Guided Modes Of Optical Planer wave-guide Solution and MATLAB code with Graphic representation...

1. Assignment-1
PHL791 (Fiber Optics)
Ajay Singh
(Physics Department, IIT Delhi)
Assignment 1
Que. Consider a planar waveguide with n1 = 2.22, n2
wavelengths of 500 nm, 1000 nm and 1500 nm.
1. Calculate the number of guided modes allowed at the three wavelengths.
2. Obtain the effective indices of the guided modes at the three wavelengths
3. Normalize the fields so that all the modes carry a total power of unity
4. Plot the power normalized field distribution Ey(x) vs. x in the region of the possible guided modes at
the three wavelengths. Plot the distributions of various guided corresponding to one wavelength in the
same graph.
5. Obtain the cut off wavelength of the waveguide

2. Computation and Plotting code (using MATLAB)
lembda_0=500e-9;
k0=2*pi/lembda_0;
n1=2.22;
n2=2.2;
d=2e-6;
V=(pi*d/lembda_0)*(n1^2-n2^2)^(1/2);
Zaai=0:0.00001:5;
Y1=Zaai.*tan(Zaai);
Y2=(V.^2-Zaai.^2).^(1/2);
plot(Zaai,Y1)
hold on;
Y3=-Zaai.*cot(Zaai);
plot(Zaai,Y3)
hold on;
Zaai1=fzero(@(Zaai) Zaai.*tan(Zaai)-(V.^2-Zaai.^2).^(1/2),1);
Zaai2=fzero(@(Zaai) -Zaai.*cot(Zaai)-(V.^2-Zaai.^2).^(1/2),2);
Zaai3=fzero(@(Zaai) Zaai.*tan(Zaai)-(V.^2-Zaai.^2).^(1/2),3);
beta1=sqrt((k0*n1)^2-(2*Zaai1/d)^2);
beta2=sqrt((k0*n1)^2-(2*Zaai2/d)^2);
beta3=sqrt((k0*n1)^2-(2*Zaai3/d)^2);
kappa1=((k0*n1)^2-beta1^2)^0.5;
kappa2=((k0*n1)^2-beta2^2)^0.5;
kappa3=((k0*n1)^2-beta3^2)^0.5;
gamma1=((beta1^2-(k0*n2)^2))^0.5;
gamma2=((beta2^2-(k0*n2)^2))^0.5;
gamma3=((beta3^2-(k0*n2)^2))^0.5;
myu=pi*4e-7;
c=3e8;
A1=((8*pi*myu*c)/(lembda_0*beta1*(d+2/gamma1)))^(0.5);
A2=((8*pi*myu*c)/(lembda_0*beta2*(d+2/gamma2)))^(0.5);
A3=((8*pi*myu*c)/(lembda_0*beta3*(d+2/gamma3)))^(0.5);
r=-1e-6:0.00000001:1e-6;
E1=A1*cos(kappa1*r);
plot(r,E1)
hold on
E2=A2*sin(kappa2*r);

3. plot(r,E2)
hold on
E3=A3*cos(kappa3*r);
plot(r,E3)
hold on
x=1e-6:0.0000001:4e-6;
E11=A1*cos(kappa1*d/2)*exp(-gamma1*(x-d/2))
plot(x,E11)
E21=A2*sin(kappa2*d/2)*exp(-gamma2*(x-d/2))
plot(x,E21)
E31=A3*cos(kappa3*d/2)*exp(-gamma3*(x-d/2))
plot(x,E31)
x1=-4e-6:0.0000001:-1e-6;
E12=A1*cos(kappa1*d/2)*exp(-gamma1*(-x1-d/2))
plot(x1,E12)
hold on
E22=-A2*sin(kappa2*d/2)*exp(-gamma2*(-x1-d/2))
plot(x1,E22)
hold on
E32=A3*cos(kappa3*d/2)*exp(-gamma3*(-x1-d/2))
plot(x1,E32)

4. Lembada_0=1000e-9;
Ko=2*pi/Lembada_0;
n1=2.22;
n2=2.2;
d=2e-6;
Vo=(pi*d/Lembada_0)*(n1^2-n2^2)^(1/2);
Zaai=0:0.000001:5;
Y1=Zaai.*tan(Zaai);
Y2=(Vo.^2-Zaai.^2).^(1/2);
plot(Zaai,Y1);
hold on;
plot(Zaai,Y2);
hold on;
Y3=-Zaai.*cot(Zaai);
plot(Zaai,Y3);
Zaai1=fzero(@(Zaai) Zaai.*tan(Zaai)-(Vo.^2-Zaai.^2).^(1/2),1);
Zaai2=fzero(@(Zaai) -Zaai.*cot(Zaai)-(Vo.^2-Zaai.^2).^(1/2),1.5);
beta1=sqrt((Ko*n1)^2-(2*Zaai1/d)^2);
beta2=sqrt((Ko*n1)^2-(2*Zaai2/d)^2);
kappa1=((Ko*n1)^2-beta1^2)^0.5;
kappa2=((Ko*n1)^2-beta2^2)^0.5;
gamma1=((beta1^2-(Ko*n2)^2))^0.5;
gamma2=((beta2^2-(Ko*n2)^2))^0.5;
myu=pi*4e-7;
c=3e8;
A1=((8*pi*myu*c)/(Lembada_0*beta1*(d+2/gamma1)))^(0.5)
A2=((8*pi*myu*c)/(Lembada_0*beta2*(d+2/gamma2)))^(0.5)
r=-1e-6:0.00000001:1e-6;
E1=A1*cos(kappa1*r);
plot(r,E1)
hold on
E2=A2*sin(kappa2*r);
plot(r,E2);
hold on
p=1e-6:0.0000001:4e-6;
E12=A1*cos(kappa1*d/2)*exp(-gamma1*(p-d/2))
plot(p,E12)

5. E22=A2*sin(kappa2*d/2)*exp(-gamma2*(p-d/2))
plot(p,E22)
q=-4e-6:0.0000001:-1e-6;
E12=A1*cos(kappa1*d/2)*exp(-gamma1*(-q-d/2))
plot(q,E12)
hold on
E22=-A2*sin(kappa2*d/2)*exp(-gamma2*(-q-d/2))
plot(q,E22)

6. lembda_0=1500e-9;
Ko=2*pi/lembda_0;
n1=2.22;
n2=2.2;
d=2e-6;
myu=pi*4e-7;
c=3e8;
Vo=(pi*d/lembda_0)*(n1^2-n2^2)^(1/2);
Zaai=0:0.00001:5;
Y1=Zaai.*tan(Zaai);
Plot(Zaai,Y1)
Y2=(Vo.^2-Zaai.^2).^(1/2);
plot(Zaai,Y2);
hold on;
Zaai= fzero(@(Zaai) Zaai.*tan(Zaai)-(Vo.^2-Zaai.^2).^(1/2),0)
beta=sqrt((Ko*n1)^2-(2*Zaai/d)^2);
kappa=((Ko*n1)^2-beta^2)^0.5;
Gama=((beta^2-(Ko*n2)^2))^0.5;
A=((8*pi*myu*c)/(lembda_0*beta*(d+2/Gama)))^(0.5);
x=-1e-6:0.00000001:1e-6;
E1=A*cos(kappa*x);
plot(x,E1)
hold on
t=1e-6:0.0000001:4e-6;
E2=A*cos(kappa*d/2)*exp(-Gama*(t-d/2))
plot(t,E2) ;
t1=-4e-6:0.0000001:-1e-6;
E3=A*cos(kappa*d/2)*exp(-Gama*(-t1-d/2))
plot(t1,E3)