# solution of matrix eigen value equation

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shiv gaur on 8 Feb 2022
Answered: Walter Roberson on 8 Feb 2022
n1=1.50;
n2=1.746;
n3=0.55-1i*11.5;
n4=1.444;
t1=5;
t2=1:70;
t3=24;
k0=2*pi/1.55;
k1=k0*sqrt(beta^2-n1^2);
k2=k0*sqrt(beta^2-n2^2);
k3=k0*sqrt(beta^2-n3^2);
k4=k0*sqrt(beta^2-n4^2);
M1=1/2(1+(k1/k2)*exp(-k1*t1) (1-(k1/k2)*exp(k1*t1);(1-(k1/k2)*exp(-k1*t1) (1+(k1/k2)*exp(k1*t1) );
M2=1/2(1+(k2/k3)*exp(-k2*t2) (1-(k2/k3)*exp(k2*t2);(1-(k2/k3)*exp(-k2*t2) (1+(k2/k3)*exp(k2*t2) );
M3=1/2(1+(k3/k4)*exp(-k3*t3) (1-(k3/k4)*exp(k3*t3);(1-(k3/k4)*exp(-k3*t3) (1+(k3/k4)*exp(k3*t3) );
M=M3*M2*M1=[m11 m12; m21 m22]
A=(A1;A2);
B=(B1;B2);
A2=0;
B1=0;
A=M*B;
m22(beta)=0;
from this equation plot(t2 vs beta)
##### 2 CommentsShowHide 1 older comment
shiv gaur on 8 Feb 2022
find the root of equation by varying t2 from 1:70

Walter Roberson on 8 Feb 2022
I had to make a bunch of guesses. In particular your M1 M2 M3 were not coded properly, and I had to guess about where to put the ) . I also had to guess about beta.
Eventually I hit the point where you have an equation relating to the undefined variables m11 m12 m21 m22 and I gave up trying to fix at that point.
You do not define A1, A2, B1, B2 before they are used, and you overwrite some of them after they are used which is confusing. You also overwrite A after you define it, which is again confusing.
There is too much wrong with the code for me to be able to fix it at this time.
n1=1.50;
n2=1.746;
n3=0.55-1i*11.5;
n4=1.444;
t1=5;
%t2=1:70;
syms t2 beta
t3=24;
k0=2*pi/1.55;
k1=k0*sqrt(beta^2-n1^2);
k2=k0*sqrt(beta^2-n2^2);
k3=k0*sqrt(beta^2-n3^2);
k4=k0*sqrt(beta^2-n4^2);
M1 = [1/2*(1+(k1/k2))*exp(-k1*t1), (1-(k1/k2)*exp(k1*t1)); (1-(k1/k2)*exp(-k1*t1)), (1+(k1/k2)*exp(k1*t1)) ]
M1 = M2 = [1/2*(1+(k2/k3))*exp(-k2*t2), (1-(k2/k3)*exp(k2*t2)); (1-(k2/k3)*exp(-k2*t2)), (1+(k2/k3)*exp(k2*t2)) ]
M2 = M3 = [1/2*(1+(k3/k4))*exp(-k3*t3), (1-(k3/k4)*exp(k3*t3)); (1-(k3/k4)*exp(-k3*t3)), (1+(k3/k4)*exp(k3*t3)) ]
M3 = M = M3*M2*M1 == [m11 m12; m21 m22]
Unrecognized function or variable 'm11'.
A = [A1;A2]
B = [B1;B2]
A2 = 0;
B1 = 0;
A = M*B;
eqn = m22*beta == 0

R2021b

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