# Determining Coupling coefficent value for mode coupling in a dual core fiber solving characterstics equation

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Deepak Sapkota am 13 Nov. 2020
Bearbeitet: Deepak Sapkota am 14 Nov. 2020
The graph obtained is not as expected. Can someone have a look on my code and figure out mistakes in it?
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
lambda=(1:0.01:2); %unit: um
%constants and variables
pi=3.14159; %Greek letter pi
c=2.99792458e14; % speed of light (unit: um/s)
a=1.95; % radius of core (unit: um)
d=2.52*4; % distance of separation between cores (unit: um)
d1=1.1; % air hole diameter (unit:um)
P=2.52; %pitch or hole-hole spacing
ko=2*pi./lambda;
dbar=d/a;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%Calculate refractive index of core material (n1) using Sellmeier's equation
G1=0.6961663; % Sellmeier's coefficients for pure silica
G2=0.4079426;
G3=0.8974794;
lambda1=.0684043; %wavelength for pure silica
lambda2=0.1162414;
lambda3=9.896161;
npower2oflambda=1+(G1*lambda.^2./(lambda.^2-power(lambda1,2)))+(G2*lambda.^2./(lambda.^2-power(lambda2,2)))+...
(G3*lambda.^2./(lambda.^2-power(lambda3,2)));
noflambda=sqrt(npower2oflambda);
n1=noflambda;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%calculate n2 in terms of n1
NA=0.20;
n2=sqrt(n1.^2-NA^2);
% calculate V-number
V=ko.*a.*(n1.^2-n2.^2 ).^(1/2);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%SOLVING BESSEL FUNCTION EIGEN VALUE EQUATION
syms U W
k1=(ko.*n1); %maxm value of beta
k2=(ko.*n2); %minimum value of beta
% beta=linspace(k2,k1,101);
beta=real(k2):real(k1-k2)/1e2:real(k1);
% n_eff=real(n2):real(n1-n2)/1e2:real(n1);
% beta=ko.*n_eff;
U=a.*sqrt(ko.^2.*n1.^2-beta.^2); %transverse mode paramter (phase constant)
W=a.*sqrt(beta.^2-ko.^2.*n2.^2); %transverse mode parameter (attenuation coefficient)
% h=U.*besselj(1,U)./besselj(0,U);
% m=W.*besselk(1,W)./besselk(0,W);
%solution=solve(U.*besselj(1,U)./besselj(0,U)==W.*besselk(1,W)./besselk(0,W), W);
%solution=double(solution)
figure(1)
plot(beta,h,'g','linewidth',2)
hold on
plot(beta,m,'r','linewidth',2)
legend('J_1(U)/U*J_0(U)','K_1(W)/W*K_0(W)')
xlabel('\delta\beta(um)')
grid on
hold off
betaroot=9.034; % first root from the plot 1
U1=a*sqrt(ko.^2.*n1.^2-betaroot.^2); %transverse mode parameter (phase constant)
W1=a*sqrt(betaroot.^2-ko.^2.*n2.^2);
%Uroot=imag(U1);
%Wroot=abs(W1);
K_0=besselk(0,W1.*dbar); %Zeroth order modified bessel function of 2nd kind
K_1=besselk(1,W1); %first order modified bessel function of 2nd kind
% %calculate coupling coefficient
R=sqrt(2*del)/a.*((U1.*U1)./(V.*V.*V)); % 1st part of coupling coefficient equation
Q=K_01./(K_1.*K_1); % 2nd part of coupling coefficient equation
q=abs(Q);
CC=R.*q;%Q;
figure(2)
plot(lambda,CC)
xlabel('wavelength (um)'); ylabel('coupling coeff. (/m)')
title('Coupling coeff. Solving characterstics equation');
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