2 Theoretical analysis

The energy diagram of a Tm:YAG crystal is shown in Figure 1, where ${\lambda}_{{P}}$ and ${{\lambda}}_{{L}}$ are the wavelengths of the pump and output laser, respectively.

The Tm³⁺ ions in the ³H₆ state can be promoted to the energy level near the ³H₅ state by stimulated absorption (SA), followed by decaying to the ³F₄ state via non-radiative transition and CR, thereby lasing at 2 μm and emitting fluorescence. Here ${\lambda}_F^{3F4}$ is the average fluorescence wavelength from the ³F₄ to³H₆ state and is given by

(1)$$\begin{align}{\lambda}_F^{3F4}=\frac{\int \varepsilon \left(\lambda \right)\lambda\;\mathrm{d}\lambda }{\int \varepsilon\left(\lambda \right)\;\mathrm{d}\lambda },\end{align}$$

where $\lambda$ is the wavelength and $\varepsilon \left(\lambda \right)$ is the intensity at the wavelength of $\lambda$. Figure 2 shows the measured fluorescence spectrum of Tm:YAG^[Reference Li, Huo, He and Cao^16]. Based on Eq.(1), the calculated average fluorescence wavelength is 1901 nm.

Figure 1 Energy diagram of a Tm:YAG crystal.

Figure 2 Fluorescence spectrum of a Tm:YAG crystal.

In addition to SE, there are two more competing transitions that may also deplete the population inversion of the ³F₄ state and increase the absorption of 1 μm photons, depending on the pumping density: UC and ESA. In the former case, an excited Tm³⁺ ion in the³F₄ state is promoted to the ³H₅ or ³H₄ state via energy transfer processes.In the latter case, an excited Tm³⁺ ion in the ³F₄ state is promoted to the ¹G₄ state by absorbing two more 1 μm photons, followed by fluorescence and non-radiative decay.The fluorescence decay from the ¹G₄ state will produce a broad fluorescence emission spectrum. Considering the transition rate and lifetimes of states, the equivalent fluorescence wavelength from ¹G₄ to lower states(³F_2,3, ³H₄,³H₅, ³F₄, and ³H₆) is given by

(2)$$\begin{align}{\lambda}_F^{1G4}=\frac{1}{\sum_{i=1}^5{\beta}_i^6\left({E}_6-{E}_i\right)},\end{align}$$

where ${E}_i\;\left(i=1,2,3,4,5\right)$ is the energy for each state and ${\beta}_i^6$ is the fluorescence branch ratio for ¹G₄ state, as shown in Table 1^[Reference Jia, Tu, Li, Zhu, You, Wang and Wu^17]. As the fluorescence branch ratio is related to the transition rate and lifetimes of the lower states, its influences have been taken into account in the model^[Reference Caird, De Shazer and Nella^18]. In addition, the³F_2,3, ³H₄, and ³H₅ states have very short lifetimes and low quantum efficiency, which can make the ${\lambda}_F^{1G4}$ blue-shifted. As a result, the equivalent fluorescence wavelength is calculated as 649.7 nm.

Table 1 The branch ratios of a Tm:YAG crystal in the ¹G₄ state.

In Figure 1, the processes of heat generation in a Tm:YAG crystal could be divided into the following four parts: quantum defect heating, non-radiative decay heating from the ³F₄ state, fluorescence heating from the ³F₄ state, and UC- and ESA-induced heating. The heating energy density due to the quantum defect caused by SE can be described as

(3)$$\begin{align}{Q}_L=\Delta n{\eta}_L\left(h{\upsilon}_P-h{\upsilon}_L\right),\end{align}$$

where $h$ is the Planck constant, ${\upsilon}_P$ is the frequency of the pump photon, ${\upsilon}_L$ is the frequency of the laser photon, and $\Delta n$ is the density of pump photons in laser medium. Here ${\eta}_L$ is the laser extraction efficiency, which is defined as the fraction of absorbed pump photons consumed by SE.

The heat energy density generated by non-radiative decay in the ³F₄ state can be described as

(4)$$\begin{align}{Q}_{NR}^{3F4}=\Delta n\left(1-{\eta}_L\right)\left(1-{\eta}_R^{3F4}\right)\left(1-{\eta}_{UC\&ESA}\right)h{\upsilon}_P,\end{align}$$

where ${\eta}_R^{3F4}$ is the radiative quantum efficiency of the ³F₄ state. Meanwhile, the heating energy density caused by fluorescence decay in the ³F₄ state can be described as

(5)$$\begin{align}\!\!\!{Q}_F^{3F4}=\Delta n\left(1-{\eta}_L\right){\eta}_R^{3F4}\left(1-{\eta}_{UC\&ESA}\right)\left(h{\upsilon}_P-h{\upsilon}_F^{3F4}\right),\end{align}$$

where ${\upsilon}_F^{3F4}$ is the frequency of average fluorescence wavelength from the ³F₄ state to the ³H₆ state and ${\eta}_{UC\& ESA}$ is the quantum efficiency of competing transitions (UC and ESA), representing the percentage of upper-level laser particles for UC and ESA. The additional absorption efficiency is then denoted by $\left(1-{\eta}_L\right){\eta}_{UC\& ESA}$, which represents the fraction of absorbed pump photons consumed by UC and ESA transitions. Here $\left(1-{\eta}_L\right)\left(1-{\eta}_{UC\& ESA}\right)\left(1-{\eta}_R^{3F4}\right)$ and $\left(1-{\eta}_L\right)\left(1-{\eta}_{UC\& ESA}\right){\eta}_R^{3F4}$ represent the fraction of absorbed pump photons consumed by non-radiative decay and fluorescence decay in the ³F₄ state, respectively.

The UC- and ESA-induced heating includes non-radiative decay heating from the ¹G₄ state ${Q}_{NR}^{1G4}$ and fluorescence heating from the ¹G₄ state ${Q}_F^{1G4}$, which can be described as

(6)$$\begin{align}{Q}_{NR}^{1G4} =\Delta n\left(1-{\eta}_L\right)\left(1-{\eta}_R^{1G4}\right){\eta}_{UC\&ESA}h{\upsilon}_P,\end{align}$$

(7)$$\begin{align}{Q}_F^{1G4}& =\Delta n\left(1-{\eta}_L\right){\eta}_{UC\&ESA}{\eta}_R^{1G4}\left(h{\upsilon}_P-h{\upsilon}_F^{1G4}/3\right),\end{align}$$

where ${\eta}_R^{1G4}$ is the radiative quantum efficiency for the ¹G₄ manifold and${\upsilon}_F^{1G4}$ is the frequency of the equivalent fluorescence wavelength from the¹G₄ state.

The total fractional thermal load of a Tm:YAG crystal is given by

(8)$$\begin{align}{\eta}_h&=\frac{\left({Q}_L+{Q}_{NR}^{3F4}+{Q}_F^{3F4}+{Q}_{NR}^{1G4}+{Q}_F^{1G4}\right)}{\Delta{n}_Rh{\upsilon}_P} =\underset{\mathrm{laser}\kern0.33em \mathrm{heating}}{\underbrace{\eta_L\left(1-\frac{\lambda_P}{\lambda_L}\right)}}\notag\\[2pt]&\quad+\underset{\begin{array}{c}\mathrm{fluorescence}\kern0.33em\mathrm{and}\kern0.33em \mathrm{non}\text{-}\mathrm{radiative}\\[-3pt] \kern0.66em\mathrm{decay}\kern0.33em \mathrm{heating}\kern0.33em \mathrm{in}\kern0.33em {}^{3}\mathrm{F}_4\kern0.33em\mathrm{state}\end{array}}{\underbrace{\left(1-{\eta}_L\right)\left(1-{\eta}_{UC\&ESA}\right)\left(1-{\eta}_R^{3F4}\frac{\lambda_P}{\lambda_F^{3F4}}\right)}}\notag\\&\quad+\underset{\mathrm{UC}\text{-}\kern0.33em \mathrm{and}\kern0.33em\mathrm{ESA}\text{-}\mathrm{induced}\kern0.33em\mathrm{heating}}{\underbrace{\left(1-{\eta}_L\right){\eta}_{UC\&ESA}\left(1-{\eta}_R^{1G4}\frac{\lambda_P}{3{\lambda}_F^{1G4}}\right)}}.\end{align}$$

It is straightforward to show that the first term of Eq. (8) represents laser heating, the second term represents fluorescence heating and non-radiative decay in the ³F₄ state, and the third term represents UC- and ESA-induced heating via fluorescence and non-radiative decay in the¹G₄ state. In addition, the laser extraction efficiency is given by

(9)$$\begin{align}{\eta}_L=\frac{\frac{I_L}{h{\upsilon}_L}{g}_L{M}_R}{\frac{I_P}{h{\upsilon}_P}{\alpha}_P},\end{align}$$

where ${I}_P$ is the average pump intensity in the crystal, ${I}_L$ is the power intensity of the circulating laser radiation inside the resonator,${M}_R$ is the number of the laser passing through the crystal per resonator round trip,${\alpha}_P$ is the absorption coefficient for pump radiation, and ${g}_L$ is the gain coefficient for laser. When the pump intensity is higher than laser threshold, the laser starts lasing and gives ${g}_L{M}_R=\delta /d$, where $d$ is the thickness of the gain medium. Here $\delta$ is the round trip loss and can be described as

(10)$$\begin{align}\delta =-\ln \left(1-{T}_{oc}\right)-\ln \left(1-{L}_{loss}\right),\end{align}$$

where ${T}_{oc}$ is the output coupler transmission and ${L}_{loss}$ accounts for residual losses, owing to the scattering during one round trip in the resonator. Equation (9) is simplified as

(11)$$\begin{align}{\eta}_L=\frac{\frac{I_L}{h{\upsilon}_L}\frac{\delta}{d}}{\frac{I_P}{h{\upsilon}_P}{\alpha}_P}=\frac{\lambda_L}{\lambda_P}\frac{I_L\delta}{I_{abs}}=\frac{\lambda_L}{\lambda_P}\frac{I_{out}\delta }{I_{abs}{T}_{oc}},\end{align}$$

where ${I}_{out}$ is the output power intensity and ${I}_{abs}$ is the absorbed pump power intensity. When the pump intensity is lower than laser threshold, the laser extraction efficiency is zero. The total fractional thermal load is simplified as

(12)$$\begin{align}{\eta}_h&=\left(1-{\eta}_{UC\&ESA}\right)\left(1-{\eta}_R^{3F4}\frac{\lambda_P}{\lambda_F^{3F4}}\right)\notag\\&\quad +{\eta}_{UC\& ESA}\left(1-{\eta}_R^{1G4}\frac{\lambda_P}{3{\lambda}_F^{1G4}}\right).\end{align}$$

Based on the absorbed pump power ${P}_{abs}$ and the total fractional thermal load ${\eta}_h$, the central temperature of Tm:YAG disk is calculated by using the finite element method.The measured temperature data are then fitted with the calculated data by adjusting ${\eta}_{UC\& ESA}$ and ${\eta}_R^{1G4}$. Consequently, the proportions and fractional thermal load of all transitions are derived. Parameters used in the simulation are listed in Table 2.

Table 2 Basic parameters used for the model.

3 Experimental setup

The experimental setup is shown in Figure 3. A multi-pass pumping scheme consisting of dual parabolic mirrors with a conjugated relationship is designed to send the pump beam through the disk 20 times, and the position of each pump spot on two parabolic mirrors is shown inFigure 3(a). In particular, this scheme enables the unabsorbed pump light to be emitted from the multi-pass pumping head, and it is thus beneficial to evaluate the absorption properties of 1 μm pump light in this laser. In addition, the temperature ofTm:YAG disk was measured by an infrared thermal imager (Testo 890-2) with a resolution of0.1°C.

Figure 3 Layout of the (a)20-pass pumping head and (b) 2 μm Tm:YAG disk laser multi-pass pumped by a 1 μm laser.

The Tm:YAG disk crystal was mounted on a water-cooled copper heatsink at 18°C with a doping concentration of 3.5%, and its thickness and pump spot size were 0.5 and 1.7 mm, respectively. In addition, the front surface of the Tm:YAG disk had an antireflection coating at both 1 and2 μm wavelengths, and the back surface had a highly reflective coating in the same wavelength band. The absorption coefficient of Tm:YAG crystal at 1 μm was around 1.37× 10^–3 mm^–1. Moreover, the range of dioptric power of the 0.5 mm disk was measured as 0.1–0.93 m^–1[Reference Chénais, Balembois, Druon, Lucas-Leclin and Georges^22]. A V-shaped cavity with large stable area was designed to match the dioptric power. M1 was a concave mirror with curvature radius of 1 m, and it had a high reflectivity at 2 μm. OC1 was a plane output coupler at 2 μm with a transmittance of 1%, which was the optimum transmissivity by measuring the highest output power. The distances between components in the cavity were L ₁ = 0.455 m and L ₂ = 0.25 m. Meanwhile, a 1 mm thick Tm:YAG disk laser was also analyzed as a comparison, which shared the same coating parameters and doping concentration as the 0.5 mm disk. To realize mode matching in terms of dioptric power of the thick disk, the cavity lengths of two arms were adjusted toL ₁ = 0.55 m and L ₂ = 0.25 m, respectively. The number of pumping passes and pumped spot size were the same as in the 0.5 mm thickness case. In addition, to study the properties of absorbed pump power and output power, P1 and P2 were used to measure the unabsorbed pump power ${P}_{unabs}$ and output laser power ${P}_{out}$, respectively.

Actually, the pump source can be replaced by any Nd³⁺- or Yb³⁺-based laser at~1 μm wavelength, as the absorption of Tm:YAG in the 1 μm spectral region is almost the same (see Figure 4). The spectra of the pump light and output laser were both measured by a spectrometer (waveScan of APE), and the central wavelengths of the pump light ${\lambda}_P$ and laser radiation ${\lambda}_L$ were 1030.9 and 2011.4 nm, respectively.

Figure 4 Absorption cross section of Tm:YAG and spectrum of pump light. Inset is the spectrum of output laser.

4 Results and discussion

During the experiments, a Yb:YAG thin disk laser was used as the pump source, and the maximum input pump power of the Tm:YAG disk laser was ${P}_{in}$ = 65.8 W. To prevent disk damage, the pump power was limited such that the disk temperature never exceeded 125°C.

4.1 Operation characteristics of a 1 μm pumped Tm:YAG disk laser

In practice, the reflection of 1 μm laser in the multi-pass pumping scheme is incomplete^[Reference Huang, Zhu, Zhu, Shang, Wang, Qi, Zhu and Guo^15]. Considering the loss of the multi-pass pumping scheme, the absorbed pump power ${P}_{abs}$ is given by

(13)$$\begin{align}{P}_{abs}={P}_{in}-{P}_{unabs}-{P}_{in}\left(1-{R}_p\right),\end{align}$$

where ${R}_p$ is the total reflectivity of the Tm:YAG multi-pass pumping scheme with the measured value of 77%.

Figure 5 shows the dependences of absorbed pump power for 0.5 and 1 mm Tm:YAG disk lasers on input pump power under non-lasing and lasing conditions. It can be seen that the absorbed pump power threshold of the 0.5 mm Tm:YAG disk laser is6.9 W. Above the threshold, the laser starts oscillating, and the output power increases linearly with the absorbed pump power, as shown in Figure 6. The maximum output power was 1.05 W with the beam quality of M_x ² = 2.02, M_y ² = 2.03, and the maximum optical-to-optical efficiency and slope efficiency were ${\eta}_{oto}= 4.8\%$ and ${\eta}_{slope} = 13.2\%$, respectively. The corresponding pump quantum efficiency was 25.8%, indicating that only a small portion of the absorbed 1 μm photons were used for emitting 2 μm lasers. At the same time, serious red and blue light was observed in experiments, indicating that the UC and ESA were more dominant than the SE in a Tm:YAG disk laser when pumped by a 1 μm laser.Compared with 0.5 mm disk, the 1 mm thick disk can absorb more pump power. At the input pump power of 38.1 W, the absorbed pump power increases from 11.9 to 16.4 W. However, because the performance of one-dimensional heat flow is poor for the thick-disk case, the 1 mm thick disk has a higher temperature than the 0.5 mm disk at the same absorbed pump power, and thereby a higher threshold of8.5 W. The output laser performances are also degraded, as presented in Figure 6.

Figure 5 Absorbed pump power of a Tm:YAG crystal versus input pump power under non-lasing and lasing conditions for 0.5 and 1 mm thickness of gain medium.

Figure 6 Output power of a Tm:YAG disk laser versus absorbed pump power for 0.5 and 1 mm thickness of gain medium. The inset shows the measured beam caustic and calculated beam quality at the output power of 1.05 W.

On the other hand, the absorbed pump power of the Tm:YAG disk is significantly different under lasing and non-lasing conditions, as shown in Figure5. Under lasing condition, the absorbed pump power of Tm:YAG decreases

obviously for both 0.5 and 1 mm thicknesses of gain medium. This abnormal phenomenon is very interesting, and shows us the dynamic absorption properties of 1 μm pump light for a Tm:YAG disk before and after lasing, which is equivalent to the consumption of population inversion on the upper laser level. In general, the depletion of upper laser level induces an increased absorption of pump light for a laser medium with simple energy level, e.g., Yb:YAG orNd:YAG^[Reference Volkov, Kuznetsov and Mukhin^23]. However, the Tm:YAG crystal shows the abnormal changes of absorbed pump power when pumped by the 1 μm light. This is attributed to the significant UC and ESA effects. To show the operation characteristics of1 μm pumped Tm:YAG disk laser clearly, an operating principle diagram under non-lasing and lasing conditions is presented in Figure 7. The absorbed pump power of Tm:YAG mainly consists of two parts: direct absorption via SA and CR, and additional absorption via UC and ESA. Above the laser threshold, the SE, UC, and ESA compete with each other to consume the population inversion on the ³F₄ state, and this shows the dynamic absorption properties of the pump light. Under the non-lasing condition, no SE occurs, and the significant UC and ESA effects allow high absorption of the 1 μm laser. At the input pump power of 57.8 W, the absorbed pump power of the 0.5 mm disk was 22.5 W. Under the lasing condition, the generation of SE makes the direct absorbed pump power increase due to the depletion of the ³F₄ state. However, the consumption of population inversion on the ³F₄ state can suppress the intensities ofUC and ESA. The additional absorbed pump power, which is used for UC and ESA, decreases accordingly. As the intensities of UC and ESA were more dominant than that of SE, the absorbed pump power of the gain medium was decreased to 18.7 W. On the other hand, the increased temperature of Tm:YAG is mainly caused by the UC and ESA when pumped by 1 μm light, and the temperature of Tm:YAG thus drops from 121.1 to91.1°C after lasing at 2 μm, as shown in Figure7.

Figure7 Operating principle diagram of the 0.5 mm Tm:YAG disk laser under (a) non-lasing and (b) lasing conditions. The thicknesses of the arrows are proportional to the intensities of the transitions.

4.2 Evaluation intensities of UC and ESA by calculating ${\eta}_{UC\& ESA}$ and ${\eta}_R^{1G4}$

As mentioned previously, the Tm:YAG disk laser has significant UC and ESA, which has been described qualitatively. In this section, the intensities of UC and ESA are evaluated quantitatively by calculating${\eta}_{UC\& ESA}$ and ${\eta}_R^{1G4}$. The finite element method is used to calculate the central temperature of the gain medium on account of ${P}_{abs}$ and ${\eta}_h$. The additional absorption efficiency ${\eta}_{UC\& ESA}$ and radiative quantum efficiency for the ¹G₄ manifold${\eta}_R^{1G4}$ are obtained from a least-squares fit to the measured temperature data.

The dependences of central temperature for a 0.5 mm Tm:YAG disk laser on absorbed pump power are shown in Figure 8(a). When the absorbed pump power is below 0.1 W, the power density is <240 W/cm³, which is less than the ESA threshold^[Reference Phua, Lai, Wu, Lim and Lau^11, Reference Chen, Wang, Dong, Wang, Chen, Qian, Zhu, Alekse and Zhu^12]. The ESA effect can then be neglected, i.e., ${\eta}_{UC\& ESA}$= 0. When the absorbed pump power is above the ESA threshold, the best fit to data gives ${\eta}_{UC\& ESA}$ = 99.6% and ${\eta}_R^{1G4}$ = 0.3% for the crystal by using the finite element method. The calculated central temperature can be obtained based on the thermal load model. It can be seen that the temperatures of Tm:YAG disk are directly proportional to the absorbed pump power, and are significantly different under lasing and non-lasing conditions. Under lasing condition, the intensities ofUC and ESA, denoted by $\left(1-{\eta}_L\right){\eta}_{UC\& ESA}$, are decreased due to the increased laser intensity ${\eta}_L$ via SE. As the increased temperature of Tm:YAG is mainly caused by the UC and ESA when pumped by 1 μm light^[12], the maximum temperature of Tm:YAG is thus decreased from122.3°C to 108.5°C at the absorbed pump power density of 2.0 kW/cm³. Moreover, the central temperature of a 1 μm pumped Tm:YAG disk crystal was comparable with the 785 nm pumped case, where the disk temperature of 150°C was reached at an absorbed pump power density of 3.1 kW/cm^3[Reference Zhang, Schulze, Mak, Pervak, Bauer, Sutter and Pronin^10]. This is due to the fact that the UC and ESA effects are significant for both 785 nm and1 μm pumped Tm:YAG disk lasers.

Figure8 Central temperature of (a) 0.5 mm Tm:YAG disk and (b) 1 mm Tm:YAG thick disk versus absorbed pump power under lasing and non-lasing conditions.

On the other hand, when the absorbed pump power is above the ESA threshold(0.2 W of absorbed pump power), the 1 mm thick disk exhibits approximately ${\eta}_{UC\& ESA}~=~99.7\%$ and ${\eta}_R^{1G4} = 0.2\%$ by using the same method. As the heat dissipation of the 1 mm thick disk is lower than the 0.5 mm disk, the temperature of the 1 mm thick disk is much higher than in the0.5 mm case at the same absorbed pump power, as shown in Figure 8(b). At the input pump power of 38.1 W, the central temperature of the gain medium has increased by 50% from 70°C to 105°C. In addition, the intensity of UC and ESA for the 1 mm thick disk is higher than in the 0.5 mm case at the same absorbed pump power, and this is attributed to the weaker intensity of SE for the 1 mm thick disk, as shown in Figure 6.

To clarify the dynamic variation of UC and ESA intensities in Tm:YAG disk lasers, the proportions of all heating factors were calculated, as shown in Figure 9. When the absorbed pump power is below the ESA threshold (0.1 W for the 0.5 mm disk case or 0.2 W for the 1 mm disk case), the proportions of laser, UC, and ESA are zero. The fluorescence and non-radiative decay from the ³F₄ state are dominant with values of 98% and 2%, respectively. At the same time, the fractional thermal loads of fluorescence and non-radiative decay from the ³F₄ state are 5.48% and 2%, respectively, as shown in Figure 10. When the absorbed pump power is above the ESA threshold, the effects of fluorescence and non-radiative decay from the³F₄ state are quite weak. For the 0.5 mm thickness of gain medium, when the pump power density is lower than the laser threshold, the proportion of UC and ESA effects is 99.6%. This is due to the fact that the absorbed pump power density at this stage is much higher than theoretically required for the onset of significant UC and ESA^[Reference Jackson and King^24]. Therefore, the UC and ESA effects are extremely strong.Based on above analysis, the radiative quantum efficiency for the ¹G₄ state${\eta}_R^{1G4}$ is only 0.3%, indicating that the UC- and ESA-induced heating in the Tm:YAG disk laser is mainly through non-radiative decay. As shown in Figure 10(a), the fractional thermal load of the gain medium is over 99%. When the absorbed pump power is higher than the laser threshold, the UC and ESA effects are partly suppressed by the increased laser intensity. The UC- andESA-induced heating is decreased accordingly. In addition, the total fractional thermal load of the gain medium is also decreased, resulting in the temperature of the Tm:YAG disk dropping after lasing, as shown in Figure  8(a). With the further increase of the absorbed pump power, the competition between laser, UC, and ESA will tend to be balanced because of the saturation of optical-to-optical efficiency.

Figure 9 Proportions of all the transitions for (a) 0.5 mm Tm:YAG disk laser and (b) 1 mm Tm:YAG thick disk laser under the lasing condition.

Figure 10 Fractional thermal loads of all transitions for (a) 0.5 mm Tm:YAG disk laser and (b) 1 mmTm:YAG thick disk laser under the lasing condition.

On the other hand, the tendencies of the 1 mm Tm:YAG thick disk are similar to the 0.5 mm case over the range of absorbed pump power. At the absorbed pump power of 16.5 W, the laser proportion of the 1 mm thick disk is 19%, which is lower than that of the 0.5 mm disk, in which a laser proportion of 24% is delivered. Conversely, compared with the 0.5 mm disk, the proportion of UC andESA for the 1 mm Tm:YAG disk increases from 75% to 82%, indicating that the 1 mm Tm:YAG disk has higher UC- and ESA-induced heating, thereby a higher total fractional thermal load. The higher heat generation, as well as poorer heat dissipation capacity, makes the temperature of the 1 mm thick gain medium much higher than that of the 0.5 mm case at the same absorbed pump power, as shown inFigure 8. Therefore, we expect that the Tm:YAG disk with lower thickness and better heat dissipation capacity can achieve higher power and efficiency via this scheme.