how measure the Reflection and refraction coefficient by using MATLAB the user will be asked to enter how many layers does he want and the MATLAB code will measure the Reflection and refraction coefficient. In addition,

function []=TransferMatrix3()

%TransferMatrix3 calculates transmission, reflection and absorption of a multilayer of planar homogenous films %inputs: %angle of incidence: thetai %wavelength of incident light: lambda %thicknesses of the layers: h %refractive index of the layers: n (may be absorbing and dispersive, but this may require a subfunction) %polarization: s or p (need one calculation for each for unpolarized light)

clear all close all

thetai=0:0.1:90; %angle of incidence (degrees) lambda=670; %vacuum wavelength (nm) h=[NaN,50,NaN,NaN]; %film thicknesses in nm, equal in length to n, start and end with NaN pol=1; %polarization, 1 for p and 0 for s n=[1.52,sqrt(Au(lambda)),1.4,1.33]; %refractive index data, NaN for frequency dependence ds=0:10:100; %film thicknesses

for b=1:length(ds) h(3)=ds(b); for a=1:length(thetai) [FR(a,b),FT(a,b),FA(a,b)]=Fresnel(lambda,thetai(a),h,n,pol); end disp([num2str(b/length(ds)*100) '% done...']) end

%plot results: figure hold on plot(thetai,FT,'b') plot(thetai,FR,'r') plot(thetai,FA,'g') xlim([thetai(1),thetai(length(thetai))]) ylim([0 1]) xlabel('incident angle (degrees)') ylabel('Fresnel coefficient') title('Fresnel coefficients for transmission (blue), reflection (red) and absorption (green)')

end

function [FR,FT,FA]=Fresnel(lambda,thetai,h,n,pol)

%Snell's law: theta(1)=thetai*pi/180; for a=1:length(n)-1 theta(a+1)=real(asin(n(a)/n(a+1)*sin(theta(a))))-1i*abs(imag(asin(n(a)/n(a+1)*sin(theta(a))))); end

%Fresnel coefficients: if pol==0 %formulas for s polarization for a=1:length(n)-1 Fr(a)=(n(a)*cos(theta(a))-n(a+1)*cos(theta(a+1)))/(n(a)*cos(theta(a))+n(a+1)*cos(theta(a+1))); Ft(a)=2*n(a)*cos(theta(a))/(n(a)*cos(theta(a))+n(a+1)*cos(theta(a+1))); end elseif pol==1 %formulas for p polarization for a=1:length(n)-1 Fr(a)=(n(a)*cos(theta(a+1))-n(a+1)*cos(theta(a)))/(n(a)*cos(theta(a+1))+n(a+1)*cos(theta(a))); Ft(a)=2*n(a)*cos(theta(a))/(n(a)*cos(theta(a+1))+n(a+1)*cos(theta(a))); end end

%phase shift factors: for a=1:length(n)-2 delta(a)=2*pi*h(a+1)/lambda*n(a+1)*cos(theta(a+1)); end

%build up transfer matrix: M=[1,0;0,1]; %start with unity matrix for a=1:length(n)-2 M=M*1/Ft(a)*[1,Fr(a);Fr(a),1]*[exp(-1i*delta(a)),0;0,exp(1i*delta(a))]; end M=M*1/Ft(length(n)-1)*[1,Fr(length(n)-1);Fr(length(n)-1),1];

%total Fresnel coefficients: Frtot=M(2,1)/M(1,1); Fttot=1/M(1,1);

%special case of single interface: if length(n)==2 Frtot=Fr(1); Fttot=Ft(1); end

%total Fresnel coefficients in intensity: FR=(abs(Frtot))^2; FT=(abs(Fttot))^2*real(n(length(n))*cos(theta(length(n))))/real(n(1)*cos(theta(1))); FA=1-FR-FT;

end

function epsilon=Au(lambda)

%analytical formula for gold based on wavelength in nm, fits J&C data: epsiloninf=1.54; lambdap=143; gammap=14500; A1=1.27; lambda1=470; phi1=-pi/4; gamma1=1900; A2=1.1; lambda2=325; phi2=-pi/4; gamma2=1060;

%other parameters, worse fit to J&C but seems more accurate often: %epsiloninf=1.53; %lambdap=155; %gammap=17000; %A1=0.94; %lambda1=468; %phi1=-pi/4; %gamma1=2300; %A2=1.36; %lambda2=331; %phi2=-pi/4; %gamma2=940;

for a=1:length(lambda) epsilon(a)=epsiloninf-1/(lambdap^2*(1/lambda(a)^2+1i/(gammap*lambda(a))))... +A1/lambda1*(exp(phi1*1i)/(1/lambda1-1/lambda(a)-1i/gamma1)+exp(-phi1*1i)/(1/lambda1+1/lambda(a)+1i/gamma1))... +A2/lambda2*(exp(phi2*1i)/(1/lambda2-1/lambda(a)-1i/gamma2)+exp(-phi2*1i)/(1/lambda2+1/lambda(a)+1i/gamma2)); end

end

[Jozef Kudelcik]

Super program

Answer 1

[Default]

Dear mohamed shafiq

I used your code and simulated it but i can not get the figure of FR (blue) and FT (red)? Could you help me to solve this problem?

Thank you very much

Best Regards

[vasanth kumar]

Hi dear Mohamed,

Did you able to solve your request brother.

[Marco A. Acevedo Z.]

%mohamed shafiq on 9 Nov 2015

% https://au.mathworks.com/matlabcentral/answers/253888-how-measure-the-reflection-and-refraction-coefficient-by-using-matlab-the-user-will-be-asked-to-ente

function []=TransferMatrix3()

%TransferMatrix3 calculates transmission, reflection and absorption of a multilayer of planar homogenous films

%inputs:

%angle of incidence: thetai

%wavelength of incident light: lambda

%thicknesses of the layers: h

%refractive index of the layers: n (may be absorbing and dispersive, but this may require a subfunction)

%polarization: s or p (need one calculation for each for unpolarized light)

clear all

close all

thetai=0:0.1:90; %angle of incidence (degrees)

lambda=670; %vacuum wavelength (nm)

h=[NaN,50,NaN,NaN]; %film thicknesses in nm, equal in length to n, start and end with NaN

pol=1; %polarization, 1 for p and 0 for s

n=[1.52,sqrt(Au(lambda)),1.4,1.33]; %refractive index data, NaN for frequency dependence

ds=0:10:100; %film thicknesses

for b=1:length(ds)

h(3)=ds(b);

for a=1:length(thetai)

[FR(a,b),FT(a,b),FA(a,b)]=Fresnel(lambda,thetai(a),h,n,pol);

end

disp([num2str(b/length(ds)*100) '% done...'])

end

%plot results:

figure

hold on

plot(thetai,FT,'b')

plot(thetai,FR,'r')

plot(thetai,FA,'g')

xlim([thetai(1),thetai(length(thetai))])

ylim([0 1])

xlabel('incident angle (degrees)')

ylabel('Fresnel coefficient')

title('Fresnel coefficients for transmission (blue), reflection (red) and absorption (green)')

end

function [FR,FT,FA]=Fresnel(lambda,thetai,h,n,pol)

% Snell's law:

theta(1)=thetai*pi/180;

for a=1:length(n)-1

theta(a+1)=real(asin(n(a)/n(a+1)*sin(theta(a))))-1i*abs(imag(asin(n(a)/n(a+1)*sin(theta(a)))));

end

% Fresnel coefficients:

if pol==0 %formulas for s polarization

for a=1:length(n)-1

Fr(a)=(n(a)*cos(theta(a))-n(a+1)*cos(theta(a+1)))/(n(a)*cos(theta(a))+n(a+1)*cos(theta(a+1)));

Ft(a)=2*n(a)*cos(theta(a))/(n(a)*cos(theta(a))+n(a+1)*cos(theta(a+1)));

end

elseif pol==1 %formulas for p polarization

for a=1:length(n)-1

Fr(a)=(n(a)*cos(theta(a+1))-n(a+1)*cos(theta(a)))/(n(a)*cos(theta(a+1))+n(a+1)*cos(theta(a)));

Ft(a)=2*n(a)*cos(theta(a))/(n(a)*cos(theta(a+1))+n(a+1)*cos(theta(a)));

end

end

% phase shift factors:

for a=1:length(n)-2

delta(a)=2*pi*h(a+1)/lambda*n(a+1)*cos(theta(a+1));

end

% build up transfer matrix:

M=[1,0;0,1]; %start with unity matrix

for a=1:length(n)-2

M=M*1/Ft(a)*[1,Fr(a);Fr(a),1]*[exp(-1i*delta(a)),0;0,exp(1i*delta(a))];

end

M=M*1/Ft(length(n)-1)*[1,Fr(length(n)-1);Fr(length(n)-1),1];

% total Fresnel coefficients:

Frtot=M(2,1)/M(1,1);

Fttot=1/M(1,1);

% special case of single interface:

if length(n)==2

Frtot=Fr(1); Fttot=Ft(1);

end

% total Fresnel coefficients in intensity:

FR=(abs(Frtot))^2;

FT=(abs(Fttot))^2*real(n(length(n))*cos(theta(length(n))))/real(n(1)*cos(theta(1)));

FA=1-FR-FT;

end

function epsilon=Au(lambda)

%analytical formula for gold based on wavelength in nm, fits J&C data:

epsiloninf=1.54;

lambdap=143;

gammap=14500;

A1=1.27;

lambda1=470;

phi1=-pi/4;

gamma1=1900;

A2=1.1;

lambda2=325;

phi2=-pi/4;

gamma2=1060;

% %other parameters, worse fit to J&C but seems more accurate often:

% epsiloninf=1.53;

% lambdap=155;

% gammap=17000;

% A1=0.94;

% lambda1=468;

% phi1=-pi/4;

% gamma1=2300;

% A2=1.36;

% lambda2=331;

% phi2=-pi/4;

% gamma2=940;

for a=1:length(lambda)

epsilon(a)=epsiloninf-1/(lambdap^2*(1/lambda(a)^2+1i/(gammap*lambda(a))))...

+A1/lambda1*(exp(phi1*1i)/(1/lambda1-1/lambda(a)-1i/gamma1)+exp(-phi1*1i)/(1/lambda1+1/lambda(a)+1i/gamma1))...

+A2/lambda2*(exp(phi2*1i)/(1/lambda2-1/lambda(a)-1i/gamma2)+exp(-phi2*1i)/(1/lambda2+1/lambda(a)+1i/gamma2));

end

end