# Chapter Three : Modulation Of Light¶

## Example 3.1, Page Number 97¶

In [1]:
print "---------------------------------------------------------------"
print " Material   Linear Electro Optic    n+      n-       Relative "
print "            Coefficient r(pm/V)                    Permittivity"
print "----------------------------------------------------------------"
print " KDP           10.6               1.51    1.47         42      "
print " KD*P          26.4               1.51    1.47         50      "
print " ADP           8.5                1.52    1.48         43   "
print " CdTe          6.8                2.6                  10.6"
print " GaAs          1.6                3.6                  11.5"
print " ZnS           2.1                2.32                 16"
print "-----------------------------------------------------------------"
print "                      Table 3.1"
l=10*(10**-3) #width of crystal
V=4000 #Applied Voltage

#From equation 3.1

#Using data in Table 3.1
dn=0.5*26.4*(10**-12)*(1.51**3)*(V/(10**-2)) #where dn is the change in refraction index
print "The Change in Refraction Index due to pockels effect is %.2e "%(dn)

---------------------------------------------------------------
Material   Linear Electro Optic    n+      n-       Relative
Coefficient r(pm/V)                    Permittivity
----------------------------------------------------------------
KDP           10.6               1.51    1.47         42
KD*P          26.4               1.51    1.47         50
CdTe          6.8                2.6                  10.6
GaAs          1.6                3.6                  11.5
ZnS           2.1                2.32                 16
-----------------------------------------------------------------
Table 3.1
The Change in Refraction Index due to pockels effect is 1.82e-05


## Example 3.2, Page Number 101¶

In [2]:
print "---------------------------------------------------------------"
print " Material   Linear Electro Optic    n+      n-       Relative "
print "            Coefficient r(pm/V)                    Permittivity"
print "----------------------------------------------------------------"
print " KDP           10.6               1.51    1.47         42      "
print " KD*P          26.4               1.51    1.47         50      "
print " ADP           8.5                1.52    1.48         43   "
print " CdTe          6.8                2.6                  10.6"
print " GaAs          1.6                3.6                  11.5"
print " ZnS           2.1                2.32                 16"
print "-----------------------------------------------------------------"
print "                      Table 3.1"

l=1.06*(10**-6) #Wavelength in meter

#Using Data from table 3.1 below

V=l/(2*10.6*(10**-12)*(1.51**3)) #Where V is the half wave voltage
V=round(V,1)
print ""
print "Using Data from table 3.1      "
print "The Half Wave Voltage for KDP is "+str(V)+" Volt"

---------------------------------------------------------------
Material   Linear Electro Optic    n+      n-       Relative
Coefficient r(pm/V)                    Permittivity
----------------------------------------------------------------
KDP           10.6               1.51    1.47         42
KD*P          26.4               1.51    1.47         50
CdTe          6.8                2.6                  10.6
GaAs          1.6                3.6                  11.5
ZnS           2.1                2.32                 16
-----------------------------------------------------------------
Table 3.1

Using Data from table 3.1
The Half Wave Voltage for KDP is 14522.4 Volt


## Example 3.3, Page Number 105¶

In [3]:
print "---------------------------------------------------------------"
print " Material   Linear Electro Optic    n+      n-       Relative "
print "            Coefficient r(pm/V)                    Permittivity"
print "----------------------------------------------------------------"
print " KDP           10.6               1.51    1.47         42      "
print " KD*P          26.4               1.51    1.47         50      "
print " ADP           8.5                1.52    1.48         43   "
print " CdTe          6.8                2.6                  10.6"
print " GaAs          1.6                3.6                  11.5"
print " ZnS           2.1                2.32                 16"
print "-----------------------------------------------------------------"
print "                      Table 3.1"

bw=10**9 #Frequency Bandwidth in Hertz
d=25*(10**-3) #Diameter of circular aperture
l=30*(10**-3) #Length
wl=633*(10**-9) #Given Wavelength
PI=3.14
k=8.85*(10**-12) #Permittivty of free space
#From equation 3.15 & data from table 3.1
P=((PI**2)*(wl**2)*PI*((d/2)**2)*bw*k*50)/(4*PI*(30**2)*((26.4*(10**-12))**2)*(1.51**6)*l) #Where P is the power requirements
P=round(P,1)

print ""
print ""
print "The Power Requirements for Modulation using a Pockels cell is "+str(P)+" W"

---------------------------------------------------------------
Material   Linear Electro Optic    n+      n-       Relative
Coefficient r(pm/V)                    Permittivity
----------------------------------------------------------------
KDP           10.6               1.51    1.47         42
KD*P          26.4               1.51    1.47         50
CdTe          6.8                2.6                  10.6
GaAs          1.6                3.6                  11.5
ZnS           2.1                2.32                 16
-----------------------------------------------------------------
Table 3.1

The Power Requirements for Modulation using a Pockels cell is 306.1 W


## Example 3.4, Page Number 114¶

In [4]:
from math import asin
from math import degrees
from math import cos
from math import sqrt

l=633*(10**-9) #Given Wavelength in meter
bw=5.0*(10**6) #Bandwidth in hertz
l1=50*(10**-3) #Modulation length
de=0.7 #Diffraction Efficiency
al=4.3*(10**-5) #Acoustic Wavelength in meter
av=3500.0 #Acoustic velocity in meter per second

#From equation 3.20

theta=asin(l/(2*al)) #where theta is the angle of diffraction
theta1=degrees(theta) #Converting it into degrees
theta1=round(theta1,2)

#From equation 3.21

phi=2*(asin(sqrt(de))) #where phi is the internal braggs angle
phi1=degrees(phi) #Converting it into degrees
phi1=round(phi1,1)

e=cos(theta1)

dn=(phi*l*e)/(3.14*2*l1) #where dn is the maximum change in refraction index

B=av/bw

print "The angle of diffraction is "+str(theta1)+" Degree"
print "The Internal Braggs Angle is "+str(phi1)+" Degree"
print "The Maximum Change in Refraction index is %.2e"%(dn)
print "The Maximum Optical Beam Width is "+str(B)+" meter"

#Answer Number 3 is Misprinted in the book

The angle of diffraction is 0.42 Degree
The Internal Braggs Angle is 113.6 Degree
The Maximum Change in Refraction index is 3.65e-06
The Maximum Optical Beam Width is 0.0007 meter


## Example 3.5, Page Number 123¶

In [5]:
from math import asin
from math import degrees

print "-----------------------------------------------"
print " Wavelength         no              nc          "
print "(Micrometer)                                    "
print "------------------------------------------------"
print " 1.06             1.4943            1.4603    "
print " 0.53             1.5132            1.4712"
print "-------------------------------------------------"

print ""
#from problem 3.10
t2=((1.4943**-2)-(1.5132**-2))/((1.4712**-2)-(0.4367))
theta1=asin(t2)

theta1=degrees(theta1) #Where theta is the phase matching angle
theta1=round(theta1,1)
print "The Phase matching angle is "+str(theta1)+" degrees"

-----------------------------------------------
Wavelength         no              nc
(Micrometer)
------------------------------------------------
1.06             1.4943            1.4603
0.53             1.5132            1.4712
-------------------------------------------------

The Phase matching angle is 26.0 degrees


## Example 3.6, Page Number 124¶

In [6]:
nw=1.5019 #Refraction index at 0.8 micrometer
n2w=1.4802 #Refraction index at 0.4 micrometer
l=0.8*(10**-6) #Vaccum wavelength at the fundamental frequency

lc=l/(4*(nw-n2w)) #Where lc is the coherance length

print "The Coherance Length is %.e meter"%(lc)

The Coherance Length is 9e-06 meter