Integration will not compute
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Hello, ive already asked this question, but im still confused and my code STILL won't compute the integral. Ive tried for a few hours now and still nothing. My problem is that P2 does not actually compute anything. Comment if you know what i can do. Thanks.
%%%%%%%%%%%Parameters %%%%%%%%%%%%
n0 = 1; %air
n1 = 1.4; %layer 1
n2 = 2.62; %layer 2
n3 = 3.5; %silicon
L0 = 650*10^(-9); %centre wavelength
L1 = 200*10^(-9): 10*10^(-9): 2200*10^(-9); %lambda from 200nm to 2200nm
x = ((pi./2).*(L0./L1)); %layer phase thickness
r01 = ((n0 - n1)./(n0 + n1)); %reflection coefficient 01
r12 = ((n1 - n2)./(n1 + n2)); %reflection coefficient 12
r23 = ((n2 - n3)./(n2 + n3)); %reflection coefficient 23
t01 = ((2.*n0)./(n0 + n1)); %transmission coefficient 01
t12 = ((2.*n1)./(n1 + n2)); %transmission coefficient 12
t23 = ((2.*n2)./(n2 + n3)); %transmission coefficient 23
Q1 = [1 r01; r01 1]; %Matrix Q1
Q2 = [1 r12; r12 1]; %Matrix Q2
Q3 = [1 r23; r23 1]; %Matrix Q3
%%%%%%%%%%%%Graph of L vs R %%%%%%%%%%%
R = zeros(size(x));
for i = 1:length(x)
P = [exp(j.*x(i)) 0; 0 exp(-j.*x(i))]; %General Matrix P
T = ((1./(t01.*t12.*t23)).*(Q1*P*Q2*P*Q3)); %Transmission
T11 = T(1,1); %T11 value
T21 = T(2,1); %T21 value
R(i) = ((abs(T21./T11))^2).*100; %Percent reflectivity
end
%%%%%%%%%%%Power Calculation %%%%%%%%%%
syms L; %General lamda
y = ((pi./2).*(L0./L)); %Layer phase thickness with variable Lamda
P1 = [exp(j.*y) 0; 0 exp(-j.*y)]; %Matrix P with variable Lambda
T1 = ((1./(t01.*t12.*t23)).*(Q1*P1*Q2*P1*Q3)); %Transmittivity matrix T1
I = ((6.16^(15))./((L.^(5)).*exp(2484./L) - 1)); %Blackbody Irradiance
Tf11 = T1(1,1); %New T11 section of matrix with variable Lambda
Tf2 = (((abs(1./Tf11))^2).*(n3./n0)); %final transmittivity
P1 = Tf2.*I; %Power before integration
L_initial = 200*10^(-9); %Lambda initial
L_final = 2200*10^(-9); %Lamba final
P2 = int(P1, L, L_initial, L_final) %Power
plot(L1,R)
title('Percent Reflectance vs. wavelength for 2 Layers')
xlabel('Wavelength (m)')
ylabel('Reflectance (%)')
1 Comment
John D'Errico
on 11 Nov 2016
If you don't understand the last answer to your last question, that is not a valid reason to repost the same question anew.
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