Z-scan Theory Analysis By Using Gaussian Decomposition Method

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.