高斯光束的matlab仿真

1、題目：根據(jù)高斯光束數(shù)學模型，模擬仿真高斯光束在諧振腔中某一位置處的歸一化強度分布并給出其二維、三維強度分布仿真圖；用Matlab讀取實際激光光斑照片中所記錄的強度數(shù)據(jù)（讀取照片中光斑的一個直徑所記錄的強度數(shù)據(jù)即可，Matlab讀取照片數(shù)據(jù)命令為imread）,用該數(shù)據(jù)畫出圖片中激光光斑的強度二維分布圖，與之前數(shù)學模型仿真圖對比。（如同時考慮高斯光束光斑有效截面半徑和等相位面特點，仿真高斯光束光強、光斑有效截面半徑以及等相位面同時隨傳播距離z的變化并給出整體仿真圖可酌情加分。）原始光斑如圖1所示，用imread命令讀入matlab后直接用imshow命令讀取即可，圖1 CCD采集的高斯光束強度分

2、布讀入的數(shù)據(jù)是一個224 X 244的矩陣，矩陣中的數(shù)值代表光強分布。用讀入的數(shù)據(jù)取中間一行（122行）畫出強度分布如圖2所示。圖2 實驗測量高斯曲線用理論上的高斯曲線公式畫出理論高斯曲線如圖3所示。圖3 理論高斯曲線M文件如下：A=imread('D:documents作業(yè)激光原理與應用高斯.bmp');A1=A(:,122);x1=1:1:224;x2=-100:1:100;a2=exp(-x2.2/10);figureimshow(A);axis offtitle('fontsize12CCD采集的高斯光束光強分布');figureplot(x2,a2,&

3、#39;linewidth',1,'color','b');axis(-40 40 0 1.2)title('fontsize12實驗測量高斯曲線')figureplot(x1,A1,'linewidth',1,'color','r')title('fontsize12理論高斯曲線')axis(50 200 0 180)畫三維強度分布。取圖片矩陣的中間層，用mesh命令畫出三維圖如圖4所示。圖4 三維強度分布由于讀入的圖片有一行白邊，需要手動去除掉，否則三維圖會有一邊整體豎起

4、來，影響觀察。最終的M文件如下。A=imread('D:documents作業(yè)激光原理與應用高斯.bmp');high, width, color = size(A);x=1:width;y=1:high-1;mesh(x', y', double(A(2:224,:,1); grid onxlabel('x'),ylabel('y'),zlabel('z');title('三維強度分布');再用matlab仿真理論上傳播過程中高斯光束的變化這次先給出M文件：%Gaussian_propagatio

5、n.m%Simulation of diffraction of Gaussian Beamclear;%Gaussian Beam%N:sampling numberN=input('Number of samples(enter from 100 to 500)=');L=10*10-3;Ld=input('wavelength of light in micrometers=');Ld=Ld*10-6;ko=(2*pi)/Ld;wo=input('Waist of Gaussian Beam in mm=');wo=wo*10-3;z_ra

6、y=(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+1 for m=1:N+1 %Space axis x(m)=(m-1)*dx-L/2; y(n)=(n-1)*dx-L/2; %Gaussian Beam in space domain Gau(n,m)=exp(-(x(m)2+y(n)2)/(wo2);%

7、Frequency axis Kx(m)=(2*pi*(m-1)/(N*dx)-(2*pi*(N)/(N*dx)/2; Ky(n)=(2*pi*(n-1)/(N*dx)-(2*pi*(N)/(N*dx)/2; %Free space transfer function H(n,m)=exp(j/(2*ko)*z*(Kx(m)2+Ky(n)2); endend%Gaussian Beam in Frequency domain FGau=fft2(Gau);FGau=fftshift(FGau);%Propagated Gaussian beam in Frequency domain FGau

8、_pro=FGau.*H; %Peak amplitude of the initial Gaussian beam Peak_ini=max(max(abs(Gau);sprintf('Initial peak amplitude is %f mm',Peak_ini)%Propagated Gaussian beam in space domain Gau_pro=ifft2(FGau_pro);Gau_pro=Gau_pro;%Peak amplitude of the propagated Gaussian beam Peak_pro=max(max(abs(Gau_p

9、ro);sprintf('Propagated peak amplitude is %f mm',Peak_pro)%Calculated Beam Width N M=min(abs(x);Gau_pro1=Gau_pro(:,M);N1 M1=min(abs(abs(Gau_pro1)-abs(exp(-1)*Peak_pro);Bw=dx*abs(M1-M)*103;sprintf('Beam width(numerical) is %fmm',Bw)%Theoretical Beam Width W=(2*z_ray)/ko*(1+(z/z_ray)2)

10、;W=(W0.5)*103;sprintf('Beam width(theoretical) is %fmm',W)%axis in mm scale x=x*103;y=y*103;figure(1);mesh(x,y,abs(Gau)title('Initial Gaussian Beam')xlabel('x mm')ylabel('y mm')axis(min(x) max(x) min(y) max(y) 0 1)axis squarefigure(2);mesh(x,y,abs(Gau_pro)title('p

11、ropagated Gaussian Beam')xlabel('x mm')ylabel('y mm')axis(min(x) max(x) min(y) max(y) 0 1)axis square程序主要根據(jù)高斯光束的傳播規(guī)律計算傳播過程中任意z處的高斯光強分布。運行結果：Number of samples(enter from 100 to 500)=500wavelength of light in micrometers=0.568Waist of Gaussian Beam in mm=1ans =Rayleigh range is 5530.972982 mmPropagation length (z) in mm100000ans =Initial peak amplitude is 1.000000 mmans =Propagated peak amplitude is 0.210252 mmans =Beam?width(numerical) is 1.940000mmans =Beam?width(theoretical) i