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How to perform integral ?

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MOHD
MOHD 2013-3-1
clear all;
clc;
close all;
dim=64;
L=531*10^-9;
k=2*pi/L;
[x,y]=meshgrid(-L:2*L/(dim-1):L);
r=sqrt(x.^2+y.^2);
alp=asin(0.95);
h=(alp)/64;
z=-32*L:1*L:31*L;
c=numel(z);
Era=zeros([dim dim c]);
Ela=zeros([dim dim c]);
Er=0;
Ez=0;
Hp=0;
for ii=1:c;
% electric field components
f=@(theta) -(cos(theta))^0.5*sin(2*theta)*bessel(1,k*r*sin(theta));
g=@(theta) -2*1i*(cos(theta))^0.5*(sin(theta))^2*bessel(0,k*r*sin(theta));%*exp(1i*k*z(ii)*cos(theta));
for jj=1:1:63
theta=(jj*h); Er=Er+(f(0)+2*f(jj*h)+f(alp));
Era(:,:,ii)=Er.*exp(1i*k*z(ii)*cos(theta));
end
for jj=1:1:63
theta=(jj*h);
Ez=Ez+(g(0)+2*g(jj*h)+g(alp));
Ela(:,:,ii)=Ez.*exp(1i*k*z(ii)*cos(theta));
end
end
Er1=(h/2)*(Era);
Ez1=(h/2)*(Ela);
Ir=Er1.*conj(Er1);
Iz=Ez1.*conj(Ez1);
Itot=Ir+Iz;
Itot=squeeze(Itot(dim/2,:,:)).';
figure(1)
imagesc(Itot),colormap gray
Hi,
By using this Program I am calculating intensity of radially polarized beam
in YZ plane.
By using this program for z=0, that is in XY plane I am getting correct
intensity pattern, but when I am varying z from -32:1:31 in YZ plane I not
getting correct intensity pattern that I am getting half part only other
half part I am missing from figure(1);
Here I am performing Integration of following function by using trepazoidal
rule
f=@(theta)
-(cos(theta))^0.5*sin(2*theta)*bessel(1,k*r*sin(theta))*exp(1i*k*z(ii)*cos(theta));
g=@(theta) -2*1i*(cos(theta))^0.5*
(sin(theta))^2*bessel(0,k*r*sin(theta))*exp(1i*k*z(ii)*cos(theta));
I have problem in Integration of this to functions
we will get intensity as a function of r and z
can any one help me in this regard,it is great help for me
thank you

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