Abstract
1 Introduction
Diode-pumped solid-state (DPSS) lasers have made great progress in the past decades. One of the enduring obstacles that DPSS lasers have faced is the restriction from high thermal gradients and aberration under intense pumping conditions. However, with the face cooling configuration of a thin, disk-shaped active medium, the diode-pumped architecture allows building high output power solid-state lasers with excellent spatial beam quality and high conversion efficiency. Following the thin disk laser concept introduced by Giesen et al.[
The spectroscopic parameters of the Nd-doped materials are superior to those of the Yb-doped materials. On the one hand, the effective emission cross-section is higher and the system is less sensitive to temperature fluctuations, which offer important practical advantages. On the other hand, the re-absorption effect is negligible. These advantages, combined with lower but reasonable upper-state lifetimes, mean that lower threshold systems might result from the use of Nd-doped materials. A thin disk Nd:GdVO4 laser was reported by Pavel and Taira[
The use of Nd:YVO4 material in thin disk geometry has attracted attention[
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For the above Nd:YVO4 thin disk laser, low absorption of the pump radiation occurs because the effective absorption path length is twice the thickness of the disk when the pump beam is reflected only once at the backside of the laser crystal. Improvement of absorption efficiency is typically achieved by re-circulating the pump beam in a multipass pumping scheme. However, this complicated and expensive multipass pumping architecture is not desirable for many applications. The double-pass pumping scheme as described by Millar et al.[
The in-band pumping directly into the emitting level is a method to reduce the thermal load in the Nd:YVO4 thin disk[
In this paper, a simple, compact double-pass pumped Nd:YVO4 thin disk laser was demonstrated. The schemes of in-band pumping, undoped end face bonds and SiC material heat sink were combined to alleviate the thermal effect. The influence of Nd doping concentration and thickness on the CW performance was experimentally investigated by using two crystals of approximately the same absorption efficiency but different doping concentrations of 1 at.% and 0.5 at.%. At the same time, a numerical analysis of the temperature distribution and thermal lens effect in the laser considering the influence of the ETU effect was presented and compared to the experimental results. The effect of the temperature dependence of the thermal conductivity tensor was also taken into account. The numerical simulations were based on the finite-element analysis methods and carried out using the COMSOL software, which matched well with experimental results. Consequently, the theoretical model can be employed as a useful tool for the design of the distributed face cooling scheme[
2 Theoretical analysis for thermal effects
Generally, the performances of Nd:YVO4 thin disk lasers are affected by thermal effects. Thus, it is significant to conduct an accurate theoretical analysis of the temperature distribution and thermal lens effect for optimum design of the double-pass pumped Nd:YVO4 thin disk laser. The detailed structure of the gain media and heat sink used in this paper is shown in Figure
2.1 Heat equation in crystal
The general steady-state temperature distribution for an anisotropic cubic laser crystal using Cartesian coordinates satisfies the following heat-conduction equation[
For a thin disk configuration, the laser crystal is mounted on a water-cooled heat sink with indium between them. It can be assumed that the four lateral surfaces of the crystal are adiabatic because the side area of the crystal is small compared to the water-cooled face dimensions. Simultaneously, we assumed that the doped end face of the crystal exchanged heat with the water-cooled heat sink and the undoped end face exchanged heat with the environment through natural convection. For a single diffusion bonded crystal, the boundary conditions are written as follows:
The solution of Equations (
2.2 Thermal conductivity
According to Ref. [
2.3 Fractional thermal loading including ETU effect
In Equation (
Here we used a rate-equation analysis to investigate the influence of the ETU effects on fractional thermal loading. For an in-band 880 nm pumped Nd:YVO4 laser, referring to the Pollnau and White models[
3 Experimental setup
The experimental setup of the double-pass pumped Nd:YVO4 thin disk laser is shown in Figure
The cavity was formed by two plane mirrors M1 and M2. Mirror M1 was high-reflection-coated at 1064 nm (
4 Experimental and numerical analysis results
The output performance of the diode double-pass pumped Nd:YVO4 thin disk laser was affected by thermal effects. First, the CW output power of the Nd:YVO4 thin disk laser was tested. A symmetrical V-type cavity was used. At the same time, a portable thermometer was used to detect the temperature at the center of the undoped end face of the crystal. In this configuration, the curves of the output power and center temperature of the undoped end face of the crystal versus the absorbed pump power are shown in Figures
As shown in Figure
As shown in Figure
In addition to the output power, output beam quality was also an important indicator of the output performance of the thin disk laser. The output beam quality of different doped systems was observed with the same cavity. We placed a charge-coupled device camera behind the mirror M1 and monitored the beam profile of the system by measuring the light leakage behind the mirror M1. The beam profiles of different doped systems at different absorbed pump powers are shown in Figures
In contrast, the output beam profile of the 0.5 at.% doped system had an evolution similar to that of the 1 at.% doped system, with a slightly different turning point. Figure
The numerical analysis was based on the finite-element method through the COMSOL Multiphysics software and MATLAB. A three-dimensional model was used for numerical analysis. According to the design of the heat dissipation system, we assumed that the temperature of the copper heat sink was equal to the temperature of the cooling water and the ambient temperature
The two-dimensional temperature distributions of the undoped end face of the 1 at.% doped crystal with
To gain a better understanding of how an undoped end cap can be used to relieve thermal effects, we plotted temperature changes in the central axis of two different doped systems with the
Based on the temperature field distribution of the crystal (calculated previously) and the theoretical model in Section
5 Conclusion
In summary, we demonstrated a simple, compact double-pass pumped Nd:YVO4 thin disk laser. The schemes of in-band pumping, undoped end face bonds and SiC material heat sink were combined to alleviate the thermal effects. The CW performances of the double-pass pumped Nd:YVO4 thin disk laser with different doping concentrations and thicknesses were investigated experimentally. The maximum CW output power of 17.71 W with an optical-to-optical efficiency relative to absorbed pump power of 46% was obtained by the 0.5 at.% doped composite crystal under an absorbed pump power of 38.8 W. In addition, a maximum CW output power of 14.87 W with an optical-to-optical efficiency relative to an absorbed pump power of 43% was obtained by the 1 at.% doped composite crystal under an absorbed pump power of 34.4 W. Furthermore, the output beam characteristics of different doped systems were compared. The 0.5 at.% doped system had a higher output power and efficiency, but the 1 at.% doped system had a better output beam quality at the maximum output power. Numerical analysis and experimental study of the temperature distribution and thermal lens effect in the double-pass pumped Nd:YVO4 thin disk laser were also presented considering the influence of the ETU effects and the temperature dependence of the thermal conductivity tensor. The simulation and experiment results were in good agreement. Moreover, both experiment and simulation results indicated that the fractional thermal loading of the 1 at.% doped system increased to 0.26 while it only increased to 0.18 for the 0.5 at.% doped system due to the influence of the ETU effect. Consequently, the theoretical model can be employed as a useful tool for the design of the distributed face cooling scheme.
Funding
Ministry of Science and Technology of the People’s Republic of China (MOST) (2016YFB1102402, 2017YFB0405202); Key Laboratory of Opto-electronic Information Technology, Ministry of Education (Tianjin University), China (2019KFKT003); Shanghai Science and Technology Achievements Transformation and Industrialization project (18511109800).
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