%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% This file is used to
% (1) Calculate the index of refraction of various glass materials
% that could be used in optical fiber
% (2) Calculate the core radius for a particular cut-off wavelength
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%Part 1 The glass materials
%
% Use the glas materials in the reference
% J. W. Fleming, "Material dispersion in lightguide glasses,"
% Electr. Lett., vol. 14, p. 326-328, May 1978.
%
% The indices of refraction are described using the Sellmeier equations
% given by
% n^2 - 1 = sum( (Ai * lambda^2)/( lambda^2 - li))
% The wavelength, lambda, is in units of micrometers
%
% These are the coefficients for the 6 materials
A1 = [ .696750; .711040; .695790; .690618; .691116; .796468];
A2 = [ .408218; .451885; .452497; .401996; .399166; .497614];
A3 = [ .890815; .704048; .712513; .898817; .890423; .358924];
L1 = [ .069066; .064270; .061568; .061900; .068227; .094359];
L2 = [ .115662; .129408; .119921; .123662; .116460; .093386];
L3 = [9.900559;9.425478;8.656641;9.098960;9.993707;5.999652];
% basic parameters
c=3e8;
% plot of the varous indices of refraction
lambda=linspace(1.2, 1.6, 201); % the wavelength in micrometers
NN=[];
NG=[];
for lp_mat=1:6
a1=A1(lp_mat);
a2=A2(lp_mat);
a3=A3(lp_mat);
l1=L1(lp_mat);
l2=L2(lp_mat);
l3=L3(lp_mat);
%calculate the refractive indices
n = sqrt(1+(a1.*lambda.^2)./(lambda.^2-l1.^2)+(a2.*lambda.^2)./(lambda.^2-l2.^2)+(a3.*lambda.^2)./(lambda.^2-l3.^2));
%make a matrix of refractive indices
NN=[NN;n];
%calculate the group refractive indices
w=2*pi*c./lambda;
dw=diff(w);
ng=n(2:end)+w(2:end).*diff(n)./diff(w);
%make a matrix of group refractive indices
NG=[NG;ng];
end
%the indices of refraction as a function of wavelength
subplot(2,1,1)
plot(lambda,NN)
subplot(2,1,2)
plot(lambda(2:end),NG)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%Part 2 Cut-off
%
% Calculate the waveguide radius for a a particular cut-off wavelength
% Use the equation 2.405 = 2*pi/lambda*a*sqrt(ncore^2-nclad^2)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
l_cutoff=1.2; %cut-off wavelength
core=2; %number for the core material
clad=1; %number for the cladding material
%check to see if these materials are valid
I=find(NN(core,:)0
'NOT VALID MATERIALS'
else
%calculate the core radius for the particular cut-off wavelength
n_core = sqrt(1+(A1(core).*l_cutoff^2)./(l_cutoff^2-L1(core).^2)+(A2(core).*l_cutoff^2)./(l_cutoff^2-L2(core).^2)+(A3(core).*l_cutoff^2)./(l_cutoff^2-L3(core).^2))
n_clad = sqrt(1+(A1(clad).*l_cutoff^2)./(l_cutoff^2-L1(clad).^2)+(A2(clad).*l_cutoff^2)./(l_cutoff^2-L2(clad).^2)+(A3(clad).*l_cutoff^2)./(l_cutoff^2-L3(clad).^2))
a=2.405*l_cutoff/(2*pi*sqrt(n_core^2-n_clad^2))
end