:GTO 激光器有望成为高效

2.1 - μ m

激光器的候选器件。

Funding 资金筹措

National Natural Science Foundation of China (NSFC) (51572053, 51802307, 61805209 and 61775053)
国家自然科学基金（NSFC）（51572053、51802307、61805209 和 61775053）

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Resonantly pumped high efficiency Ho:GdTaO 4 4 _(4){ }_{4} laser 共振泵浦高效 Ho:GdTaO 4 4 _(4){ }_{4} 激光器

Abstract 摘要

1. Introduction 1.导言

2. Spectral properties 2.光谱特性

3. Experimental setup 3.实验装置

4. Experimental results 4.实验结果

5. Summary 5.总结

Funding 资金筹措

References 参考资料

Resonantly pumped high efficiency Ho:GdTaO $_{4}$ laser
共振泵浦高效 Ho:GdTaO $_{4}$ 激光器