solve the equation reflectivity vs wavenumber plot

function kps5
K0 = 1550e-6:1e-6:1600e-6;
for j=1:numel(K0)
    
    k3 = K0(j);
    p0 = 0.5;
    p1 = 1;
    p2 = 1.5;
    TOL = 10^-8;
    N0 = 100; format long
    h1 = p1 - p0;
    h2 = p2 - p1;
    DELTA1 = (f(p1,k0) - f(p0,k0))/h1;
    DELTA2 = (f(p2,k0) - f(p1,k0))/h2;
    d = (DELTA2 - DELTA1)/(h2 + h1);
    i=3;
    while i <= N0 
        
        b = DELTA2 + h2*d;
        D = (b^2 - 4*f(p2,k0)*d)^(1/2);
        
        if abs(b-D) < abs(b+D)
            E = b + D;
        else
            E = b - D;
        end
        
        h = -2*f(p2,k0)/E;
        p = p2 + h;
        
        if abs(h) < TOL      
            disp(p) 
            break
        end
        
        p0 = p1;
        p1 = p2;
        p2 = p;
        h1 = p1 - p0;
        h2 = p2 - p1;
        DELTA1 = (f(p1,k0) - f(p0,k0))/h1;
        DELTA2 = (f(p2,k0) - f(p1,k0))/h2;
        d = (DELTA2 - DELTA1)/(h2 + h1);
        i=i+1;
        
    end
    
    if i > N0
        
        formatSpec = string('The method failed after N0 iterations,N0= %d \n');
        fprintf(formatSpec,N0);
    end
    P(j)=real(p);
    R(j)=real(r)
end
plot(K0,R)
end
function  y=f(x,k0)



n0=1.3707;
n1=1.3;
n2=1.59;
n3=1.45
n4=3.46;
na=1.36;
t1=2.10e-6;
t2=0.198e-6;
t3=1e-6;
t4=0.002e-6;
x=1.36-1i*0.0123;
k1=k0*sqrt(n1.^2-x.^2);
k2=k0*sqrt(n2.^2-x.^2);
k3=k0*sqrt(n3.^2-x.^2);
k4=k0*sqrt(n4.^2-x.^2);


m11= cos(t1*k1)*cos(t2*k2)-(k2/k1)*sin(t1*k1)*sin(t2*k2);
m12=(1/k2)*(cos(t1*k1)*sin(t2*k2)*1i) +(1/k1)*(cos(t2*k2)*sin(t1*k1)*1i);
m21= (k1)*cos(t2*k2)*sin(t1*k1)*%i +(k2)*cos(t1*k1)*sin(t2*k2)*%i;
m22=cos(t1*k1)*cos(t2*k2)-(k1/k2)*sin(t1*k1)*sin(t2*k2);

m34= cos(t3*k3)*cos(t4*k4)-(k4/k3)*sin(t3*k3)*sin(t4*k4);
m32=(1/k4)*(cos(t3*k3)*sin(t4*k4)*1i) +(1/k3)*(cos(t4*k4)*sin(t3*k3)*1i);
m23= (k3)*cos(t4*k4)*sin(t3*k3)*1i +(k4)*cos(t3*k3)*sin(t4*k4)*1i;
m33=cos(t3*k3)*cos(t4*k4)-(k3/k4)*sin(t3*k3)*sin(t4*k4);
M11=m11*m34+m12*m23;
M12=m11*m32+m12*m33;
M21=m21*m34+m22*m23;
M22=m21*m32+m22*m33;

g0=sqrt(x.^2-n0.^2)*k0;
ga= sqrt(x.^2-na.^2)*k0;


y= 1i*(g0*M11/n0^2+ga*M22/na^2)-M21+(g0*ga/n0^2*na^2)*M12 ;

r=(na^2*g0*M11-n0^2*ga*M22+g0*ga*M12-na^2*n0^2*M21)/(na^2*g0*M11+n0^2*ga*M22+g0*ga*M12+na^2*n0^2*M21);
end

[shiv gaur]

this is the program of transcedental equation by varying the wavenumber k0 to find the the value of r and plot

[KSSV]

What is your question?

[shiv gaur]

question is that if we vary the value of k0 the what is the value of r at varying the k0 and plot between k0 vs r

[shiv gaur]

figure like attach file

[shiv gaur]

not K3 i e K0

[shiv gaur]

function kps5

K0 = 1550e-6:1e-6:1600e-6;

for j=1:numel(K0)

k0 = K0(j);

p0 = 0.5;

p1 = 1;

p2 = 1.5;

TOL = 10^-8;

N0 = 100; format long

h1 = p1 - p0;

h2 = p2 - p1;

DELTA1 = (f(p1,k0) - f(p0,k0))/h1;

DELTA2 = (f(p2,k0) - f(p1,k0))/h2;

d = (DELTA2 - DELTA1)/(h2 + h1);

i=3;

while i <= N0

b = DELTA2 + h2*d;

D = (b^2 - 4*f(p2,k0)*d)^(1/2);

if abs(b-D) < abs(b+D)

E = b + D;

else

E = b - D;

end

h = -2*f(p2,k0)/E;

p = p2 + h;

if abs(h) < TOL

disp(p)

break

end

p0 = p1;

p1 = p2;

p2 = p;

h1 = p1 - p0;

h2 = p2 - p1;

DELTA1 = (f(p1,k0) - f(p0,k0))/h1;

DELTA2 = (f(p2,k0) - f(p1,k0))/h2;

d = (DELTA2 - DELTA1)/(h2 + h1);

i=i+1;

end

if i > N0

formatSpec = string('The method failed after N0 iterations,N0= %d \n');

fprintf(formatSpec,N0);

end

P(j)=real(p);

R(j)=real(r)

end

plot(K0,R)

end

function y=f(x,k0)

n0=1.3707;

n1=1.3;

n2=1.59;

n3=1.45

n4=3.46;

na=1.36;

t1=2.10e-6;

t2=0.198e-6;

t3=1e-6;

t4=0.002e-6;

k1=k0*sqrt(n1.^2-x.^2);

k2=k0*sqrt(n2.^2-x.^2);

k3=k0*sqrt(n3.^2-x.^2);

k4=k0*sqrt(n4.^2-x.^2);

m11= cos(t1*k1)*cos(t2*k2)-(k2/k1)*sin(t1*k1)*sin(t2*k2);

m12=(1/k2)*(cos(t1*k1)*sin(t2*k2)*1i) +(1/k1)*(cos(t2*k2)*sin(t1*k1)*1i);

m21= (k1)*cos(t2*k2)*sin(t1*k1)*%i +(k2)*cos(t1*k1)*sin(t2*k2)*%i;

m22=cos(t1*k1)*cos(t2*k2)-(k1/k2)*sin(t1*k1)*sin(t2*k2);

m34= cos(t3*k3)*cos(t4*k4)-(k4/k3)*sin(t3*k3)*sin(t4*k4);

m32=(1/k4)*(cos(t3*k3)*sin(t4*k4)*1i) +(1/k3)*(cos(t4*k4)*sin(t3*k3)*1i);

m23= (k3)*cos(t4*k4)*sin(t3*k3)*1i +(k4)*cos(t3*k3)*sin(t4*k4)*1i;

m33=cos(t3*k3)*cos(t4*k4)-(k3/k4)*sin(t3*k3)*sin(t4*k4);

M11=m11*m34+m12*m23;

M12=m11*m32+m12*m33;

M21=m21*m34+m22*m23;

M22=m21*m32+m22*m33;

g0=sqrt(x.^2-n0.^2)*k0;

ga= sqrt(x.^2-na.^2)*k0;

y= 1i*(g0*M11/n0^2+ga*M22/na^2)-M21+(g0*ga/n0^2*na^2)*M12 ;

r=(na^2*g0*M11-n0^2*ga*M22+g0*ga*M12-na^2*n0^2*M21)/(na^2*g0*M11+n0^2*ga*M22+g0*ga*M12+na^2*n0^2*M21);

end

[shiv gaur]

modified program plot k0 vs r

[shiv gaur]

any one pl help to plot between k0 vs r