10: Optical Materials

Example number 10.1, Page number 10.61

In [32]:
#importing modules
import math
from __future__ import division

#Variable declaration
h=6.626*10**-34;       #plancks constant(J s)
c=3*10**8;     #velocity of light(m/s)
Eg=1.44*1.6*10**-19;    #band gap(J)

#Calculation
lamda=h*c/Eg;      #wavelength of emission(m)

#Result
print "wavelength of emission is",round(lamda*10**10),"angstrom"

wavelength of emission is 8628.0 angstrom

Example number 10.2, Page number 10.61

In [33]:
#importing modules
import math
from __future__ import division

#Variable declaration
lamda=1.55;     #wavelength(micro m)

#Calculation
Eg=1.24/lamda;     #band gap(eV)

#Result
print "band gap is",Eg,"eV"

band gap is 0.8 eV

Example number 10.3, Page number 10.61

In [34]:
#importing modules
import math
from __future__ import division

#Variable declaration
eta=0.65;     #quantum efficiency
n=5*10**5;    #number of photons incident

#Calculation
N=eta*n;      #number of electron-hole pairs

#Result
print "number of electron-hole pairs is",N/10**5,"*10**5"

number of electron-hole pairs is 3.25 *10**5

Example number 10.4, Page number 10.61

In [35]:
#importing modules
import math
from __future__ import division

#Variable declaration
eta=0.6;     #quantum efficiency
q=1.6*10**-19;    #charge(coulomb)
lamda=1.3*10**-6;    #lamda(m)
h=6.625*10**-34;       #plancks constant(J s)
c=3*10**8;     #velocity of light(m/s)

#Calculation
R=eta*q*lamda/(h*c);     #responsibility(A/W)

#Result
print "responsibility is",round(R,3),"A/W"

responsibility is 0.628 A/W

Example number 10.5, Page number 10.61

In [36]:
#importing modules
import math
from __future__ import division

#Variable declaration
eta=0.7;     #quantum efficiency
q=1.6*10**-19;    #charge(coulomb)
lamda=863*10**-9;    #lamda(m)
P0=0.5*10**-6;     #optical power(W)
h=6.625*10**-34;       #plancks constant(J s)
c=3*10**8;     #velocity of light(m/s)
IT=10*10**-6;    #current(A)

#Calculation
IP=eta*q*lamda*P0/(h*c);
M=IT/IP;       #multiplication factor

#Result
print "multiplication factor is",int(M)

multiplication factor is 41

Example number 10.6, Page number 10.62

In [37]:
#importing modules
import math
from __future__ import division

#Variable declaration
n2=1.47;              #refractive index of cladding
n1=1.5;    #refractive index of core

#Calculation
phi_c=math.asin(n2/n1);     #critical angle(radian)
phi_c=phi_c*180/math.pi;    #critical angle(degrees)
NA=math.sqrt(n1**2-n2**2);     #numerical aperture
phi_max=math.asin(NA);       #acceptance angle(radian)
phi_max=phi_max*180/math.pi;    #acceptance angle(degrees)

#Result
print "critical angle is",round(phi_c,1),"degrees"
print "numerical aperture is",round(NA,1)
print "acceptance angle is",round(phi_max,1),"degrees"

critical angle is 78.5 degrees
numerical aperture is 0.3
acceptance angle is 17.4 degrees

Example number 10.7, Page number 10.62

In [38]:
#importing modules
import math
from __future__ import division

#Variable declaration
d=50*10**-6;     #diameter(m)
NA=0.2;      #numerical aperture(m)
lamda=1*10**-6;    #wavelength(m)

#Calculation
N=4.9*(d*NA/lamda)**2;     #total number of guided modes

#Result
print "total number of guided modes is",N

total number of guided modes is 490.0

Example number 10.8, Page number 10.62

In [41]:
#importing modules
import math
from __future__ import division

#Variable declaration
d=5*10**-6;     #diameter(m)
n2=1.447;              #refractive index of cladding
n1=1.45;    #refractive index of core
lamda=1*10**-6;    #wavelength(m)

#Calculation
NA=math.sqrt(n1**2-n2**2);      #numerical aperture
N=4.9*(d*NA/lamda)**2;     #total number of guided modes

#Result
print "total number of guided modes is",int(N)

total number of guided modes is 1

Example number 10.9, Page number 10.63

In [42]:
#importing modules
import math
from __future__ import division

#Variable declaration
n1=1.46;    #refractive index of core
delta=0.05;    #refractive index difference

#Calculation
NA=n1*math.sqrt(2*delta);     #numerical aperture

#Result
print "numerical aperture is",round(NA,2)

numerical aperture is 0.46

Example number 10.10, Page number 10.63

In [44]:
#importing modules
import math
from __future__ import division

#Variable declaration
a=50;
n2=1.5;              #refractive index of cladding
n1=1.53;    #refractive index of core
lamda0=1;    #wavelength(micro m)

#Calculation
V_number=round(2*math.pi*a*math.sqrt(n1**2-n2**2)/lamda0,2);     #V number
n=V_number**2/2;     #maximum number of modes

#Result
print "V number is",V_number
print "maximum number of modes is",round(n)

V number is 94.72
maximum number of modes is 4486.0

Example number 10.11, Page number 10.63

In [45]:
#importing modules
import math
from __future__ import division

#Variable declaration
a=100*10**-6;
NA=0.3;      #numerical aperture(m)
lamda=850*10**-9;    #wavelength(m)

#Calculation
V_number=round(2*math.pi**2*a**2*NA**2/lamda**2);     #number of modes

#Result
print "total number of modes is",2*V_number

total number of modes is 49178.0

Example number 10.12, Page number 10.63

In [46]:
#importing modules
import math
from __future__ import division

#Variable declaration
a=25*10**-6;
n1=1.48;    #refractive index of core
delta=0.01;    #refractive index difference
V=25;     #Vnumber

#Calculation
lamda=2*math.pi*a*n1*math.sqrt(2*delta)/V;      #cutoff wavelength(m)

#Result
print "cutoff wavelength is",round(lamda*10**6,3),"micro m"

cutoff wavelength is 1.315 micro m

Example number 10.13, Page number 10.63

In [48]:
#importing modules
import math
from __future__ import division

#Variable declaration
V=2.405;     #Vnumber
lamda=1.3;    #wavelength(micro m)
NA=0.05;      #numerical aperture(m)

#Calculation
amax=V*lamda/(2*math.pi*NA);     #maximum value of core radius(micro m)

#Result
print "maximum value of core radius is",round(amax,2),"micro m"

maximum value of core radius is 9.95 micro m