FIBER OPTIC COMMUNCIATION ASSIGNMENT
ASSIGNMENT 2
Manish Shankar : 108118079
Solving Eigen value or modal characteristics equations for TE01 and TM01 mode
using MATLAB. Explain the results with graphical representations and justify.
Code
clc();
a = 10e-6;
k = 2*pi/1.55e-6;
n1 = 1.4;
n2 = 1.33;
k1 = n1*k;
k2 = n2*k;
kz = linspace(k2,k1,100000);
kz(1) = [];
kz(end) = [];
u = sqrt(k1^2 - kz.^2);
w = sqrt(kz.^2 - k2^2);
Jv = besselj(1,u*a)./(k1.*besselj(0,u*a));
Jvm = mean(abs(Jv));
Jv(abs(Jv)>3*Jvm) = nan;
Kv = besselk(1,w*a)./(w.*besselk(0,w*a));
Kvm = mean(abs(Kv));
Kv(abs(Kv)>3*Kvm) = nan;
figure(1)
plot(kz,Jv,kz,-Kv)
%ylim([-2e-5 2e-5])
grid on
figure(2)
plot(kz,k1^2*Jv,kz,-k2^2*Kv)
grid on
kzroot = 5.4617301149e6;
k1root = sqrt(n1^2*k^2 - kzroot^2);
k2root = sqrt(n2^2*k^2 - kzroot^2);
alpha = besselj(1,k1root*a)/besselh(1,1,k2root*a);
TE_E1 =
besselj(1, k1root*a)
TE_E2 = alpha*besselh(1,1,k2root*a)
TE_H1 =
k1root*besselj(0, k1root*a)
TE_H2 = alpha*k2root*besselh(0,1,k2root*a)
kzroot = 5.470410e6;
k1root = sqrt(n1^2*k^2 - kzroot^2);
k2root = sqrt(n2^2*k^2 - kzroot^2);
alpha = besselj(1,k1root*a)/besselh(1,1,k2root*a);
TM_E1 =
besselj(1, k1root*a)
TM_E2 = alpha*besselh(1,1,k2root*a)
TM_H1 =
k1root*besselj(0, k1root*a)
TM_H2 = alpha*k2root*besselh(0,1,k2root*a)
*********
We consider the case with following parameters
Core radius: 10 um
Wavelength: 1.55 um
Core refractive index, n1 = 1.4
Cladding refractive index, n2 = 1.33
From the modal equation, we get
For TE0m, we have v = 0 from the above equation. Hence RHS = LHS = 0. In the LHS we have 2 factors:
(Jv + Kv) = 0
(K12Jv + k22 Kv)=0
Case 1: TE01
(Jv + Kv) = 0
We find this by equation Jv = -Kv
We get the point of intersection as 5.4617301149 * 106
From here we find the values of electric and magnetic field
Output
Case2: TM01
(K12Jv + k22 Kv)=0
We find this by plotting Jv and -Kv and finding the first point of intersection
(TM01) Jv = -Kv
We get the point of intersection as 5.470410 * 106
From here we find the values of electric and magnetic field
Output