How can I calculate and plot rayleigh scattering equation?

hi, I want to plot and calculate rayleigh equation.I wrote it , calculated and plotted.But it does not match the graph in my book.Here is my code.Thx for your help.

clear all

freq=6.*10.^8;

omeg=2.*pi.*freq;

eps0=(10.^-9)./(36.*pi);

mu0=4.*pi.*10.^-7;

k=omeg.*sqrt(eps0.*mu0);

lambda=2.*pi./k;

R=0.01:0.00366:0.07957;

N_cut=20;

for n=1:N_cut

    hankel2(n,:)=sqrt(pi*k*R).*besselh(n+0.5,1,k*R);

    hankel2der(n,:)=-

n.*sqrt(pi.*k./(2.*R)).*besselh(n+0.5,2,k.*R)+k.*sqrt(pi.*k.*R./2).*besselh(n-

0.5,2,k.*R);

    A_e(n,:)=(((-1).^n)).*(2.*n+1)./(hankel2(n,:).*hankel2der(n,:));

end

Ae=sum(A_e,2);

f_Ae=((lambda.^2)./(4.*pi)).*(abs(Ae)).^2;

figure

plot(R,f_Ae)

grid on

[Ahmed A. Selman]

Please use formatted syntax, clarify the specific equation you want to plot, and it would be helpful for anyone if you could refer to the (graph in your book) with something on the internet for comparison of what this nicely-written code produces. At least, mention the book you are referring to. I've copied the code to my editor, and couldn't see why is it not working for you. If you clarified it better, someone could properly assist you.

[Burak]

my book is Time-Harmonic Electromagnetic Fields Syracuse University (McGraw-Hill Electrical and Electronic Engineering Series).page 295 and this is my eq. http://i45.tinypic.com/vnz2c3.jpg thanks for help.

Answer 1

[Youssef Khmou]

hi, How is the graph you are expecting ? i altered the oscillating frequency to F=6Ghz . take a look at this code , and try also with f=6E+8 Hz ( the original freq you posted ), N_cut is augmented to 200 points .

 clear all
freq=6.*10^9; % 6 GHz
omeg=2.*pi.*freq; % Angular frequency in RAD/Second

 eps0=(10.^-9)./(36.*pi); % Absolute permittivity in FARAD/Meter
mu0=4.*pi.*10.^-7; % Absolute permeability
k=omeg.*sqrt(eps0.*mu0); % Wave Vector
lambda=2.*pi./k;  %wavelength in Meter
N_cut=200; 
R=linspace(0.01,0.07957,N_cut); % Radius....

 for n=1:N_cut

    hankel2(n,:)=sqrt(pi*k*R).*besselh(n+0.5,1,k*R);
    A=-n.*sqrt(pi.*k./(2.*R)).*besselh(n+0.5,2,k.*R);
    B=+k.*sqrt(pi.*k.*R./2).*besselh(n-0.5,2,k.*R);

    hankel2der(n,:)=A+B;
    A_e(n,:)=(((-1).^n)).*(2.*n+1)./(hankel2(n,:).*hankel2der(n,:));
end
Ae=sum(A_e,2);
f_Ae=((lambda.^2)./(4.*pi)).*(abs(Ae)).^2;
figure,plot(R,f_Ae),grid on
figure, plot(R,f_Ae), grid on, axis([0.01 0.02 0 0.012])

[Burak]

Really thanks it worked at 6 GHz and graph looks like what I want.my graph should've looked like this (<http://i48.tinypic.com/2vkc2gn.jpg>) and now it matches.God bless you :)

[Youssef Khmou]

ok nice.