Chapter7 - Source to fiber power launching and photodetectors

Example 7.2.1, page 7-11

In [2]:
from __future__ import division
from numpy import pi, sqrt, log10
n1=3.4     #refractive index of optical source
n=1.46      #refractive index of silica fiber
r=((n1-n)/(n1+n))**2     #computing Frensel reflection
L=-10*log10(1-r)       #computing loss
print "Frensel reflection is %.3f.\nPower loss is %.2f dB." %(r,L) 

Frensel reflection is 0.159.
Power loss is 0.75 dB.

Example 7.2.2, page 7-11

In [3]:
r=35*10**-6         #radius
R=150       #Lambertian emission pattern
NA=0.2      #Numerical aperture
Pled = pi**2*r**2*R*NA**2 
Pled=Pled*10**7 
print "Optical power for larger core of 35 micrometer is %.3f mW." %(Pled) 
r1=25*10**-6 
Pled1=(r1/r)**2*Pled 
print "Optical power for smaller core of 25 micrometer is %.2f mW." %(Pled1) 

Optical power for larger core of 35 micrometer is 0.725 mW.
Optical power for smaller core of 25 micrometer is 0.37 mW.

Example 7.2.3, page 7-12

In [4]:
r=25*10**-6         #radius
R=39       #Lambertian emission pattern
NA=0.25     #numerical aperture
a=35*10**-6     #area
Pc1= pi**2*a**2*R*NA**2   #computing coupled power when r<a
Pc1=Pc1*10**7 
Pc= pi**2*r**2*R*NA**2    #computing coupled power when r>a
Pc=Pc*10**7 
print "Optical power when r>a is %.2f mW.\nOptical power when r<a is %.3f mW." %(Pc,Pc1) 

Optical power when r>a is 0.15 mW.
Optical power when r<a is 0.295 mW.

Example 7.5.1, page 7-23

In [6]:
h=6.626*10**-34     #plank's constant
c=3*10**8       #speed of light
e=1.6*10**-19   #charge of electron
q=1.43      #Bandgap energy
lamda=h*c/(q*e)*10**9     #computing wavelength
print "Wavelength is %d nm" %(lamda) 

Wavelength is 868 nm

Example 7.5.2, page 7-23

In [7]:
R=0.6       #responsivity
Pin=15      #optical power in microwatt
Ip=R*Pin        #computing photocurrent
print "Photocurrent generated is %d microAmpere." %Ip 

Photocurrent generated is 9 microAmpere.

Example 7.5.3, page 7-23

In [8]:
lamda1=1300*10**-9 
lamda2=1600*10**-9 
h=6.625*10**-34     #plank's constant
c=3*10**8       #speed of light
q=1.6*10**-19   #charge of electron
eta=90/100  #quantum efficiency
E=0.73       #energy gap in eV
R1=eta*q*lamda1/(h*c) 
R2=eta*q*lamda2/(h*c) 
lamdac=1.24/E 
print "Responsivity at 1300nm is %.2f A/W.\nResponsivity at 1600nm is %.2f A/W.\nCut-off wavelength is %.1f micrometer." %(R1,R2,lamdac) 
#R1 is calculated wrong.

Responsivity at 1300nm is 0.94 A/W.
Responsivity at 1600nm is 1.16 A/W.
Cut-off wavelength is 1.7 micrometer.

Example 7.5.4, page 7-24

In [10]:
lamda=0.8*10**-6 
h=6.625*10**-34     #plank's constant
c=3*10**8       #speed of light
q=1.6*10**-19   #charge of electron
ne=1.8*10**11   #electrons collected
np=4*10**11     #photons incident
eta=ne/np       #computing quantum efficiency
R=eta*q*lamda/(h*c)     #computing responsivity
print "Responsivity of photodiode at 0.8 micrometer is %.3f A/W." %R 
#answer in the book is wrong. 

Responsivity of photodiode at 0.8 micrometer is 0.290 A/W.

Example 7.5.5, page 7-24

In [17]:
E=1.8*10**-19  # Energy of photon
nq=70/100  # Quantum
Ip=3  # current in uA
h=6.625*10**-34     #plank's constant
c=3*10**8       #speed of light
lamda=h*c/E*10**6  # wavelength in micro meter
print "Photodiode operates at %0.2f micro meter" %lamda
q=1.6*10**-19   #charge of electron
R=nq*q/E     #computing responsivity
Popt=Ip/R
print "Incident optical power required =  %.3f uW." %Popt 

Photodiode operates at 1.10 micro meter
Incident optical power required =  4.821 uW.

Example 7.5.6, page 7-25

In [18]:
h=6.626*10**-34     #plank's constant
c=3*10**8       #speed of light
q=1.6*10**-19   #charge of electron
E=1.35       #energy gap in eV
lamda=h*c/(q*E)    #computing wavelength
lamda=lamda*10**6 
print "The InP photodetector will stop operation above %.2f micrometer." %(lamda) 
#calculation error in the book.

The InP photodetector will stop operation above 0.92 micrometer.

Example 7.5.7, page 7-26

In [19]:
h=6.626*10**-34     #plank's constant
c=3*10**8       #speed of light
eta=65/100  #quantum efficiency
I=2.5*10**-6      #photocurrent 
E=1.5*10**-19   #energy of photns
q=1.6*10**-19   #charge of electron
lamda=h*c/E    #computing wavelength
R=eta*q*lamda/(h*c)     #computing responsivity
Popt=I/R        #computing optical power
lamda=lamda*10**6 
Popt=Popt*10**6 
print "Wavelength is %.3f micrometer.\nResponsivity is %.3f A/W.\nIncident optical power required is %.1f microWatt." %(lamda,R,Popt) 
#answer of R(responsivity) in the book is calculated as 0.694 A/W, deviation of 0.001.

Wavelength is 1.325 micrometer.
Responsivity is 0.693 A/W.
Incident optical power required is 3.6 microWatt.

Example 7.5.8, page 7-26

In [20]:
ne=3.9*10**6   #electrons collected
np=6*10**6     #photons incident
eta=100*ne/np   #computing efficiency
print "Quantum efficiency is %d percent." %(eta) 

Quantum efficiency is 65 percent.

Example 7.8.1, page 7-37

In [21]:
w=25*10**-6     #width
v=1*10**5       #velocity
r=40*10**-6     #radius
eps=12.5*10**-13 
t=w/v       #computing drift time
c=eps*3.14*(r)**2/w      #computing junction capacitance
c=c*10**16 
print "Drift time %.1e sec.\nJunction capacitance %.1f pf." %(t,c) 
#calculation error in drift time answer.

Drift time 2.5e-10 sec.
Junction capacitance 2.5 pf.

Example 7.8.2, page 7-38

In [22]:
w=20*10**-6     #width
v=4*10**4       #velocity
t=w/v       #computing drift time
BW=(2*pi*t)**-1         #computing bandwidth
rt=1/BW     #computing response time
rt=rt*10**9 
print "Maximum response time is %.1f ns." %(rt)
#Calculation error in the book.

Maximum response time is 3.1 ns.

Example 7.9.1, page 7-43

In [23]:
lamda=1.4*10**-6 
h=6.626*10**-34     #plank's constant
c=3*10**8       #speed of light
q=1.6*10**-19   #charge of electron
eta=65/100  #quantum efficiency
I=10*10**-9     #current
NEP= h*c*sqrt(2*q*I)/(eta*q*lamda) 
D=NEP**-1 
print "Noise equivalent power is %.3e W.\nSpecific directivity is %.2e." %(NEP,D) 
#answers in the book for NEP & D is wrong.

Noise equivalent power is 7.723e-14 W.
Specific directivity is 1.29e+13.

Example 7.9.2, page 7-44

In [24]:
lamda=1300*10**-9 
h=6.626*10**-34     #plank's constant
c=3*10**8       #speed of light
q=1.6*10**-19   #charge of electron
eta=90/100  #quantum efficiency
P0=300*10**-9   #optical power
Id=4     #dark current
B=20*10**6      #bandwidth
K=1.39*10**-23  #Boltzman constant
T=298       #temperature
R=1000      #load resister
Ip= 10**9*eta*P0*q*lamda/(h*c) 
Its=10**9*(2*q*B*(Ip+Id)) 
Its=sqrt(Its) 
print "rms shot noise current is %.2f nA." %(Its) 
It= 4*K*T*B/R 
It=sqrt(It) 
print "Thermal noise is %.2e A." %(It) 
#answer given in book for shot noise & Thermal noise are wrong.

rms shot noise current is 1.35 nA.
Thermal noise is 1.82e-08 A.

Example 7.10.1, page 7-51

In [27]:
from numpy import floor
lamda=0.85*10**-6 
h=6.626*10**-34     #plank's constant
c=3*10**8       #speed of light
q=1.6*10**-19   #charge of electron
eta=75/100  #quantum efficiency
P0=0.6*10**-6   #incident optical power
Im=15*10**2    #avalanche gain
R= eta*q*lamda/(h*c)    #computing responsivity
Ip=10**8*P0*R        #computing photocurrent
Ip=floor(Ip) 
M=Im/Ip         #computing multiplication factor
print "Multiplication factor is %d." %(M) 

Multiplication factor is 50.

Example 7.10.2, page 7-51

In [46]:
from __future__ import division
lamda=900*10**-9  # Wavelength in m
P0=0.5 # Optical power
Im=10  # Photocurrent
h=6.626*10**-34     #plank's constant
c=3*10**8       #speed of light
q=1.6*10**-19   #charge of electron
eta=65.0/100  #quantum efficiency
R= eta*q*lamda/(h*c)    #computing responsivity
Ip=P0*R        #computing photocurrent 
M=Im/Ip         #computing multiplication factor
print "Multiplication factor is %0.2f." %(M) 
# Answer is wrong in the textbook.

Multiplication factor is 42.47.

Example 7.10.3, page 7-52

In [47]:
lamda=900*10**-9 
h=6.626*10**-34     #plank's constant
c=3*10**8       #speed of light
q=1.6*10**-19   #charge of electron
eta=65/100  #quantum efficiency
P0=0.5*10**-6   #incident optical power
Im=10*10**2    #avalanche gain
R= eta*q*lamda/(h*c)    #computing responsivity
Ip=10**8*P0*R        #computing photocurrent
M=Im/Ip         #computing multiplication factor
print "Multiplication factor is %d." %(M) 
#answer in the book is wrong.

Multiplication factor is 42.

Example 7.10.3, page 7-52

In [48]:
lamda=900*10**-9 
h=6.626*10**-34     #plank's constant
c=3*10**8       #speed of light
q=1.6*10**-19   #charge of electron
eta=65/100  #quantum efficiency
P0=0.5*10**-6   #incident optical power
Im=10*10**2    #avalanche gain
R= eta*q*lamda/(h*c)    #computong responsivity
Ip=10**8*P0*R        #computing photocurrent
M=Im/Ip         #computing multiplication factor
print "Multiplication factor is %d." %M 

Multiplication factor is 42.