文献翻译Effect of defects on long-pulse laser-induced damage of two kinds of optical thin films.docx

Effect of defects on long-pulse laser-induced damage of two kinds of optical thin films两种光学薄膜的缺陷对长脉冲激光造成薄膜的损伤的影响In order to study the effect of defects on the laser-induced damage of different optical thin films, we carried out damage experiments on two kinds of thin films with a 1 ms long-pulse laser. Surface-defect and subsurface-defect damage models were used to explain the damage morphology. The two-dimensional finite element method was applied to calculate the temperature and thermal-stress fields of these two films. The results show that damages of the two films are due to surface and subsurface defects,respectively. Furthermore, the different dominant defects for thin films of different structures are discussed. 激光对缺陷不同的光学薄膜会造成的不同损伤，为了研究，我们用1ms长脉冲激光对两种薄膜进行了实验。我们用表面缺陷和下表面缺陷的损伤模型来解释损伤的形态，用二维有限元法来计算这两种薄膜的温度场和热应力场。结果表明，两种薄膜的损伤分别由表面缺陷和下表面缺陷造成。另外，我们还讨论了不同结构的薄膜的不同主导缺陷。1. Introduction前言Optical coatings are important components in a laser system but are easily damaged. Damage to these components induced by the laser beam limit the output power and energy of the lasers. It is generally believed that defects in films initiate the damage 1. Currently, two damage models, the interfacial layer model and inclusion model, are widely used for film damage analysis. In the interfacial layer model, interface absorption in films, especially in multilayer films, is taken into account for analysis and calculation. The interface absorption is considered to take place at the boundaries between the coating and substrate, air/coating, or film/film interfaces. And the overall interface absorption can be as large or even larger than that in the entire coating volume 24. In the inclusion model, it is believed that defects, such as contaminants, impurities, and void fillers whose size can range from a few to several hundred nanometers, will be included in the film due to the impurity of the raw material and inhomogeneous film growth during the deposition process 5,6. High absorption of laser energy by these inclusions causes film damage. The distribution density, depth, and type of inclusions influence the damage properties. Evidence for the first assumption comes from the fact that laser damage of optical coatings most often occurs in isolated spots. Furthermore, artificial nanoparticles of a known size, depth, and even distribution density are introduced into film coatings for experimental and theoretical studies 710, which were focused on film damage induced by a short pulse laser with a pulse width of nanoseconds and below. Film damage induced by a long-pulse laser with a pulse width of milliseconds was not mentioned.光学镀层是激光系统的重要组成部分，但很容易损伤。激光束会造成这些部件损伤，这会限制激光的输出功率和能量。人们普遍认为，损伤是由薄膜的缺陷造成的1。目前，有两种损伤模型被广泛用于分析膜损伤，即界面层模型和包容模型。在界面层模型中，主要分析和计算薄膜中的吸收界面，特别是多层薄膜中的吸收界面。假设界面吸收发生在镀层和衬底，空气/镀层，或薄膜/薄膜界面之间的边界。并且整体界面的吸收会很大，甚至比在整个镀层的量更大2-4。在包容模型中，人们认为，在沉积过程中像污染物、杂质和几纳米到几百纳米的空隙填充物这样的缺陷，会由于原料中的杂质和薄膜的非均匀生长而进入薄膜中5,6。这些杂质吸收的大量激光能量会导致薄膜损伤。密度分布、深度和内含物的类型会影响损伤的特性。光学薄膜的激光损伤最常发生在孤立点，这证实了第一个假设。此外，薄膜镀层的实验和理论研究已引入了已知大小、厚度和均匀密度的人造纳米颗粒7-10，其侧重于纳秒宽度的短脉冲激光导致的薄膜损伤，如下文。而毫秒宽度的长脉冲激光导致的薄膜损伤则未提及。The long-pulse laser has more and more applications in the field of laser processing because of its advantages of smaller loss during transmission, no plasma shielding, no self-focus, larger pulse energy, and high efficiency of energy coupling. It is significant to develop higher energy output long-pulse lasers and do research on the long-pulse laserinduced damage of optical films. Also, neither the interfacial layer model nor the inclusion model can explain all film damage properties. The interfaciallayer model cannot explain isolated damage spots, while the inclusion model cannot explain the rear surface damage of a substrate induced by the 1 ms long-pulse laser in our experiment. It can be confirmed that laser damage of films is induced by different defects in different situations. However, no study has reported on how to distinguish these situations. In addition, previous researches on the interfacial layer model considered substrate thickness as infinite compared with the film. The interfacial absorption of the rear surface of the substrate was neglected. This neglect was acceptable for high reflection (HR) coatings but was not advisable for other kinds of coatings such as antireflection (AR) coatings. The interfacial absorption of the rear surface of the substrate will be taken into consideration in this paper. The factors that can induce laser damage in films are grouped into two categories. First, the surfaces of the film and substrate can absorb moisture and contaminants during transportation and storage. The surface absorption layers can transform laser energy into heat deposition effectively, and then this leads to damage of the films. This is defined as the surface-defect model. Second, as described in the inclusion model, high absorptive defects included in films are linked to damage of the films. This is defined as the subsurface-defect model.长脉冲激光在传输过程中损耗更小、无等离子体屏蔽、无自聚焦、脉冲能量较大并且能量耦合效率高，这些优点使长脉冲激光越来越多应用在激光加工领域。这对开发输出更高能量的长脉冲激光器和研究光学薄膜的长脉冲激光损伤很有意义。此外，无论是界面层模型，还是包容模型都不能解释所有薄膜的损伤特性。界面层模型不能解释孤立点的损伤，而我们的实验中1ms长脉冲激光对衬底背面造成的损伤，不能用包容模型解释。可以确认的是，薄膜的激光损伤是由不同情况下的不同缺陷造成的。然而，现在还没有如何区分这些情况的研究报告。此外，以往研究界面层模型时，总是拿假设厚度无穷大的衬底与薄膜相比较，忽略掉衬底背面的吸收。可忽略高反射(HR)镀层，但对于其他种类的镀层，如抗反射(AR)涂层，却不可忽略。本文将会考虑衬底背面的吸收。激光引起的薄膜损伤的因素可分为两大类。第一，薄膜和衬底表面在运输和贮存过程中会受潮与污染。表面的吸收层会有效地把激光能量转换成热量积累，这会导致薄膜损伤。这定义为表面缺陷模型。第二，正如包容模型所描述的，薄膜的高吸收性缺陷与薄膜的损伤相关。这被定义为下表面缺陷模型。In the present study, we carried out damage experiments of two different kinds of optical coatings (AR and HR coatings). It is found that damage morphologies of the two films are distinguished from each other easily. Then the surface-defect model and subsurface-defect model were used to explain the damage morphologies of the two films, respectively. The two-dimensional finite element method (FEM) was applied to calculate the temperature and thermal-stress fields. To go further in our study, the problem of which kind of defects actually dominates laser damage for thin films of different structures was discussed.本研究中，我们对两种不同的光学镀层（AR和HR镀层）进行了损伤实验。结果发现，很容易辨别两种薄膜的损伤形态。然后用表面缺陷模型和下表面缺陷模型来分别解释两种薄膜的损伤形态，用二维有限元法（FEM）来计算温度场和热应力场。为了进一步研究，我们将讨论不同结构的薄膜的激光损伤实际上是由哪一种缺陷问题主导的。Fig. 1. Coating structures of the two films.图1 两种薄膜的镀层结构2. Experiment 实验A. Test SamplesThe film coatings used in the experiment were deposited on the substrate of the K9 glass by ion beam sputtering. The substrate was polished at its six surfaces, and its size was 29 mm 15 mm 1.8 mm. Figure 1 shows the coating structures of the two films. Film A Fig. 1(a) is a SiO2/Al2O3 AR coated (0=1064 nm), and film B Fig. 1(b) is a SiO2= TiO2 HR coated (0=635 nm). The two films will be labeled film A and film B, respectively, in the following text.A.测试样本 在实验中使用的薄膜镀层沉积在经离子喷镀的K9玻璃的衬底上。对大小为29mm15mm1.8mm的衬底的六个面进行抛光。图1显示了两种薄膜的镀层结构。薄膜A图1(a)用SiO2/Al2O3 AR镀膜(0=1064 nm)，薄膜B图1(b)用SiO2= TiO2 HR镀膜(0=635 nm)。两种薄膜在下文中将记为薄膜A与薄膜B。B. Experimental SetupOur experimental setup is shown in Fig. 2. It involves a single-mode Nd3+:YAG long-pulse laser beam with a 1064 nm wavelength and 0.52.5 ms pulse duration.The pulse energy delivered can be measured by an energy meter at each shot and varied from 1 to 50 J. In additional to this shot beam, a visible HeNe probe laser beam is used to allow the region under study to be located accurately. The two beams of the Nd3+:YAG shot laser and HeNe probe laser are aligned and can be focused at the test film components. The size and location of the beam focused on the film surface can be controlled by the threedimensional precision displacement platform. In our experiment, the Nd3+:YAG laser pulse duration was fixed at 1 ms and the beam radius focused on the film surface at 350 m. The energy density per surface unit (called the fluence) irradiated on the film was adjusted by changing the single pulse energy.B.实验装置图2为实验装置。这需要一束波长为1064nm、持续时间为0.5-2.5ms的单一模式的Nd3+:YAG长脉冲激光束。从1J到50J的每次发射中，可用能量计测量脉冲传递的能量。在这个附加的发射束中，用可见的He-Ne探测激光束来研究该区域的精确定位。为测试薄膜组件，把两束Nd3+:YAG发射激光对准HeNe激光探头。聚焦在薄膜表面的激光束的大小和位置可以用三维精密位移平台来控制。在我们的实验中，Nd3+:YAG激光脉冲的持续时间固定为1ms，聚焦在薄膜表面的激光束的半径为350m。通过改变单脉冲的能量，可调整照射到单位面积的薄膜上的能量密度（这叫做通量）。Fig. 2. Experimental setup for laser damage of film components.图2 薄膜组件的激光损伤的实验装置C. Damage MorphologyBy using different laser fluences in the damage experiments of films A and B, we can get a series of damage morphologies.C.损伤形态学通过用不同能量密度的激光对薄膜A与薄膜B进行损伤实验，我们可以得到一系列的损伤形态。Figure 3 shows the damage morphologies of film A induced by different laser fluences. The photos were taken from the side of the test samples. The film surface is facing up and the substrate surface is facing down. The laser beam irradiated on the film surface and laser fluence increased from Figs. 3(a)3(c). It was found that both the film surface and the substrate surface of film Awere damaged, while the middleof film A was undamaged. As the laser fluence increased, the damage extended inward from the two surfaces and linked together.图3显示了不同能量密度的激光对薄膜A造成的损伤形态。这是测试样本一侧的照片。薄膜表面朝上，衬底表面朝下。从图3(a)3(c)可看出，激光束照射在薄膜表面并且激光的能量密度增大。结果发现，薄膜表面和Awere薄膜的衬底表面都受损，而薄膜A的中部是完好的。随着激光的能量密度增加，损伤从两表面向内延伸，最后连在一起。Fig. 3. Damage morphologies of film A induced by different laser fluences.图3 不同能量密度的激光对薄膜A造成的损伤形态Figure 4 shows the damage morphologies of film B induced by different laser fluences. The photographs of Figs. 4(a)4(c) were taken from the film surface of the samples, and Fig. 4(d) was taken from the side. Figures 4(a)4(c) showed that the damage of film B first occurred in isolated spots at the laser fluence 114 J/cm2, and the isolated spots gradually connected to a whole as fluence increased. It is widely acknowledged that the morphology of isolated damage spots was caused by the subsurface nanoparticles included in films 11. Observation of damage morphologies from the side showed that there was no cone-shaped damage inside film samples induced by laser fluence 114, 215, and 281 J/cm2. But when the laser fluence increased to 945 J/cm2, coneshaped damage could be found inside see Fig. 4(d). It should be noticed that there was no damage on the back surface of the substrate for film B, which was perceived in film A.图4显示了不同能量密度的激光对薄膜B造成的损伤形态。图4(a)4(c)与图4(d)的照片分别是薄膜样品的表面与侧面。图4(a)4(c)显示，能量密度为114 J/cm2的激光在孤立点对薄膜B造成的损伤。随着能量密度增大，孤立点逐渐与整体连接。人们普遍承认，孤立点的损伤形态是由薄膜下表面中的纳米微粒造成的11。从侧面观察损伤形态，薄膜样品内部没有由能量密度为114，215，和281 J/cm2的激光造成的锥形损伤。但是，当激光能量密度提高到945 J/cm2时，可能就会对内部造成锥形损伤见图4(d)。应当注意到，薄膜B的衬底背面没有损伤，于是认为损伤在薄膜A。Fig. 4. Damage morphologies of film B induced by different laser fluences.图4 不同能量密度的激光对薄膜B造成的损伤形态3. Numerical Computation 数值计算A. Model and Theory To verify that the laser damage of film coatings is initialized by different kinds of defects, it is first necessary to confirm that the film damage is caused by defect absorption rather than intrinsic absorption. So the case that there are not any absorption defects in film coatings (we call it the “perfect model”) is supposed at first. Analysis of the perfect model irradiated by a laser is needed. Then the surface-defect and subsurface-defect models can be investigated for further study.A. 模型与理论为了验证薄膜镀层的激光损伤最先是由不同种类的缺陷造成的，首先要确认薄膜损伤是由缺陷吸收造成的，而不是本征吸收造成的。因此，首先假定薄膜的镀层中没有任何吸收缺陷（我们称之为“完美模型”）。为了再进一步研究表面缺陷模型和下表面缺陷模型，很有必要分析激光照射的完美模型。A scheme of the film model used for our calculation is illustrated in Fig. 5. Because of the axisymmetric property of the laser irradiating film, an axisymmetric model is established. The size of the film and substrate is consistent with that of the actual sample. The material is assumed to be homogeneous and isotropic. Surface convection and heat emission are ignored.图5表示的是我们计算薄膜模型所用的方法。因为照射薄膜的激光成轴对称，所以建立一个轴对称模型。薄膜和衬底的尺寸与实际样品一致。假定材料均匀且和各向同性，忽略表面对流和热辐射。Fig. 5. Scheme of model of film irradiated by a laser.图5 激光照射薄膜的模型方法For the perfect model of film, the flow of heat in the film/substrate system during laser irradiation can be described by the heat conduction equations as follows 2:对于薄膜的完美模型，激光照射期间在薄膜/衬底系统中的热流量可以通过热传导方程描述，如下2：where Eqs. (2) and (3) are boundary conditions and initial condition, respectively. T(r,z, t) is the temperature of location r, z at time t. ci, i, and i, respectively, indicate specific heat, density, and thermal conductivity of layer i. s is the heat conductivity of the substrate. T0 is the ambient temperature, which is 300 K. qi(r, z, t) is the source term and can be expressed as其中方程(2)和(3)分别为边界条件和初始条件。T(r,z, t)表示t时刻在位置R,z的温度。 ci, i和i分别表示比热容，密度和i层的导热系数。s表示衬底的热传导率。T0表示300K的室温。qi(r, z, t)是源项并且可表示为where i is the absorption coefficient of layer i. E(z) indicates the electric field intensity (EFI) distribution in the film/substrate system, which can be obtained from the Maxwell equations and the characteristic matrix of the film. ni is the refractive index of layer i, and I(r, t) is the intensity of the incident laser, which can be written as式中，i表示i层的吸收系数。E(z)表示薄膜/衬底系统的电场强度分布(EFI)，可由麦克斯韦方程和薄膜的特征矩阵推导而得。 ni表示i层的折射率，I(R,T)表示入射激光的强度，它可以写作where f (r) and g(t) are the space and time distributions of the laser beam, respectively. I0 is the peak power density. For the Gaussian beam at the TEM00 mode:其中，f(r)和g(t)分别表示激光束的空间和时间的分布。I0表示峰值功率密度。TEM00模型中的高斯光束表示为：where r0 is the beam radius. And g(t) is taken as其中r0表示光束半径，g(t)取为Here is the pulse width of the laser.这里的表示激光脉冲的宽度。At a certain time of t, the inhomogeneous temperature rise in material will cause thermal stress. The thermoelastic equation is described as 12在某个t时刻，材料的温度非均匀上升会导致热应力。热弹性方程写作12The constitutive relationships are expressed as follows:本构关系可如下表示：The geometric deformation relationships are described as几何形变关系表示为：where =r+ +z, =(r+z)(1 + 2)/, r|r=L=0, uz|z=0,r=L=0, , , and represent the Young modulus, Poisson ratio, and linear coefficient of expansion, respectively. , , and u stand for stress, strain, and displacement, respectively. The subscripts r, z, , and zr indicate the direction of the radius, axis, hoop, and tangential, respectively.其中，=r+ +z, =(r+z)(1 + 2)/, r|r=L=0, uz|z=0,r=L=0, , 和分别表示杨氏模量、泊松比和线性膨胀系数。, 和u分别表示应力、应变和位移。下标r,z,和zr分别表示半径、长度、角度和切向。 Similarly, for the surface-defect model, a strong absorption layer of 50 nm thickness is put on the surfaces of the film and substrate, respectively, without considering subsurface defects, while for the subsurface-defect model, a cylinder high absorption region of 50 nm radius and 50 nm height is introduced into the film without considering the surface absorption layers 6,13.类似地，表面缺陷模型中，把50nm厚的强吸收层分别置于不考虑表面缺陷的薄膜和衬底的表面上。下表面缺陷模型中，把半径50nm和高50nm的柱形高吸收区引入不考虑表面吸收层的薄膜中6,13。B. Results and AnalysisThe FEM is applied to calculate the thermal and stress distribution of the film under the three analytical models. The parameters of films and substrate are summarized in Table 1. In our calculations, the absorption coefficient of surface absorption layers and subsurface defects are 2 orders of magnitude higher than that of the bulk material, while the heat conductivity is 1 order lower 4.B.结果与分析用有限元法计算三个分析模型中薄膜的热和应力的分布。薄膜和衬底的参数列于表1中。在我们的计算中，表面吸收层及下表面缺陷的吸收系数比本体材料高两个数量级，而热导率低一个数量级4。Materials 材料K9SiO2Al2O3TiO2Melting point熔点(K)1673197323132128Tensile strength拉伸强度(MPa)2811025551.6Compressive strength压缩强度(MPa)65015002945688Refractive index折射率1.521.4651.612.609Absorption coefficient吸收系数(m-1)1.181141.72611815905Specific heat比热容J/(kgK)858841880700Thernductivity 导热系数W/(mK)1.51.193511.9Young modulus杨氏模量(GPa)8187375228Poisson ratio 泊松比0.2080.160.220.27Linear expansibility线性膨胀系数(K-1)7.1x10-60.5x10-68.4x10-69x10-6Density 密度(kg/m3)2510250039804000Table 1. Summary of Parameters Used for Calculations and Analysis表1 用于计算与分析的参数汇总1. Film A: Surface-Defect ModelFor the convenience of comparing with the experiment, the laser parameters used for calculations for film A are the same as that marked in Fig. 3(a) with laser fluence 2.7 103 J/cm2. According to the experimental results, in order to investigate the feature of damage morphologies,we pay special attention to the thermal and stress distributions on the surfaces of film and substrate at the end of the laser pulse t = 1 ms. It is assumed that the film sample is damaged if the calculated maximum temperature is bigger than the melting point of the material or the maximum stress exceeds the tensile/compressive strength. The melting point or the tensile/compressive strength of the material is defined as the damage critical value. Figure 6 shows the temperature distribution on the surface of the top layer of film A along the radial direction under the three models, and Fig. 7 shows the thermal-stress distribution, where negative numbers represent compressive stress and positive numbers represent tensile stress. Rear surface distributions of temperature and thermal stress on the substrate are shown in Figs. 8 and 9, respectively.1.薄膜A：表面缺陷模型为了便于与实验对比，用于计算薄膜A的激光参数与图3(a)中能量密度为2.7103J/cm2的激光相同。根据实验结果，为了研究损伤形态的特征，我们要特别注意，在t=1ms时刻激光脉冲末尾处的薄膜和衬底表面上的热和应力的分布。据推测，如果计算出的最高温度大于该材料的熔点，或最大应力超过拉伸/压缩强度，那薄膜样品会损伤。熔点或该材料的拉伸/压缩强度定义为损伤的临界值。图6显示三种模型中沿径向的薄膜A的顶层表面上的温度分布。图7显示热应力分布，其中负值表示压缩应力，正值代表拉伸应力。图8和图9分别显示衬底背面的温度与热应力的分布。Fig. 6. Top layer surface temperature distributions of film A along the radial direction (t =1 ms).图6 沿径向的薄膜A的顶层表面温度的分布(t=1ms)Fig. 7. Top layer surface thermal-stress distributions of film A along the radial direction (t=1ms): (a) perfect model, (b) surface-defect model, and (c) subsurface-defect model.图7 沿径向的薄膜A的顶层表面的热应力分布(t=1ms)：(a)完美的模型，(b)表面缺陷模型，(c)下表面缺陷模型Fig. 8. Substrate surface temperature distributions of film A along the radial direction (t=1 ms).图8 沿径向的薄膜A的衬底表面温度的分布(t=1ms)Fig. 9. Substrate surface thermal-stress distributions of film A along radial direction (t =1 ms): (a) perfect model, (b) surface-