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高斯分解法在Z扫描理论分析中的应用

Z-scan Theory Analysis by Using Gaussian Decomposition Method

【作者】 王奉敏

【导师】 彭慰先;

【作者基本信息】 吉林大学 , 光学, 2006, 硕士

【摘要】 在过去的十年里,Z扫描方法作为测量一些材料非线性光学参数的简单精确方法而被广泛应用。Z扫描(Z-scan)方法是由Sheik-Bahae等最先提出的,该方法的显著特点是灵敏度高和采用单光束测量,由于在测量过程中要求被测试样品沿单光束传输的光轴方向移动,因而将该方法称之为Z扫描法。它采用单一激光束灵敏地测量光学材料的非线性系数的符号及大小。本文介绍了Z扫描(Z-scan)技术的一般理论和发展,然后用高斯分解法研究了非完美高斯光束的情况,并得到了通过非线性介质后激光束的远场模型。本文分为四个部分:第一部分简要介绍了非线性光学的发展以及Z扫描技术在非线性光学中的应用。第二部分介绍了三阶非线性光学效应和三阶非线性光学系数的测量方法。第三部分详细介绍了Z扫描技术的一般理论和发展,分无非线性吸收和有非线性吸收两种情况来阐述了该理论。第四部分用高斯分解法研究了近高斯光束入射情况下的Z扫描理论,并且给出了距样品出射面任意距离D的变形光束的电场模型。还将近高斯光束的Z扫描理论同纯高斯光束的Z扫描理论进行了对比,从几方面说明了二者的不同,表明近高斯光束的Z扫描理论具有更普遍的适用性。

【Abstract】 Mansoor Sheik Bahae introduced a high sensitive single-beamZ-scan technique in 1989. It requires relatively simple experimentalapparatus and simple analysis. Z-scan technique has been widelyemployed since it was reported. Now, it has become an importantmethod used in studying the nonlinear optical characteristics.This thesis introduces the general theory and its development ofZ-scan technique from two aspects. We study the near-Gaussianincident beam Z-scan theory by using Gaussian decomposition method,and give the electric field pattern of the distorted beam at any desireddistance D from the exit plane of the sample. Therefore, the near-Gaussian incident beam Z-scan theory and the pure-Gaussian incidentbeam Z-scan theory are compared from several aspects. It is concludedthat the near-Gaussian incident beam Z-scan theory can be widelyemployed.First this thesis introduced general theory. It supposes circularity-Gaussian incident beam(TEM00). The electric field of a circularity-Gaussian beam is given by.Thecomplex electric field of the beam at the exit plane of the sample isdecomposed into a sum of Gaussian beams through a Taylor expansionof e i( z,r,t). Each beam is propagated to the plane. Finally all thesebeams are summed to reconstruct the far field pattern of the resultingbeam. E a ( r,t)= E(z,r=0,t)e? α L2?[ ( )]∑?Φ???? ??+????∞m = mmmmmmiRrikrm0 i 0 !z , t?? 0exp?2222θ, The variationbetween peak and valley can be got from the normalized Z-scanmeasured curve, and using the formulae ?Τ p ?v≈0 .406(1?S)0.25??0,and ?? 0 =( 2πλ)γI 0(1?e?αL )α, the nonlinear refractive index ofthe sample γ(m2/w) can be calculated.But the beams produced by most laser systems are not perfectGaussians but contain also a small amount of higher-ordermodes(TEMlm). In this thesis the Gaussian decomposition method isemployed, which is introduced by Weaire et al. and further developedby Sheik-Bahae et al. According to the method, complex electric fieldof the beam at the exit plane of the sample is decomposed into a sumof Gaussian beams with decreasing waist dimensions through a Taylorexpansion of the induced phase shift. Each individual Gaussian beamis propagated far away from the sample and finally all these beams aresummed to reconstruct the far field pattern of the resulting beam. FirstThe electric field of a near-Gaussian beam is given byE ( x,y,z,t)= c0 E0(x,y,z,t)+εEh(x,y,z,t), =∑lmEh xyztclmElmxyzt,( ,,,)(,,,)Where Ek is a sum over the higher-order Hermite–Gaussian modes;E0(x, y, z, t) is the zero-order Gaussian mode(TEM00). Then theelectric field pattern at the exit plane of the sample is decomposd to alinear combination of Hermite–Gaussian modes through the Gaussiandecomposition method and the electric field pattern of the distortedbeam at any desired distance D from the exit plane of the sample canbe obtained.In this thesis the near-Gaussian incident beam Z-scan theory andthe pure-Gaussian incident beam Z-scan theory are compared. Sincethe beams produced by most laser systems are not perfect Gaussiansbut contain also a small amount of higher-order modes(TEMlm), thenear-Gaussian incident beam Z-scan theory are more widelyemployed.

【关键词】 Z扫描高斯分解近高斯光束三阶非线性
  • 【网络出版投稿人】 吉林大学
  • 【网络出版年期】2006年 10期
  • 【分类号】O437
  • 【被引频次】8
  • 【下载频次】398
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