Chapter 8: Optical Fiber Communication System

Example 1: PgNo-339

In [33]:
import math

# Variable initialisation
tr=40.0     # rediative life time in ns
tnr=60.0    # nonrediative life time in ns
i=35*math.pow(10,-3) # drive current in amp
y=0.85*math.pow(10,-6)# wavelength in m
h=6.626*math.pow(10,-34)# plank constant
c=3*math.pow(10,8)# the speed of light in m/s
eq=1.602*math.pow(10,-19)# charge

# calculations
t=tr*tnr/(tr+tnr)# total carrier recombination lifetime ns
ni=t/tr     # internal quantam efficiency
pil=(ni*h*c*i)/(eq*y)# internal power in watt
p_int=pil*math.pow(10,3)# internal power in mW

# Results
print ('%s %.f %s' %(" The total carrier recombination lifetime = ",t,"ns"))
print ('%s %.2f %s' %("\n The internal power = ",p_int,"mW"))
print ("\n The answer is wrong in textbook ")

 The total carrier recombination lifetime =  24 ns

 The internal power =  30.66 mW

 The answer is wrong in textbook

Example 2: PgNo-341

In [34]:
import math

# Initialisation of variables
tr=30.0 # rediative life time in ns
tnr=50.0  # nonrediative life time in ns
i=40*math.pow(10,-3)  # drive current in amp
pil=28.4*math.pow(10,-3) # internal power in watt
h=6.626*math.pow(10,-34) # plank constant
c=3*math.pow(10,8)  # the speed of light in m/s
eq=1.602*math.pow(10,-19) # charge
t=tr*tnr/(tr+tnr) # total carrier recombination lifetime ns
ni=t/tr    # internal quantam efficiency
y=(ni*h*c*i)/(eq*pil) # peak emission wavelength in m

# Results
print ('%s %.2f %s' %(" The total carrier recombination lifetime = ",t,"ns"))
print ('%s %.2f %s' %("\n The peak emission wavelength = ",y*pow(10,6),"um"))

 The total carrier recombination lifetime =  18.75 ns

 The peak emission wavelength =  1.09 um

Example 3: PgNo-345

In [35]:
import math

# Variable initialisation
nx=3.6  # refractive index
Fn=0.68 # transmission factor
pe_pi=(Fn)/(4*math.pow(nx,2))
pi_p=0.3
nep=pe_pi*pi_p # external power efficiency

# Results
print ('%s %.2f %s' %("The external power efficiency = ",nep*100,"%"))

The external power efficiency =  0.39 %

Example 4: PgNo-347

In [36]:
import math

# Variable initialisation
n=3.6 # core refractive index
NA=0.15 # numerical aperture
nc=math.pow(NA,2) # coupling efficiency
l_s=-10*math.log(nc)/math.log(10) # loss in db
pe_pi=0.023*0.0013  # from ex 8.3
pc=-10*math.log(pe_pi)/math.log(10) # loss in decibels relative to Pint

# Results
print ('%s %.2f %s' %(" The coupling efficiency = ",nc*100,"%"))
print ('%s %.3f %s' %("\n The loss = ",l_s,"db"))
print ('%s %.2f %s' %("\n The loss in decibels relative to Pint= ",pc,"db"))

 The coupling efficiency =  2.25 %

 The loss =  16.478 db

 The loss in decibels relative to Pint=  45.24 db

Example 5: PgNo-348

In [37]:
import math

# Variable initialisation
r=45*math.pow(10,-6) # radius in m
NA=0.3 # numerical aperture
rd=40 # radiance
A=3.14*math.pow((r*100),2) # area in cm^2
pe=3.14*(1-r)*A*rd*math.pow(NA,2) # optical power coupled into the fiber
Pe=pe*math.pow(10,4) # optical power coupled into the fiber uW

# Results
print ('%s %.3f %s' %(" The optical power coupled into the fiber = ",Pe,"uW"))

 The optical power coupled into the fiber =  7.187 uW

Example 6: PgNo-351

In [38]:
import math

# Variable initialisation
pc=150*math.pow(10,-6) # coupling power W
p=20*math.pow(10,-3)*2 # optical power W
npc=pc/p # overall efficiency
Npc=npc*100 # percentage of overall efficiency

# Results
print ('%s %.2f %s' %(" The percentage of overall efficiency = ",Npc,"%"))

 The percentage of overall efficiency =  0.37 %

Example 7: PgNo-357

In [39]:
import math

# Variable initialisation
n=1.5 # refractive index
L=0.05  #crystal length in m
y=0.5*math.pow(10,-6) #  wavelength in m
c=3*math.pow(10,8) # speed of light in m/s
q=2*n*L/y # the number of longitudinal modes
df=c/(2*n*L) # frequency separation of the modes in Hz
Df=df/math.pow(10,9) # frequency separation of the modes in GHz

# Results
print ('%s %d ' %(" The number of longitudinal modes = ",q))
print ('%s %.2f %s' %("\n The frequency separation of the modes = ",Df,"GHz"))

 The number of longitudinal modes =  300000 

 The frequency separation of the modes =  2.00 GHz

Example 8: PgNo-358

In [40]:
import math

# Variable declaration
Eg=1.43 # bandgap energy in eV
dy=0.15*math.pow(10,-9);
c=3*math.pow(10,8) # speed of light in m/s
y=1.24/Eg  # in um
y1=y*math.pow(10,-6) # wavelength of optical emission in m
df=(c*dy)/math.pow(y1,2) # the line width in Hz
Df=df/math.pow(10,9) # the line width in GHz

# Results
print ('%s %.2f %s' %(" The wavelength of optical emission  = ",y,"um"))
print ('%s %.4f %s' %("\n The frequency separation of the modes = ",Df,"GHz"))

 The wavelength of optical emission  =  0.87 um

 The frequency separation of the modes =  59.8468 GHz

Example 9: PgNo-362

In [41]:
import math

# Variable initialisation
n=3.6 # refractive index
c=3*math.pow(10,8)# speed of light in m/s
y=0.85*math.pow(10,-6)# wavelength in m
df=275*math.pow(10,9) # frequency separation of the modes in Hz
L=c/(2*n*df) # crystal length in m
L1=L*math.pow(10,6) # crystal length in um
q=2*n*L/y # the number of longitudinal modes

# results
print ('%s %.2f %s' %(" The crystal length = ",L1,"um"))
print ('%s %d' %("\n The the number of longitudinal modes = ",int(q)))
print ("\n answer is wrong in textbook ")

 The crystal length =  151.52 um

 The the number of longitudinal modes =  1283

 answer is wrong in textbook

Example 10: PgNo-364

In [42]:
import math

# Initialisation of variables
nt=0.20# total efficiency
Eg=1.43# bandgap energy in eV
V=2.2# applied voltage in volts
nep=(nt*Eg)/V# external power efficiency
Nep=nep*100#  percentage of external power efficiency

# Results
print ('%s %.2f %s' %(" The external power efficiency = ",Nep,"%"))

 The external power efficiency =  13.00 %

Example 11: PgNo-367

In [43]:
import math

# Initialisation of variables
h=0.35*math.pow(10,-3)# irradiance W/cm^2
po=0.45*math.pow(10,-3)# power output in watt
d=1.5 # separation distance in cm
x=math.sqrt((4*po)/(3.14*math.pow(d,2)*h)) # divergence angle in radians
X=(x*180)/3.14 # divergence angle in degree

# Results
print ('%s %.3f %s' %(" The divergence angle = ",X,"degree "))

 The divergence angle =  48.909 degree

Example 12: PgNo-369

In [44]:
import math

# Initialisation of variables
ni=0.09 # normal efficiency
d=2*2.54 # separation distance in cm
x=0.2 # divergence angle in radians
vf=2.0 # forward voltage in volts
i_f=65*math.pow(10,-3) # forward current in amp
pil=vf*i_f # input power in Watt
po=ni*pil # output power in Watt
H=4*po/(3.14*math.pow(d,2)*math.pow(x,2)) # irradiance in watt/cm^2
H1=H*1000 # irradiance in mwatt/cm^2

# Results
print ('%s %.2f %s' %(" The irradiance = ",H1,"mwatt/cm^2 "))

 The irradiance =  14.44 mwatt/cm^2

Example 13: PgNo-372

In [45]:
import math

# variable declaration
tr=3.5 # relative life time in ms
tnr=50 # nonrelative life time in ms
ni=tnr/(tr+tnr) # internal quantam efficiency

# results
print ('%s %.2f %s' %(" The internal quantam efficiency = ",ni*100,"%"))

 The internal quantam efficiency =  93.46 %

Example 14: PgNo-375

In [46]:
import math

# initialisation of variables
ni=0.15 # internal quantam efficiency
vf=2.0  # forward voltage in volts
i_f=15*math.pow(10,-3) # forward current in amp
x=25    # acceptance angle in degree
pil=vf*i_f # input power in Watt
po=ni*pil # output power in Watt
NA=(math.sin(x*math.pi/180))
nc=math.pow(NA,2) # numerical aperture
pf=nc*po # optical power coupled into optical fiber in w

# Results
print ('%s %.2f %s' %(" The optical power coupled into optical fiber = ",pf*1000,"mW"))

 The optical power coupled into optical fiber =  0.80 mW

Example 15: PgNo-378

In [47]:
import math

# Initialisation of variables
tnr=10  # nonrediative life time in ns
n_inj=0.80 # injection efficiency
n_ex=0.60 # extraction efficiency
nt=0.025 # total efficiency
nr=nt/(n_inj*n_ex) # non rediative life time in ns
tr=((1/nr)-1)*tnr # rediative life time in ns
# Results
print ('%s %.1f %s' %(" The rediative life time = ",tr,"ns"))

 The rediative life time =  182.0 ns

Example 16: PgNo-381

In [48]:
import math

# Variable initialisation
tr=30*math.pow(10,-9) # rise time in s
Bw=0.35/tr # bandwidth in Hz

# Results
print ('%s %.3f %s' %(" The bandwidth = ",Bw/math.pow(10,6),"MHz"))

 The bandwidth =  11.667 MHz

Example 17: PgNo-384

In [49]:
import math

# Initialisation of variables
y=630*math.pow(10,-9)# operating wavelength in m
w=25*math.pow(10,-6) # spot size in m
x=2*y/(math.pi*w) # divergence angle in radians
x1=x*180/math.pi #  divergence angle in degree

# Results
print ('%s %.3f %s' %(" The  divergence angle = ",x,"radians"))
print ('%s %.3f %s' %("\n The  divergence angle = ",x1,"degree"))

 The  divergence angle =  0.016 radians

 The  divergence angle =  0.919 degree

Example 18: PgNo-388

In [50]:
import math

# Variable initialisation
y1=550*math.pow(10,-3)# peak of eyes response in um
y2=10.6 # standard wavelength in um
y3=2.39 # predominant IR line of He-Ne laser in um
E1=1.24/y1 # energy in electron volts
E2=1.24/y2 # energy in electron volts
E3=1.24/y3 # energy in electron volts

# results
print ('%s %.3f %s' %(" The  energy = ",E1,"electron volts"))
print ('%s %.3f %s' %("\n The energy = ",E2,"electron volts"))
print ('%s %.3f %s' %("\n The energy = ",E3,"electron volts"))

 The  energy =  2.255 electron volts

 The energy =  0.117 electron volts

 The energy =  0.519 electron volts

Example 19: PgNo-391

In [51]:
import math

# variable initialisation
Eg=1.4 # energy in electron volts
y=1.24/Eg # cut off wavelength in um
y1=y*1000 # cut off wavelength in nm
# Results
print ('%s %.4f %s' %(" The  cut off wavelength = ",y1,"nm"))

 The  cut off wavelength =  885.7143 nm

Example 20: PgNo-394

In [52]:
import math

# Variable initialisation
y=1200*math.pow(10,-9)# operating wavelength in m
w=5*math.pow(10,-6)# spot size in m
x=2*y/(math.pi*w)# divergence angle in radians
x1=x*180/math.pi #  divergence angle in degree

# Results
print ('%s %.3f %s' %(" The  divergence angle = ",x,"radians"))
print ('%s %.3f %s' %("\n The  divergence angle = ",x1,"degree"))

 The  divergence angle =  0.153 radians

 The  divergence angle =  8.754 degree

Example 21: PgNo-395

In [53]:
import math

# Initialisation of variables
n1=1.48 # core refractive index
n2=1.46 # cladding refractive index 
NA=math.sqrt(math.pow(n1,2)-math.pow(n2,2)) # numerical aperture
xa=(math.asin(NA))*(180/math.pi) # acceptance angle in degree
nc=math.pow(NA,2) # coupling efficiency

# Results
print ('%s %.2f %s' %(" The  acceptance angle = ",xa,"degree"))
print ('%s %.2f %s' %("\n The coupling efficiency = ",nc*100,"%"))

 The  acceptance angle =  14.03 degree

 The coupling efficiency =  5.88 %

Example 22: PgNo-398

In [54]:
import math

# Initialisation of variables
c=3*math.pow(10,8)  # speed of light in m/s
n=3.66 # for GaAs
L=150*math.pow(10,-6) # cavity length in m
dv=c/(2*n*L) #frequency separation in Hz
dv1=dv/math.pow(10,12) # frequency separation in GHz
h=6.64*math.pow(10,-34) # plank constant
q=1.6*math.pow(10,-19) # charge of an electron
dE=(h*dv)/q # energy separation eV

# Results
print ('%s %.4f %s' %(" The frequency separation = ",dv1,"GHz"))
print ('%s %.3f %s' %("\n The energy separation = ",dE*1000,"meV"))

 The frequency separation =  0.2732 GHz

 The energy separation =  1.134 meV

Example 23: PgNo-400

In [55]:
import math

# variable initialisation
po=2*math.pow(10,-3)# optical power in watts
I=100*math.pow(10,-3)# current in amp
V=2 # applied voltage in volt
pe=I*V # electrical power in watts
n=(po/pe)*100 # conversion efficiency
# Results
print ('%s %.2f %s' %(" The conversion efficiency = ",n,"%"))

 The conversion efficiency =  1.00 %

Example 24: PgNo-403

In [56]:
import math

# variable initialisation
c=3*math.pow(10,8)  # speed of light in m/s
h=6.64*math.pow(10,-34) # plank constant
Eg=1.43 # gap energy in eV
y=(1.24*math.pow(10,-6))/Eg # wavelength in m
dy=0.1*math.pow(10,-9) # in m
df=(dy*c)/math.pow(y,2) # width in Hz
# Results
print ('%s %.3f %s' %(" The wavelength = ",y*pow(10,6),"um"))
print ('%s %.4f %s' %("\n The width = ",df/pow(10,9),"GHz"))

 The wavelength =  0.867 um

 The width =  39.8979 GHz

Example 25: PgNo-407

In [57]:
import math

# Variable declaration
tr=25.0 # rediative life time in ns
tnr=90.0 # nonrediative life time in ns
i=3.5*math.pow(10,-3) # drive current in amp
y=1.31*math.pow(10,-6) # wavelength in m
h=6.625*math.pow(10,-34) # plank constant
c=3*math.pow(10,8) # the speed of light in m/s
eq=1.6*math.pow(10,-19 )# charge
t=tr*tnr/(tr+tnr) # total carrier recombination lifetime ns
ni=t/tr # internal quantam efficiency
pil=(ni*h*c*i)/(eq*y) # internal power in watt
p_int=pil*pow(10,3) # internal power in mW
P=p_int/(ni*(ni+1)) # power emitted in mW

# Results
print ('%s %.2f %s' %(" The total carrier recombination lifetime = ",t,"ns"))
print ('%s %.2f ' %("\n The internal quantam efficiency = ", ni))
print ('%s %.2f %s' %("\n The internal power = ",p_int,"mW"))
print ('%s %.2f %s' %("\n The power emitted = ",P,"mW"))

 The total carrier recombination lifetime =  19.57 ns

 The internal quantam efficiency =  0.78 

 The internal power =  2.60 mW

 The power emitted =  1.86 mW

Example 26: PgNo-409

In [58]:
import math

# Variable initialisation
nt=0.18 # total efficiency
Eg=1.43 # band gape energy eV
V=2.5 # appied voltage in volt
n_ex=(nt*(Eg/V))*100 # external efficiency

# Results
print ('%s %.2f %s' %(" The external efficiency = ",n_ex,"%"))

 The external efficiency =  10.30 %

Example 27: PgNo-411

In [59]:
import math

# Initialisation of variables
c=3*math.pow(10,8)   # speed of light in m/s
n=3.6      # for GaAs
df=278*math.pow(10,9)  # separation in Hz
y=0.87*math.pow(10,-6) # wavelength in m
L=c/(2*n*df) # cavity length in m
l=L*math.pow(10,6) # cavity length in um
L1=math.floor(l)*math.pow(10,-6) # cavity length in m
q=(2*n*L1)/y  # number of longitudinal modes
# Results
print ('%s %.3f %s' %(" The cavity length = ",l,"um"))
print ('%s %d' %( "\n The number of longitudinal modes = ",int(q)))

 The cavity length =  149.880 um

 The number of longitudinal modes =  1233

Example 28: PgNo-415

In [60]:
import math

# Initialisation of variables
ac=14 # acceptance angle in degree
nc=math.pow((math.sin(ac*math.pi/180)),2) # coupling efficiency
l_s=-10*math.log(nc)/math.log(10) # loss in decibels

# results
print ('%s %.3f ' %(" The coupling efficiency = ",nc))
print ('%s %.3f %s' %("\n The loss = ",l_s,"decibels"))

 The coupling efficiency =  0.059 

 The loss =  12.326 decibels

Example 29: PgNo-417

In [61]:
import math

# Variable initialisation
c=3*math.pow(10,8)# speed of light in m/s
n=3.7 # for GaAs
L=500*math.pow(10,-6) # cavity length in m
y=850*math.pow(10,-9)
df=c/(2*n*L) #frequency separation in Hz
df1=df/math.pow(10,9)  # frequency separation in GHz
dy=(y*y)/(2*L*n) # wavelength in m
dy1=dy*math.pow(10,9) # wavelength in nm

# Resultsh
print ('%s %.4f %s' %(" The frequency separation = ",df1,"GHz"))
print ('%s %.3f %s' %("\n The wavelength separation = ",dy1,"nm"))

 The frequency separation =  81.0811 GHz

 The wavelength separation =  0.195 nm