# Ch-8 : Optical Sources¶

## Ex:8.1 Pg: 335¶

In :
from math import pi
from __future__ import division
tr=40## rediative life time in ns
tnr=60## nonrediative life time in ns
i=35*10**-3## drive current in amp
y=0.85*10**-6## wavelength in m
h=6.626*10**-34## plank constant
c=3*10**8## the speed of light in m/s
e=1.602*10**-19## charge
t=tr*tnr/(tr+tnr)## total carrier recombination lifetime ns
ni=t/tr## internal quantam efficiency
pi=(ni*h*c*i)/(e*y)## internal power in watt
p_int=pi*10**3## internal power in mW
print "The total carrier recombination lifetime =%d ns"%( t)#
print "\n The internal power =%0.2f mW"%( p_int)#
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


## Ex:8.2 Pg: 335¶

In :
from math import pi
from __future__ import division
tr=30## rediative life time in ns
tnr=50## nonrediative life time in ns
i=40*10**-3## drive current in amp
pi=28.4*10**-3## internal power in watt
h=6.626*10**-34## plank constant
c=3*10**8## the speed of light in m/s
e=1.602*10**-19## charge
t=tr*tnr/(tr+tnr)## total carrier recombination lifetime ns
ni=t/tr## internal quantam efficiency
y=(ni*h*c*i)/(e*pi)## peak emission wavelength in m
print "The total carrier recombination lifetime =%0.2f ns"%( t)#
print "\n The peak emission wavelength =%0.2f um"%( y*10**6)

The total carrier recombination lifetime =18.75 ns

The peak emission wavelength =1.09 um


## Ex:8.3 Pg: 336¶

In :
from math import pi
from __future__ import division
nx=3.6## refractive index
Fn=0.68## transmission factor
pe_pi=(Fn)/(4*nx**2)#
pi_p=0.3#
nep=pe_pi*pi_p## external power efficiency
print "The external power efficiency =%0.2f %%"%( nep*100)

The external power efficiency =0.39 %


## Ex:8.4 Pg: 337¶

In :
from math import pi,log
from __future__ import division
n=3.6## core refractive index
NA=0.15## numerical aperture
nc=NA**2## coupling efficiency
l_s=-10*log(nc)/log(10)## loss in db
pe_pi=0.023*0.0013## from ex 8.3
pc=-10*log(pe_pi)/log(10)## loss in decibels relative to Pint
print "The coupling efficiency =%0.2f %%"%( nc*100)#
print "\n The loss =%0.2f db"%( l_s)#
print "\n The loss in decibels relative to Pint=%0.2f db"%( pc)

The coupling efficiency =2.25 %

The loss =16.48 db

The loss in decibels relative to Pint=45.24 db


## Ex:8.5 Pg: 337¶

In :
from __future__ import division
NA=0.3## numerical aperture
A=3.14*(r*100)**2## area in cm**2
pe=3.14*(1-r)*A*rd*NA**2## optical power coupled into the fiber
Pe=pe*10**4## optical power coupled into the fiber uW
print "The optical power coupled into the fiber =%0.2f uW"%( Pe)

The optical power coupled into the fiber =7.19 uW


## Ex:8.6 Pg: 337¶

In :
from __future__ import division
pc=150*10**-6## coupling power W
p=20*10**-3*2## optical power W
npc=pc/p## overall efficiency
Npc=npc*100## percentage of overall efficiency
print "The percentage of overall efficiency =%0.2f %%"%( Npc)

The percentage of overall efficiency =0.37 %


## Ex:8.7 Pg: 338¶

In :
from __future__ import division
n=1.5## refractive index
L=0.05## crystal length in m
y=0.5*10**-6## wavelength in m
c=3*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/10**9## frequency separation of the modes in GHz
print "The number of longitudinal modes =%0.2f"%( q)#
print "\n The frequency separation of the modes =%0.2f GHz"%( Df)

The number of longitudinal modes =300000.00

The frequency separation of the modes =2.00 GHz


## Ex:8.8 Pg: 338¶

In :
from __future__ import division
Eg=1.43## bandgap energy in eV
dy=0.15*10**-9#
c=3*10**8## speed of light in m/s
y=1.24/Eg## in um
y1=y*10**-6## wavelength of optical emission in m
df=(c*dy)/(y1**2)## the line width in Hz
Df=df/10**9## the line width in GHz
print "The wavelength of optical emission  =%0.2f um"%( y)#
print "\n The frequency separation of the modes =%d GHz"%( Df)

The wavelength of optical emission  =0.87 um

The frequency separation of the modes =59 GHz


## Ex:8.9 Pg: 338¶

In :
from __future__ import division
n=3.6## refractive index
c=3*10**8## speed of light in m/s
y=0.85*10**-6## wavelength in m
df=275*10**9## frequency separation of the modes in Hz
L=c/(2*n*df)## crystal length in m
L1=L*10**6## crystal length in um
q=2*n*L/y## the number of longitudinal modes
print "The crystal length =%0.2f um"%( L1)#
print "\n The the number of longitudinal modes =%d"%( q)#
print "\n answer is wrong in textbook"

The crystal length =151.52 um

The the number of longitudinal modes =1283



## Ex:8.10 Pg: 339¶

In :
from __future__ import division
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
print "The external power efficiency =%0.2f %%"%( Nep)

The external power efficiency =13.00 %


## Ex:8.11 Pg: 339¶

In :
from math import sqrt
from __future__ import division
po=0.45*10**-3## power output in watt
d=1.5## separation distance in cm
X=(x*180)/3.14## divergence angle in degree
print "The divergence angle =%0.2f degree "%( X)

The divergence angle =48.91 degree


## Ex:8.12 Pg: 339¶

In :
from math import pi
from __future__ import division
ni=0.09## normal efficiency
d=2*2.54## separation distance in cm
vf=2.0## forward voltage in volts
i_f=65*10**-3## forward current in amp
pi=vf*i_f## input power in Watt
po=ni*pi## output power in Watt
print "The irradiance =%0.2f mwatt/cm**2 "%( H1)

The irradiance =14.44 mwatt/cm**2


## Ex:8.13 Pg: 340¶

In :
from __future__ import division
tr=3.5## relative life time in ms
tnr=50## nonrelative life time in ms
ni=tnr/(tr+tnr)## internal quantam efficiency
print "The internal quantam efficiency =%0.2f %%"%( ni*100)

The internal quantam efficiency =93.46 %


## Ex:8.14 Pg: 340¶

In :
from math import pi,sin
from __future__ import division
ni=0.15## internal quantam efficiency
vf=2.0## forward voltage in volts
i_f=15*10**-3## forward current in amp
x=25## acceptance angle in degree
pi=vf*i_f## input power in Watt
po=ni*pi## output power in Watt
NA=(sin(x*3.14/180))#
nc=NA**2## numerical aperture
pf=nc*po## optical power coupled into optical fiber in w
print "The optical power coupled into optical fiber =%0.2f mW "%( pf*1000)

The optical power coupled into optical fiber =0.80 mW


## Ex:8.15 Pg: 340¶

In :
from __future__ import division
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
print "The rediative life time =%d ns"%( tr)

The rediative life time =182 ns


## Ex:8.16 Pg: 341¶

In :
from __future__ import division
tr=30*10**-9## rise time in s
Bw=0.35/tr## bandwidth in Hz
print "The bandwidth =%0.2f MHz"%( Bw/10**6)

The bandwidth =11.67 MHz


## Ex:8.17 Pg: 341¶

In :
from __future__ import division
y=630*10**-9## operating wavelength in m
w=25*10**-6## spot size in m
x1=x*180/3.14##  divergence angle in degree
print "The  divergence angle =%0.2f radians"%( x)#
print "\n The  divergence angle =%0.2f degree"%( x1)

The  divergence angle =0.02 radians

The  divergence angle =0.92 degree


## Ex:8.18 Pg: 341¶

In :
from __future__ import division
y1=550*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
print "The  energy =%0.2f electron volts"%( E1)#
print "\n The energy =%0.2f electron volts"%( E2)#
print "\n The energy =%0.2f electron volts"%( E3)

The  energy =2.25 electron volts

The energy =0.12 electron volts

The energy =0.52 electron volts


## Ex:8.19 Pg: 342¶

In :
from __future__ import division
Eg=1.4## energy in electron volts
y=1.24/Eg## cut off wavelength in um
y1=y*1000## cut off wavelength in nm
print "The  cut off wavelength =%d nm"%( y1)

The  cut off wavelength =885 nm


## Ex:8.20 Pg: 342¶

In :
from __future__ import division
y=1200*10**-9## operating wavelength in m
w=5*10**-6## spot size in m
x1=x*180/3.14##  divergence angle in degree
print "The  divergence angle =%0.2f radians"%( x)#
print "\n The  divergence angle =%0.2f degree"%( x1)

The  divergence angle =0.15 radians

The  divergence angle =8.76 degree


## Ex:8.21 Pg: 342¶

In :
from math import pi,asin
from __future__ import division
n1=1.48## core refractive index
NA=sqrt(n1**2-n2**2)## numerical aperture
xa=(asin(NA))*(180/pi)## acceptance angle in degree
nc=NA**2## coupling efficiency
print "The  acceptance angle =%0.2f degree"%( xa)#
print "\n The coupling efficiency =%0.2f %%"%( nc*100)

The  acceptance angle =14.03 degree

The coupling efficiency =5.88 %


## Ex:8.22 Pg: 343¶

In :
from __future__ import division
c=3*10**8## speed of light in m/s
n=3.66## for GaAs
L=150*10**-6## cavity length in m
dv=c/(2*n*L)##frequency separation in Hz
dv1=dv/10**12## frequency separation in GHz
h=6.64*10**-34## plank constant
q=1.6*10**-19## charge of an electron
dE=(h*dv)/q## energy separation eV
print "The frequency separation =%0.2f GHz"%( dv1)#
print "\n The energy separation =%0.2f meV"%( dE*1000)

The frequency separation =0.27 GHz

The energy separation =1.13 meV


## Ex:8.23 Pg: 343¶

In :
from __future__ import division
po=2*10**-3## optical power in watts
I=100*10**-3## current in amp
V=2## applied voltage in volt
pe=I*V## electrical power in watts
n=(po/pe)*100## conversion efficiency
print "The conversion efficiency =%d %%"%( n)

The conversion efficiency =1 %


## Ex:8.24 Pg: 343¶

In :
from __future__ import division
c=3*10**8## speed of light in m/s
h=6.64*10**-34## plank constant
Eg=1.43## gap energy in eV
y=(1.24*10**-6)/Eg## wavelength in m
dy=0.1*10**-9## in m
df=(dy*c)/y**2## width in Hz
print "The wavelength =%0.2f um"%( y*10**6)#
print "\n The width =%d GHz"%( df/10**9)

The wavelength =0.87 um

The width =39 GHz


## Ex:8.25 Pg: 344¶

In :
from __future__ import division
tr=25## rediative life time in ns
tnr=90## nonrediative life time in ns
i=3.5*10**-3## drive current in amp
y=1.31*10**-6## wavelength in m
h=6.625*10**-34## plank constant
c=3*10**8## the speed of light in m/s
e=1.6*10**-19## charge
t=tr*tnr/(tr+tnr)## total carrier recombination lifetime ns
ni=t/tr## internal quantam efficiency
pi=(ni*h*c*i)/(e*y)## internal power in watt
p_int=pi*10**3## internal power in mW
P=p_int/(ni*(ni+1))## power emitted in mW
print "The total carrier recombination lifetime =%0.2f ns"%( t)#
print "\n The internal quantam efficiency =%0.2f "%( ni)#
print "\n The internal power =%0.2f mW"%( p_int)#
print "\n The power emitted =%0.2f mW"%( P)

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


## Ex:8.26 Pg: 344¶

In :
from __future__ import division
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
print "The external efficiency =%0.2f %%"%( n_ex)

The external efficiency =10.30 %


## Ex:8.27 Pg: 345¶

In :
from math import floor
from __future__ import division
c=3*10**8## speed of light in m/s
n=3.6## for GaAs
df=278*10**9## separation in Hz
y=0.87*10**-6## wavelength in m
L=c/(2*n*df)## cavity length in m
l=L*10**6## cavity length in um
L1=floor(l)*10**-6## cavity length in m
q=(2*n*L1)/y## number of longitudinal modes
print "The cavity length =%d um"%( l)#
print "\n The number of longitudinal modes =%d"%( q)

The cavity length =149 um

The number of longitudinal modes =1233


## Ex:8.28 Pg: 345¶

In :
from math import log,sin
from __future__ import division
ac=14## acceptance angle in degree
nc=(sin(ac*3.14/180))**2## coupling efficiency
l_s=-10*log(nc)/log(10)## loss in decibels
print "The coupling efficiency =%0.2f"%( nc)#
print "\n The loss =%0.2f decibels"%( l_s)

The coupling efficiency =0.06

The loss =12.33 decibels


## Ex:8.29 Pg: 346¶

In :
from __future__ import division
c=3*10**8## speed of light in m/s
n=3.7## for GaAs
L=500*10**-6## cavity length in m
y=850*10**-9##
df=c/(2*n*L)##frequency separation in Hz
df1=df/10**9## frequency separation in GHz
dy=(y*y)/(2*L*n)## wavelength in m
dy1=dy*10**9## wavelength in nm
print "The frequency separation =%d GHz"%( df1)#
print "\n The wavelength separation =%0.2f nm"%( dy1)

The frequency separation =81 GHz

The wavelength separation =0.20 nm