傳輸矩陣的Matlab簡易編程o

n0=1;%n0為空氣折射率a0=0;%初始入射角為0，即正入射n1=1.444;n2=1.7514;d1=3.4886;d2=4.6373;d=1.55;p1=2*pi*n1*d1/d;p2=2*pi*n2*d2/d;u0=4*pi*1e-7;%真空磁導率e0=1e-9/(36*pi);%真空介電常數b=sqrt(e0/u0);c1=b*n1;%波阻抗c2=b*n2;c0=b*n0;c00=b*n0;A1=cos(p1);B1=-i*sin(p1)/c1;C1=-i*c1*sin(p1);D1=cos(p1);M1=[A1B1;C1D1];%介質1的傳輸矩陣A2=cos(p2);B2=-i*sin(p2)/c2;C2=-i*c2*sin(p2);D2=cos(p2);M2=[A2B2;C2D2];%介質2的傳輸矩陣M=M1*M2;%兩個介質層的總傳輸矩陣A=M(1,1);B=M(1,2);C=M(2,1);D=M(2,2);r=(A*c0+B*c0*c00-C-D*c00)/(A*c0+B*c0*c00+C+D*c00)%反射系數t=(2*c0)/(A*c0+B*c0*c00+C+D*c00)%透射系數R=r*conj(r)T=t*conj(t)以上可作為TE波和TM波的一特列，即垂直入射n0=1;%n0為空氣折射率a0=input('請輸入入射角a0:');%初始入射角n1=input('請輸入介質1的折射率n1:');n2=input('請輸入介質2的折射率n2:');d1=input('請輸入介質1的厚度d1:');d2=input('請輸入介質2的厚度d2:');d=input('請輸入入射光波長d:');a1=asin(n0*sin(a0)/n1);%光在介質1中的傳播角度a2=asin(n1*sin(a1)/n2);%光在介質2中的傳播角度a3=asin(n2*sin(a2)/n0);%射出介質時的出射角p1=2*pi*n1*d1*cos(a1)/d;%相位厚度p2=2*pi*n2*d2*cos(a2)/d;u0=4*pi*1e-7;%真空磁導率e0=1e-9/(36*pi);%真空介電常數b=sqrt(e0/u0);c1=b*n1*cos(a1);%波阻抗c2=b*n2*cos(a2);c0=b*n0*cos(a0);c00=b*n0*cos(a3);A1=cos(p1);B1=-i*sin(p1)/c1;C1=-i*c1*sin(p1);D1=cos(p1);M1=[A1B1;C1D1];%介質1的傳輸矩陣A2=cos(p2);B2=-i*sin(p2)/c2;C2=-i*c2*sin(p2);D2=cos(p2);M2=[A2B2;C2D2];%介質2的傳輸矩陣M=M1*M2;%兩個介質層的總傳輸矩陣A=M(1,1);B=M(1,2);C=M(2,1);D=M(2,2);r=(A*c0+B*c0*c00-C-D*c00)/(A*c0+B*c0*c00+C+D*c00)%反射系數t=(2*c0)/(A*c0+B*c0*c00+C+D*c00)%透射系數R=r*conj(r)T=t*conj(t)以上為TE波的例子。若為TM波則，只有波阻抗表達不同，即：n0=1;%n0為空氣折射率a0=input('請輸入入射角a0:');%初始入射角n1=input('請輸入介質1的折射率n1:');n2=input('請輸入介質2的折射率n2:');d1=input('請輸入介質1的厚度d1:');d2=input('請輸入介質2的厚度d2:');d=input('請輸入入射光波長d:');a1=asin(n0*sin(a0)/n1);%光在介質1中的傳播角度a2=asin(n1*sin(a1)/n2);%光在介質2中的傳播角度a3=asin(n2*sin(a2)/n0);%射出介質時的出射角p1=2*pi*n1*d1*cos(a1)/d;%相位厚度p2=2*pi*n2*d2*cos(a2)/d;u0=4*pi*1e-7;%真空磁導率e0=1e-9/(36*pi);%真空介電常數b=sqrt(e0/u0);c1=b*n1/cos(a1);%波阻抗c2=b*n2/cos(a2);c0=b*n0/cos(a0);c00=b*n0/cos(a3);A1=cos(p1);B1=-i*sin(p1)/c1;C1=-i*c1*sin(p1);D1=cos(p1);M1=[A1B1;C1D1];%介質1的傳輸矩陣A2=cos(p2);B2=-i*sin(p2)/c2;C2=-i*c2*sin(p2);D2=cos(p2);M2=[A2B2;C2D2];%介質2的傳輸矩陣M=M1*M2;%兩個介質層的總傳輸矩陣A=M(1,1);B=M(1,2);C=M(2,1);D=M(2,2);r=(A*c0+B*c0*c00-C-D*c00)/(A*c0+B*c0*c00+C+D*c00)%反射系數t=(2*c0)/(A*c0+B*c0*c00+C+D*c00)%透射系數R=r*conj(r)T=t*conj(t)若入射光中TE波，TM波都存在且TE占e%比例，TM占m%比例，則計算方法如下：n0=1;%n0為空氣折射率e=input('請輸入e:');m=input('請輸入m:');a0=input('請輸入入射角a0:');%初始入射角n1=input('請輸入介質1的折射率n1:');n2=input('請輸入介質2的折射率n2:');d1=input('請輸入介質1的厚度d1:');d2=input('請輸入介質2的厚度d2:');d=input('請輸入入射光波長d:');a1=asin(n0*sin(a0)/n1);%光在介質1中的傳播角度a2=asin(n1*sin(a1)/n2);%光在介質2中的傳播角度a3=asin(n2*sin(a2)/n0);%射出介質時的出射角p1=2*pi*n1*d1*cos(a1)/d;%相位厚度p2=2*pi*n2*d2*cos(a2)/d;u0=4*pi*1e-7;%真空磁導率e0=1e-9/(36*pi);%真空介電常數b=sqrt(e0/u0);c1m=b*n1/cos(a1);%波阻抗c2m=b*n2/cos(a2);c0m=b*n0/cos(a0);c00m=b*n0/cos(a3);A1m=cos(p1);B1m=-i*sin(p1)/c1m;C1m=-i*c1m*sin(p1);D1m=cos(p1);M1m=[A1mB1m;C1mD1m];%介質1中TM的傳輸矩陣A2m=cos(p2);B2m=-i*sin(p2)/c2m;C2m=-i*c2m*sin(p2);D2m=cos(p2);M2m=[A2mB2m;C2mD2m];%介質2中TM的傳輸矩陣Mm=M1m*M2m;%兩個介質層的TM的總傳輸矩陣Am=Mm(1,1);Bm=Mm(1,2);Cm=Mm(2,1);Dm=Mm(2,2);rm=(Am*c0m+Bm*c0m*c00m-Cm-Dm*c00m)/(Am*c0m+Bm*c0m*c00m+Cm+Dm*c00m)%TM的反射系數和透射系數tm=(2*c0m)/(Am*c0m+Bm*c0m*c00m+Cm+Dm*c00m)Rm=rm*conj(rm)Tm=tm*conj(tm)%計算TM波的反射率和透射率c1e=b*n1*cos(a1);%波阻抗c2e=b*n2*cos(a2);c0e=b*n0*cos(a0);c00e=b*n0*cos(a3);A1e=cos(p1);B1e=-i*sin(p1)/c1e;C1e=-i*c1e*sin(p1);D1e=cos(p1);M1e=[A1eB1e;C1eD1e];%介質1中TE的傳輸矩陣A2e=cos(p2);B2e=-i*sin(p2)/c2e;C2e=-i*c2e*sin(p2);D2e=cos(p2);M2e=[A2eB2e;C2eD2e];%介質2中TE的傳輸矩陣Me=M1e*M2e;%兩個介質層的TE的總傳輸矩陣Ae=Me(1,1);Be=Me(1,2);Ce=Me(2,1);De=Me(2,2);re=(Ae*c0e+Be*c0e*c00e-Ce-De*c00e)/(Ae*c0e+Be*c0e*c00e+Ce+De*c00e)%TE的反射系數和透射系數te=(2*c0e)/(Ae*c0e+Be*c0e*c00e+Ce+De*c00e)Re=re*conj(re)Te=te*conj(te)%計算TM波的反射率和透射率R=(e*Re+m*Rm)/(e+m)T=(e*Te+m*Tm)/(e+m)用傳輸矩陣計算周期性光子晶體的反射和透射的簡易編程:n0=1;%n0為空氣折射率a0=0;%初始入射角為0，即正入射d1=3.4886;d2=4.6373;n1=1.444;n2=1.7514;d=1.55;p1=2*pi*n1*d1/d;p2=2*pi*n2*d2/d;u0=4*pi*1e-7;%真空磁導率e0=1e-9/(36*pi);%真空介電常數b=sqrt(e0/u0);c1=b*n1;%波阻抗c2=b*n2;c0=b*n0;c00=b*n0;A1=cos(p1);B1=-i*sin(p1)/c1;C1=-i*c1*sin(p1);D1=cos(p1);M1=[A1B1;C1D1];%介質1的傳輸矩陣A2=cos(p2);B2=-i*sin(p2)/c2;C2=-i*c2*sin(p2);D2=cos(p2);M2=[A2B2;C2D2];%介質2的傳輸矩陣s=0;forN=1:1:200M=(M1*M2)^N;%介質層的總傳輸矩陣A=M(1,1);B=M(1,2);C=M(2,1);D=M(2,2);r=(A*c0+B*c0*c00-C-D*c00)/(A*c0+B*c0*c00+C+D*c00