Chapter03:Optical Sources and Transmitters

Ex3.2.1:Pg-3.10

In [6]:
#Given
x= 0.07 
Eg= 1.424+1.266*x+0.266*x**2 
lamda= 1.24/Eg 
print " The emitted wavelength in um =",round(lamda,2) 
 The emitted wavelength in um = 0.82

Ex3.2.2:Pg-3.10

In [7]:
#Given
x= 0.26 
y=0.57 
Eg= 1.35-0.72*y+0.12*y**2 
lamda = 1.24/Eg 
print " The wavelength emitted in um =",round(lamda,2) 
 The wavelength emitted in um = 1.27

Ex3.2.3:Pg-3.12

In [8]:
#Given

Tr = 60*10**-9    # radiative recombination time
Tnr= 90*10**-9    # non radiative recomb time
I= 40*10**-3      # current
t = Tr*Tnr/(Tr+Tnr)      # total recomb time
t=t*10**9     # Converting in nano secs...
print " The total carrier recombination life time in ns =",int(t) 
t=t/10**9 
h= 6.625*10**-34      # plancks const
c= 3*10**8 
q=1.602*10**-19 
lamda= 0.87*10**-6 
Pint=(t/Tr)*((h*c*I)/(q*lamda)) 
Pint=Pint*1000   # converting inmW...
print " \n\nThe Internal optical power in mW =",round(Pint,2) 
 The total carrier recombination life time in ns = 36
 

The Internal optical power in mW = 34.22

Ex3.2.4:Pg-3.13

In [9]:
#Given
lamda = 1310*10**-9 
Tr= 30*10**-9 
Tnr= 100*10**-9 
I= 40*10**-3 
t= Tr*Tnr/(Tr+Tnr) 
t=t*10**9    # converting in nano secs...
print " Bulk recombination life time in ns =",round(t,2) 
t=t/10**9 
n= t/Tr 
print " \n\nInternal quantum efficiency =",round(n,3) 
h= 6.625*10**-34      # plancks const
c= 3*10**8 
q=1.602*10**-19 
Pint=(0.769*h*c*I)/(q*lamda)*1000 
print " \n\nThe internal power level in mW =",round(Pint,3) 
print " \n\n***NOTE: Internal Power wrong in text book.. Calculation Error.." 
 Bulk recombination life time in ns = 23.08
 

Internal quantum efficiency = 0.769
 

The internal power level in mW = 29.131
 

***NOTE: Internal Power wrong in text book.. Calculation Error..

Ex3.2.5:Pg-3.14

In [11]:
#Given
nx= 3.6 
TF= 0.68 
n= 0.3 
 # Pe=Pint*TF*1/(4*nx**2) 
 # ne= Pe/Px*100     ..eq0
 # Pe = 0.013*Pint      # Eq 1
 # Pint = n*P     # Eq 2
 # substitute eq2 and eq1 in eq0
ne = 0.013*0.3*100 
print " The external Power efficiency in % =",round(ne,3) 
 #  Wrongly printed in textbook. it should be P instead of Pint in last step
 The external Power efficiency in % = 0.39

Ex3.2.6:Pg-3.15

In [12]:
#Given

lamda= 0.85*10**-6 
Nint = 0.60 
I= 20*10**-3 
h= 6.625*10**-34      # plancks const
c= 3*10**8 
e=1.602*10**-19 
Pint = Nint*h*c*I/(e*lamda) 
print " The optical power emitted in W =",round(Pint,4) 

TF= 0.68 
nx= 3.6 
Pe= Pint*TF/(4*nx**2)*1000000 
print " \n\nPower emitted in the air in uW =",round(Pe,1) 
Pe=Pe/1000000 
Nep=Pe/Pint*100 
print " \n\nExternal power efficiency in % =",round(Nep,1) 
 The optical power emitted in W = 0.0175
 

Power emitted in the air in uW = 229.7
 

External power efficiency in % = 1.3

Ex3.2.7:Pg-3.16

In [15]:
#Given

lamda = 0.87*10**-6 
Tr= 50*10**-9 
I= 0.04 
Tnr= 110*10**-9 
t= Tr*Tnr/(Tr+Tnr) 
t=t*10**9    # converting in ns...
print " Total carrier recombination life time in ns =",round(t,2) 
t=t/10**9 
h= 6.625*10**-34      # plancks const
c= 3*10**8 
q=1.602*10**-19 
n= t/Tr 
print " \n\nThe efficiency in % ",round(n,3) 
Pint=(n*h*c*I)/(q*lamda)*1000 
print " \n\nInternal power generated in mW =",round(Pint,2) 
print " \n\n***NOTE- Internal Power wrong in book... "
 Total carrier recombination life time in ns = 34.38
 

The efficiency in %  0.688
 

Internal power generated in mW = 39.22
 

***NOTE- Internal Power wrong in book... 

Ex3.2.8:Pg-3.16

In [16]:
#Given
 

V= 2 
I= 100*10**-3 
Pc= 2*10**-3 
P= V*I 
Npc= Pc/P*100 
print " The overall power conversion efficiency in % =",int(Npc) 
 The overall power conversion efficiency in % = 1

Ex3.3.1:Pg-3.25

In [17]:
#Given
import math

r1= 0.32 
r2= 0.32 
alpha= 10 
L= 500*10**-4 
temp=math.log(1/(r1*r2)) 
Tgth = alpha + (temp/(2*L)) 
print " The optical gain at threshold in /cm =",round(Tgth,2) 
 The optical gain at threshold in /cm = 32.79

Ex3.3.2:Pg-3.27

In [18]:
#Given
 
n= 3.7 
lamda = 950*10**-9 
L= 500*10**-6 
c= 3*10**8 
DELv = c/(2*L*n)*10*10**-10   # converting in GHz...
print " The frequency spacing in GHz =",int(DELv) 
DEL_lamda= lamda**2/(2*L*n)*10**9   # converting to nm..
print " \n\nThe wavelength spacing in nm =",round(DEL_lamda,2) 

print " \n\n***NOTE- The value of wavelength taken wrongly in book" 
 #  value of lamda taken wrongly while soving for DEL_LAMDA inthe book..
 The frequency spacing in GHz = 81
 

The wavelength spacing in nm = 0.24
 

***NOTE- The value of wavelength taken wrongly in book

Ex3.3.3:Pg-3.30

In [20]:
 #Given
 
L= 0.04 
n= 1.78 
lamda= 0.55*10**-6 
c= 3*10**8 
q= 2*n*L/lamda 
q=q/10**5 
print " Number of longitudinal modes  =",round(q,2),"x 10^5" 
del_f= c/(2*n*L) 
del_f=del_f*10**-9 
print " \n\nThe frequency seperation in GHz =",round(del_f,1) 
 Number of longitudinal modes  = 2.59 x 10^5
 

The frequency seperation in GHz = 2.1

Ex3.3.4:Pg-3.33

In [22]:
#Given

Nt= 0.18 
V= 2.5 
Eg= 1.43 
Nep= Nt*Eg*100/V 
print " The total efficiency in % =",round(Nep,3) 
 The total efficiency in % = 10.296

Ex3.3.5:Pg-3.33

In [24]:
#Given

n= 3.6 
BETA= 21*10**-3 
alpha= 10 
L= 250*10**-4 

r= (n-1)**2/(n+1)**2 
Jth= 1/BETA *( alpha + (math.log(1/r)/L)) 
Jth=Jth/1000   # converting for displaying...
print " The threshold current density =",round(Jth,3),"x 10**3" 
Jth=Jth*1000 
Ith  =Jth*250*100*10**-8 
Ith=Ith*1000   # converting into mA...
print " \n\nThe threshold current in mA =",round(Ith,1) 
 The threshold current density = 2.65 x 10**3
 

The threshold current in mA = 662.4

Ex3.3.6:Pg-3.34

In [26]:
#Given

T= 305.0 
T0 = 160.0 
T1= 373.0

Jth_32 = exp(T/T0) 
Jth_100 = exp(T1/T0) 
R_j = Jth_100/Jth_32 
print " Ratio of current densities at 160K is =",round(R_j,2) 
print " \n\n***NOTE- Wrong in book...\nJth(100) calculated wrongly..." 
To = 55 
Jth_32_new = exp(T/To) 
Jth_100_new = exp(T1/To) 
R_j_new = Jth_100_new/Jth_32_new 
print " \n\nRatio of current densities at 55K is  ",round(R_j_new,2) 
 # wrong in book...
 Ratio of current densities at 160K is = 1.53
 

***NOTE- Wrong in book...
Jth(100) calculated wrongly...
 

Ratio of current densities at 55K is   3.44

Ex3.4.1:Pg-3.42

In [27]:
#Given
import math

Bo= 150 
rs= 35*10**-4 
a1= 25*10**-6 
NA= 0.20 
a2= 50*10**-6 

Pled = (a1/rs)**2 * (math.pi**2*rs**2*Bo*NA**2) 
Pled=Pled*10**10   # converting in uW...
print " The power coupled inthe fibre in uW =",int(Pled) 
Pled_new = (math.pi**2*rs**2*Bo*NA**2) 
Pled_new=Pled_new*10**6   # converting in uW...
print " \n\nThe Power coupled for case 2 in uW =",round(Pled_new,2) 
 The power coupled inthe fibre in uW = 370
 

The Power coupled for case 2 in uW = 725.42

Ex3.4.2:Pg-3.43

In [28]:
#Given
import math
n= 1.48 
n1= 3.6 
R= (n1-n)**2/(n1+n)**2 
print " The Fresnel Reflection is  ",round(R,4) 
L= -10*math.log10(1-R) 
print " \n\nPower loss in dB =",round(L,2) 
 The Fresnel Reflection is   0.1742
 

Power loss in dB = 0.83

Ex3.4.3:Pg-3.44

In [29]:
#Given
import math

NA= 0.20 
Bo= 150 
rs= 35*10**-6 
Pled = math.pi**2*rs**2*Bo*NA**2 
Pled=Pled*10**10   # convertin in uW for displaying...
print " The optical power coupled in uW =",round(Pled,2) 
 The optical power coupled in uW = 725.42

Ex3.4.4:Pg-3.44

In [30]:
#Given
import math

n1= 1.5 
n=1 
R= (n1-n)**2/(n1+n)**2 
L= -10*math.log10(1-R) 
 # Total loss is twice due to reflection
L= L+L 
print " Total loss due to Fresnel Reflection in dB =",round(L,2) 
 Total loss due to Fresnel Reflection in dB = 0.35

Ex3.4.5:Pg-3.51

In [39]:
#Given
import math
 
n1= 1.5 
n=1.0 
y=5.0 
a= 25.0 
temp1=(1-(y/(2*a)**2))**0.5 
temp1=temp1*(y/a) 
temp=2*math.acos(0.9996708)  #  it should be acos(0.1) actually... due to approximations
    
    #  answer varies a lot... 
temp=math.degrees(temp)-temp1 
 # temp=temp 
tem= 16*(1.5**2)/(2.5**4) 
tem=tem/math.pi 
temp=temp*tem 
Nlat= temp 
print " The Coupling efficiency is =",round(Nlat,3) 
L= -10*math.log10(Nlat) 
print " \n\nThe insertion loss in dB =",round(L,2) 
temp1=(1-(y/(2*a)**2))**0.5 
temp1=temp1*(y/a) 
temp=2*math.acos(0.9996708)  #  it should be acos(0.1) actually... due to approximations
    #  answer varies a lot... 
temp=math.degrees(temp)-temp1 
temp=temp/math.pi 
N_new =temp  
print " \n\nEfficiency when joint index is matched =",round(N_new,3) 
L_new= -10*math.log10(N_new) 
print " \n\nThe new insertion loss in dB =",round(L_new,2) 
 The Coupling efficiency is = 0.804
 

The insertion loss in dB = 0.95
 

Efficiency when joint index is matched = 0.872
 

The new insertion loss in dB = 0.59