FILMS demonstrates thin-film coatings
$$\mathcal{M} = \mathcal{M}_1 \mathcal{M}_2 %%
by Chuck DiMarzio Northeastern University May 2009
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Contents
Set up parameters
lambda=(250:10:2500)*1e-9; % meters, Wide bandwidth to see what happens lambdadesign=500e-9; % Design wavelength n0=1; % Start in air ncoating=1.35; % Magnesium fluoride nt=1.5; % Nominal glass value kdesign=2*pi./lambdadesign; s=pi/2/kdesign/ncoating; % Quarter wave coating %
Compute Reflection as a function of wavelength
rho=zeros(size(lambda)); for nlambda=1:length(lambda); k=2*pi/lambda(nlambda); m=[cos(ncoating*k*s),1i/ncoating*sin(ncoating*k*s);... 1i*ncoating*sin(ncoating*k*s),cos(ncoating*k*s)]; A=m(1,1);B=m(1,2);C=m(2,1);D=m(2,2); rho(nlambda)=(A*n0+B*nt*n0-C-D*nt)/(A*n0+B*nt*n0+C+D*nt); end;
Repeat for ideal coating
ncoating1=sqrt(nt); s1=pi/2/kdesign/ncoating1; % Quarter wave coating rho1=zeros(size(lambda)); for nlambda=1:length(lambda); k=2*pi/lambda(nlambda); m=[cos(ncoating1*k*s1),1i/ncoating1*sin(ncoating1*k*s1);... 1i*ncoating1*sin(ncoating1*k*s1),cos(ncoating1*k*s1)]; A=m(1,1);B=m(1,2);C=m(2,1);D=m(2,2); rho1(nlambda)=(A*n0+B*nt*n0-C-D*nt)/(A*n0+B*nt*n0+C+D*nt); end;
Plot results
fig1=figure;plot(lambda*1e9,abs(rho).^2,'-',... lambda*1e9,abs(rho1).^2,'--');grid on; xlabel('\lambda, Wavelength, nm'); ylabel('R, Reflectivity'); legend('MgFl','Perfect','Location','SouthEast');
