粗糙表面散热模型及其在激光器热分析中的应用
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摘要
本文研究了激光二极管端面泵浦固体激光器中采用金属热沉夹持圆棒晶体散热时的相关热效应问题。实际中，通常采用两块金属热沉夹持圆棒状激光晶体散热，晶体棒与热沉的接触面具有一定的粗糙度。由于圆棒晶体的特殊结构，装配压强在晶体侧面形成不均匀分布，在晶体棒侧面产生非轴对称的接触热导。对于轴对称的高斯型泵浦光分布，晶体棒侧面散热的不均匀导致晶体棒温度呈非轴对称空间分布，在晶体中产生随圆周发生变化的热效应。本文的研究重点是建立圆棒晶体与热沉间的接触散热模型，研究热界面物质厚度、热沉装配压力、晶体棒与热沉接触面粗糙度对二者间接触热导、晶体棒温度空间分布的影响。研究装配压力、泵浦功率、泵浦光半径对晶体棒端面温度非轴对称性的影响。研究装配压力、泵浦功率对出射光波前畸变、光斑形状以及光束质量因子的影响。论文主要内容分为四部分：
第一部分：
在采用两块带有半圆型凹槽的金属热沉夹持圆棒晶体散热结构的中，晶体棒侧面受到热沉装配的压强沿圆周方向发生变化，形成非轴对称分布的接触热导。在截断高斯型粗糙表面模型下，建立了晶体棒与热沉间塑性形变接触热导模型和弹性形变接触热导模型，得到了无热界面物质情况下、采用厚度相当于平均间隙厚度和远大于平均间隙厚度的热界面物质时晶体棒与热沉间的接触热导，提出间隙热导的概念描述晶体棒与热沉的整体接触性能。研究了装配压力、等效均方根粗糙度、等效平均绝对值斜率对晶体棒与热沉间接触热导及晶体棒温度分布的影响。研究结果表明：不采用热界面物质时，在塑性形变接触热导模型和弹性形变接触热导模型下，晶体棒与热沉间接触热导沿圆周角变化较大，接触热导在热沉凹槽底部达到最大，在两块热沉接触面方向最小；装配压力增大、等效均方根粗糙度减小、或等效平均绝对值斜率增大时，晶体棒与热沉间接触热导数值整体变大，沿圆周方向分布的均匀性变差，晶体棒温度整体降低。使用铟箔作为热界面物质时，接触热导及其均匀性得到很大提高，晶体棒温度整体降低，近似呈轴对称分布。
第二部分：
对于采用两块热沉夹持圆棒晶体散热的二极管端面泵浦固体激光器，不采用热界面物质时，晶体棒侧面的接触热导呈非轴对称分布，导致晶体棒温度梯度沿圆周方向发生变化，使得圆棒晶体中的热效应呈椭圆型分布。端面泵浦时，热耗主要集中在晶体棒泵浦端面附近，在截断高斯型粗糙表面模型和塑性形变接触热导模型基础上，主要研究了装配压力、泵浦功率、泵浦光半径对晶体棒端面温度分布非轴对称的影响。针对采用两块热沉夹持晶体散热时，圆棒晶体与热沉空间接触的不均匀性，研究了采用三块、四块热沉来夹持圆棒晶体散热时的热效应问题。研究结果表明：装配压力开始增大时，晶体棒与热沉间接触热导整体提高，而晶体棒侧面接触散热的均匀性变差，使得晶体棒端面同一圆周上的温差起伏变大；装配压力进一步增大，晶体棒侧面不同圆周角处的接触热导足够大时，晶体棒端面温度分布趋于轴对称。泵浦光半径从小变大的过程中，晶体棒端面同一圆周上的最大温差先减小后增大。增加泵浦功率，同一圆周上的温差最大值增大。采用三块热沉夹持圆棒晶体散热时，晶体棒侧面的压强、接触热导及晶体棒端面温度的周向均匀性得到改善，端面中心温度降低，采用四块热沉时，晶体棒侧面接触热导及端面温度沿周向变化最小，端面中心温度最低。
第三部分：
两块热沉夹持圆棒晶体散热时，晶体棒侧面的散热具有非轴对称的空间分布。此时，圆棒晶体温度空间分布呈三维变化，使得晶体中的热效应问题变得复杂。利用有限元方法计算晶体棒温度，从衍射积分理论出发，研究非轴对称的相位分布对激光光场模式的调制，得到激光光场分布，对光斑形状和激光光束质量因子进行研究。研究结果表明：采用两块热沉夹持晶体散热时，波前畸变呈非轴对称分布，中心波前畸变最大，随着半径增大而减小；波前畸变沿圆周方向发生变化，在热沉凹槽底部方向最大，在两块热沉接触面方向最小。装配压力增大，出射光波前畸变整体变小，周向均匀性提高，激光光斑偏圆度降低，热沉装配正侧面的光束质量因子同时减小；泵浦功率增大，波前畸变整体变大，周向均匀性变差，激光光斑偏圆度升高，正侧面的光束质量因子同时变大。采用三块、四块热沉夹持散热时，晶体热效应产生的附加相位具有周向较均匀的分布，激光光斑接近于圆形，光束质量质量因子减小。通过实验研究了采用两块热沉夹持圆棒晶体散热，不采用热界面物质，晶体棒侧面存在不均匀分布的接触热导时的激光光斑形状和光束质量因子。实验测量与理论计算结果基本一致。
This dissertation studys the problem of thermal effect in the laser-diodeend-pumped solid-state laser. In practice, two metal heat sinks are usually used to holdround rod crystal and dissipatie heat. The contact surfaces of crystal and heat sinks areboth rough. Due to the special structure of the crystal, the assembly pressure is unevenlydistributed in the side-face of crystal, which forms the nonaxisymmetric thermal contactconductance in the side face of crystal. In the case of the axisymmetry distribution ofGaussian pumping source, the uneven dissipation of the side face of crystal makes thespatial distribution of temperature in the crystal nonaxisymmetric, and makes thethermal effect change in the circumferential direction. The key contents of this study areto establish the heat-dissipating model of the crystal, to discuss the influences of theassembly force, the performance of the rough surface between the crystal and heat sinksto the thermal contact conductance and the spatial distribution of the temperature in thecrystal. Then discuss the influence of the assembly force, pumping power, and rudias ofthe pumping light to the nonaxisymmetriy of the end face temperature. Study therelationship between the assembly force, the pumping power and the wavefrontdistortion, the laser spot pattern, along with the factors of beam quality of the outputlaser. The main contents of this paper contact four parts:
The first part:
For the special structure of using two heat sinks with half-round groove holding theround rod crystal，the assembly pressure in the side face of the crystal changes in thecircumferential direction, which forms nonaxisymmetric thermal contact conductance inthe side face of crystal. Under the model of the truncated-Gaussian rough surface, thethermal contact conductance models of plastic-deformation and elastic-deformation areestablished. Under this circumstance, three kinds of thermal contact conductance modelare established, including not using thermal interface material, using thermal interfacematerial with its thickness equal to the average thickness of the gap and using thermalinterface material with its thickness much thicker than the thickness of the gap. And theconcept of the gap thermal conductanse is proposed to describe the contant performanceof the crystal and heat sinks. The influences of the assembly force, the equivalentroot-mean-square (RMS) roughness and the equivalent mean-absolute slope on thermalcontact conductance and the spatial distribution of the temperature are discussed. Theresults show that without using thermal interface material, the thermal contact conductance between the crystal and the heat sinks changes significantly in thecircumferential direction, which reaches a maximum point on the bottom of the grooveand a minimum point on the direction of the contact areas of the heat-sink couple usingthe thermal contact conductance models of plastic-deformation and elastic-deformation.With the assembly force increasing, the equivalent root-mean-square roughnessdecreasing or the equivalent mean-absolute surface slope increasing, the thermal contactconductance gets larger but more nonuniform, and the temperature of the crystal rodreduces. When the indium foil is used as thermal interface material, the thermal contactconductance gets larger and more uniform, the temperature of the crystal rod reduces aswell and its distribution becomes axisymmetric.
The second part:
For the LD end-pumped solid-state laser working with round-rod material holdedby two heat sinks, the thermal contant conductance in the side face of the crystalpresents nonaxisymmetric without using thermal interface material. It causes thegradient of the temperature in the crystal to change in the circumferential direction andthe thermal effect of the crystal to be elliptic distribution. In the case of end-pumping,the heat consumption is mainly near the pumped end-face of the crystal. Using themodels of the truncated-Gaussian rough surface and the thermal contact conductance ofplastic-deformation, the effect of assembly force, the pumping power, and the rudias ofthe pumping source to the nonaxisymmetriy of the end face temperature is studied. Inorder to improve the spatial uniformity of the contact between the crystal and the heatsinks in the case of using two heat sinks, the methods of using three or four heat sinks tohold crystal to dissipate heat is proposed. The results show that when the assembly forcegets larger，the thermal contact conductance between the crystal and heat sinks becomeslarger overall, and the uniformity of thermal contact conductance gets worse, whichcause the fluctuation of the temperature in the same concyclic in the end face of thecrystal to get larger. As the assembly force gets larger further, the value of the thermalcontact conductance gets much larger, and the distribution of the temperature in thecrystal tends to become axial symmetry. As the pumping radius becomes larger, thefluctuation of the temperature on the same concyclic firstly gets smaller, and then getslarger. When the pumping power increases, the fluctuation of the temperature on thesame concyclic gets larger. In the method of using three heat sinks, the uniformity of thepressure、the thermal contact conductance and the distribution of temperature inside thecrystal is greatly improved, and the central value of the end-face temperature is reducedat the same time. Using four heat sinks, the result is best and the temperature in the center of end-face becoems lowest.
The third part:
In the case of using two heat sinks to hold the crystal and dissipate heat, the spatialdistribution of heat-dissipating of the crystal is nonaxisymmetric. The temperature ofthe crystal changes in three directions, and the thermal effect in the crystal becomesvery complex. The finite element method is used to calculate the temperature whilethere is nonuniform thermal contact conductance between the crystal and the heat sinksin the side face of crystal. Under the theory of the diffraction integral, the modulation ofthe nonaxisymmetrical phase to the models of optical field is studied, and thedistribution of optical field is obtained. The laser spot pattern and the factors of beamquality are stuied. The results show that the distribution of the wavefront distortion isnonaxisymmetrical, which decreases as the the radius increase and have a maximumpoint in the center. The wavefront distortion changes in the circumferential direction,which reaches a maximum point on the bottom of the heat-sink groove and a minimumpoint in the direction of the contact areas of the heat-sink couple. As the assembly forceincreases, the wavefront distortion gets smaller and more uniform, and the partialroundness of the laser spot gets smaller. Otherwise, the factors of beam quality in twodirection of X and Y decrease at the same time. While the pumping power increases, thewavefront distortion gets larger and more nonuniform, and the partial roundness of thelaser spot gets larger. The factors of beam quality in two directions of X and Y decreaseat the same time. In the method of using three or four heat sinks to hold the crystal rod,the additional phase caused by thermal effect presents the uniform distribution in thecircumferential direction. Under this circumstance, the laser spot pattern is close to acircular spot, and the factors of beam quality in two directions of X and Y decreaseconsiderably. Through the experiment of using two heat sinks holding crystal in thecase of not using thermal interface material, the laser spot pattern and the factors ofbeam quality are stuied when there is nonuniform thermal contact conductance betweenthe crystal and the heat sinks. The experimental results in and theoretical calculationresults are basically the same.
第一部分：
在采用两块带有半圆型凹槽的金属热沉夹持圆棒晶体散热结构的中，晶体棒侧面受到热沉装配的压强沿圆周方向发生变化，形成非轴对称分布的接触热导。在截断高斯型粗糙表面模型下，建立了晶体棒与热沉间塑性形变接触热导模型和弹性形变接触热导模型，得到了无热界面物质情况下、采用厚度相当于平均间隙厚度和远大于平均间隙厚度的热界面物质时晶体棒与热沉间的接触热导，提出间隙热导的概念描述晶体棒与热沉的整体接触性能。研究了装配压力、等效均方根粗糙度、等效平均绝对值斜率对晶体棒与热沉间接触热导及晶体棒温度分布的影响。研究结果表明：不采用热界面物质时，在塑性形变接触热导模型和弹性形变接触热导模型下，晶体棒与热沉间接触热导沿圆周角变化较大，接触热导在热沉凹槽底部达到最大，在两块热沉接触面方向最小；装配压力增大、等效均方根粗糙度减小、或等效平均绝对值斜率增大时，晶体棒与热沉间接触热导数值整体变大，沿圆周方向分布的均匀性变差，晶体棒温度整体降低。使用铟箔作为热界面物质时，接触热导及其均匀性得到很大提高，晶体棒温度整体降低，近似呈轴对称分布。
第二部分：
对于采用两块热沉夹持圆棒晶体散热的二极管端面泵浦固体激光器，不采用热界面物质时，晶体棒侧面的接触热导呈非轴对称分布，导致晶体棒温度梯度沿圆周方向发生变化，使得圆棒晶体中的热效应呈椭圆型分布。端面泵浦时，热耗主要集中在晶体棒泵浦端面附近，在截断高斯型粗糙表面模型和塑性形变接触热导模型基础上，主要研究了装配压力、泵浦功率、泵浦光半径对晶体棒端面温度分布非轴对称的影响。针对采用两块热沉夹持晶体散热时，圆棒晶体与热沉空间接触的不均匀性，研究了采用三块、四块热沉来夹持圆棒晶体散热时的热效应问题。研究结果表明：装配压力开始增大时，晶体棒与热沉间接触热导整体提高，而晶体棒侧面接触散热的均匀性变差，使得晶体棒端面同一圆周上的温差起伏变大；装配压力进一步增大，晶体棒侧面不同圆周角处的接触热导足够大时，晶体棒端面温度分布趋于轴对称。泵浦光半径从小变大的过程中，晶体棒端面同一圆周上的最大温差先减小后增大。增加泵浦功率，同一圆周上的温差最大值增大。采用三块热沉夹持圆棒晶体散热时，晶体棒侧面的压强、接触热导及晶体棒端面温度的周向均匀性得到改善，端面中心温度降低，采用四块热沉时，晶体棒侧面接触热导及端面温度沿周向变化最小，端面中心温度最低。
第三部分：
两块热沉夹持圆棒晶体散热时，晶体棒侧面的散热具有非轴对称的空间分布。此时，圆棒晶体温度空间分布呈三维变化，使得晶体中的热效应问题变得复杂。利用有限元方法计算晶体棒温度，从衍射积分理论出发，研究非轴对称的相位分布对激光光场模式的调制，得到激光光场分布，对光斑形状和激光光束质量因子进行研究。研究结果表明：采用两块热沉夹持晶体散热时，波前畸变呈非轴对称分布，中心波前畸变最大，随着半径增大而减小；波前畸变沿圆周方向发生变化，在热沉凹槽底部方向最大，在两块热沉接触面方向最小。装配压力增大，出射光波前畸变整体变小，周向均匀性提高，激光光斑偏圆度降低，热沉装配正侧面的光束质量因子同时减小；泵浦功率增大，波前畸变整体变大，周向均匀性变差，激光光斑偏圆度升高，正侧面的光束质量因子同时变大。采用三块、四块热沉夹持散热时，晶体热效应产生的附加相位具有周向较均匀的分布，激光光斑接近于圆形，光束质量质量因子减小。通过实验研究了采用两块热沉夹持圆棒晶体散热，不采用热界面物质，晶体棒侧面存在不均匀分布的接触热导时的激光光斑形状和光束质量因子。实验测量与理论计算结果基本一致。
This dissertation studys the problem of thermal effect in the laser-diodeend-pumped solid-state laser. In practice, two metal heat sinks are usually used to holdround rod crystal and dissipatie heat. The contact surfaces of crystal and heat sinks areboth rough. Due to the special structure of the crystal, the assembly pressure is unevenlydistributed in the side-face of crystal, which forms the nonaxisymmetric thermal contactconductance in the side face of crystal. In the case of the axisymmetry distribution ofGaussian pumping source, the uneven dissipation of the side face of crystal makes thespatial distribution of temperature in the crystal nonaxisymmetric, and makes thethermal effect change in the circumferential direction. The key contents of this study areto establish the heat-dissipating model of the crystal, to discuss the influences of theassembly force, the performance of the rough surface between the crystal and heat sinksto the thermal contact conductance and the spatial distribution of the temperature in thecrystal. Then discuss the influence of the assembly force, pumping power, and rudias ofthe pumping light to the nonaxisymmetriy of the end face temperature. Study therelationship between the assembly force, the pumping power and the wavefrontdistortion, the laser spot pattern, along with the factors of beam quality of the outputlaser. The main contents of this paper contact four parts:
The first part:
For the special structure of using two heat sinks with half-round groove holding theround rod crystal，the assembly pressure in the side face of the crystal changes in thecircumferential direction, which forms nonaxisymmetric thermal contact conductance inthe side face of crystal. Under the model of the truncated-Gaussian rough surface, thethermal contact conductance models of plastic-deformation and elastic-deformation areestablished. Under this circumstance, three kinds of thermal contact conductance modelare established, including not using thermal interface material, using thermal interfacematerial with its thickness equal to the average thickness of the gap and using thermalinterface material with its thickness much thicker than the thickness of the gap. And theconcept of the gap thermal conductanse is proposed to describe the contant performanceof the crystal and heat sinks. The influences of the assembly force, the equivalentroot-mean-square (RMS) roughness and the equivalent mean-absolute slope on thermalcontact conductance and the spatial distribution of the temperature are discussed. Theresults show that without using thermal interface material, the thermal contact conductance between the crystal and the heat sinks changes significantly in thecircumferential direction, which reaches a maximum point on the bottom of the grooveand a minimum point on the direction of the contact areas of the heat-sink couple usingthe thermal contact conductance models of plastic-deformation and elastic-deformation.With the assembly force increasing, the equivalent root-mean-square roughnessdecreasing or the equivalent mean-absolute surface slope increasing, the thermal contactconductance gets larger but more nonuniform, and the temperature of the crystal rodreduces. When the indium foil is used as thermal interface material, the thermal contactconductance gets larger and more uniform, the temperature of the crystal rod reduces aswell and its distribution becomes axisymmetric.
The second part:
For the LD end-pumped solid-state laser working with round-rod material holdedby two heat sinks, the thermal contant conductance in the side face of the crystalpresents nonaxisymmetric without using thermal interface material. It causes thegradient of the temperature in the crystal to change in the circumferential direction andthe thermal effect of the crystal to be elliptic distribution. In the case of end-pumping,the heat consumption is mainly near the pumped end-face of the crystal. Using themodels of the truncated-Gaussian rough surface and the thermal contact conductance ofplastic-deformation, the effect of assembly force, the pumping power, and the rudias ofthe pumping source to the nonaxisymmetriy of the end face temperature is studied. Inorder to improve the spatial uniformity of the contact between the crystal and the heatsinks in the case of using two heat sinks, the methods of using three or four heat sinks tohold crystal to dissipate heat is proposed. The results show that when the assembly forcegets larger，the thermal contact conductance between the crystal and heat sinks becomeslarger overall, and the uniformity of thermal contact conductance gets worse, whichcause the fluctuation of the temperature in the same concyclic in the end face of thecrystal to get larger. As the assembly force gets larger further, the value of the thermalcontact conductance gets much larger, and the distribution of the temperature in thecrystal tends to become axial symmetry. As the pumping radius becomes larger, thefluctuation of the temperature on the same concyclic firstly gets smaller, and then getslarger. When the pumping power increases, the fluctuation of the temperature on thesame concyclic gets larger. In the method of using three heat sinks, the uniformity of thepressure、the thermal contact conductance and the distribution of temperature inside thecrystal is greatly improved, and the central value of the end-face temperature is reducedat the same time. Using four heat sinks, the result is best and the temperature in the center of end-face becoems lowest.
The third part:
In the case of using two heat sinks to hold the crystal and dissipate heat, the spatialdistribution of heat-dissipating of the crystal is nonaxisymmetric. The temperature ofthe crystal changes in three directions, and the thermal effect in the crystal becomesvery complex. The finite element method is used to calculate the temperature whilethere is nonuniform thermal contact conductance between the crystal and the heat sinksin the side face of crystal. Under the theory of the diffraction integral, the modulation ofthe nonaxisymmetrical phase to the models of optical field is studied, and thedistribution of optical field is obtained. The laser spot pattern and the factors of beamquality are stuied. The results show that the distribution of the wavefront distortion isnonaxisymmetrical, which decreases as the the radius increase and have a maximumpoint in the center. The wavefront distortion changes in the circumferential direction,which reaches a maximum point on the bottom of the heat-sink groove and a minimumpoint in the direction of the contact areas of the heat-sink couple. As the assembly forceincreases, the wavefront distortion gets smaller and more uniform, and the partialroundness of the laser spot gets smaller. Otherwise, the factors of beam quality in twodirection of X and Y decrease at the same time. While the pumping power increases, thewavefront distortion gets larger and more nonuniform, and the partial roundness of thelaser spot gets larger. The factors of beam quality in two directions of X and Y decreaseat the same time. In the method of using three or four heat sinks to hold the crystal rod,the additional phase caused by thermal effect presents the uniform distribution in thecircumferential direction. Under this circumstance, the laser spot pattern is close to acircular spot, and the factors of beam quality in two directions of X and Y decreaseconsiderably. Through the experiment of using two heat sinks holding crystal in thecase of not using thermal interface material, the laser spot pattern and the factors ofbeam quality are stuied when there is nonuniform thermal contact conductance betweenthe crystal and the heat sinks. The experimental results in and theoretical calculationresults are basically the same.
引文
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