# Chapter3 - Wave propagation in planor waveguides¶

## Example 3.1 : Page 45¶

In [1]:
from math import pi, sqrt
#range of propagation constants and maximum no. of modes
n1=1.5##core refractive index
t=9.83##thickness of guided layer in micro meter
h=0.85##wavelength in µm
b1=((2*pi*n1)/(h*10**-6))##phase propagation constant in m**-1
b2=((2*pi*n2)/(h*10**-6))##phase propagation constant in m**-1
m=((4*t)/h)*(sqrt(n1**2-n2**2))##number of modes
print "range of propagation constant is %0.5e"%(b1)," to %0.4e"%(b2)," m**-1"
print"number of modes are",round(m/2)

range of propagation constant is 1.10880e+07  to 1.1014e+07  m**-1
number of modes are 4.0


## Example 3.2 : Page 51¶

In [2]:
from math import sqrt
#thickness
n1=3.6##core refractive index
h=0.85##wavelength in µm
a=((h/(2*sqrt(n1**2-n2**2))))##thickness in µm
print "thicknes of the slab should not be greater than %0.3f"%(a)," µm"

thicknes of the slab should not be greater than 0.794  µm


## Example 3.3 : Page 52¶

In [1]:
from math import pi, sqrt
from numpy import nditer
#no. of modes
print "part (a)"
n1=1.5##core refractive index
t=10.11##thickness of guided layer in micro meter
h=1.55##wavelength in µm
b1=((2*pi*n1)/(h*10**-6))##phase propagation constant in m**-1
b2=((2*pi*n2)/(h*10**-6))##phase propagation constant in m**-1
m=((2*pi*t)/h)*(sqrt(n1**2-n2**2))##number of modes
print "number of modes are : ",round(m/2)

print "part (b)"
t1=10.11##thickness of guided layer in micro meter
t=t1/2#
h=1.55##wavelength in µm
b1=((2*pi*n1)/(h*10**-6))##phase propagation constant in m**-1
b2=((2*pi*n2)/(h*10**-6))##phase propagation constant in m**-1
mo=(((2*pi*t1)/h)*(sqrt(n1**2-n2**2)))/2##number of modes
uma0=1.30644## for m=0 from the curve
uma1=2.59574## for m=1 from the curve
uma2=3.83747## for m=2 from the curve
uma3=4.9063## for m=3 from the curve
wma0=4.8263## for m=0 from the curve
wma1=4.27342## for m=1 from the curve
wma2=3.20529## for m=2 from the curve
wma3=0.963466## for m=3 from the curve
um0=uma0/(t*10**-6)##in m**-1
um1=uma1/(t*10**-6)##in m**-1
um2=uma2/(t*10**-6)##in m**-1
um3=uma3/(t*10**-6)##in m**-1
wm0=wma0/(t*10**-6)##in m**-1
wm1=wma1/(t*10**-6)##in m**-1
wm2=wma2/(t*10**-6)##in m**-1
wm3=wma3/(t*10**-6)##in m**-1
bm0=((wm0*t*10**-6)/mo)**2##for m=0
bm1=((wm1*t*10**-6)/mo)**2##for m=1
bm2=((wm2*t*10**-6)/mo)**2##for m=2
bm3=((wm3*t*10**-6)/mo)**2##for m=3
m0=sqrt((bm0*(b1**2-b2**2))+b2**2)##for m=0 in m**-1
m1=sqrt((bm1*(b1**2-b2**2))+b2**2)##for m=1 in m**-1
m2=sqrt((bm2*(b1**2-b2**2))+b2**2)##for m=2 in m**-1
m3=sqrt((bm3*(b1**2-b2**2))+b2**2)##for m=3 in m**-1
for x in params:
print x,'\t',

print '\n'
a = range(0,4)
b = [uma0, uma1, uma2, uma3]
c = [um0, um1, um2, um3]
d = [wma0, wma1, wma2, wma3]
e = [wm0, wm1, wm2, wm3]
f = [bm0, bm1, bm2, bm3]
for k,l,m,n,o,p in nditer([a,b,c,d,e,f]) :
print k,'    ',l,'        %0.4e'%m,'      ',n,'        %0.4e'%o,'       %0.5f'%p

part (a)
number of modes are :  5.0
part (b)

0      1.30644         2.5845e+05        4.8263         9.5476e+05        0.93077
1      2.59574         5.1350e+05        4.27342         8.4538e+05        0.72974
2      3.83747         7.5914e+05        3.20529         6.3408e+05        0.41053
3      4.9063         9.7058e+05        0.963466         1.9060e+05        0.03709


## Example 3.4 : Page 56¶

In [4]:
from math import sin, cos, pi
#G factor
d=0.793##in micro meter
v=pi/2##point of intersection
ua=0.934##
wa=1.262##
Y=(wa*(1+(sin(ua*pi/180))*(cos(ua*pi/180))/ua))
G=(1+((cos(ua*pi/180))**2)/Y)**(-1)
print "G factor is %0.4f"%G
#answer is wrong in the textbook

G factor is 0.5622