Up conversion and excited state absorption analysis in the Tm:YAG disk laser multi-pass pumped by 1 μm laser

Enmao Song; Guangzhi Zhu; Hailin Wang; Hantian Chen; Yefeng Qian; Kozlov Aleksei; Xiao Zhu

doi:10.1017/hpl.2020.55

Abstract

We present a 2 μm Tm:YAG disk laser multi-pass pumped by a 1 μm laser. The transitions in competition of up conversion (UC) and excited state absorption (ESA) are analyzed in detail based on a numerical model that considers stimulated emission, fluorescence, non-radiative decay, UC, andESA, showing good agreement with experiments. The proportions and fractional thermal loads of all transitions are derived quantitatively. The results show that UC and ESA are critical in Tm:YAG disk lasers, resulting in a decrease in the absorbed pump power and temperature after lasing for two different disk thicknesses. In addition, although the absorbed pump power of the 0.5 mm disk is lower than in the 1 mm case, its relatively weak UC and ESA and low total fractional thermal load can improve laser performance. A 0.5 mm Tm:YAG disk laser thus delivered the maximum output power of1.05 W with beam quality of M_x² = 2.02 and M_y² = 2.03.

Keywords

mid-infrared laser thermal effects thulium

1 Introduction

Tm:YAG lasers operating at 2 μm wavelengths have attracted a lot of attention owing to their strong absorption in water, as well as the eye-safe wavelength bands, which have been utilized extensively in soft-material processing, medical diagnostics, direct optical communications, and so on [1 - 3] . One of the main challenges is related to the induced laser performance degeneration that arises from waste heat generated inside the crystal, which is detrimental to the cited applications. Increasing the heat dissipation capability and analyzing thermal problems in Tm:YAG lasers are thus critical for laser developers.

Efficient heat removal is realized by increasing the surface-to-volume ratio of the gain medium, as in fiber, slab, and disk lasers [4 - 7] . Among them, disk architectures have several advantages, including efficient cooling capacity, weak nonlinear effect, and power scaling without compromising beam quality [8] . The highest published output power of a Tm:YAG disk laser is 24 W with M 2 value of 11.7 and slope efficiency of 31% when pumped at 785 nm, in which the presence of cross-relaxation (CR) can increase the pump quantum efficiency [9, 10] . In addition, the use of a 1 μm laser as the pump source has also proved successful in generating 2 μm radiation [11] . This is a readily available and cost-effective pump method, because the 1 μm laser (e.g., lamp-pumped Nd:YAG laser,Yb 3+ doped laser) is commercially mature with high power, high reliability, and mass production.Very recently, an intra-cavity pumped Tm:YAG disk laser in multi-transverse mode operation was reported with an average output power of 760 mW in quasi-continuous wave mode and 17 mW in continuous wave mode [12] . The relatively low absorption coefficient of 1 μm laser for a disk-shaped gain medium is compensated by the intra-cavity pumping method [11] .Nevertheless, its poor pumping stability and strong nonlinear coupling can degrade the output laser performances significantly [13, 14] . It is then difficult to study the operation characteristics of 1 μm pumped Tm:YAG disk laser in detail.

On the other hand, because a high population inversion is necessary to compensate for the limitation of the disk’s thickness, the intensities of transitions in competition, up conversion (UC) and excited state absorption (ESA), cannot be ignored, as is done in rod and fiber-shaped lasers [4] . The enhancement of output power is then limited and more heat is generated in Tm:YAG disk lasers. Therefore, verifying the proportions of all transitions and evaluating their effects on operation characteristics and heat generation are extremely important forTm:YAG disk lasers.

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In the present paper, a dual parabolic mirror 20-pass pumping scheme is designed for the1 μm pumped Tm:YAG disk laser. The multi-pass pumping method ensures high pumping stability and efficient thermal management of the gain medium[15]. This scheme can also enable the measurement of the unabsorbed pump power in real time. The absorption properties of 1 μm pump light are then studied efficiently. In addition, a numerical model considering stimulated emission (SE), fluorescence, non-radiative decay, UC, and ESA is developed to evaluate the proportions and fractional thermal loads of all transitions quantitatively in view of the absorption, output, and temperature properties in this laser.Experimental and theoretical results show that the UC, ESA, and SE compete with each other to consume the1 μm pump photons, and the proportions of UC and ESA are more dominant than that of SE in a1 μm pumped Tm:YAG disk laser, leading the absorbed pump power to decrease abnormally after lasing. The strong UC and ESA effects are the main part of total heat generation for two thicknesses of gain medium. In addition, the small thickness of gain medium with better heat dissipation capacity has relatively weak UC and ESA and low total fractional thermal load, which can improve the output laser performances. Consequently, a 0.5 mm Tm:YAG disk laser delivered an average power of 1.05 W with slope efficiency of 13.2%, and the measurement of it yielded Mx2 = 2.02 and My2 = 2.03.

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.

Energy diagram of a Tm:YAG crystal.

Figure 1.Energy diagram of a Tm:YAG crystal.

Figure 2.Fluorescence spectrum of a Tm:YAG crystal.

Parameters	Value
Loss factor for laser in resonator(${L}_{loss}$)	2%
Cu–W plate thickness (${d}_{CuW}$)	2 mm
Thermal conductivity of Cu–W plate(${k}_{CuW}$)	385 W/(m·K)
Thermal conductivity of Tm:YAG crystal(${k}_{Tm: YAG}$)	7 W/(m·K)^[¹⁹^]
Convective heat transfer coefficient(${K}_{heat}$)	10 W/(m²·K)^[²⁰^]
Radiative quantum efficiency of³F₄ state (${\eta}_R^{3F4}$)	0.98^[²¹^]
Temperature of coolant fluid (${T}_{cool}$)	292 K

Table 2. Basic parameters used for the model.

View all Tables

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 3 F 4 state, fluorescence heating from the 3 F 4 state, and UC- and ESA-induced heating. The heating energy density due to the quantum defect caused by SE can be described as

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

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 3 F 4 state can be described as

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

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

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

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

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

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

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.

Table Infomation Is Not Enable

3 Experimental setup

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[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 L1 = 0.455 m and L2 = 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 toL1 = 0.55 m and L2 = 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.

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[15]. Considering the loss of the multi-pass pumping scheme, the absorbed pump power ${P}_{abs}$ is given by

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

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

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

Image Infomation Is Not Enable

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.

Image Infomation Is Not Enable

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.

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.

5 Conclusion

In summary, we have reported a 2 μm Tm:YAG disk laser pumped by a 1 μm laser via a 20-pass pumping scheme. This scheme enables the evaluation of absorption, output, and temperature properties. The competitive transitions of UC and ESA particularly challenge the scaling of output powers for 2 μm disk lasers. To analyze the effects of UC and ESA, a numerical model accounting forSE, fluorescence, non-radiative decay, UC, and ESA has been developed. More broadly, the proportions and fractional thermal loads of all transitions have been derived quantitatively based on the model.Experimental and theoretical results show that the UC and ESA effects are dominant in 1 μm pumped Tm:YAG disk lasers, leading the absorbed pump power to decrease abnormally after lasing. The strongUC and ESA are the main sources of total heat generation of the gain medium. In addition, although theTm:YAG disk with small thickness has a lower absorbed pump power, its higher heat dissipation capacity enables the relatively weak UC and ESA and low total fractional thermal load, which are conducive to the promotion of laser performance. As a result, the 0.5 mm Tm:YAG disk has a maximum output power of1.05 W, limited only by the available pump power, and the measurement of it yielded Mx2 = 2.02, My2 = 2.03. Finally, this model can be used for any Tm3+-doped disk laser, which lays the groundwork for analyzing the operation characteristics and evaluating the dynamic processes of all transitions for disk-shaped Tm3+-doped lasers. Further reducing the thickness of the gain medium, together with increasing pump number and spot size, will be propitious to scaling the Tm3+ disk lasers’ output power without compromising beam quality and mode stability in the near future.

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