Chapter 6 - Optical sources 1: the laser

Example 6.1, page 301

In [1]:
import math

#Variable declaration
c=2.998*10**8                              #speed of light in m/s
h=0.5*10**-6                               #operating wavelength in um
t=1000                                     #tempreture in K

#Calculation
f=c/h                                                 #operating frequency
r=1/math.exp((6.626*10**-34*f)/(1.381*10**-23*t))     #ratio

#Result
print'Ratio = %.1f x 10^-13 '%(r*10**13)

Ratio = 3.2 x 10^-13

Example 6.2, page 306

In [2]:
#Variable declaration
n=1.78                                   #refractive index
L=0.04                                   #length in meter
h=0.55*10**-6                            #peak emission wavelength in um
c=2.998*10**8                            #speed of light in meter

#Calculation
q=2*n*L/h                                #no of longitudinal modes
sf=c/(2*n*L)                             #frequency separation modes

#Result
print'No of longitudinal modes = %.1f x 10^5'%(q/10**5)
print'Frequency separation modes = %.1f GHz'%(sf/10**9)

No of longitudinal modes = 2.6 x 10^5
Frequency separation modes = 2.1 GHz

Example 6.3, page 308

In [3]:
#Variable declaration
a=30                                    #active cavity losses
L=0.06                                  #length in meter
r=0.3                                   #reflectivity


#Calculation
gm=a+(1/L)+(1/r)                           #laser gain coefficient


#Result
print'Laser gain coefficient = %.1f cm^-1'%gm

Laser gain coefficient = 50.0 cm^-1

Example 6.4, page 315

In [4]:
import math

#Variable declaration
Bt1=7.21*10**-10                                  #recombination coefficient of GaAs
Bt2=1.79*10**-15                                  #recombination coefficient of Si
N=10**18                                          #hole concentration 

#Calculation
tr1=(Bt1*N)**-1                                   #radiative carrier lifetime of GaAs
tr2=(Bt2*N)**-1                                   #radiative carrier lifetime of Si

#Result
print'Radiative carrier lifetime of silicon = %.2f ms'%(tr2*1000)
print'Radiative carrier lifetime of gallium arsenide = %.2f ns'%(tr1*10**9)

Radiative carrier lifetime of silicon = 0.56 ms
Radiative carrier lifetime of gallium arsenide = 1.39 ns

Example 6.5, page 322

In [5]:
import math

#Variable declaration
n=3.6                                         #refractive index
B=21*10**-3                                   #gain factor
a=10                                          #loss coefficient per cm
L=250*10**-4                                  #optical cavity length
w=100*10**-4                                  #optical cavity width

#Calculation
r=((n-1)/(n+1))**2                             #reflectivity
jth=(1/B)*(a+math.log(1/r)/L)                  #threshold current density
area=L*w                                       #area
ith=jth*area                                   #threshold current
 
#Result
print'Threshold current = %.1f mA'%(ith*1000)

Threshold current = 662.4 mA

Example 6.6, page 330

In [6]:
import math

#Variable declaration
nt=0.18                                  #total efficiency
E=1.43                                   #bandgap energy
V=2.5                                    #voltage


#Calculation
nep=nt*(E/V)*100                            #external power efficiency

#Result
print'External power efficiency = %d percent'%nep

External power efficiency = 10 percent

Example 6.7, page 352

In [7]:
import math

#Variable declaration
t1=20+273                               #tempreture 20 °C convert to kelvin
t2=80+273                               #tempreture 80 °C convert to kelvin
L1=160                                  #tempreture 160K
L2=55                                   #tempreture 55K

#Calculation
a=t1*L1**-1                          
b=t2*L1**-1
c=t1*L2**-1
d=t2*L2**-1
Ja1=math.exp(a)                           #For the AlGaAs device
Ja2=math.exp(b)                           #For the AlGaAs device
Ja=Ja2/Ja1                                #ratio of the current densities
Jb1=math.exp(c)                           #For the InGaAsP device
Jb2=math.exp(d)                           #For the InGaAsP device
Jb=Jb2/Jb1                                #ratio of the current densities

#Result
print'Threshold current density at 20 °C = %.2f'%Ja
print'                          at 80 °C = %.2f' %Jb

Threshold current density at 20 °C = 1.45
                          at 80 °C = 2.98

Example 6.8, page 359

In [8]:
import math

#Variable declaration
s=10**-15                            #RIN value    
f=100*10**6                          #bandwidth
e=1.602*10**-19                      #1 electron volt
n=0.6                                #quantum efficiency
h=1.55*10**-6                        #wavelength in um
pe=2*10**-3                          #power incident
B=100*10**6                          #bandwidth
h1=6.626*10**-34                     #plancks constant
c=2.998*10**8                        #speed of light

#Calculation
sr=s*f                                 
rin=math.sqrt(sr)                                 #RMS value of power fluctuation
irn=e*n*h*rin*pe*math.sqrt(B)*10**-4/(h1*c)       #RMS noise current

#Result
print'(a) RMS value of power fluctuation = %.2f x 10^-4 W'%(rin*10**4)
print'(b) RMS noise current = %.2f x 10^-7 A'%(irn*10**7)

(a) RMS value of power fluctuation = 3.16 x 10^-4 W
(b) RMS noise current = 4.74 x 10^-7 A