how to solve this error ?
In this code, MATLAB gives me the following issue: For the solving function, how can I correct this error?
Error using sym/vpasolve:
Unable to find variables in equations.
Error in ni_water_simulationburgemanforchatgbt (line 99):
`solutions = vpasolve(eq, epsilon_mg, min(epsi, epsh), max(epsi, epsh));`
clear all
lambda = 500*10^-3:10*10^-3:2500*10^-3; % in microns
A1= 1.4182;
B1= 0.021304;
n_pc=sqrt(1+(A1.*lambda.^2)./(lambda.^2-B1));
wp= 15.92; % eV
f0 = 0.096;
Gamma0 = 0.048; % eV
f1 = 0.100;
Gamma1 = 4.511; % eV
omega1 = 0.174; % eV
f2 = 0.135;
Gamma2 = 1.334; % eV
omega2 = 0.582; % eV
f3 = 0.106;
Gamma3 = 2.178; % eV
omega3 = 1.597; % eV
f4 = 0.729;
Gamma4 = 6.292; % eV
omega4 = 6.089; % eV
OmegaP = sqrt(f0) * wp; % eV
eV = 4.13566733e-1 * 2.99792458 ./ lambda;
epsilon = 1 – OmegaP^2 ./ (eV .* (eV + 1i * Gamma0));
epsilon = epsilon + f1 * wp^2 ./ ((omega1^2 – eV.^2) – 1i * eV * Gamma1);
epsilon = epsilon + f2 * wp^2 ./ ((omega2^2 – eV.^2) – 1i * eV * Gamma2);
epsilon = epsilon + f3 * wp^2 ./ ((omega3^2 – eV.^2) – 1i * eV * Gamma3);
epsilon = epsilon + f4 * wp^2 ./ ((omega4^2 – eV.^2) – 1i * eV * Gamma4);
n = real(sqrt(epsilon));
k = imag(sqrt(epsilon));
nMetal = n+1i.*k;
%NWATER
NWATER = 0.0738.*lambda.^6 – 0.6168.*lambda.^5 + 2.0263.*lambda.^4 – 3.3315.*lambda.^3 + 2.8708.*lambda.^2 – 1.2367.*lambda + 1.5411;
nAir=1+0.05792105./(238.0185-(lambda.^(-2)))+0.00167917./(57.362-(lambda.^(-2)));
% permetivity
epsMetal = nMetal.^2;
epsWATER=NWATER.^2;
%parmenter for each axes
%1 specific volume
ni=n_pc;
nt=NWATER;
%angels
thetaI =0; % incidence angle
thetaI = thetaI/180*pi;
beta=20;
beta = beta/180*pi;
fi=0;
fi=fi/180*pi;
%%%%%
a=20*10.^-9;
b=5*10.^-9;
d=2*a*cos(beta);
fi=0.3;
fh=1-fi;
Rpp = [];
Rsp = [];
Rps = [];
Rss = [];
Tpp = [];
Tsp = [];
Tps = [];
Tss = [];
% epsilon for compost materals SHAPE Factor
e= sqrt(1-(b/a)^2);
la=((1-e^.2)/e^2)*((log((1+e)/(1-e)))/2*e^2 -1);
lb=0.5*(1-la);
% Symbolic variable for epsilon_mg
syms epsilon_mg
%%%%%%%%
for i=1:size(lambda,2)
%snel law §
thetaT=asin(ni(i)*sin(thetaI)/nt(i));
k0=2*pi/(lambda(i)*10^-6);
VX=ni(i)*sin(thetaI);
epsi=epsMetal(i);
epsh=epsWATER(i);
% Bruggeman mixing formula
eq = fi * (epsi – epsilon_mg) / (epsilon_mg + la * (epsi – epsilon_mg)) +(1 – fi) * (epsh – epsilon_mg) / (epsilon_mg + lb * (epsh – epsilon_mg)) == 0;
% Solve equation with positive imaginary part
solutions = vpasolve(eq, epsilon_mg, [min(epsi, epsh), max(epsi, epsh)]);
positive_imaginary = solutions(imag(solutions) > 0);
if ~isempty(positive_imaginary)
epsilon_mg = positive_imaginary(1);
else
error(‘No solution with positive imaginary part found at index %d’, i);
end
eps1=epsilon_mg;
eps2=epsilon_mg;
eps3=epsilon_mg;
exx=eps2 +(eps1.*cos(beta).*cos(beta) +eps3.*sin(beta).*sin(beta) -eps2).*cos(fi).*cos(fi);
exy=0.5.*(eps1.*cos(beta).*cos(beta) +eps3.*sin(beta).*sin(beta) – eps2).*sin(2.*fi);
exz=0.5.*(eps3-eps1).*sin(2.*beta).*cos(fi);
eyy=eps2 +(eps1.*cos(beta).*cos(beta) +eps3.*sin(beta).*sin(beta) – eps2).*sin(fi).*sin(fi);
eyz=0.5.*(eps3-eps1).*sin(2.*beta).*sin(fi);
ezz=eps1 +(eps3 -eps1).*cos(beta).*cos(beta);
eyx=exy;
ezx=exz;
ezy=eyz;
del = [-VX.*ezx./ezz 1-(VX.*VX)./ezz -VX.*ezy./ezz 0; exx-(exz.*ezx)./ezz -VX.*exz./ezz exy-exz.*ezy./ezz 0; 0 0 0 1; eyx-(eyz.*ezx)./ezz -VX.*eyz./ezz eyy-(VX.*VX)-(eyz.*ezy)./ezz 0];
P=exp(1)^(1i.*k0.*d.*del);
a1 = ni(i).*(nt(i).*P(1,2)-cos(thetaT).*P(2,2))+cos(thetaI).*(nt(i).*P(1,1)-cos(thetaT).*P(2,1));
a2 = ni(i).*(nt(i).*P(1,2)-cos(thetaT)*P(2,2))-cos(thetaI).*(nt(i).*P(1,1)-cos(thetaT).*P(2,1));
a3 = (nt(i).*P(1,3)-cos(thetaT).*P(2,3))+ni(i).*cos(thetaI).*(nt(i).*P(1,4)-cos(thetaT).*P(2,4));
a4 = (nt(i).*P(1,3)-cos(thetaT).*P(2,3))-ni(i).*cos(thetaI).*(nt(i).*P(1,4)-cos(thetaT).*P(2,4));
a5 = ni(i).*(nt(i).*cos(thetaT).*P(3,2 )-P(4,2)) +cos(thetaI).*(nt(i).*cos(thetaT).*P(3,1)-P(4,1));
a6 = ni(i).*(nt(i).*cos(thetaT).*P(3,2) -P(4,2))-cos(thetaI).*(nt(i).*cos(thetaT).*P(3,1)-P(4,1));
a7 = (nt(i).*cos(thetaT).*P(3,3)-P(4,3))+ni(i).*cos(thetaI).*(nt(i).*P(3,4).*cos(thetaT)-P(4,4));
a8 = (nt(i).*cos(thetaT).*P(3,3)-P(4,3))-ni(i).*cos(thetaI).*(nt(i).*P(3,4).*cos(thetaT)-P(4,4));
b1 = (ni(i).*P(2,2)+cos(thetaI).*P(2,1))./nt(i);
b2 = (ni(i).*P(2,2)-cos(thetaI).*P(2,1))./nt(i);
b3 = (P(2,3)-ni(i).*cos(thetaI).*P(2,4))./nt(i);
b4 = (P(2,3)+ni(i).*cos(thetaI).*P(2,4))./nt(i);
b5 = ni(i).*P(3,2)+cos(thetaI).*P(3,1);
b6 = ni(i).*P(3,2)-cos(thetaI).*P(3,1);
b7 = P(3,3)-ni(i).*cos(thetaI).*P(3,4);
b8 = P(3,3)+ni(i).*cos(thetaI).*P(3,4);
rpp=(a1.*a8-a4.*a5)./(a4.*a6-a2.*a8);
rps=(a3.*a8-a4.*a7)./(a4.*a6-a2.*a8);
rsp=(a2.*a5-a1.*a6)./(a4.*a6-a2.*a8);
rss=(a2.*a7-a6.*a3)./(a4.*a6-a2.*a8);
tpp=b1+b2.*rpp+b3.*rsp;
tps=b4+b2.*rps+b3.*rss;
tsp=b5+b6.*rpp+b7.*rsp;
tss=b8+b6.*rps+b7.*rss;
Rpp = [Rpp (abs(rpp))^2];
Rsp = [Rsp (abs(rsp))^2];
Rps = [Rps (abs(rps))^2];
Rss = [Rss (abs(rss))^2];
Tpp = [Tpp (nt(i) .* cos(thetaI) ./ ni(i) .* cos(real(thetaT))).*(abs(tpp )^2)];
Tss = [Tss (nt(i) .* cos(real(thetaT)) ./ ni(i) .* cos(thetaI)).*(abs(tss )^2)];
Tsp = [Tsp (nt(i) .* cos(real(thetaT)) ./ ni(i) .* cos(thetaI)).*(abs(tsp )^2)];
Tps = [Tps (nt(i) .* cos(real(thetaT)) ./ ni(i) .* cos(thetaI)).*(abs(tps )^2)];
T=(Tpp+Tsp+Tps+Tss)/2;
R=(Rpp+Rsp+Rps+Rss)/2;
A=1-R-T;
end
figure(1)
hold on
plot(lambda*10^3,A*100,’LineWidth’, 3)
hold on
xlabel(‘Wavelength (nm)’,’fontsize’,16)
hold on
ylabel(‘Absorbtion’,’fontsize’, 16)
figure(2)
hold on
plot(lambda*10^3,T*100,’LineWidth’, 3)
hold on
xlabel(‘Wavelength (nm)’,’fontsize’,16)
hold on
ylabel(‘Transmission’,’fontsize’, 16)In this code, MATLAB gives me the following issue: For the solving function, how can I correct this error?
Error using sym/vpasolve:
Unable to find variables in equations.
Error in ni_water_simulationburgemanforchatgbt (line 99):
`solutions = vpasolve(eq, epsilon_mg, min(epsi, epsh), max(epsi, epsh));`
clear all
lambda = 500*10^-3:10*10^-3:2500*10^-3; % in microns
A1= 1.4182;
B1= 0.021304;
n_pc=sqrt(1+(A1.*lambda.^2)./(lambda.^2-B1));
wp= 15.92; % eV
f0 = 0.096;
Gamma0 = 0.048; % eV
f1 = 0.100;
Gamma1 = 4.511; % eV
omega1 = 0.174; % eV
f2 = 0.135;
Gamma2 = 1.334; % eV
omega2 = 0.582; % eV
f3 = 0.106;
Gamma3 = 2.178; % eV
omega3 = 1.597; % eV
f4 = 0.729;
Gamma4 = 6.292; % eV
omega4 = 6.089; % eV
OmegaP = sqrt(f0) * wp; % eV
eV = 4.13566733e-1 * 2.99792458 ./ lambda;
epsilon = 1 – OmegaP^2 ./ (eV .* (eV + 1i * Gamma0));
epsilon = epsilon + f1 * wp^2 ./ ((omega1^2 – eV.^2) – 1i * eV * Gamma1);
epsilon = epsilon + f2 * wp^2 ./ ((omega2^2 – eV.^2) – 1i * eV * Gamma2);
epsilon = epsilon + f3 * wp^2 ./ ((omega3^2 – eV.^2) – 1i * eV * Gamma3);
epsilon = epsilon + f4 * wp^2 ./ ((omega4^2 – eV.^2) – 1i * eV * Gamma4);
n = real(sqrt(epsilon));
k = imag(sqrt(epsilon));
nMetal = n+1i.*k;
%NWATER
NWATER = 0.0738.*lambda.^6 – 0.6168.*lambda.^5 + 2.0263.*lambda.^4 – 3.3315.*lambda.^3 + 2.8708.*lambda.^2 – 1.2367.*lambda + 1.5411;
nAir=1+0.05792105./(238.0185-(lambda.^(-2)))+0.00167917./(57.362-(lambda.^(-2)));
% permetivity
epsMetal = nMetal.^2;
epsWATER=NWATER.^2;
%parmenter for each axes
%1 specific volume
ni=n_pc;
nt=NWATER;
%angels
thetaI =0; % incidence angle
thetaI = thetaI/180*pi;
beta=20;
beta = beta/180*pi;
fi=0;
fi=fi/180*pi;
%%%%%
a=20*10.^-9;
b=5*10.^-9;
d=2*a*cos(beta);
fi=0.3;
fh=1-fi;
Rpp = [];
Rsp = [];
Rps = [];
Rss = [];
Tpp = [];
Tsp = [];
Tps = [];
Tss = [];
% epsilon for compost materals SHAPE Factor
e= sqrt(1-(b/a)^2);
la=((1-e^.2)/e^2)*((log((1+e)/(1-e)))/2*e^2 -1);
lb=0.5*(1-la);
% Symbolic variable for epsilon_mg
syms epsilon_mg
%%%%%%%%
for i=1:size(lambda,2)
%snel law §
thetaT=asin(ni(i)*sin(thetaI)/nt(i));
k0=2*pi/(lambda(i)*10^-6);
VX=ni(i)*sin(thetaI);
epsi=epsMetal(i);
epsh=epsWATER(i);
% Bruggeman mixing formula
eq = fi * (epsi – epsilon_mg) / (epsilon_mg + la * (epsi – epsilon_mg)) +(1 – fi) * (epsh – epsilon_mg) / (epsilon_mg + lb * (epsh – epsilon_mg)) == 0;
% Solve equation with positive imaginary part
solutions = vpasolve(eq, epsilon_mg, [min(epsi, epsh), max(epsi, epsh)]);
positive_imaginary = solutions(imag(solutions) > 0);
if ~isempty(positive_imaginary)
epsilon_mg = positive_imaginary(1);
else
error(‘No solution with positive imaginary part found at index %d’, i);
end
eps1=epsilon_mg;
eps2=epsilon_mg;
eps3=epsilon_mg;
exx=eps2 +(eps1.*cos(beta).*cos(beta) +eps3.*sin(beta).*sin(beta) -eps2).*cos(fi).*cos(fi);
exy=0.5.*(eps1.*cos(beta).*cos(beta) +eps3.*sin(beta).*sin(beta) – eps2).*sin(2.*fi);
exz=0.5.*(eps3-eps1).*sin(2.*beta).*cos(fi);
eyy=eps2 +(eps1.*cos(beta).*cos(beta) +eps3.*sin(beta).*sin(beta) – eps2).*sin(fi).*sin(fi);
eyz=0.5.*(eps3-eps1).*sin(2.*beta).*sin(fi);
ezz=eps1 +(eps3 -eps1).*cos(beta).*cos(beta);
eyx=exy;
ezx=exz;
ezy=eyz;
del = [-VX.*ezx./ezz 1-(VX.*VX)./ezz -VX.*ezy./ezz 0; exx-(exz.*ezx)./ezz -VX.*exz./ezz exy-exz.*ezy./ezz 0; 0 0 0 1; eyx-(eyz.*ezx)./ezz -VX.*eyz./ezz eyy-(VX.*VX)-(eyz.*ezy)./ezz 0];
P=exp(1)^(1i.*k0.*d.*del);
a1 = ni(i).*(nt(i).*P(1,2)-cos(thetaT).*P(2,2))+cos(thetaI).*(nt(i).*P(1,1)-cos(thetaT).*P(2,1));
a2 = ni(i).*(nt(i).*P(1,2)-cos(thetaT)*P(2,2))-cos(thetaI).*(nt(i).*P(1,1)-cos(thetaT).*P(2,1));
a3 = (nt(i).*P(1,3)-cos(thetaT).*P(2,3))+ni(i).*cos(thetaI).*(nt(i).*P(1,4)-cos(thetaT).*P(2,4));
a4 = (nt(i).*P(1,3)-cos(thetaT).*P(2,3))-ni(i).*cos(thetaI).*(nt(i).*P(1,4)-cos(thetaT).*P(2,4));
a5 = ni(i).*(nt(i).*cos(thetaT).*P(3,2 )-P(4,2)) +cos(thetaI).*(nt(i).*cos(thetaT).*P(3,1)-P(4,1));
a6 = ni(i).*(nt(i).*cos(thetaT).*P(3,2) -P(4,2))-cos(thetaI).*(nt(i).*cos(thetaT).*P(3,1)-P(4,1));
a7 = (nt(i).*cos(thetaT).*P(3,3)-P(4,3))+ni(i).*cos(thetaI).*(nt(i).*P(3,4).*cos(thetaT)-P(4,4));
a8 = (nt(i).*cos(thetaT).*P(3,3)-P(4,3))-ni(i).*cos(thetaI).*(nt(i).*P(3,4).*cos(thetaT)-P(4,4));
b1 = (ni(i).*P(2,2)+cos(thetaI).*P(2,1))./nt(i);
b2 = (ni(i).*P(2,2)-cos(thetaI).*P(2,1))./nt(i);
b3 = (P(2,3)-ni(i).*cos(thetaI).*P(2,4))./nt(i);
b4 = (P(2,3)+ni(i).*cos(thetaI).*P(2,4))./nt(i);
b5 = ni(i).*P(3,2)+cos(thetaI).*P(3,1);
b6 = ni(i).*P(3,2)-cos(thetaI).*P(3,1);
b7 = P(3,3)-ni(i).*cos(thetaI).*P(3,4);
b8 = P(3,3)+ni(i).*cos(thetaI).*P(3,4);
rpp=(a1.*a8-a4.*a5)./(a4.*a6-a2.*a8);
rps=(a3.*a8-a4.*a7)./(a4.*a6-a2.*a8);
rsp=(a2.*a5-a1.*a6)./(a4.*a6-a2.*a8);
rss=(a2.*a7-a6.*a3)./(a4.*a6-a2.*a8);
tpp=b1+b2.*rpp+b3.*rsp;
tps=b4+b2.*rps+b3.*rss;
tsp=b5+b6.*rpp+b7.*rsp;
tss=b8+b6.*rps+b7.*rss;
Rpp = [Rpp (abs(rpp))^2];
Rsp = [Rsp (abs(rsp))^2];
Rps = [Rps (abs(rps))^2];
Rss = [Rss (abs(rss))^2];
Tpp = [Tpp (nt(i) .* cos(thetaI) ./ ni(i) .* cos(real(thetaT))).*(abs(tpp )^2)];
Tss = [Tss (nt(i) .* cos(real(thetaT)) ./ ni(i) .* cos(thetaI)).*(abs(tss )^2)];
Tsp = [Tsp (nt(i) .* cos(real(thetaT)) ./ ni(i) .* cos(thetaI)).*(abs(tsp )^2)];
Tps = [Tps (nt(i) .* cos(real(thetaT)) ./ ni(i) .* cos(thetaI)).*(abs(tps )^2)];
T=(Tpp+Tsp+Tps+Tss)/2;
R=(Rpp+Rsp+Rps+Rss)/2;
A=1-R-T;
end
figure(1)
hold on
plot(lambda*10^3,A*100,’LineWidth’, 3)
hold on
xlabel(‘Wavelength (nm)’,’fontsize’,16)
hold on
ylabel(‘Absorbtion’,’fontsize’, 16)
figure(2)
hold on
plot(lambda*10^3,T*100,’LineWidth’, 3)
hold on
xlabel(‘Wavelength (nm)’,’fontsize’,16)
hold on
ylabel(‘Transmission’,’fontsize’, 16) In this code, MATLAB gives me the following issue: For the solving function, how can I correct this error?
Error using sym/vpasolve:
Unable to find variables in equations.
Error in ni_water_simulationburgemanforchatgbt (line 99):
`solutions = vpasolve(eq, epsilon_mg, min(epsi, epsh), max(epsi, epsh));`
clear all
lambda = 500*10^-3:10*10^-3:2500*10^-3; % in microns
A1= 1.4182;
B1= 0.021304;
n_pc=sqrt(1+(A1.*lambda.^2)./(lambda.^2-B1));
wp= 15.92; % eV
f0 = 0.096;
Gamma0 = 0.048; % eV
f1 = 0.100;
Gamma1 = 4.511; % eV
omega1 = 0.174; % eV
f2 = 0.135;
Gamma2 = 1.334; % eV
omega2 = 0.582; % eV
f3 = 0.106;
Gamma3 = 2.178; % eV
omega3 = 1.597; % eV
f4 = 0.729;
Gamma4 = 6.292; % eV
omega4 = 6.089; % eV
OmegaP = sqrt(f0) * wp; % eV
eV = 4.13566733e-1 * 2.99792458 ./ lambda;
epsilon = 1 – OmegaP^2 ./ (eV .* (eV + 1i * Gamma0));
epsilon = epsilon + f1 * wp^2 ./ ((omega1^2 – eV.^2) – 1i * eV * Gamma1);
epsilon = epsilon + f2 * wp^2 ./ ((omega2^2 – eV.^2) – 1i * eV * Gamma2);
epsilon = epsilon + f3 * wp^2 ./ ((omega3^2 – eV.^2) – 1i * eV * Gamma3);
epsilon = epsilon + f4 * wp^2 ./ ((omega4^2 – eV.^2) – 1i * eV * Gamma4);
n = real(sqrt(epsilon));
k = imag(sqrt(epsilon));
nMetal = n+1i.*k;
%NWATER
NWATER = 0.0738.*lambda.^6 – 0.6168.*lambda.^5 + 2.0263.*lambda.^4 – 3.3315.*lambda.^3 + 2.8708.*lambda.^2 – 1.2367.*lambda + 1.5411;
nAir=1+0.05792105./(238.0185-(lambda.^(-2)))+0.00167917./(57.362-(lambda.^(-2)));
% permetivity
epsMetal = nMetal.^2;
epsWATER=NWATER.^2;
%parmenter for each axes
%1 specific volume
ni=n_pc;
nt=NWATER;
%angels
thetaI =0; % incidence angle
thetaI = thetaI/180*pi;
beta=20;
beta = beta/180*pi;
fi=0;
fi=fi/180*pi;
%%%%%
a=20*10.^-9;
b=5*10.^-9;
d=2*a*cos(beta);
fi=0.3;
fh=1-fi;
Rpp = [];
Rsp = [];
Rps = [];
Rss = [];
Tpp = [];
Tsp = [];
Tps = [];
Tss = [];
% epsilon for compost materals SHAPE Factor
e= sqrt(1-(b/a)^2);
la=((1-e^.2)/e^2)*((log((1+e)/(1-e)))/2*e^2 -1);
lb=0.5*(1-la);
% Symbolic variable for epsilon_mg
syms epsilon_mg
%%%%%%%%
for i=1:size(lambda,2)
%snel law §
thetaT=asin(ni(i)*sin(thetaI)/nt(i));
k0=2*pi/(lambda(i)*10^-6);
VX=ni(i)*sin(thetaI);
epsi=epsMetal(i);
epsh=epsWATER(i);
% Bruggeman mixing formula
eq = fi * (epsi – epsilon_mg) / (epsilon_mg + la * (epsi – epsilon_mg)) +(1 – fi) * (epsh – epsilon_mg) / (epsilon_mg + lb * (epsh – epsilon_mg)) == 0;
% Solve equation with positive imaginary part
solutions = vpasolve(eq, epsilon_mg, [min(epsi, epsh), max(epsi, epsh)]);
positive_imaginary = solutions(imag(solutions) > 0);
if ~isempty(positive_imaginary)
epsilon_mg = positive_imaginary(1);
else
error(‘No solution with positive imaginary part found at index %d’, i);
end
eps1=epsilon_mg;
eps2=epsilon_mg;
eps3=epsilon_mg;
exx=eps2 +(eps1.*cos(beta).*cos(beta) +eps3.*sin(beta).*sin(beta) -eps2).*cos(fi).*cos(fi);
exy=0.5.*(eps1.*cos(beta).*cos(beta) +eps3.*sin(beta).*sin(beta) – eps2).*sin(2.*fi);
exz=0.5.*(eps3-eps1).*sin(2.*beta).*cos(fi);
eyy=eps2 +(eps1.*cos(beta).*cos(beta) +eps3.*sin(beta).*sin(beta) – eps2).*sin(fi).*sin(fi);
eyz=0.5.*(eps3-eps1).*sin(2.*beta).*sin(fi);
ezz=eps1 +(eps3 -eps1).*cos(beta).*cos(beta);
eyx=exy;
ezx=exz;
ezy=eyz;
del = [-VX.*ezx./ezz 1-(VX.*VX)./ezz -VX.*ezy./ezz 0; exx-(exz.*ezx)./ezz -VX.*exz./ezz exy-exz.*ezy./ezz 0; 0 0 0 1; eyx-(eyz.*ezx)./ezz -VX.*eyz./ezz eyy-(VX.*VX)-(eyz.*ezy)./ezz 0];
P=exp(1)^(1i.*k0.*d.*del);
a1 = ni(i).*(nt(i).*P(1,2)-cos(thetaT).*P(2,2))+cos(thetaI).*(nt(i).*P(1,1)-cos(thetaT).*P(2,1));
a2 = ni(i).*(nt(i).*P(1,2)-cos(thetaT)*P(2,2))-cos(thetaI).*(nt(i).*P(1,1)-cos(thetaT).*P(2,1));
a3 = (nt(i).*P(1,3)-cos(thetaT).*P(2,3))+ni(i).*cos(thetaI).*(nt(i).*P(1,4)-cos(thetaT).*P(2,4));
a4 = (nt(i).*P(1,3)-cos(thetaT).*P(2,3))-ni(i).*cos(thetaI).*(nt(i).*P(1,4)-cos(thetaT).*P(2,4));
a5 = ni(i).*(nt(i).*cos(thetaT).*P(3,2 )-P(4,2)) +cos(thetaI).*(nt(i).*cos(thetaT).*P(3,1)-P(4,1));
a6 = ni(i).*(nt(i).*cos(thetaT).*P(3,2) -P(4,2))-cos(thetaI).*(nt(i).*cos(thetaT).*P(3,1)-P(4,1));
a7 = (nt(i).*cos(thetaT).*P(3,3)-P(4,3))+ni(i).*cos(thetaI).*(nt(i).*P(3,4).*cos(thetaT)-P(4,4));
a8 = (nt(i).*cos(thetaT).*P(3,3)-P(4,3))-ni(i).*cos(thetaI).*(nt(i).*P(3,4).*cos(thetaT)-P(4,4));
b1 = (ni(i).*P(2,2)+cos(thetaI).*P(2,1))./nt(i);
b2 = (ni(i).*P(2,2)-cos(thetaI).*P(2,1))./nt(i);
b3 = (P(2,3)-ni(i).*cos(thetaI).*P(2,4))./nt(i);
b4 = (P(2,3)+ni(i).*cos(thetaI).*P(2,4))./nt(i);
b5 = ni(i).*P(3,2)+cos(thetaI).*P(3,1);
b6 = ni(i).*P(3,2)-cos(thetaI).*P(3,1);
b7 = P(3,3)-ni(i).*cos(thetaI).*P(3,4);
b8 = P(3,3)+ni(i).*cos(thetaI).*P(3,4);
rpp=(a1.*a8-a4.*a5)./(a4.*a6-a2.*a8);
rps=(a3.*a8-a4.*a7)./(a4.*a6-a2.*a8);
rsp=(a2.*a5-a1.*a6)./(a4.*a6-a2.*a8);
rss=(a2.*a7-a6.*a3)./(a4.*a6-a2.*a8);
tpp=b1+b2.*rpp+b3.*rsp;
tps=b4+b2.*rps+b3.*rss;
tsp=b5+b6.*rpp+b7.*rsp;
tss=b8+b6.*rps+b7.*rss;
Rpp = [Rpp (abs(rpp))^2];
Rsp = [Rsp (abs(rsp))^2];
Rps = [Rps (abs(rps))^2];
Rss = [Rss (abs(rss))^2];
Tpp = [Tpp (nt(i) .* cos(thetaI) ./ ni(i) .* cos(real(thetaT))).*(abs(tpp )^2)];
Tss = [Tss (nt(i) .* cos(real(thetaT)) ./ ni(i) .* cos(thetaI)).*(abs(tss )^2)];
Tsp = [Tsp (nt(i) .* cos(real(thetaT)) ./ ni(i) .* cos(thetaI)).*(abs(tsp )^2)];
Tps = [Tps (nt(i) .* cos(real(thetaT)) ./ ni(i) .* cos(thetaI)).*(abs(tps )^2)];
T=(Tpp+Tsp+Tps+Tss)/2;
R=(Rpp+Rsp+Rps+Rss)/2;
A=1-R-T;
end
figure(1)
hold on
plot(lambda*10^3,A*100,’LineWidth’, 3)
hold on
xlabel(‘Wavelength (nm)’,’fontsize’,16)
hold on
ylabel(‘Absorbtion’,’fontsize’, 16)
figure(2)
hold on
plot(lambda*10^3,T*100,’LineWidth’, 3)
hold on
xlabel(‘Wavelength (nm)’,’fontsize’,16)
hold on
ylabel(‘Transmission’,’fontsize’, 16) solve function, matalb code, sav, vpasolve MATLAB Answers — New Questions
