【作者】 刘祥志；

【导师】 卢霏；

【作者基本信息】 山东大学 ， 无线电物理， 2008， 博士

【摘要】 离子注入作为一种制备光波导的有效技术，具有在任意温度下对离子注入的剂量和深度可以精确控制，从而改变材料表面性质的优越性，引起了人们的广泛关注。迄今为止，利用该技术在光学晶体、玻璃、半导体和有机聚合物等光学材料上形成光波导结构方面取得了重要进展。由于折射率分布对于确定离子注入型光波导的性质有着至关重要的作用，因此对其折射率分布的确定显得尤其重要。为此人们提出了多种确定折射率分布的方法，如反射率计算方法(reflectivity calculation method，RCM)，参数折射率重构方法(parameterized index profile reconstruction，PIPR)和反向Wentzel-Kramer-Brillouin方法(iWKB)。其中RCM方法假设一个由高斯函数结合线性函数的折射率分布模型，按该折射率分布模型对光波导进行分层，调整函数参数，计算光在层与层之间界面上发生的反射和折射，使计算出的模式值和实验测得的导模的模式值(通常使用棱镜耦合方法测量)误差最小，就认为该折射率分布为实际存在的折射率分布。PIPR方法与其类似．，也是将折射率分布用线性函数和指数函数进行描述，调整函数参数使计算出的模式值和实验得到的模式值偏差最小，该折射率分布就认为是波导中实际的折射率分布。iWKB方法则是从量子力学原理出发，通过渐变型曲线的参数调整使计算出的模式值和实验测得的导模的模式有效折射率误差最小，就认为此曲线所代表的折射率分布就是波导的实际折射率分布。其中iWKB方法由于其使用渐变函数描述折射率分布，决定了该方法适用于分析内(外)扩散形成的波导，扩散形成的波导其折射率分布随着深度的变化是逐步改变的，但对于外延生长、离子注入形成的波导，由于其折射率分布改变比较剧烈，特别是位垒的出现，使用iWKB方法将会带来较大误差。RCM和PIPR对于改变比较剧烈的折射率分布比较合适，一般将其用来分析离子注入型波导的折射率分布。以上三种方法的共同特点就是假设折射率分布，通过计算出的模式有效折射率和实验测得的进行比较，确定实际的折射率分布曲线。为了达到较小的误差，一般要求在光波导上测量到的模式阶数不小于三。既然常规的确定折射率分布的方法要求模式阶数不小于三，探索出一种在导模阶数低于二，甚至在单模情况下仍然能够确定光波导折射率分布的方法具有重要意义。本文中将尝试使用数值分析方法来解决该问题。光束传播法(Beam Propagation Method，BPM)由于其概念清晰、基础技术易于实现和掌握，能够仿真计算复杂几何形状的光学器件性质而在光电子器件计算机辅助设计(Computer Aided Design，CAD)方面得到广泛应用，基于此技术的众多商业仿真软件得到开发和推广，尝试将该数值分析计算技术引入到离子注入型光波导的折射率分布和其它离子注入型光波导所特有的物理现象的研究具有重要的理论价值和应用前景。虽然利用光束传播法可以仿真计算光线在离子注入型光波导中的传播过程，但为了确定出单模光波导的折射率分布，需要对仿真计算出的结果和实验结果进行相似度比较，这就涉及到数字图像处理的相关内容。本文使用欧几里德(Euclid)距离来衡量两幅灰度图的相似程度，实践中采用的是其数学变形表达式：其中：Sim(m，s)为相似程度，N为灰度级别，对于灰度图，其值为255，m_i和s_i分别为实验测量和仿真计算得到的灰度图中第i阶灰度直方图值，P为仿真计算中所选颜色空间的样点数。本文数值分析的理论基础为BPM和数字图像处理技术，通过它们仿真计算出离子注入型单(双)模条形(平面)光波导的折射率分布，同时尝试使用数值分析技术设计条形波导的离子注入参数，研究离子注入型光波导所特有的物理现象，并分析其物理机理。主要结果如下：在MeV能级通过重离子注入铌酸锂已经成功制备出了折射率增加型的条形和平面光波导，而且其模式为单模(1539 nm)或双模(633 nm)，长期以来一直找不到一个在不破坏样品的情况下确定出波导折射率分布的方法。本文提出了光强计算方法(Intensity Calculation Method，ICM)确定单模条形和平面波导的折射率分布，该方法使用光束传播法仿真光线在波导中的传输过程，将仿真计算出的光强图和实验获得的光强图进行数字图像分析比较，精确确定出单模平面(条形)波导的折射率分布。该方法可以推广到分析其它离子注入型单模波导的折射率分布，这对于分析离子注入型光波导的物理性质及对其进行应用开发具有重要意义。在633 nm下，对多能量氧离子注入铌酸锂进行棱镜耦合测量，发现其为双模波导，同时使用端面耦合发现光强图中两模式耦合在一起，无法区分开，这样无法再使用确定单模情况下铌酸锂波导中折射率分布的ICM方法，需要提出新的方法来确定该类光波导的折射率分布。在本论文中，提出了一种基于折射率分布理论模型的数值计算方法来确定双模光波导的折射率分布。通过该折射率分布模型，调整模型参数，对不同参数下折射率分布所对应模式的有效折射率进行数值计算，计算出的模式有效折射率和实验测得的模式有效折射率的方差最小时所对应的折射率分布模型即认为是光波导中实际的折射率分布。一般情况下离子注入型光波导的损伤分布情况可以通过SRIM(The Stoppingand Range of Ions in Matter)软件能够仿真计算出来，并且通过ICM方法能够确定条形波导在离子注入方向的折射率分布，在折射率分布已知的情况下，利用数值计算方法对不同宽度下的条形波导在宽度方向上的模式分布情况进行仿真计算，最后对仿真计算结果和实验测量出的结果进行比较，发现计算值和实际测得的数据吻合较好，这为将来设计光波导的注入条件进行了有益的尝试。在离子注入形成的光波导中观察到一些比较特别的物理现象，比如奇异模(Strange Mode)和双位垒(Double Barrier)，对于这些现象，科研工作者相继提出了一些模型进行解释。对于奇异模现象，科研人员提出的模型认为是由晶体损伤区的主光位垒(the main nuclear damage optical barrier)旁存在一个小的光势阱(thesubsidiary optical well)造成的。本论文中尝试从损伤分布曲线出发，建立理论模型，使用数值计算方法验证该模型是否能有奇异模的存在。对离子注入铌酸锂晶体，注入离子的种类、能量和剂量不同会在注入后的晶体内部出现双位垒现象，在使用传统方法RCM计算结果的基础上，利用数值计算方法BPM计算在该双位垒型光波导中存在的模式有效折射率，将其和棱镜耦合实验测得的进行比较，方差较小时所对应的折射率分布曲线即认为是双位垒现象下离子注入晶体形成的光波导的折射率分布曲线。通过比较RCM和数值计算结果所对应的误差，发现数值计算方法能进一步提高RCM计算结果的精度。更多还原

【Abstract】 Ion implantation, as an outstanding method to modify the surface property of materials, is confirmed to be an effective method for fabricating various waveguide structures. Up to now, many waveguide structures have been formed by ion implantation in most optical materials such as optical crystals, glass, semiconductors and polymers etc.Since the refractive index distribution plays a critical role in determine the natureof optical waveguides, the reconstruction of refractive index profile （RIP） is animportant goal of scientific research. For this reason, scientists have made a variety ofmethods to determine the refractive index distribution, such as reflectance calculationmethod （RCM）, the parameterized index profile reconstruction （PIPR） andinverse-Kramer-Brillouin-Wentzel method （iWKB）. RCM, which combined aGaussian function with a linear function, assumes the model of refractive indexdistribution in waveguide firstly and then the waveguide is divided layer by layeraccording to the refractive index distribution model. By adjusting function parameters,the reflection and refraction between the layers are calculated. For a given set of curveparameters, a numerical routine is used to calculate the corresponding waveguidemode indices. A numerical optimization technique is then used to adjust theparameters of the RIP such that the sum of the square of the errors between measured（usually measured using coupling prism-module） and calculated mode indices isminimized. The result corresponding to the minimum error is believed to describe thereal RIP in waveguide. PIPR assumed that the surface index change due to theimplantation is described by a straight line, and the index barrier is approximated bytwo half Gaussians. Then the free parameters are adjusted to best match the measuredmode indices. The PIPR and RCM have some similarity. Both assume that thewaveguide index profile can be described approximately by two half-Gaussian curves.RCM and PIPR are ideally suitable for the following cases, such as epitaxial growth,and ion implanted waveguides, in which the index profile has a steep index function, even an optical barrier. The iWKB method is typically used to determine RIP showing a monotic index change of optical waveguide from the measured mode indices and cannot be applied to characterize waveguides formed by ion implantation. The iWKB has been proved to be remarkably accurate in some cases, such as in-diffused or ion-exchanged waveguides in which the index is gradually changing with penetration depth. In order to achieve smaller error in employing these methods （RCM, PIPR and iWKB）, the number of measured waveguide mode greater than or equal to three is generally required.Since the conventional methods of determining the refractive index distribution are usually applicable to the waveguides with the mode number more than two, to develop a new method which can describe the RIP of waveguide with guiding modes less than two, or even in the case of single-mode waveguides is of great significance. In this dissertation, numerical method has been used to solve this problem.Beam propagation method （BPM）, with clear concept and easy to implement and master, is capable of simulating complex geometry of the optical device in the field of optoelectronic devices. It has been extensively applied in computer-aided design （CAD）. Based on this technology many commercial simulation softwares are developed and promoted. The introduction of numerical analysis to the study of refractive index profile in ion implantation optical waveguide, as well as other waveguide-specific physical phenomena has important theoretical value and application prospects.The BPM can be used to simulate the light propagation process in ion implanted waveguide. However, in order to determine the refractive index profile of single-mode waveguides, the similarity comparison between the results of simulation and experimental measured results is required. It involves the relevant content of digital iImage processing. In this paper, both measured and simulated intensity image are converted into 256-level gray scale ones and every pixel of the image is corresponding to a value between 0 and 255. Two image’s comparability is Euclidean distance defined as Where Ed（m, s） is the Euclidean distance, N is the color orders, for 256-level gray scale image, N is equal to 255, s_i and m_i are the gray scale histogram value of simulated and measured, respectively.In order to express comparability clearly, another equation in percentage described as Eq. （2） is adopted in intensity calculation.Where Sim（m, s） is the comparability value, P is the count of gray levels calculated in the simulation process, else parameters are the same meaning as those in Eq. （1）. If measured and simulated intensity image are identical, the Sim（m, s） is equal to 100%.Based on the BPM and digital image processing technique, numerical method has been used to determine the RIP of single （or double） mode channel （or planar） ion-implantation optical waveguide. Besides those works, numerical method has been used to design the parameters of ion-implantation waveguide, and also applied to investigate some special physics phenomenon of ion-implantation waveguide, such as "strange mode" and "double-barrier" structure. The main results are as follows:Lithium niobate crystal has unique electro-optical, photoelastic, piezoelectric, non-linear properties, and exhibits excellent mechanical and chemical stability. It has been widely used in a variety of integrated optics and active acousto-optical devices, such as modulators, multiplexers, switches, and waveguide amplifiers. In the recent works, it has been reported that the fabrication of channel and planar waveguides in lithium niobate crystal by MeV heavy ion implantation (O²⁺), and the guiding modes of the formed waveguides are single- （1539 nm） or double-mode （633 ran）. Positive changes of n_e refractive index happened in the waveguide region. As is known, the RIP dominates the properties of the waveguide, however the RIP of the single mode channel waveguides formed by ion implantation could not determined by the conventional methods directly. A method （which is named as Intensity Calculation Method （ICM）） is developed to decide the RIP in those waveguides. It can be used to determine the index profile in channel and planar waveguides formed by ion implantation without bringing any damage to the sample. In this dissertation, ICM has been applied to predict the refractive index profile in O² ion-implanted LiNbO₃ （LN） single- and double-mode waveguide successfully. In this method, BPM is applied to simulate the light wave propagates in the optical waveguide. The measured near-field intensity distributions of guiding mode by end-fire out-coupling and that from calculation by BPM are analyzed and compared, the refractive index profile in the channel （or planar） waveguide could be finally obtained based on these analyses.Double-mode planar waveguide was formed by O²⁺ ion implantation at three energies of （3.0, 3.6 and 4.5 MeV） and respective doses of （1.8, 2.2 and 4.8）×10¹⁴ ions/cm2 in vacuum at room temperature. ICM shows some difficulties in dealing with the multimode ion-implanted waveguide simply because the total output intensity cannot be clearly distinguished into each guided modes by our present experimental devices. The extraordinary RIP of a double-mode waveguide will be reconstructed by using BPM combining with Hu’s theoretical model. Through BPM calculation of RIP from Hu’s model, the calculated mode indices of different modes can be obtained. The calculated modes corresponding to the minimum variance of the experimental values of the modes is considered to be the actual distribution of the refractive index in optical waveguides.The damage profile in the ion-implantation optical waveguide can be usually simulated out by SRIM （The Stopping and Range of Ions in Matter） software, while the RIP of ion-implantation single-mode optical waveguide can be determined by the ICM. Once those parameters are well defined, numerical simulation is carried out to simulate lateral mode profiles from channel waveguides with different strip widths. The final results of the simulation and the measured results are compared. The result that the calculated and the actual measured data agree well suggests that the analysis method can be used in the design of the waveguide structure.Some special physical phenomena, such as strange mode and double-barrier have been observed in the waveguides formed by ion implantation. For these phenomena, researchers have made a number of models to explain. Some analyses attribute the "strange mode" to the existence of a subsidiary optical well next to the main nuclear damage optical barrier. They can be observed when measured using varying wavelengths or suffering surface polishing. In this dissertation, numerical calculation method is employed to testify the reasonableness of the existence of "strange modes". The waveguide with double index barriers can be formed by mutli-enregy ion implantation. The RIP in the waveguide is unknown and difficult to reconstruct using the conventional methods mentioned before. In the dissertation a successful analysis is introduced to deal with this problem. A hypothetical index profile based on the lattice damage is firstly assumed, following the RCM is used to calculate the effective modes of waveguide. Meanwhile, the results of BPM numerical calculation for double-barrier-mode optical waveguides can also be obtained. Then the comparison between the calculated values and the measured results by coupling prism is carried out, the parameters corresponding to the smallest variance is believed to describe the actual index distribution in the waveguide. By comparison of RCM and BPM calculation, it is found that the accuracy of the results can be enhanced by additional BPM amendment.更多还原