# Chapter 11: Optical amplifires¶

## Example 11.1, Page Number: 397¶

In [1]:
import math

#variable declaration
Vg = 2*10**8                             #group velocity (m/s)
h = 6.625*10**-34                        #planks constant (J*s)
C = 3*10**8                              #free space velocity (m/s)
Lam_bda = 1550*10**-9                    #operating wave length(nm)
V = C/Lam_bda                            #frequency (Hz)
w = 5*10**-6                             #width of optical amplifier (meters)
d = 0.5*10**-6                           #thickness of optical amplifier (meter)
Ps = 10**-6                              #optical signal of power

#calculation
Nph = Ps/(Vg*h*V*w*d)                   #photon density

#result
print "The photon density Nph = " ,round(Nph*1e-16,2),"e+6 photons/m3"

The photon density Nph =  1.56 e+6 photons/m3


## Example 11.2, Page Number: 397¶

### Example 11.2(a)¶

In [2]:
import math

#varible declaration
I = 100.0*10**-3                                    #bias current (Amps)
w = 3.0*10**-6                                      #active area width (meters)
L = 500.0*10**-6                                    #amplifier lenght (meters)
d = 0.3*10**-6                                      #active area thick ness(meters)
q = 1.6*10**-19                                     #charge (coulombs)
Tuo = 0.3                                           #The confinement factor
a = 2*10**-20                                       #gain coefficient (square meter)
J = I/(w*L)                                         #3bias current density (Amp/squre meter)
nth = 10**24                                        #threshold density (per cubic meter)
Tuor = 10**-9;                                      #Time constant (seconds)

#calculation
Rp = I/(q*d*w*L)                                    # The pumping rate((electron/m3)/s)

#result
print "The pumping rate Rp = " , round(Rp*1e-33,2)*10**33," (electron/m3)/s"

The pumping rate Rp =  1.39e+33  (electron/m3)/s


### Example 11.2(b)¶

In [3]:
import math

#varible declaration
I = 100.0*10**-3                                    #bias current (Amps)
w = 3.0*10**-6                                      #active area width (meters)
L = 500.0*10**-6                                    #amplifier lenght (meters)
d = 0.3*10**-6                                      #active area thick ness(meters)
q = 1.6*10**-19                                     #charge (coulombs)
Tuo = 0.3                                           #The confinement factor
a = 2*10**-20                                       #gain coefficient (square meter)
J = I/(w*L)                                         #3bias current density (Amp/squre meter)
nth = 10**24                                        #threshold density (per cubic meter)
Tuor = 10**-9;                                      #Time constant (seconds)

#calculation
Rp=I/(q*d*w*L)                                                  #The pumping rate((electron/m3)/s)
g0 = Tuo*a*Tuor*(round(Rp*1e-33,2)*10**33-(nth/Tuor))           #The zero singal(1/cm)

#result
print "The zero singal g0 = " ,round(g0),"1/m =", round(g0/100,1),"1/cm"

The zero singal g0 =  2340.0 1/m = 23.4 1/cm


## Example 11.3, Page Number: 404¶

In [4]:
import math

#variable declaration
Lambda_p = 980.0*10**-9                     #pump wavelength(nm)
Lambda_s = 1550.0*10**-9                    #signal wavelength(nm)
Pp_in = 30.0*10**-3                         #input pump power (watts)
G = 1.0*10**2                               #gain

#calculation
Ps_in = (Lambda_p/Lambda_s)*Pp_in/(G-1)         #maximum input power(W)
Ps_out = Ps_in+(Lambda_p/Lambda_s)*Pp_in        #maximum output power(W)
Ps_out_db = 10*(math.log10(Ps_out*10**3))       #maximum output power(dBm)

#result
print "The maximum input power = " , round(Ps_in*10**6) , "uW"
print "The maximum output power = " , round(Ps_out*10**3,1),"mW"
print "The maximum output power = " , round(Ps_out_db,1),"dBm"

The maximum input power =  192.0 uW
The maximum output power =  19.2 mW
The maximum output power =  12.8 dBm


## Example 11.6, Page Number: 412¶

In [7]:
import math

#variable declarion
Q = 6                                        #Q factor of 6

#calculation
OSNR = 0.5*Q*(Q+math.sqrt(2))
OSNR_DB = 10*(math.log10(OSNR))              #The optical signal to noise ratio(dB)

#result
print "The optical signal to noise ratio (OSNR) = " ,round(OSNR,2),"=", round(OSNR_DB,1),"dB"

The optical signal to noise ratio (OSNR) =  22.24 = 13.5 dB


## Example 11.7, Page Number: 413¶

In [8]:
import math

#variable declaration
Lambda_p = 980*10**-9                              #pump wavelength (meters)
Lambda_s = 1540*10**-9                             #signal wavelength (meters)
Ps_out = 10*10**-3                                 #output signal power(mW)
Ps_in = 10**-3                                     #input signal power(mW)

#calculation
Pp_in = (Lambda_s/Lambda_p)*(Ps_out-Ps_in)         #pump power at input(mW)

#result
print "Pump power = " , round(Pp_in*10**3) ,"mW"

Pump power =  14.0 mW


## Example 11.8, Page Number: 413¶

In [9]:
import math

#variable declaration
P_ASE1 = -22                     #ASE level (dBm)
P_ASE2 = -16                     #ASE level (dBm)
Pout = 6                         #amplified signal level (dBm)

#calculation
OSNR1 = Pout-P_ASE1
OSNR2 = Pout-P_ASE2              #The optical signal to noise ratio(dBm)

#result
print "Optical SNR OSNR1 = " , round(OSNR1) , "dBm"
print "Optical SNR OSNR2 = " , round(OSNR2) , "dBm"

Optical SNR OSNR1 =  28.0 dBm
Optical SNR OSNR2 =  22.0 dBm


## Example 11.9, Page Number: 414¶

In [10]:
import math

#variable declaration
G1 = 10**(30/10)                            #gain(dB)
G2 = 10**(20/10)

#calculation
Fpath1 = (((G1-1)/math.log(G1))**2)/G1             #noise penalty factor for G1
fpath_db1=10*math.log10(Fpath1)                    #noise penalty factor(dB)
Fpath2 = (((G2-1)/math.log(G2))**2)/G2             #noise penalty factor for G2
fpath_db2=10*math.log10(Fpath2)                    #noise penalty factor(dB)

#result
print "Noise penalty factor for G1 = ",round(fpath_db1,1),"dB"
print "Noise penalty factor for G2 = ",round(fpath_db2,1),"dB"

Noise penalty factor for G1 =  13.2 dB
Noise penalty factor for G2 =  6.6 dB


## Example 11.10, Page Number: 415¶

In [11]:
import math

#variable declaration
etta = 0.65                                     #quantum efficiency
nsp = 2                                         #population inversion
Lambda = 1550*10**-9                            #oprating wavelength(meters)
T = 300                                         #room temperature(kelvin)
h = 6.625*10**-34                               #planks constant(J*s)
C = 3*10**8                                     #free space velocity(m/s)
kB = 1.38*10**-23                               #boltzmann's constant
V = C/ Lambda                                   #(Hz)
q = 1.6*10**-19                                 #Charge (coulombs)

#calculation
Ps_in = kB*T*h*V/(R*nsp*(etta**2)*(q**2))           #maxiamum input optical power level(Watt)

#result
print "Upper bound input otical power level <",round(Ps_in*10**6,1),"uW"

Upper bound input otical power level < 490.8 uW