program of two variable df/dna/df/dx vs da value

function shiv8

clear all

close all

na=1.432;

n=linspace(1.43,1.50,10)

D1= linspace(1e-9,3e-7,15);

for j=1:numel(D1)

for k=1: numel(n)

da = D1(j);

na=n(k);

p0 = 1;

p1 = 1.5;

p2 = 2;

TOL = 10^-8;

N0 = 100; format long

h1 = p1 - p0;

h2 = p2 - p1;

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

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

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

i=3;

while i <= N0

b = DELTA2 + h2*d;

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

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

E = b + D;

else

E = b - D;

end

h = -2*f(p2,na,da)/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,na,da ) - f(p0,na,da ))/h1;

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

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

i=i+1;

end

end

%pv(j)=p;

P(j)=real(p();

%R(j)=real(r);

end

plot(D1,P)

end

function y=f(x,na,da)

l=6330*(10)^(-10);

k0=2*pi/l;

nc=1.33;

ec=nc^2;

%na=1.43;

ea=na.^2;

nf=1.59;

ef=nf^2;

nm=0.064+1i*4;

em=nm^2;

ns=1.495;

es=ns^2;

df=0.5e-6;

dm=0.03e-6;

%kx=(2*pi/l)*np*sin(a);

kc=k0*sqrt(x^2-ec);

ka=k0*sqrt(ea-x^2);

kf=k0*sqrt(ef-x^2);

km=k0*sqrt(em-x^2);

ks=k0*sqrt(x^2-es);

rfm=(kf-km)/(kf+km);

rms=(km-ks)/(ks+km);

rfa=(kf-ka)/(kf+ka);

rac=(ka-kc)/(ka+kc);

a=(1-rfm)/(1+rfm);

b=(1-rms*exp(2*1i*dm*km))/(1+rms*exp(2*1i*dm*km));

c=(1-rfa)/(1+rfa);

f=(1-rac*exp(2*1i*da*ka))/(1+rac*exp(2*1i*da*ka));

pfms=2*atan(1i*a*b);

pfac=2*atan(1i*c*f);

y=2*kf*df-pfms-pfac;

end

pl plot df/dna/df/dx vs da