1-5
用公式(1-54),(1-58)
matlab代码:
a=0:0.01:pi/2,angle=a.*180./pi,
b=asin(a/(1.8-i*7.1)),cp=(1.8-i*7.1)*cos(b), u=real(cp),v=imag(cp),
s=(cos(a)-cp)./(cos(a)+cp),
p=(cp-cos(a).*(u.^2-v.^2+2.*i.*u.*v+sin(a).^2))./(cp+cos(a).* (u.^2- v.^2+2.*i.*u.*v+sin(a).^2)),
Rs=real(s).^2+imag(s).^2,
Rp=real(p).^2+imag(p).^2,
ans=phase(s),anp=phase(p),
plot(angle,Rs, 'r-+',angle,Rp, 'g-d') ,
plot(angle,ans, 'r-+',angle,anp, 'g-d')
加号是Rs,s-光的反射位相,菱形是Rp,p的反射位相,横坐标是入射角
反射率
位相:
1-9
公式(1-73)及下方的计算位相厚度的公式,(1-74),波堆:光程,(1-95)上方的公式
n0=1,nH=2.35,nL=1.38,ng=1.52, inputangle=0,num=[3,5,7],
for n=1:1:2000,
g(n)=(n-1)/1000+0.1,
aH=pi/2*cos(inputangle) /g(n),
aL= pi/2*cos(inputangle)/g(n),
MH=[cos(aH),i*sin(aH)/nH; i*sin(aH)*nH,cos(aH)],
ML=[cos(aL),i*sin(aL)/nL; i*sin(aL)*nL,cos(aL)],
for p=1:1:3
M=(MH*ML)^num(p)*MH*[1;ng],
B=M(1,1),C=M(2,1),
cp=(n0*B-C)/(n0*B+C),
R(p,n)=real(cp).^2+imag(cp).^2
end
end
x=1./g,
plot(x,R)
1-13
用(1-110)公式
n0=1;nh=2.35;nl=1.38;ng=1.52;
Mh=[0,1i/nh;1i*nh,0],Ml=[0,1i/nl;1i*nl,0],
M=cat(2,Mh,Ml,Mh,Ml,Mh),n=cat(2,nh,nl,nh,nl,nh)
G=[1;ng];
D(1)=G(2,1)/G(1,1);
syms x,
syms y,
syms f(x,y),
f(x,y)=x^2+y^2-(abs(D(1))^2+n(1)^2)*x/real(D(1))+n(1)^2,
for i=1:4,
H=G,
G=[M(1,2*i-1),M(1,2*i);M(2,2*i-1),M(2,2*i)]*H, %计算等效基底%
D(1+i)=G(2,1)/G(1,1),
syms g(x,y),
g(x,y)=f(x,y),
f(x,y)=(x^2+y^2-(abs(D(i+1))^2+n(i+1)^2)*x/real(D(1+i))+n(i+1)^2)*g(x,y),
%用乘积的
把多个曲线画在一个图上%
end
figure();
ezplot(f);
grid on;
axis([0,6,-20,20])
2-1
理想增透膜:(1-74)可知:Y=n0,及导纳轨迹最后落到实轴上,且坐标为n0;而半波长层不会影响导纳轨迹终点
n=2.35; ng=1.52;
syms x,
syms y,
syms f(x,y),
f(x,y)=x^2+y^2-(abs(ng)^2+n^2)*x/real(ng)+n^2,
figure();
ezplot(f);
grid on;
axis([1.5,4,-1.5,1.5])
2-3
用的矢量法,把矢量和关于膜厚的二维曲面画出来,然后找到最小值对应的膜厚,范围都是40到220算出 石英: 216,42 玻璃:210,44
缩小范围在这个值附近,并增加步长,算出石英:216.29, 42.01 玻璃 209,44
和参考答案有出入:
n0=1,n1=1.45,n2=2.3,ng=1.45,wave=632.8,
r1=(n0-n1)/(n0+n1),
r2=(n1-n2)/(n1+n2),
r3=(n2-ng)/(n2+ng),
[x,y]=meshgrid(200:0.01:220, 40:0.01:45);
z= abs(r1+ r2*exp(i*4*pi.*x/wave)+ r3*exp(i*(4*pi.*x/wave+4*pi.*y/wave)));
surf(z), [rows,cols]=find(z== min(z(:)))
r=rows, c=cols,
n1d1=x(r,c),n2d2=y(r,c)