LD端面泵浦连续Nd：GdVO_4激光的理论研究
摘要
激光二极管(laser diode, LD)泵浦的固体激光器集半导体激光器和固体激光器的优势于一体,在民用、军事等领域有重要而广泛的应用,是新一代的优质相干光源,也是激光技术的重要发展领域。其中LD端面泵浦固体激光器系统因其结构紧凑、转换效率高、空间模式好等特点而受到广泛关注。Nd:GdVO4晶体,作为一种较新型的激光材料,其优良的光学和热学特性使之成为一种非常适合LD泵浦的激光晶体,尤其适合于高功率运转。
本论文发展了LD端面泵浦连续激光的理论计算方法,并对LD端面泵浦的连续Nd:GdVO4激光特性进行了理论模拟研究。首先在不考虑热效应的情况下,对端泵1063 nm(四能级结构)连续Nd:GdVO4激光进行了数值模拟;然后详细计算了端泵方式下Nd:GdVO4晶体中的热效应问题;最后在考虑热效应的情况下,分别对高功率LD端泵Nd:GdVO4 1063 nm和准三能级结构的912 nm连续激光进行了数值模拟研究,详细讨论了较高功率情况下激光器参数对激光输出特性和热效应的影响规律。
本论文的研究工作,为高功率LD端面泵浦的连续激光研究探索出一种更加合理的理论计算方法,也有助于对Nd:GdVO4激光动力学过程的深入了解,为实际激光系统和器件的优化设计提供理论参考。
Laser-diode (LD)-pumped solid-state laser combines the advantages of semiconductor laser with those of solid-state laser. It has important applications in civil and military fields, and has become a new generation of coherent source of high quality. In particular, much attention has been paid to the LD end-pumped solid-state laser owing to its compactness, high conversion efficiency and good mode. In order to provide effective theoretical guidelines for experimental design, it is very necessary to theoretically study in detail the performance of LD end-pumped solid-state laser. In the theoretical models previously reported, there are some obvious limitations in the procedure of calculations for laser behaviors and thermal effects. In the present thesis, we developed a theoretical method for simulating LD end-pumped continuous wave (CW) lasers. Taking a newer laser crystal Nd:GdVO4 as the laser medium, we presented numerical simulations on the LD end-pumped CW Nd:GdVO4 laser and the thermal effects in the crystal, and discussed the cavity parameters influencing the laser operation with a view to optimizing laser performance. The thesis consists of the four parts: as follows
Firstly, numerical simulations on end-pumped 1063 nm (four-level system) CW Nd:GdVO4 laser without consideration of thermal effects.
In this part, we presented a more reasonable theoretical model for end-pumped CW laser, in which the rate equations and propagation equations have been employed, and the point-by-point iteration method has been used to numerically solve these equations. Since the propagation equations could demonstrate the spatial evolutions of the pump and the laser powers in the cavity, our model will be applicable to both low- and high-gain lasers.
With this theoretical model the performance of end-pumped 1063 nm CW Nd:GdVO4 laser was numerically simulated. The good agreement between the calculated and the published experimental data validated our theoretical model. In addition, we investigated the influences on laser performance from some parameters including the reflectivity of output coupler, the spot size of laser beam and the crystal length, and the optimum parameter values were obtained. The optimum output reflectivity R2 opt is a decreasing function of the incident pump power; the optimum spot-size ratioαopt between the laser and pump beams is an increasing function of the incident power, and under higher pump power it is larger than unity; the optimum crystal length lo pt for Nd:GdVO4 hardly changes with the incident power.
Secondly, theoretical calculations on thermal effect in LD end-pumped CW Nd:GdVO4 laser.
At first we introduced the theoretical methods for thermal effect in laser medium. And then taking Nd:GdVO4 as an example, we calculated the thermal effects in 1063 nm laser, including numerically solving the steady-state heat-conduction equation by the finite difference method to obtain temperature distribution in the crystal, with the temperature distribution calculating the optical path difference generating when the cavity mode passing through the medium, determining the thermal lens focal length by fitting the optical path difference to a parabolic reference surface, with the Strehl intensity ratio estimating the thermally-induced diffraction loss. From the calculated results, one can see the influences of some parameters, such as incident pump power, spot sizes of pump and laser beams, focal position of pump beam and so on, on the thermal effects, from which some methods for mitigating thermal effects were inspired. A larger waist radius of pump beam can effectively mitigate thermal effects in the crystal; Shift of pump beam focus from the surface into interior of the medium can reduce the end-face temperature; diminishing of the spot size of laser cavity mode especially less than that of pump beam is helpful to reduce the thermally induced diffraction loss and to improve laser beam quality; uniformity of transverse intensity distribution of pump beam through reshaping can also relieve thermal effects.
Thirdly, numerical simulations on high-power LD end-pumped 1063 nm CW Nd:GdVO4 laser by considering thermal effects.
For high-power LD-pumped solid-state lasers, the thermal effects in laser medium are the main limitation factor for stepping up output power. Therefore, it is crucial to include thermal effects into theoretical studies of this kind of laser. In this part, we presented a more reasonable calculation method considering thermal effects for simulating high-power LD end-pumped CW lasers. The advantage of our model is the entire considerations for the pump absorption saturation and the interactions between thermal effects and laser oscillation. As a result, it is applicable to both the case of lasing including three-level and four-level systems and the case of nonlasing.
With this theoretical model we simulated the performance of high-power LD end-pumped 1063 nm CW Nd:GdVO4 laser, and meanwhile we obtained the results of thermal effects. The calculated results and the published experimental data agreed well with each other. In order to provide guidelines for resonator design, we investigated the input-output characteristics for different cavity lengths. It is found that a too short or long cavity is not favorable to achieve higher-efficient laser output. Also we investigated the relationship between the optimum spot-size ratio ( )ωsωpaopt and the incident pump power with and without thermal effects included. It can be seen that ( )ωsωpaopt without thermal effects included is an increasing function of the pump power and it is larger than unity for slightly high pump power. In contrast, ( )ωsωpaoptincluding thermal effects is a decreasing function of pump power and it is less than unity for slightly high pump power.
Fourthly, numerical simulations on LD end-pumped 912 nm (quasi-three-level system) CW Nd:GdVO4 laser.
According to the characteristics of a quasi-three-level system, some changes have to been made in the theoretical model included thermal effects. Here we investigated the case that the pump beam passes twice through laser medium. Because of the lower efficiency for 912 nm laser, the heat generation in the medium cannot be completely attributed to the quantum defect. Therefore, according to the definition of the laser extraction efficiencyηl, we made use of laser intensity and population density to determineηl and hence the fractional thermal loadingηh. Then a numerical simulation on LD end-pumped 912 nm CW Nd:GdVO4 laser was performed. And a good agreement between the calculated results and the published experimental data was achieved. By comparing the calculated results for two-pass pumping with those for one-pass case, it is found that the slope efficiency for the latter was much lower than that for the former. We also calculated the axial and the transverse distributions of the fractional thermal loading, and the results indicated that it is very necessary to calculate in detail the fractional thermal loading for a quasi-three-level system.
The studies in this thesis presented a more reasonable theoretical method for LD end-pumped CW lasers. They are helpful to a better understanding for the kinetic behaviours of CW Nd:GdVO4 laser, and to theoretical guidelines for optimizing design of the practical laser system.
本论文发展了LD端面泵浦连续激光的理论计算方法,并对LD端面泵浦的连续Nd:GdVO4激光特性进行了理论模拟研究。首先在不考虑热效应的情况下,对端泵1063 nm(四能级结构)连续Nd:GdVO4激光进行了数值模拟;然后详细计算了端泵方式下Nd:GdVO4晶体中的热效应问题;最后在考虑热效应的情况下,分别对高功率LD端泵Nd:GdVO4 1063 nm和准三能级结构的912 nm连续激光进行了数值模拟研究,详细讨论了较高功率情况下激光器参数对激光输出特性和热效应的影响规律。
本论文的研究工作,为高功率LD端面泵浦的连续激光研究探索出一种更加合理的理论计算方法,也有助于对Nd:GdVO4激光动力学过程的深入了解,为实际激光系统和器件的优化设计提供理论参考。
Laser-diode (LD)-pumped solid-state laser combines the advantages of semiconductor laser with those of solid-state laser. It has important applications in civil and military fields, and has become a new generation of coherent source of high quality. In particular, much attention has been paid to the LD end-pumped solid-state laser owing to its compactness, high conversion efficiency and good mode. In order to provide effective theoretical guidelines for experimental design, it is very necessary to theoretically study in detail the performance of LD end-pumped solid-state laser. In the theoretical models previously reported, there are some obvious limitations in the procedure of calculations for laser behaviors and thermal effects. In the present thesis, we developed a theoretical method for simulating LD end-pumped continuous wave (CW) lasers. Taking a newer laser crystal Nd:GdVO4 as the laser medium, we presented numerical simulations on the LD end-pumped CW Nd:GdVO4 laser and the thermal effects in the crystal, and discussed the cavity parameters influencing the laser operation with a view to optimizing laser performance. The thesis consists of the four parts: as follows
Firstly, numerical simulations on end-pumped 1063 nm (four-level system) CW Nd:GdVO4 laser without consideration of thermal effects.
In this part, we presented a more reasonable theoretical model for end-pumped CW laser, in which the rate equations and propagation equations have been employed, and the point-by-point iteration method has been used to numerically solve these equations. Since the propagation equations could demonstrate the spatial evolutions of the pump and the laser powers in the cavity, our model will be applicable to both low- and high-gain lasers.
With this theoretical model the performance of end-pumped 1063 nm CW Nd:GdVO4 laser was numerically simulated. The good agreement between the calculated and the published experimental data validated our theoretical model. In addition, we investigated the influences on laser performance from some parameters including the reflectivity of output coupler, the spot size of laser beam and the crystal length, and the optimum parameter values were obtained. The optimum output reflectivity R2 opt is a decreasing function of the incident pump power; the optimum spot-size ratioαopt between the laser and pump beams is an increasing function of the incident power, and under higher pump power it is larger than unity; the optimum crystal length lo pt for Nd:GdVO4 hardly changes with the incident power.
Secondly, theoretical calculations on thermal effect in LD end-pumped CW Nd:GdVO4 laser.
At first we introduced the theoretical methods for thermal effect in laser medium. And then taking Nd:GdVO4 as an example, we calculated the thermal effects in 1063 nm laser, including numerically solving the steady-state heat-conduction equation by the finite difference method to obtain temperature distribution in the crystal, with the temperature distribution calculating the optical path difference generating when the cavity mode passing through the medium, determining the thermal lens focal length by fitting the optical path difference to a parabolic reference surface, with the Strehl intensity ratio estimating the thermally-induced diffraction loss. From the calculated results, one can see the influences of some parameters, such as incident pump power, spot sizes of pump and laser beams, focal position of pump beam and so on, on the thermal effects, from which some methods for mitigating thermal effects were inspired. A larger waist radius of pump beam can effectively mitigate thermal effects in the crystal; Shift of pump beam focus from the surface into interior of the medium can reduce the end-face temperature; diminishing of the spot size of laser cavity mode especially less than that of pump beam is helpful to reduce the thermally induced diffraction loss and to improve laser beam quality; uniformity of transverse intensity distribution of pump beam through reshaping can also relieve thermal effects.
Thirdly, numerical simulations on high-power LD end-pumped 1063 nm CW Nd:GdVO4 laser by considering thermal effects.
For high-power LD-pumped solid-state lasers, the thermal effects in laser medium are the main limitation factor for stepping up output power. Therefore, it is crucial to include thermal effects into theoretical studies of this kind of laser. In this part, we presented a more reasonable calculation method considering thermal effects for simulating high-power LD end-pumped CW lasers. The advantage of our model is the entire considerations for the pump absorption saturation and the interactions between thermal effects and laser oscillation. As a result, it is applicable to both the case of lasing including three-level and four-level systems and the case of nonlasing.
With this theoretical model we simulated the performance of high-power LD end-pumped 1063 nm CW Nd:GdVO4 laser, and meanwhile we obtained the results of thermal effects. The calculated results and the published experimental data agreed well with each other. In order to provide guidelines for resonator design, we investigated the input-output characteristics for different cavity lengths. It is found that a too short or long cavity is not favorable to achieve higher-efficient laser output. Also we investigated the relationship between the optimum spot-size ratio ( )ωsωpaopt and the incident pump power with and without thermal effects included. It can be seen that ( )ωsωpaopt without thermal effects included is an increasing function of the pump power and it is larger than unity for slightly high pump power. In contrast, ( )ωsωpaoptincluding thermal effects is a decreasing function of pump power and it is less than unity for slightly high pump power.
Fourthly, numerical simulations on LD end-pumped 912 nm (quasi-three-level system) CW Nd:GdVO4 laser.
According to the characteristics of a quasi-three-level system, some changes have to been made in the theoretical model included thermal effects. Here we investigated the case that the pump beam passes twice through laser medium. Because of the lower efficiency for 912 nm laser, the heat generation in the medium cannot be completely attributed to the quantum defect. Therefore, according to the definition of the laser extraction efficiencyηl, we made use of laser intensity and population density to determineηl and hence the fractional thermal loadingηh. Then a numerical simulation on LD end-pumped 912 nm CW Nd:GdVO4 laser was performed. And a good agreement between the calculated results and the published experimental data was achieved. By comparing the calculated results for two-pass pumping with those for one-pass case, it is found that the slope efficiency for the latter was much lower than that for the former. We also calculated the axial and the transverse distributions of the fractional thermal loading, and the results indicated that it is very necessary to calculate in detail the fractional thermal loading for a quasi-three-level system.
The studies in this thesis presented a more reasonable theoretical method for LD end-pumped CW lasers. They are helpful to a better understanding for the kinetic behaviours of CW Nd:GdVO4 laser, and to theoretical guidelines for optimizing design of the practical laser system.
引文
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