# Chapter 6 :Integrated Optics and Photonic Circuits¶

## Example 6.1 , Page no:121¶

In [1]:
import math
from __future__ import division

#initialisation of variables
lamda=1.55;  #wavelength in um
n1=1.51;  #Film refractive index
n2=1.5;  #substrate refractive index

#CALCULATIONS
t=(lamda)/(2*3.14*math.sqrt(n1*n1-n2*n2));  #Thickness of film in um

#RESULTS
print"Film thickness=",round(t,5),"um";

Film thickness= 1.42262 um


## Example 6.2 , Page no:121¶

In [2]:
import math
from __future__ import division

#initialisation of variables
b=0.5;  #normalized propoagation constant
lamda=1.3;  #wavelength in um
n1=2.21;  #Film refractive index
n2=2.2;  #substrate refractive index

#CALCULATIONS
V=(2*math.atan(b/(1-b))/(math.sqrt(1-b)));  #normalized frequency
t=(lamda)/(2*3.14*math.sqrt(n1*n1-n2*n2));  #Thickness of film in um

#RESULTS
print"Normalized frequency=",round(V,5);
print"Film thickness=",round(t,5),"um";

Normalized frequency= 2.22144
Film thickness= 0.98574 um


## Example 6.3 , Page no:121¶

In [3]:
import math
from __future__ import division

#initialisation of variables
lamda=1.3;  #wavelength in um
nf=1.51;  #Film refractive index
t=1.5;  #Film thickness in um
ns=1.5;  #Waveguide refractive index
na=1;  #refractive index of air

#CALCULATIONS
V=(2*3.14*t/lamda)*math.sqrt(nf**2-ns**2);  #V-number
a=(ns**2-na**2)/(nf**2-ns**2);  #asymmetry parameter of the waveguide
Vc=math.atan(a**0.5);  #cutoff V-number

#RESULTS
print"V-number=",round(V,5);
print"symmetry parameter of the waveguide=",round(a,5);
print"Cutoff V-number=",round(Vc,5);

V-number= 1.25716
symmetry parameter of the waveguide= 41.52824
Cutoff V-number= 1.41685


## Example 6.4 , Page no:121¶

In [4]:
import math
from __future__ import division

#initialisation of variables
delta_phi=3.14;
d=4*10**-6;  #seperation between electrodes
n=2.2;  #approximate inder in absence of voltage
r13=30*10**-12;  #poper electro optic coefficient
row=0.4;  #overlap factor
lambda1=1300*1e-9;  #wavelength in m
L=8*10**-3;  #length of electrode in m

#CALCULATIONS
delta_n=delta_phi*lambda1/(2*3.14*L);  #change in refractive index
V_pi=2*d*delta_n/(n**3*row*r13);  #Voltahe required for using the device as BPSK modulator

#RESULTS
print"Voltage required for using the device as BPSK modulator=",round(V_pi,5),"V";
print"Voltage length product for unit length is=",round(V_pi,5),"VM";

Voltage required for using the device as BPSK modulator= 5.08703 V
Voltage length product for unit length is= 5.08703 VM


## Example 6.5 , Page no:122¶

In [5]:
import math
from __future__ import division

#initialisation of variables
d=10*10**-6;  #seperation between electrodes
ne=2.2;  #approximate inder in absence of voltage
r33=32*10**-12;  #poper electro optic coefficient
lambda1=1*1e-6;  #wavelength in m
L=5*10**-3;  #length of electrode in m

#CALCULATIONS
V=d*lambda1/(2*3.14*ne**3*r33*L);  #Voltahe required for using the device as BPSK modulator

#RESULTS
print"Voltage required for using the device as BPSK modulator=",round(V,5);
print"The answer is different because of rounding off error";

Voltage required for using the device as BPSK modulator= 0.93466
The answer is different because of rounding off error


## Example 6.6 , Page no:122¶

In [6]:
import math
from __future__ import division

#initialisation of variables
delta_L=1/100;  #error in effective interaction length

#CALCULATIONS
P=(3.14/2*delta_L)**2;  #cross talk power output in W
PdB=10*math.log10(P);  #power in dB

#RESULTS
print"cross talk power output=",round(P*10**4,5),"x10^-4W";  #multiplication by 10^4 to convert unit from W to 10^-4 W
print"cross talk power output=",round(PdB,5),"dB";

cross talk power output= 2.4649 x10^-4W
cross talk power output= -36.08201 dB