# Chepter 5: Power launching and coupling¶

## Example 5.1, Page Number: 192¶

In [14]:
import math

#variable declartion
phi = 0                                        #lateral coordinate(degree)
Half_power = 10                                #half power beam width(degree)

#calculation
teta = Half_power/2
L = math.log(0.5)/math.log(math.cos(teta_rad))      #power distribution co-efficient

#result
print "Power distribution co-efficient L = " ,round(L)

Power distribution co-efficient L =  182.0


## Example 5.2, Page Number: 194¶

In [1]:
import math

#variable declartion
rs = 35.0*1e-6                                        #the source radius (meter)
a = 25.0*1e-6                                         #the core radius of stepindex fiber (meter)
NA = 0.20                                             #the numerical aperture value
Bo = 150.0*1e4                                        #radiance ( W/cm^2 * sr)

#calculation
Ps = ((math.pi**2)*(rs**2))*Bo                        #power emitted by the source
PLED_step = Ps*(NA**2)                                #for larger core fiber(W)
PLED_step1 = (((a/rs)**2)*Ps)*(NA**2)                 #for smaller core fiber at the end face(W)

#result
print "For larger core fiber optical power emitted from the LED light source = " , round(PLED_step*1e3,3),"mW"
print "For smaller core fiber then area optical power coupled to step index fiber on W = " , round(PLED_step1*1e3,3),"mW"

For larger core fiber optical power emitted from the LED light source =  0.725 mW
For smaller core fiber then area optical power coupled to step index fiber on W =  0.37 mW


## Example 5.3, Page Number: 194¶

In [16]:
import math

#variable declartion
n1 = 3.6                                                #refractive index of optical source
n = 1.48                                                #refractive index of silica fiber

#calculation
R = ((n1-n)/(n1+n))**2                                  #fresnel reflection
L = -10*(math.log10(1-R))                               #power loss(dB)

#result
print"Fresnel reflection = ",round(R,3)," = ",round(R*100,1),"%"
print"Power loss = " , round(L,2),"dB"

Fresnel reflection =  0.174  =  17.4 %
Power loss =  0.83 dB


## Example 5.4, Page Number: 205¶

In [17]:
import math

#variable declartion
d = 0.3*a                                #axial offset

#calculation
PT_P = (2/math.pi)*(math.acos(d/(2*a))-(1-(d/(2*a))**2)**0.5*(d/(6*a))*(5-0.5*(d/a)**2))
PT_P_dB = 10*(math.log10(PT_P))                                #power coupled between two fibers(dB)

#result
print "Power coupled between two graded index fibers = " , round(PT_P_dB,2),"dB"

Power coupled between two graded index fibers =  -1.26 dB


## Example 5.5, Page Number: 211¶

In [2]:
import math

#variable declartion
V = 2.4                                   #normalized frequency
n1 = 1.47                                 #core refractive index
n2 = 1.465                                #cladding refractive index
a = (9.0/2.0)*10**-6                      #core radii (meters)
d = 1*10**-6                              #lateral offset (meters)

#calculation
W = a*(0.65+1.619*V**(-1.5)+2.879*V**-6)            #mode field diameter (um)
Lsm = -10*(math.log10(math.exp(-(d/W)**2)))         #Loss between identical fibers(dB)

#result
print "Mode field diameter = " , round(W*1e6,2),"um"
print "Loss between single mode fibers due to lateral misalignment = " , round(Lsm,2),"dB"

Mode field diameter =  4.95 um
Loss between single mode fibers due to lateral misalignment =  0.18 dB


## Example 5.6, Page Number: 212¶

In [3]:
import math

#variable declartion
V = 2.4                                       #normalized frequency
n1 = 1.47                                     #core refractive index
n2 = 1.465                                    #cladding refractive index
a = (9.0/2.0)*1e-6                            #coreradii in meters
d = 1*1e-6                                    #lateral offset (m)
teta = 1                                      #in (degrees)

Loss between single mode fibers due to angular misalignment =  0.41 dB