高斯光束的mb仿真

1、题目：根据高斯光束数学模型，模拟仿真高斯光束在谐振腔中某一位置处 的归一化强度分布并给出其二维、三维强度分布仿真图；用Matlab读取 实际激光光斑照片中所记录的强度数据（读取照片中光斑的一个直径所记 录的强度数据即可，Matlab读取照片数据命令为imread），用该数据画出 图片中激光光斑的强度二维分布图，与之前数学模型仿真图对比。（如同 时考虑高斯光束光斑有效截面半径和等相位面特点，仿真高斯光束光强、 光斑有效截面半径以及等相位面同时随传播距离z的变化并给出整体仿真 图可酌情加分。）原始光斑如图1所示，用imread命令读入matlab后直接用imshow命令 读取即可，图1 CCD采集

2、的高斯光束强度分布读入的数据是一个224 X 244的矩阵，矩阵中的数值代表光强分布。用读 入的数据取中间一行（122行）画出强度分布如图2所示。图2实验测量高斯曲线用理论上的高斯曲线公式画出理论高斯曲线如图3所示。图3理论高斯曲线M文件如下：A=imread（D:documents作业、激光原理与应用、高斯.bmp）;A1=A（:,122）;x1=1:1:224;x2=-100:1:100;a2二exp（-x2.“2/10）;figureimshow(A);axis offtitle(fontsize12CCD采集的高斯光束光强分布);figureplot(x2,a2, linewidth

3、,1, color ,b);axis(-40 40 0 1.2)title(fontsize(12实验测量高斯曲线)figureplot(x1,A1, linewidth ,1, color ,r)title(fontsize12理论高斯曲线)axis(50 200 0 180)画三维强度分布。取图片矩阵的中间层，用mesh命令画出三维图如图4所示。图4三维强度分布由于读入的图片有一行白边，需要手动去除掉，否则三维图会有一边整体竖起来，影响观察。最终的M文件如下。A=imread(D:documents作业、激光原理与应用、高斯.bmp);high, width, color = size(A

4、);x=1:width;y=1:high-1;mesh(x, y, double(A(2:224,:,1);grid on xlabel(x),ylabel(y),zlabel(z);title(三维强度分布)；再用matlab仿真理论上传播过程中高斯光束的变化这次先给出M文件：%Gaussian_propagation.m%Simulation of diffraction of Gaussian Beam clear;%Gaussian Beam%N:sampling numberN=input(Number of samples(enter from 100 to 500)=);L=10

5、*10-3;Ld二input(wavelength of light in micrometers)；Ld二Ld*10、6;ko=(2*pi)/Ld;wo=input(Waist of Gaussian Beam in mm=)； wo=wo*10 -3;z_ray=(ko*wo2)/2*103;sprintf(Rayleigh range is %f mm ,z_ray) z_ray=z_ray*10 -3;z=input(Propagation length (z) in mm);z=z*10 -3;%dx:step size dx=L/N;for n=1:N+1for m=1:N+1%S

6、pace axisx(m) = (m-1)*dx-L/2;y(n) = (n-1)*dx-L/2;%Gaussian Beam in space domainGau(n,m)=exp(-(x(m) 2+y(n) 2)/(wo 2);%Frequency axisKx(m) = (2*pi*(mT)/(N*dx)-(2*pi*(N)/(N*dx)/2;Ky(n) = (2*pi*(nT)/(N*dx)-(2*pi*(N)/(N*dx)/2;%Free space transfer functionH(n,m)=exp(j/(2*ko)*z*(Kx(m)“2+Ky(n)“2);endend%Gau

7、ssian Beam in Frequency domainFGau=fft2(Gau);FGau二fftshift(FGau);%Propagated Gaussian beam in Frequency domainFGau_pro=FGau.*H;%Peak amplitude of the initial Gaussian beamPeak_ini=max(max(abs(Gau);sprintf(lnitial peak amplitude is %f mm,Peak_ini)%PropagatedGaussian beam in space domainGau_pro=ifft2(

8、FGau_pro);Gau_pro=Gau_pro;%Peak amplitude of the propagated Gaussian beamPeak_pro=max(max(abs(Gau_pro);sprintf(Propagated peak amplitude is %fmm,Peak_pro)%Calculated Beam WidthN M=min(abs(x);Gau_pro1=Gau_pro(:,M);N1 M1=min(abs(abs(Gau_pro1)-abs(exp(-1)*Peak_pro);Bw二dx*abs(M1-M)*103;sprintf(Beam widt

9、h(numerical) is %fmm,Bw)%Theoretical BeamWidthW=(2*z_ray)/ko*(1+(z/z_ray)“2);W=(W0.5)*103;sprintf(Beam width(theoretical) is %fmm,W)%axis in mm scalex=x*103;y=y*103;figure(1);mesh(x,y,abs(Gau)title(lnitial Gaussian Beam)ylabel(y mm)axis(min(x) max(x) min(y) max(y) 0 1) axis square figure(2);mesh(x,y

10、,abs(Gau_pro)title(propagated Gaussian Beam)xlabel(x mm)ylabel(y mm)axis(min(x) max(x) min(y) max(y) 0 1)axis square程序主要根据高斯光束的传播规律计算传播过程中任意z处的高斯光强分 布。运行结果：Number of samples(enter from 100 to 500)=500 wavelength of light in micrometers=0.568Waist of Gaussian Beam in mm=1 ans =Rayleigh range is 5530.972982 mmPropagation length (z) in mm100000 ans =Initial peak amplitude is 1.000000 mm ans =Propagated peak amplitude is 0.210252 mm ans =Beam?width(numerical) is 1.940000mm ans =Beam?width(theoretical) is 18.107635mm 束腰半径处的理想高斯光强分布传播1m处的理想高斯光强分布传