matrix multiplication and root finding

Mj=[cos (kj hj) i*sin(kj hj) /kj ; i*kj*sin(kj hj) cos (kj hj) ];

kj=sqrt(nj2*k02-x2);

Take n1=1.521;n2=2.66;k0=1;h1=1.5e-6;h2=1e-6

We take M=M1*M2;

Where M=( m11 m12;m21 m22) as usual in

Matrix;

How to multiply this matrix for M find the multiplication of matrix and find the value of

x;

and solve the eq

ns=1.512;

nc=1.2-i7;

gs=x2-ns2k02;

gc= x2-ns2k02;

f(x)=igsm11+gcm22)-m21+gsgcm12;

and solve the eq and value of x

Answer 1

[Vidhi Agarwal]

Hi @shiv gaur,

To solve the issue follow the given below steps:

• Define the matrices.
• Compute the matrix multiplication.
• Formulate the function.
• Solve the equation.

Modified code for the same is given below:

% Given values
n1 = 1.521;
n2 = 2.66;
k0 = 1;
h1 = 1.5e-6;
h2 = 1e-6;
ns = 1.512;
nc = 1.2 - 1i*7;

% Define symbolic variable for x
syms x

% Calculate k1 and k2
k1 = sqrt(n1^2 * k0^2 - x^2);
k2 = sqrt(n2^2 * k0^2 - x^2);

% Define M1 and M2 matrices
M1 = [cos(k1 * h1), 1i * sin(k1 * h1) / k1;
      1i * k1 * sin(k1 * h1), cos(k1 * h1)];

M2 = [cos(k2 * h2), 1i * sin(k2 * h2) / k2;
      1i * k2 * sin(k2 * h2), cos(k2 * h2)];

% Multiply matrices to get M
M = M1 * M2;

% Extract elements from M
m11 = M(1,1);
m12 = M(1,2);
m21 = M(2,1);
m22 = M(2,2);

% Define gs and gc
gs = x^2 - ns^2 * k0^2;
gc = x^2 - nc^2 * k0^2;

% Define the function f(x)
f = 1i * (gs * m11 + gc * m22) - m21 + gs * gc * m12;

% Use vpasolve for numerical solution
x_solution = vpasolve(f == 0, x);

% Display the solutions
disp('Numerical solutions for x:')
disp(x_solution)

For better understanding of basic matrix operation in MATLAB refer to the documentation https://www.mathworks.com/help/matlab/math/basic-matrix-operations.html.

Hope this helps!

[shiv gaur]

thanks for answer.what will be change in program if we varying h2 from 1e-3 to 1e-6 pl provide the solution

[shiv gaur]

plot h2(x axis) vs x(real or x imaginary)