Thermal analysis and laser performance of a GYSGG/Cr,Er,Pr:GYSGG composite laser crystal operated at 2.79 &#x03BC;m

Zhongqing Fang; Dunlu Sun; Jianqiao Luo; Huili Zhang; Xuyao Zhao; Cong Quan; Lunzhen Hu; Maojie Cheng; Qingli Zhang; Shaotang Yin

doi:10.1364/OE.25.021349

1. Introduction

Laser region of 2.7–3 μm can be obtained by the transition from ⁴I_11/2 to ⁴I_13/2 of the trivalent erbium ions, which are widely utilized in laser surgery and laser radar measurements of atmospheric humidity owing to the strong water absorption bands in this range [1-2]. In addition, this laser waveband is also an ideal pumping source for Optical Parameter Oscillator (OPO) in realizing 3-5 and 8-12 μm mid-infrared laser [3]. To date, the majority of research on erbium doped oxide laser have focused on Er:YAG (Er:Y₃Al₅O₁₂) [4], Er:YSGG (Er:Y₃Sc₂Ga₃O₁₂) [5], Er:GSGG (Gd₃Sc₂Ga₃O₁₂) [6] and Er:GYSGG (Gd_1.17Y_1.83Sc₂Ga₃O₁₂) [7] etc. The Er:GYSGG has a lower phonon energy (732 cm⁻¹) comparing with the Er:YAG (846 cm⁻¹) and Er:GSGG (741 cm⁻¹). Low phonon energy can decrease non-radiation transition probability, which is benefited to decrease the lifetime of ⁴I_13/2 level and improve laser efficiency. Moreover, the outstanding advantage of Er:GYSGG is its excellent radiation-resistance ability, which can be applied in the radiation environments. However, the Er:GYSGG has a shortcoming of long lifetime of the lower laser level, which influences the laser threshold and efficiency. In our previous work, appropriately increasing concentration of Cr³⁺ ions (3 at.%) can improve the output energy of Cr,Er:YSGG laser crystal and Ho³⁺ or Pr³⁺ ions [8–10] as deactivator can efficiently deactivate the level ⁴I_13∕2 and increase the 2.79 μm laser efficiency. Duan [11] et al reported that with the increasing concentration of Pr³⁺, 2.7 μm emission is restrained significantly due to the concentration quenching of Pr³⁺ ions. Thus, it is essential and meaningful to further optimize the concentrations of doping Cr³⁺, Er³⁺, Pr³⁺ ions. In addition, the Cr,Er,Pr:GYSGG crystal has relatively low thermal conductivity, which the generated thermal effect would limit the improvement of laser performance. Thermal bonding is an effective way to depress the thermal effect of laser crystal. Due to the absence of active ions in the GYSGG crystal, the GYSGG end caps can act as suitable cooling structure to improve cooling efficiency for the Cr,Er,Pr:GYSGG crystal. To the best of our knowledge, no reports about Cr,Er,Pr:GYSGG composite crystal can be found until now.

In this work, a Cr,Er,Pr:GYSGG crystal was grown successfully by the Czochralski (Cz) method and the concentrations of sensitization Cr³⁺, activation Er³⁺ and deactivation Pr³⁺ were further optimized. A GYSGG/Cr,Er,Pr:GYSGG composite crystal was obtained by thermal bonding with un-doped GYSGG crystals as the end cap. The temperature distribution in the two crystal rods and laser properties of flash lamp side-pumping were analyzed and compared.

2. Experimental setup

The Cr,Er,Pr:GYSGG crystal was grown by the Cz method. The concentrations of Cr³⁺, Er³⁺ and Pr³⁺ in the polycrystalline materials are 3 at.%, 20 at.% and 0.15at.%, respectively. Cr₂O₃ and Sc₂O₃ powders (99.99% purity), as well as Gd₂O₃, Pr₆O₁₁, Y₂O₃, Ga₂O₃ and Er₂O₃ (99.999% purity) were used as starting raw materials and weighed according to the molecular formula of (Er_0.6Pr_0.0045Gd_0.75Y_1.6455)(Cr_0.6Sc_1.94)Ga₃O₁₂. Ga₂O₃ was overweighed by 2 wt.% to compensate for its evaporation loss during the crystal growth. The crystal was cut and processed into crystal rods with sizes of Φ 4 mm × 89 mm and Φ 4 mm × 79 mm, respectively. Two pure GYSGG crystals(Φ 4 mm × 5 mm) were bonded thermally at 1200 °C for 10 h to the shorter crystal rod, as shown in Fig. 1. The two end faces of the crystal rods were optically polished and antireflection coated near 2.79 μm.

Fig. 1 Photograph of the single Cr,Er,Pr:GYSGG crystal and the bonding GYSGG/Cr,Er,Pr:GYSGG crystal.

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In the laser experiment, the pumping source is a xenon flash lamp with an arc length of 80 mm and an inner diameter of 5 mm. The xenon flash lamp and crystal rods were both placed into a close-coupled diffusing ceramic cavity and cooled with circulating water, which was maintained at a temperature of 20 °C. A simple plane-plane resonator cavity formed by two mirrors with a cavity-length of 246 mm was employed to demonstrate mid-infrared laser, as shown in Fig. 2. M₁ is a plane mirror with reflectivity of 100% around 2.79 μm. The transmission of the output mirrors (M₂) was 30% at 2.79 μm. The laser output energy was measured by an energy meter (Ophir PE50-DIF-C). The laser beam profile and M² factor were determined by pyroelectric array camera (Ophir-Spiricon PY-III-HR).

Fig. 2 Schematic of the GYSGG/Cr,Er,Pr:GYSGG composite crystal laser pumped by the xenon lamp.

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3. Results and discussion

3.1 Level lifetime

In this work, The lifetimes of the upper level ⁴I_11/2 and the lower level ⁴I_13/2 are 0.63 and 0.86 ms respectively in the Cr,Er,Pr:GYSGG crystal with 3 at.% Cr³⁺, 20 at.% Er³⁺, and 0.15 at.% Pr³⁺, as shown in Fig. 3. The lifetime ratio between the ⁴I_13/2 level and ⁴I_11/2 level is 1.365, in comparison with the value of 1.424 in the previous work [10], which the lifetimes are 0.59 and 0.84 ms for the ⁴I_11/2 level and ⁴I_13/2 level in Cr,Er,Pr:GYSGG crystal with doping 2 at.% Cr³⁺, 18 at.% Er³⁺ and 0.2 at.% Pr³⁺, respectively. This result indicates that the lifetime ratio of lower and upper levels is further decreased due to the optimized doping concentrations, which should be helpful to further improve the laser performance.

Fig. 3 Fluorescence decay curves of the Cr,Er,Pr:GYSGG crystal.

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3.2 Temperature distribution

The temperature distributions of the Cr,Er,Pr:GYSGG and GYSGG/Cr,Er,Pr:GYSGG composite crystals side-pumped by flash lamp are the simulated using the simulation software COMSOL Multiphysics. The mathematical model for unstable diffusion of heat in a body is a parabolic partial differential equation. The general differential equation of heat conduction for a stationary, homogenous, isotropic solid with heat generation within the body is [12]:

\nabla • (k (T) • \nabla T) + Q = ρ c_{P} \frac{\partial T}{\partial t}

where Q is the heat intensity,

ρ

the density, c_p the specific heat at constant pressure, K the thermal conductivity, and

\nabla

denotes the gradient operator. In steady state, assuming K = constant, then Eq. (1) becomes:

\nabla^{2} T = \frac{\partial^{2} T}{\partial r^{2}} + \frac{1}{r} \frac{\partial T}{\partial r} + \frac{\partial^{2} T}{\partial z^{2}} + \frac{1}{r^{2}} \frac{\partial^{2} T}{\partial θ^{2}} = - \frac{Q}{K}

In cylindrical coordinate system, we assume the heat flow is strictly radial, and azimuthal ( $θ$ ) variations in T can be ignored. The temperature is a function of radial (r) and longitudinal (z). The Eq. (2) can be written as:

\frac{\partial^{2} T}{\partial r^{2}} + \frac{1}{r} \frac{\partial T}{\partial r} + \frac{\partial^{2} T}{\partial z^{2}} = - \frac{Q (r, z)}{K}

The Neumann boundary S between the edge of the rod and the coolant:

K • {\frac{\partial T}{\partial s} |}_{S} = h • (T_{C} - {T |}_{S})

where h is the heat transfer coefficient, T_C the coolant temperature, and the first derivative is taken with respect to the normal to the surface S.

To calculate the heat conduction differential equations, The following parameters are used in the numerical calculations of the temperature profile in the crystal: rod length l = 89 mm; doped Cr,Er,Pr:GYSGG crystal length l_e = 79 mm (also efficient rod length); pure GYSGG length l_p = 5*2 mm; rod radius r = 2 mm; heat transfer coefficient between crystal and cooling water h₁ = 1 W/cm²·K; heat transfer coefficient between crystal and air h₂ = 0.005 W/cm²; K₁ = 4.6 W/(m·K), is the thermal conductivity of doped Cr,Er,Pr:GYSGG crystal; K₂ = 6 W/(m·K), is the thermal conductivity of pure GYSGG crystal; the heat density Q = 1000 W/cm³; the temperature of cooling water and condition T_C = 293.15 K. Figure 4 shows the relative temperature distributions of the Cr,Er,Pr:GYSGG crystal and the GYSGG/Cr,Er,Pr:GYSGG composite crystal.

Fig. 4 Relative temperature distribution models of single Cr,Er,Pr:GYSGG crystal rod and GYSGG/Cr,Er,Pr:GYSGG composite crystal rod. (a) the whole laser rods; (b) cross-sections at bonding or corresponding position. The red represents high temperature and blue represents low temperature.

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The efficient pumping lengths are the same on the two laser rods. The surface temperature of two rods are all close to 350 K at heat density 588 W/cm³ (corresponding to pumping energy 14.7 J at repetition rate 40 Hz). But at the end cap, the thermal conductivity of un-doping GYSGG crystal is larger than that of Cr,Er,Pr:GYSGG, resulting in an increasing thermal diffusion in GYSGG/Cr,Er,Pr:GYSGG composite crystal. In cross-sections at bonding or corresponding position, the maximum temperature of GYSGG/Cr,Er,Pr:GYSGG composite crystal (376.6 K) is lower than that of Cr,Er,Pr:GYSGG crystal (387.7 K). When the heat density up to 1000 W/cm³, the maximum temperature of two crystal are 432.2 and 450.1 K, respectively. With the increasing of heat density, the difference value of maximum temperature at bonding section is larger, as shown in Fig. 5. Composite crystal produces lower buildup and lower gradients, which is benefitted to reduce the thermal lens effects. This indicates the GYSGG/Cr,Er,Pr:GYSGG composite crystal is more suitable for high pumping energy.

Fig. 5 Relative maximum temperature at the bonding section of two crystals.

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3.3 Laser performance

The output pulse energy as a function of pump energy for the Cr,Er,Pr:GYSGG crystal with 30% output coupler transmission operated at 1, 5, 10, 20, 40 and 60 Hz is shown in Fig. 6. We can note that the output energy stays linear as a function of the pump energy indicating that the crystal is not saturated. A maximum laser energy 315.8 mJ operated at 5 Hz with a pumped energy of 39.7 J is obtained, corresponding electrical-to-optical efficiency 0.79% and laser thresholds about 9.1 J. We obtain maximum slope efficiency 1.22% at the repetition rate of 40 Hz and electrical-to-optical efficiency 0.85% at 10 Hz. Luo et al [10] have reported a maximum pulse energy 278 mJ and a slope efficiency of 0.7% operated at 10 Hz with flash-pumping on the 2 at.% Cr³⁺, 18 at.% Er³⁺ and 0.2 at.% Pr³⁺ doped GSYGG crystal. This indicates the laser performances of Cr,Er,Pr:GYSGG are improved successfully by optimizing the concentration of the doping ions in this work. The single pulse energy increases with the repetition rate under the same pump energy, maybe resulting from that only the partial crystal rod can absorb the pumping light at the low repetition rate.

Fig. 6 Output pulse energy for Cr,Er,Pr:GYSGG crystal versus pump energy at different repetition rate.

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Using 30% output coupler transmission, the results operated at various repetition rates of the GYSGG/Cr,Er,Pr:GYSGG composite crystal are presented in Fig. 7. The thresholds of the GYSGG/Cr,Er,Pr:GYSGG composite crystal is about 9.1 J similar to the Cr,Er,Pr:GYSGG crystal, because the thermal effect is not obvious at low pumping energy. A maximum laser energy 342.8 mJ operated at 5 Hz with a pumped energy 39.7 J is obtained, corresponding to electrical-to-optical efficiency 0.86%. It is 27 mJ larger than that of the Cr,Er,Pr:GYSGG crystal. A maximum slope efficiency 1.34% at the repetition rate of 40 Hz and a maximum electrical-to-optical efficiency 0.89% at 10 Hz are realized. Table 1 lists the optical parameters of two crystals. With the repetition rate increasing, the difference values of the single-pulse output energy of two crystals under the same pumping energy become larger, suggesting the merit of the cooling effect of GYSGG end cap of GYSGG/Cr,Er,Pr:GYSGG composite crystal can be well exhibited at high repetition rate. Therefore, the GYSGG/Cr,Er,Pr:GYSGG composite crystal has obvious advantages in improving laser performances, which is more suitable to be operated at high pumping energy and high repetition rate.

Fig. 7 Output pulse energy for GYSGG/Cr,Er,Pr:GYSGG composite crystal versus pump energy at different repetition rates.

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Table 1. Concentration, lifetime and laser parameters of Cr,Er,Pr:GYSGG crystals.

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3.4 Thermal focal length and M² factors

The thermal focal lengths of the two rods were measured to illustrate the influence of GYSGG/Cr,Er,Pr:GYSGG composite crystal on the thermal lensing effect. Thermal focal lengths of two crystals as a function of pump power are shown in Fig. 8. We find that the thermal focal length decreases with the pump power increasing. When pump power is 130 W, the thermal focal length of GYSGG/Cr,Er,Pr:GYSGG composite crystal is 97 mm and that of Cr,Er,Pr:GYSGG crystal is only 87 mm. The thermal focal length of GYSGG/Cr,Er,Pr:GYSGG composite crystal is close to 66 mm when the pump power is up to 280 W. However, the thermal focal length of the Cr,Er,Pr:GYSGG crystal is 66 mm when the pump power is 225 W. These results indicate that the GYSGG/Cr,Er,Pr:GYSGG composite crystal can decrease the thermal lensing effect and is highly advantageous to the thermal stability of output power.

Fig. 8 Thermal focal lengths of two crystals as a function of pump power.

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The laser beam profile, M² factor and far-field divergence were determined to analysis the influence of bonding with pure GYSGG crystals as end cap on laser beam quality. After focusing laser beam through the lens with focal length 305.72 mm at 100 mJ output energy, we moved the camera near the position of the lens focal point to record the horizontal and vertical diameter. The beam waist diameter and far-field divergence were determined through the hyperbolic fitting [13], the result is shown in Fig. 9. The laser quality M² factor can be calculated as [14]:

M^{2} = \frac{ϖ Θ π}{4 λ}

where ω is the beam waist diameter, Θ the far-field divergence and λ the wavelength. We obtained the M_x²/M_y² factors are 3.23/3.08 in the x and y direction for Cr,Er,Pr:GYSGG, and 3.10/2.89 for GYSGG/Cr,Er,Pr:GYSGG composite crystal, respectively. The far-field divergence (Θ_x/Θ_y) of two crystals are 3.93/3.77 and 3.79/3.64 mrad, respectively. The laser of two rods were operated in multimode regime, resulting in the M² factor and the far-field divergence relative large. But the M² factor and the far-field divergence of composite crystal are less than those of single crystal. It is observed that the GYSGG/Cr,Er,Pr:GYSGG composite crystal presents a higher laser beam quality than that of the Cr,Er,Pr:GYSGG crystal at equal output energy.

Fig. 9 Beam diameter versus propagation distance of two crystals. (a) Cr,Er,Pr:GYSGG crystal; (b) GYSGG/Cr,Er,Pr:GYSGG composite crystal.

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4. Conclusions

A GYSGG/Cr,Er,Pr:GYSGG composite crystal is obtained by thermal bonding with un-doped GYSGG crystals as end cap. The thermal analysis indicates the GYSGG/Cr,Er,Pr:GYSGG composite crystal can decrease the thermal buildup and thermal gradients, which inhibits thermal lens effects effectively. The measurement of thermal focal length also indicates thermal lensing effects can be reduced effectively. A maximum pulse energy 342.8 mJ is obtained on the GYSGG/Cr,Er,Pr:GYSGG composite crystal, corresponding to electrical-to-optical efficiency of 0.86% and slope efficiency of 1.08%. With the repetition rate increasing, the difference values of the single-pulse output energy of two crystal under the same pumping energy become larger. The GYSGG/Cr,Er,Pr:GYSGG composite crystal is more suitable to be operated at high pumping energy and high repetition rate. The M² factor and the far-field divergence of GYSGG/Cr,Er,Pr:GYSGG composite crystal are less than those of Cr,Er,Pr:GYSGG crystal. All these results suggest that the GYSGG/Cr,Er,Pr:GYSGG composite crystal has great advantages in reducing thermal effects and improving laser performances.

Funding

National Key Research and Development Program of China (2016YFB1102301); the National Natural Science Foundation of China (51272254, 61405206, 51502292, and 51702322); and Open Research Fund of the State Key Laboratory of Pulsed Power Laser Technology, Electronic Engineering Institute (SKL2015KF01).

References and links

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Thermal analysis and laser performance of a GYSGG/Cr,Er,Pr:GYSGG composite laser crystal operated at 2.79 μm

Abstract

1. Introduction

2. Experimental setup