Chapter 2 - Optical sources 2: the light-emitting diode

Example 7.1, page 401

import math

#Variable declaration
tr=60*10**-9                             #radiative ecombination lifetime
tnr=100*10**-9                           #nonradiative ecombination lifetime
h=6.626*10**-34                          #plancks const
c=2.998*10**8                           #speed of light
i=40*10**-3                             #drive current
e=1.602*10**-19                          #1 electron volt
h1=0.87*10**-6                           #wavelength

#Calculation
t=(tr*tnr)/(tr+tnr)                      #total carrier recombination lifetime
n=t/tr                                   #quantum efficiency 
pin=n*h*c*i/(e*h1)                       #internal power generated

#Result
print'Total carrier recombination lifetime = %.1f ns'%(t*10**9)
print'Power internally generated = %.1f mW'%(pin*10**3)

Total carrier recombination lifetime = 37.5 ns
Power internally generated = 35.6 mW

Example 7.2, page 402

import math

#Variable declaration
F=0.68                                       #crystal–air interface
n=1                                           #refractive index of air
nx=3.6                                        #refractive index of Ga


#Calculation
pe=(F*n**2)/(4*nx**2)                         #Optical power emitted
n1=pe*100/2                                   #External power efficiency

#Result
print'Optical power emitted = %.3f *Pint'%(pe)
print'External power efficiency = %.2f percent'%n1

Optical power emitted = 0.013 *Pint
External power efficiency = 0.66 percent

Example 7.3, page 404

import math

#Variable declaration
NA=0.2                                 #numerical aperture
pe=0.013                               #optical power emitted

#Calculation
nc=NA**2                               #coupling efficiency
Loss=-10*math.log10(nc)                #optical loss
pc=nc*pe                               #coupling power
Loss1=-10*math.log10(pc)               #internal power relative loss

#Result
print'Coupling efficiency = %.2f'%nc
print'Optical loss = %.1f dB'%Loss
print'Loss due internal optical power = %.1f dB'%Loss1

Coupling efficiency = 0.04
Optical loss = 14.0 dB
Loss due internal optical power = 32.8 dB

Example 7.4, page 409

import math

#Variable declaration
r=0.01                                       #fresnel reflection coefficient 
Rd=30                                        #radiance
NA=0.15                                      #numerical aperture
a=25*10**-4                                  

#Calculation
A=math.pi*a**2                               #emission area
pc=math.pi*(1-r)*A*Rd*NA**2                  #optical power

#Result
print'Optical power = %.1f uW'%(pc*10**6)

Optical power = 41.2 uW

Example 7.5, page 421

import math

#Variable declaration
pc=190*10**-6                              #optical power
p=25*10**-3                                #forward current
v=1.5                                     #voltage


#Calculation
n=(pc/(p*v))*100                        #power efficiency

#Result
print'Overall power efficiency = %.1f percent'%n

Overall power efficiency = 0.5 percent

Example 7.7, page 430

import math

#Variable declaration
pdc=300*10**-6                            #optical output power
f=20*10**6                                #frequency in hertz
ti=5*10**-9                               #minority carrier recombination lifetime
f2=100*10**6                              #frequency in hertz
t=10**-8
w=math.sqrt(3)

#Calculation
pe1=pdc/math.sqrt(1+(2*math.pi*f*ti)**2)     #Optical output power (f=20 MHz)
pe2=pdc/math.sqrt(1+(2*math.pi*f2*ti)**2)    #Optical output power (f=100 MHz)
f=w/(math.pi*t)
B=f/math.sqrt(2)

#Result
print'(a) Optical output power (f=20 MHz) = %.2f uW'%(pe1*10**6)
print'(b) Optical output power (f=100 MHz) = %.2f uW'%(pe2*10**6)
print'Electrical bandwidth = %.1f MHz'%(B*10**-6)

(a) Optical output power (f=20 MHz) = 254.02 uW
(b) Optical output power (f=100 MHz) = 90.99 uW
Electrical bandwidth = 39.0 MHz

Example 7.8, page 435

import math

#Variable declaration
bo=1.84*10**7                                       #proportionality constant
e=-1.602*10**-19                                    #charge of electron
k=1.38*10**-23                                      #boltzman constant
t1=290                                               #tempreture in kelvin
exp=0.67



#Calculation
bt=bo*math.exp(e/(k*t1))                         #degradation rate
t=-math.log(exp)/bt                                #operating lifetime

#Result
print'CW operating lifetime = %.1f x 10^9 h'%(t*10**-9)

CW operating lifetime = 5.3 x 10^9 h