# Chapter 10: WDM concepts and Components¶

## Example 10.1, Page Number: 343¶

In [20]:
import math

#variable declaration
Lambda2 = 1520.0*10**-9                           #spectral bandwidth(nHz)
Lambda1 = 1420.0*10**-9
C = 3.0*10**8                                     #free space velocity(m/s)
delta_Lambda1=100.0*10**-9                        #spectral band(nm)
delta_Lambda2=105.0*10**-9

#calculation
delta_v1= C*delta_Lambda1 /(Lambda1**2)           #optical bandwidth(Hz)
delta_v2= C*delta_Lambda2/(Lambda2**2)

#result
print "Usable spectral band for 100 nm = ",round(delta_v1*10**-12,1),"THz"
print "Usable spectral band for 100 nm = ",round(delta_v2*10**-12),"THz"

Usable spectral band for 100 nm =  14.9 THz
Usable spectral band for 100 nm =  14.0 THz


## Example 10.2, Page Number: 343¶

In [21]:
import math

#variable declaration
c=3.0*pow(10,8)                                    #free space velocity(m/s)
delta_lambda=0.8*pow(10,-9)                        #spectral band (meter)
lam_bda=1550*pow(10,-9)                            #wavwlenth (meter)

#calculation
delta_v=(c*delta_lambda)/lam_bda**2                #Mean freqency spacing(GHz)

#result
print "Mean freqency spacing = " , round(delta_v*(pow(10,-9))),"GHz"

Mean freqency spacing =  100.0 GHz


## Example 10.3, Page Number: 348¶

In [22]:
import math

#variable declaration
p0=200.0*pow(10,-6)                              #input optical power level (watts)
p1=90.0*pow(10,-6)                               #output power at port-1
p2=85.0*pow(10,-6)                               #output power at port-2
p3=6.3*pow(10,-9)                                #output power at port-3

#calculation
coupling_ratio=(p2/(p1+p2))*100                    #Coupling ratio(%)
Excess_loss=10*(math.log10(p0/(p1+p2)))            #Excess loss(dB)
Insertion_loss_0_1=10*(math.log10(p0/p1))          #Insertion loss(dB)
Insertion_loss_0_2=10*(math.log10(p0/p2))
Return_loss = 10*(math.log10(p3/p0))               #Return loss(dB)

#result
print "Coupling ratio = " , round(coupling_ratio,1) , "%"
print "Excess loss = " , round(Excess_loss,2) , "dB"
print "Insertion loss (port0 to port1 = " , round(Insertion_loss_0_1,2), "dB"
print "Insertion loss (port0 to port2 = " , round(Insertion_loss_0_2,2), "dB"
print "Return loss = " , round(Return_loss), "dB"

Coupling ratio =  48.6 %
Excess loss =  0.58 dB
Insertion loss (port0 to port1 =  3.47 dB
Insertion loss (port0 to port2 =  3.72 dB
Return loss =  -45.0 dB


## Example 10.6, Page Number: 353¶

In [23]:
import math

#variable declaration
k = 0.6/(10**-3)                           #Coupling coefficint (per mm)
m = 1                                      #mode=1

#calculation
L = ((math.pi)*(m+1))/(2*k)                #coupling length(mm)

#result
print "Coupling length L = ",round(L*(10**3),2),"mm"

Coupling length L =  5.24 mm


## Example 10.7, Page Number: 355¶

In [24]:
import math

#variable declaration
Power_Lost = 5.0/100.0                      #lost power%
FT = 1-Power_Lost                           #power coupled
N = 32

#calculation
Excess_Loss = -10*(math.log10(FT**(math.log10(N)/math.log10(2))))               #Excess Loss(dB)
Splitting_Loss = -10*math.log10(N)                                              #Splitting Loss(dB)
Total_Loss = (-Excess_Loss) + Splitting_Loss

#result
print "Excess Loss = " , round(Excess_Loss,1) ,"dB"
print "Splitting Loss = " , round(abs(Splitting_Loss)) ,"dB"
print "Total Loss experienced in Star Couplers = " , round(-Total_Loss,1) , "dB"

Excess Loss =  1.1 dB
Splitting Loss =  15.0 dB
Total Loss experienced in Star Couplers =  16.2 dB


## Example 10.8, Page Number: 357¶

### Example 10.8(a)¶

In [28]:
import math

#variable declaration
delta_lambda=0.08*pow(10,-9)                         #wavelength spacing (nm)
lam_bda=1550*pow(10,-9)                              #wavelength (meters)
neff=1.5                                             #effective refractive index in the waveguide
c=3*10**8                                            #free space velocity(m/s)

#calculation
delta_v1=10*10**9                                    #Frequency sepration
delta_l1=c/(2*neff*delta_v1)                         #Waveguide length(mm)

#result
print "Waveguide length1 diffrence = " , round(delta_l1*10**3) ,"mm"

Waveguide length1 diffrence =  10.0 mm


### Example 10.8(b)¶

In [29]:
import math

#variable declaration
delta_lambda=0.08*pow(10,-9)                         #wavelength spacing (nm)
lam_bda=1550*pow(10,-9)                              #wavelength (meters)
neff=1.5                                             #effective refractive index in the waveguide
c=3*10**8                                            #free space velocity(m/s)

#calculation
delta_v2=130*10**9                                   #Frequency sepration
delta_l2=c/(2*neff*delta_v2)                         #Waveguide length(mm)

#result
print "Waveguide length2 diffrence = " , round(delta_l2*10**3,2) ,"mm"

Waveguide length2 diffrence =  0.77 mm


## Example 10.9, Page Number: 364¶

### Example 10.9(a)¶

In [30]:
import math

#variable declaration
kl=1.0                            #coupling coeffiecint and length
k2=2.0
k3=3.0

#calculation
rmax1=math.tanh(kl)**2                       #peak reflectivity Rmax
rmax2=math.tanh(k2)**2
rmax3=math.tanh(k3)**2

#result
print "For k1 Rmax = " , round(rmax1*100) ,"%"
print "For k2 Rmax = " , round(rmax2*100) ,"%"
print "For k3 Rmax = " ,round(rmax3*100) ,"%"

For k1 Rmax =  58.0 %
For k2 Rmax =  93.0 %
For k3 Rmax =  99.0 %


### Example 10.9(b)¶

In [31]:
import math

#variable declaration
L=0.5                                             #length (cm)
lam_bda_brg = 1530*10**-9                         #reflaaction wavelength(nm)
n_eff = 1.48                                      #mode effective index of core
delta_n = 2.5*10**-4
etta = 0.82                                       #efficiency(%)

#calculation
k = (math.pi*delta_n*etta)/(lam_bda_brg)                                                         #coupling coefficint
delta_lambda = (lam_bda_brg**2)*(math.sqrt(((k/100*L)**2)+math.pi**2))/(math.pi*n_eff*L)         #bandwidth

#result
print "Coupling coefficint = ", round(k/100,1), "1/cm"
print "Total bandwidth = ", round(delta_lambda*10**11,2),"nm"

Coupling coefficint =  4.2 1/cm
Total bandwidth =  0.38 nm


## Example 10.10, Page Number: 372¶

In [32]:
import math

#variable declaration
lambda_c=1550*pow(10,-9)                         #wavelength(nm)
nc=1.45                                          #refrective index of grating array waveguide
ns=1.45                                          #refrective index of teh star coupler
ng=1.47                                          #group index of grating array waveguide
x=5*10**-6                                       #spacing between input waveguide(um)
d=5*10**-6                                       #spacing between output waveguide(um)
m=1                                              #mode
lf=10*10**-3                                     #distance between Tx to Rx

#calculation
delta_l=m*lambda_c/nc                            #waveguide length diffrence(um)
delta_lambda=(x/lf)*(ns*d/m)*(ns/ng)             #channel spacing(nm)

#result
print "Waveguide length diffrence = " , round(delta_l*10**6,3), "um"
print "Channel spacing interms of wavelength = " , round(delta_lambda*10**9,2) ,"nm"

Waveguide length diffrence =  1.069 um
Channel spacing interms of wavelength =  3.58 nm


## Example 10.11, Page Number: 373¶

In [33]:
import math

#variable declaration
nc=1.45                                            #refractive index
Lambda_C = 1550.5*pow(10,-9)                       #center wavelength(nm)
delta_Lambda = 32.2*pow(10,-9)                     #free spectral range(nm)
c=3*10**8                                          #free space velocity(m/s)

#calculation
delta_L = Lambda_C**2/(nc*delta_Lambda)            #length diffrence(um)

#result
print "Length diffrence between adjacent array waveguide = " , round(delta_L*10**6,2) , "um"

Length diffrence between adjacent array waveguide =  51.49 um


## Example 10.12, Page Number: 383¶

In [34]:
import math

#variable declaration
Lam_bda = 1550*pow(10,-9)                                 #DBR laser wavelength(nm)
delta_neff = 0.0065                                       #index change

#calculation
delta_Lambda_tune = Lam_bda*delta_neff                    #tuning range (meter)
delta_Lambda_signal = 0.02*pow(10,-9)                     #spectral width(meter)
delta_Lambda_channel = 10*delta_Lambda_signal             #channal width
N = delta_Lambda_tune/delta_Lambda_channel                #The number of channels

#result
print "Tuning wavelength = " , round(delta_Lambda_tune*10**9) , "nm"
print "The number of channels that can operate in this tuning range is N = " , round(N)

Tuning wavelength =  10.0 nm
The number of channels that can operate in this tuning range is N =  50.0