7.56-W continuous-wave Pr<sup>3+</sup>-based green laser via managing thermally induced effects

Shouyan Zhang; Shuxian Wang; Shuxian Wang; Gang Lian; Zhengping Wang; Haohai Yu; Haohai Yu; Huaijin Zhang

doi:10.1364/OE.511076

1. Introduction

Over the past decades, green lasers have aroused growing attention in the fields of data storage, optical communication, display, and medicine and have demonstrated widespread application demand in the development of deep-ultraviolet laser sources [1–6]. They can be generated through the second harmonic generation (SHG) of near-infrared lasers (Nd³⁺, Yb³⁺), up-conversion lasers (Ho³⁺, Er³⁺), argon ion lasers [7–12], as well as blue-laser-diode-pumped Pr³⁺- or Tb³⁺-based lasers. Along with the technological advances in commercial blue laser diodes and laser gain materials, there is a mounting interest in Pr³⁺-based green lasers owing to their apparent advantages in developing high-efficiency laser devices with simple and compact configuration designs [13–16].

The first continuous-wave (CW) Pr³⁺-based green laser was achieved in Pr³⁺:LiYF₄ (Pr:YLF) crystal with the lasing wavelength at ∼522 nm [17]. Since the blue laser diode was applied in pumping Pr³⁺- doping crystals first in 2004 [18], Pr³⁺-based CW green lasers pumped by blue laser diodes have gradually become the dominating operation way due to their superiority in the aspects of miniaturization and production cost. In 2014, P. W. Metz et al. realized a 2.9-W CW green laser output in a single-blue-laser-diode-pumped Pr:YLF crystal with a slope efficiency of 72% [19]. That high-efficiency Pr³⁺-doped laser output is enviable, but the watt-level output power of a single blue laser diode limits the attainable output of green lasers. Ostroumov and co-authors developed a dual-end-pumped technique that can effectively improve the whole available pumping power. On that basis, a CW green output power of 4.3 W at 522 nm was obtained under 10-W pumping by two blue laser diodes, which is the highest output power of green lasers in Pr³⁺-doped gain media so far [14]. Recently, the research group of B. Xu also achieved a similar CW green laser output using the dual-end-pumped configuration, yielding an output power of 3.43 W at 522 nm [20]. Additionally, with the development of Pr³⁺-based green lasers, the fiber gain materials were also extensively explored apart from the single-crystalline gain media, recently demonstrating a 3.6-W CW green laser at 521 nm [21–23].

The selection of gain media is intricately related to the lasing performance. Pr³⁺-doped fluoride materials own lower host phonon energies in comparison to oxide hosts [24,25], benefiting the reduction of non-radiative transitions and the improvement of lasing output efficiency [26,27]. Hence, fluoride gain media represented by Pr:YLF crystal manifest a growing prevalence in the development of Pr³⁺-based lasers. The high-power lasing operation is usually accompanied by a serious generation of heat owing to the existence of the intrinsic quantum defect of active ions. If managed unreasonably, the thermally induced effects will make the lasing performance worse, even resulting in the cracking of gain media. The hurdle of thermally induced effects limits the progress of high-power Pr³⁺-based CW green lasers. Albeit there have been several theoretical simulations on the thermal effects of Pr³⁺-based CW lasers [28,29], the relevant experimental validation is absent, and the attainable output power of green lasers still stays at 4.3 W [14]. Herein, combining the theoretical analysis of thermally induced effects and the concrete experimental feedback, we achieved the optimal Pr³⁺ doping concentration and machining dimensions of Pr:YLF gain media. On that basis, we realized a 7.56-W CW laser output at 522 nm by optimizing the mode matching between the pump and green lasers. To the best of our knowledge, this is the maximum output power of Pr³⁺-based CW green lasers. Moreover, the obtained 522-nm laser also manifests excellent output stability (RMS = 1.27%), slope efficiency (56.50%), and beam quality (M² = 1.30 × 1.12), further clarifying the importance of considering the thermally induced impacts. Our findings provide useful insight into developing high-power blue-laser-diode-pumped visible lasers.

2. Result and discussion

The laser cavity of the 522-nm experiment is shown in Fig. 1(a). The pump source was integrated with six laser diodes (LD, FFKJ444-24B1), allowing a maximum pump power of 24 W with a beam quality factor (M²) of 7.82 × 6.67. To ensure stable temperature during high-power operation, the pump source surface contacted a copper block cooled at 25 °C. The pump laser was focused by a lens with a focal length ranging from 100 mm to 150 mm. A concave-plane laser cavity was used to generate the green laser. The input mirror (IM) (R = 100 mm) was the concave mirror with anti-reflection (T > 99.9%) at 444 nm and high-reflection (R > 99.9%) at 522 nm. An a-cut Pr:YLF crystal without coating was wrapped in indium foil and then inserted into a copper block maintained at 20 °C. The output coupler (OC) mirror was a flat mirror with a transmittance of 4% at 522 nm. The total cavity length was ∼99 mm. The losses of intracavity were calculated at 0.3% by Findlay-Clay method δ=ln(1/R)/[2 l(P_thr/P_t)-1] [30] caused by absorption, scattering, and optical inhomogeneity, where P_thr is the threshold pump power in the laser cavity (0.29 W with T = 4%), P_t is the threshold pump power with high-reflection output coupling (0.15 W with T = 0.01%), δ is the intracavity optical losses, R is the reflectance of the output coupling mirror (R = 96%) and l is the length of laser crystal (7 mm).

Fig. 1. Experimental analysis of the thermal lens effect. (a) Resonant cavity with lasing wavelength at 522 nm. IM: input mirror, OC: output coupling mirror. (b) Effective thermal focal lengths of different gain media.

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To begin, three a-cut Pr:YLF crystals with different doping concentrations were used to study the thermal lens effect. The Pr³⁺ doping concentrations correspond to 0.43 at.% (Gain_H), 0.30at.% (Gain_M), and 0.21at.% (Gain_L), and the relevant crystal dimensions are 3 × 3 × 7 mm³ (Gain_H) and 2 × 2 × 7 mm³ (Gain_M and Gain_L). The thermal lens effect is intricately associated with the temperature variation inside the gain media and the related equation can be expressed as [31],

(1)$${f_T} = \frac{{\pi {K_c}\omega _p^2}}{{\xi {P_{abs}}(1 - {e^{ - \alpha l}})\left[ {\frac{{dn}}{{dt}} + n(1 + \mu ){\alpha_T}} \right]}}$$

where f_T describes the thermal lens focal length, K_c is the thermal conductivity of Pr:YLF crystal (4.1 W/m/K along the a-axis direction) [32], ω_p is the half of waist spot of the pump beam (∼75 µm), μ is the Poisson ratio (0.33), n is the refractive index of the gain crystal (1.47). ξ is the fractional thermal loading (14.9%). dn/dt is the thermo-optic coefficient (π: −4.3 × 10⁻⁶) [33]. α is the absorption coefficient of the gain crystal (Gain_H =1.96 cm⁻¹, Gain_M = 1.37 cm⁻¹, Gain_L = 0.96 cm⁻¹), l is the length of the gain crystal (7 mm), and α_T is the thermal expansion coefficient (a-cut: 13 × 10⁻⁶ K⁻¹). Subsequently, the thermal focal lengths of the Pr:YLF crystals at different pump powers were measured via the same laser experiments of 522 nm. The corresponding thermal focal lengths under different pump powers were determined when the output power was dropped to 70% of maximum power at the stable cavity by moving d₂ to increase the cavity length [31,34]. d₁ and d₂ were measured according to the experimental setup shown in Fig. 1(a).

(2)$$\frac{1}{{{f_{th}}}} = \frac{1}{{{d_2} + l(\frac{1}{n} - 1)}} - \frac{1}{{r - {d_1}}}$$

where d₁ and d₂ are the distances from the pumped facet of the gain crystal to the input mirror and output coupler, respectively. l is the length of the gain crystal and r is the radius of curvature of the input mirror. As displayed in Fig. 1(b) and Fig. S1 in Supplement 1, combined with the experimental data and theoretical simulation, the thermal focal lengths of different gain media were established. It can be observed that under the same absorbed pump power, the effective focal length of Gain_H is smaller than those of Gain_M and Gain_L meaning the increase in Pr³⁺ doping content will make the thermal lens effect more obvious [35].

2.1 522-nm CW lasers of different gain crystals

The schematic diagram of the CW laser experiments is shown in Fig. 1(a). As shown in Fig. 2(a), Gain_H was conducted first. When the absorbed pump power reaches 0.5 W, the green laser can be observed at 522 nm. Augmenting the pump power, the output power gradually increases. Unfortunately, the Gain_H crystal starts to crack when the absorbed pump power reaches 11.7 W, yielding a maximum output power of 4.83 W and a slope efficiency of 46.82%. The cracking of Gain_H indicates the Pr:YLF gain crystal with high doping concentrations cannot support high-power laser output due to the severe thermally induced effects inside the crystal.

Fig. 2. 522-nm Output power of Gain_H (a), Gain_M (b), and Gain_L (c) crystals. The inset is the lasing wavelength.

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To reduce the thermally induced effects of the gain crystal, Gain_L was applied to the CW laser experiment. The square aperture is changed from 3 × 3 mm² (Gain_H) to 2 × 2 mm² (Gain_L) and the crystal length remains unchanged (7 mm). As demonstrated in Fig. 2(c), the green CW laser is observed as the absorbed pump power attains the threshold value (0.7 W). The largest 522-nm output power of 3.75 W is obtained under the maximum absorbed pump power (12 W). Note that Gain_L can maintain the laser oscillation even if under the absorbed pump power that causes the cracking of Gain_H, indicating the importance of adjusting the distribution of heat in the gain media. However, the slope efficiency of Gain_L (32.92%) is smaller than that of Gain_H. That consequence is primarily caused by the impact of the thermal lens effect on the mode matching between the pump and green lasers.

Considering the laser performances of Gain_H and Gain_L, it needs to pursue a balance between the reduction of thermally induced effects and the improvement of output power. Hence, Gain_M is further employed to optimize the output of the green laser. As Fig. 2(b) shows, the green laser starts to oscillate when the absorbed pump power reaches 0.3 W. The output power presents a non-linear increasing behavior as the absorbed pump power is below 5 W. This mainly stems from the alteration of the lasing wavelength of the blue laser diode depending on the pump power, giving rise to an absorption change of Pr:YLF crystal [36]. When the absorbed pump power is above 5 W, there is a good overlap between the pump wavelength and absorption wavelength. The gain medium maintains a nearly stable absorptivity of the pump laser (∼61.5%), yielding a linear rise in output power. Finally, the maximum output power of 7.56 W is obtained when the absorbed pump power reaches 14.76 W, corresponding to a slope efficiency of 56.50%, superior to those of Gain_H and Gain_L. Such a result indicates that it is imperative to understand the influence mechanism of thermally induced effects on the performance of Pr³⁺-based lasers.

2.2 Thermal effect analysis of gain crystals

In this part, we theoretically analyze the temperature-field distribution within the Pr:YLF gain crystals using the finite element method. When one gain crystal is located in thermal equilibrium, its temperature distribution can be expressed as follows [37],

(3)$$\begin{aligned} &\frac{{{\partial ^2}T(x,y,z)}}{{\partial {x^2}}} + \frac{{{\partial ^2}T(x,y,z)}}{{\partial {y^2}}} + \frac{{{\partial ^2}T(x,y,z)}}{{\partial {z^2}}} ={-} \frac{{Q(x,y,z)}}{{{K_c}}}\\ &Q(x,y,z) = \frac{{2\xi \alpha \exp ( - \alpha z)[1 - \exp ( - \alpha l)]}}{{\pi \omega _p^2}}\exp ( - \frac{{2{{({x^2} + {y^2})}^2}}}{{\omega _p^2}}) \end{aligned}$$

where T (r, z) is the temperature, Q (r, z) is the distribution function of heat flux, α is the absorption coefficient of the gain crystal, The surface temperature of the gain crystal was treated as a constant temperature of 293 K, the boundary conditions for thermal stability of the gain crystal was ∂T(r,z)/∂z|_z = 0 = 0, ∂T(r,z)/∂z|_z = l = 0 and the three-dimensional coordinates of the gain crystal is shown in Fig. 3(a). The related simulation parameters are given in Supplement 1, Table S1. The absorbed pump power is set according to the experimental data. The obtained axial temperature distributions (x = y = 0) of the three gain crystals are demonstrated in Fig. 3(b). The maximum temperatures of Gain_H, Gain_M, and Gain_L are 342 K, 325 K, and 310 K, respectively. This indicates that even if under a lower absorbed pump power, Gain_H manifests a maximum temperature, obviously larger than those of Gain_M and Gain_L. The maximum axial temperature gradient of Gain_H is −8.64 K/mm (z = 0.047 mm), ∼2.12 times of Gain_M (−4.07 K/mm at z = 0.052 mm) and ∼5.61 times of Gain_L (−1.54 K/mm at z = 0.058 mm). The main reason for this phenomenon is that the absorption of gain media presents an exponentially declining trend, resulting in the strongest utilization of the pump laser at the front face of gain media. A low doping concentration of active ions will effectively reduce the maximum temperature and the temperature gradient. Additionally, as shown in Fig. 3(c), the alteration of radial temperature is more evident in comparison to the axial temperature distribution. The maximum radial temperature gradient of Gain_H reaches −372 K/mm (r = 0.003 mm), a value that is ∼1.67 times of Gain_M (−222.1 K/mm at r = 0.003 mm) and ∼3.1 times of Gain_L (−119.7 K/mm at r = 0.004 mm). Such a large temperature gradient along the radial direction suggests the lasing performance will suffer a degradation influence caused by thermally induced effects. Fig. 3(d-i) shows the three-dimensional temperature distribution of Gain_H, Gain_M, and Gain_L in the (x, y, 0) and (x, 0, z) plane.

Fig. 3. (a) Three-dimensional graph of the gain crystal. (b) Axial temperature distributions of the three gain media under the largest absorbed pump power (x = y = 0). (c) Radial temperature distributions of the three gain media under the largest absorbed pump power (z = 0). (d-f) Three-dimensional temperature distributions of Gain_H, Gain_M, and Gain_L in the (x, y, 0) plane. (g-i) Three-dimensional temperature distribution of Gain_H, Gain_M, Gain_L in the (x, 0, z) plane.

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The non-uniformity of the temperature distribution inside the gain crystal will give rise to thermally induced stress [38]. If controlled unreasonably, the Pr³⁺-based lasers are susceptible to the cracking of gain media. Combined with the radial temperature difference inside the gain crystal, the radial and tangential components of thermally induced stress can be described as [39],

(4)$$\begin{aligned} &{\sigma _r}(r,z) = \frac{{\alpha E}}{{1 - \nu }}[\frac{1}{{r_0^2}}\int_0^{{r_0}} {T(r,z)rdr - \frac{1}{{r_{}^2}}} \int_0^r {T(r,z)rdr} ]\\ &{\sigma _\theta }(r,z) = \frac{{\alpha E}}{{1 - \nu }}[\frac{1}{{r_0^2}}\int_0^{{r_0}} {T(r,z)rdr + \frac{1}{{r_{}^2}}} \int_0^r {T(r,z)rdr - T(r,z)} ] \end{aligned}$$

where σ_r (r, z) and σ_θ (r, z) denote the radial and tangential stress, respectively, ν and E correspond to the Poisson’s ratio and Elastic modulus of the gain crystal. The calculated stress results are elucidated in Fig. 4. The maximum σ_r and σ_θ of Gain_H are −68.6 MPa and −16.9 MPa, respectively. By contrast, through lessening the square aperture (from 3 × 3 mm² to 2 × 2 mm²) and Pr³⁺ doping concentration, the three kinds of thermally induced stress within Gain_M are reduced by 35.2% and 37.2%, respectively, yielding the values of −44.4 MPa and −10.6 MPa respectively. For Gain_L, the thermally induced stress will be further reduced due to the decline in Pr³⁺ doping concentration, and the largest σ_r and σ_θ become −23.9 MPa and −5.8 MPa, respectively. For the cracking of Gain_H under an absorbed pump power of 11.7 W, it is mainly because the thermally induced maximum stress is obviously larger than the actual fracture limit of YLF (∼ 40 MPa) [40]. Gain_M still has excellent laser performance even if under the thermally induced stress close to the fracture limit of YLF. Gain_L shows a lower thermally induced stress than those of Gain_H and Gain_M, hence being more suitable for the laser operation under a high pump power.

Fig. 4. Thermally induced stress of different Pr:YLF gain media. (a) The distribution of radial stress in the (x, y, 0) plane. (b) The distribution of tangential stress in the (x, y, 0) plane.

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2.3 Optimization of CW green lasers

To gain a deeper insight into the thermally induced effects on the mode matching between the pump laser and the green laser, the lasing performance of Gain_M was further optimized by changing the pump focusing system. Three different focus lenses were used to adjust the beam distribution of the pump laser, and their focal lengths correspond to 100 mm (F₁), 125 mm (F₂), and 150 mm (F₃). As shown in Fig. 5(a), The pump threshold values of the three kinds of cases are 0.15 W, 0.29 W, and 0.78 W, respectively. This accords with the consequence that a lower pump power density needs a higher pump power to satisfy the laser oscillation. It is worth noting that the maximum output powers and slope efficiencies of the three 522-nm lasers are similar, indicating the strong thermal lensing effect of the Pr:YLF gain crystal under the high-power pump power. As the pump laser through F₁, F₂, and F₃, the waist spot sizes were 125 µm × 133 µm, 148 µm × 167 µm, and 205 µm × 201 µm, respectively. When the thermal lensing effect of Gain_M was considered under an absorbed pump power of 14.76 W, those waist spots were altered as 82 µm × 88 µm, 101 µm × 115 µm, and 135 µm × 132 µm, well matching with the waist diameter of the intracavity green laser (87 µm for F₁, 111 µm for F₂, and 135 µm for F₃). For Gain_M, the overlap efficiencies of the focus systems of F₁, F₂, and F₃ under the maximum absorbed pump power were 82.3%, 83.3%, and 80.3%, respectively. This verifies that compared to the optimization of the pump focusing system, the meticulous consideration of gain media is more essential in improving the mode matching condition owing to the concentration-dependent thermal lensing effect. As Fig. 5(b) shows, the achievement of the 522-nm CW laser in this study is superior to those previously reported results and becomes the maximum output power, to the beat of our knowledge.

Fig. 5. Optimization of the laser performance of Gain_M. (a) Output power of 522-nm lasers under different pump focusing systems. F₁ = 100 mm, F₂ = 125 mm, F₃ = 150 mm. (b) Performance comparison of 522-nm CW lasers between our experimental result and previously reported data. [14,19–21,33,41–48]. (c) Beam quality of the 522-nm laser under F₂ = 125 mm. The inset is the CCD image. (d) Output power stability of the optimal 522-nm laser (with F₂ = 125 mm). RMS = 1.95%, 0.92%, 0.79%, 0.77%, and 1.27% for the absorbed pump power (P_abs) from 1.87 W to 14.76 W.

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Then, the laser beam quality factor (M²) and output power stability of the optimal 522-nm laser were measured. Fig. 5(c) shows the laser spot radius focused by a lens with a focal length of 50 mm. The laser beam quality factor (M²) is determined to be 1.30 × 1.12, suggesting that the beam quality does not reverse even if under a high-power lasing operation. Fig. 5(d) shows the output power stability of the green laser under different absorbed pump powers, The RMS under the maximum absorbed pump power (14.76 W) is 1.27%, manifesting fascinating output stability. Those obtained results further verify the importance of considering the thermally induced effects in developing high-power Pr³⁺-based visible lasers.

3. Conclusion

In summary, we report a high-power CW green laser of Pr:YLF crystal by carefully managing the accompanying thermally induced effects. The effective optimization of heat distribution inside the gain crystal yields good mode matching and excellent resilience against cracking under high-power laser operation. The maximum output power of the green laser reaches 7.56 W with a slope efficiency of 56.50%, manifesting an apparent power advantage compared to the previously reported results. Moreover, our obtained green laser also demonstrates remarkable beam quality and output stability due to addressing the thermally induced effects reasonably. Our observation here offers a reference pathway to resolve the thermally induced questions that limit the development of Pr³⁺-based high-power visible lasers.

Funding

Key Technology Research and Development Program of Shandong (2022CXGC010104); National Natural Science Foundation of China (52025021); Natural Science Foundation of Shandong Province (ZR2022LLZ005); the Future Plans of Young Scholars at Shandong University, and the Fundamental Research Funds for the Central Universities (2022JC024)

Disclosures

The authors declare no conflicts of interest.

Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

Supplemental document

See Supplement 1 for supporting content.

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7.56-W continuous-wave Pr³⁺-based green laser via managing thermally induced effects

Abstract

1. Introduction

2. Result and discussion

2.1 522-nm CW lasers of different gain crystals

2.2 Thermal effect analysis of gain crystals

2.3 Optimization of CW green lasers

3. Conclusion

Funding

Disclosures

Data availability

Supplemental document

Reference

Supplementary Material (1)

Data availability

Cited By

Figures (5)

Equations (4)

Optics Express