1. Supervisor: Dr. Munazza Zulfiqar Ali
Co‐Supervisor: Dr. Muhammad Sabieh Anwar
Presented By: Hafiz Muhammad Ahmed Masood
Roll No: P06‐10
B S (H ) Ph iB.Sc (Honors) Physics
Session (2006‐2010)
11،‫فروری‬11 1

2. Outlines
Part I
Polarization of light
J C l l
Part II
Birefringence
Schematic of ExperimentJones Calculus
Magneto Optics
Differential detection
Schematic of Experiment
Results
References
Schematic of the experiment
Results
11،‫فروری‬11 2

3. Polarization of lightPolarization of light
Linear Polarization
• Electric field vector oscillates
along a fixed direction
Unpolarized light
along a fixed direction.
• Plane of oscillation contains E and k vectors.
• Electromagnetic wave with
fi ld ill i ll l E field oscillating parallel to
y axis.
Linearly polarized
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4. Linear polarization (cont )
Horizontally polarized light propagating in z‐direction
Linear polarization (cont…)
)cos(),(
^
wtkzEitzE xx  
)( tE ),( tzEx
Vertically Polarized light propagating along
z‐direction at phase difference ε
)cos(),( 0
^
 wtkzEjtzE xx
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5. Linear polarization (cont )Linear polarization (cont…)
S iti f th t •Superposition of the two waves
)cos()cos(),( 0
^
0
^
 wtkzEjwtkzEitzE yx
11،‫فروری‬11 5

6. l l
• Two orthogonal components
Circular polarization
Two orthogonal components
of electric field are equal, i.e.
•Phase difference of
•Electric field is time varying and magnitude remains constant

90
yx EE  
•Electric field is time varying and magnitude remains constant
a) Right Circular Polarization
•Phase difference of
•Rotating clock wise
 m22/ 
)]sin()cos([
^^
wtkzjwtkziEE  )]sin()cos([ wtkzjwtkziEE 
11،‫فروری‬11 6

7. Ci l l i ti ( t )Circular polarization (cont…)
Right circular
b) Left Circularly Polarized light
•Phase shift of  m22/ 
Right circular
•Rotates anticlockwise
)]sin()cos([ tkzjtkziEE o  

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8. Ci l l i ti ( t )Circular polarization (cont…)
Linearly polarized light is the sum of left circularly polarized
d i h i l l l i d li h
left circular
and right circularly polarized light.
)cos(2),( tkziEtzE o 

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9. Elli ti l P l i ti
•Two orthogonal components are not equal
Elliptical Polarization
in amplitude
•General case of linear and circularly polarized light
•Resultant field vector rotates as well as changesResultant field vector rotates as well as changes
the magnitude
The endpoint of electric field vector sweeps
lli i dout an ellipse as it rotates once around.
11،‫فروری‬11 9

10. Jones Calculus
 R. Clark Jones in 1941
Jones Calculus
J 94
 For perfectly polarized light

)cos()cos(),(   tkzEjtkzEitzE oyox



 oxE y
 F li l l i d li ht






 i
oy
ox
eE
tzE ),(
y
 For linearly polarized light





cos
)( tzE
 x



 sin
),( tzE
11،‫فروری‬11 10

11. Jones Calculus (cont )Jones Calculus (cont…)
 Incident Jones vector is related to transmitted jones
vector through matrix, M
iE
tE
it MEE 
 For beam passing through a series of optical elements
int EMMMME 123...
11،‫فروری‬11 11

12. Magneto Optics
I i f li h d i•Interaction of light and magnetism
Historyy
•1813 Morrichini
•1814 Faraday
•1826 S. H. Christie
•1834 Faraday
•1844 Faraday44 y
•Faraday Effect
•Kerr Effect
11،‫فروری‬11 12
Kerr Effect

13. Faraday Effect
Faraday rotation
•Magnetically induced birefringence
•Pl f l i ti f li ht i t t d h •Plane of polarization of light is rotated when passes
through an optically inactive medium placed in magnetic field
•Non reciprocal
11،‫فروری‬11 13

14. •For uniform magnetic field
Faraday Effect (cont…)
g
VBd
•For non uniform magnetic field•For non‐uniform magnetic field

d
dzzBV
0
)(
0
•V=Verdet constant
•B=Magnetic field
•d length of the medium•d= length of the medium
•V is function of wavelength and temperature
•Very small, of the order of micro radians per gauss
11،‫فروری‬11 14

15. Schematic of the experimentSchematic of the experiment
•Light Source
•Polarization rotation elements
11،‫فروری‬11 15
•Polarization rotation elements
•Detecting mechanism

16. Schematic of the experiment (cont…)Schematic of the experiment (cont…)
Light Source
•Laser
The gain medium is placed inside
a Febry‐Perot resonator
The basic three level
scheme for lasers
AlGaN diode laser
11،‫فروری‬11 16

17. S h ti f th i t ( t )
Linear polarizer
Schematic of the experiment (cont…)
p
Mauls' law
Un polarized light is polarized by
means of a linear polarizer
11،‫فروری‬11 17

18. Schematic of the experiment (cont )
Source of magnetic field
DC S
Schematic of the experiment (cont…)
•DC Source
Large ,bulky, expensive magnets required
•AC Source
Helmholtz coil, Solenoid
to replace DC magnetic source
H l h lt C ilHelmholtz Coil
Two identical coils with separation equal
to their common radius.
...)1( 6
6
4
4  xcxcBB o
In superposition
N4
i
a
N
B o23
)
5
4
(
11،‫فروری‬11 18

19. Schematic of the experiment (cont )Schematic of the experiment (cont…)
Helmholtz Coil
11،‫فروری‬11 19

20. Schematic of the experiment (cont…)
 Parameters of coil
8 i d
Schematic of the experiment (cont…)
• 18 gauge copper wire, d=1.2 mm
• N=324 , l=2.7 cm , R=1.5Ω
• D1=6.5 cm, D2=10.2 cm , a=4.8 cm5 , , 4
• L=7 mH
Connected a capacitor of Connected a capacitor of
0.97µF to resonate the coil
at 1.22 kHz to maximize
LCf
2
1

the current and hence B
2
11،‫فروری‬11 20

21. S h i f h i ( )Schematic of the experiment (cont…)
11،‫فروری‬11 21

22. Working Principle
One sided detection Differential detection
11،‫فروری‬11 22

23. Working Principle (cont…)
B li•Beam splitter
11،‫فروری‬11 23

24. Working Principle (cont…)
Jones vector of a linearly polarized Jones vector of a linearly polarized
After passing through the sample
)(
0
1
),( wtkzi
eAtzE 






 
After passing through the sample
)(
sin
cos
),( wtkzi
eAtzE 






 


After the beam splitter
)(
sincoscossin
sinsincoscos
),( wtkzeAtzE i








 



Beam splitter is at
)(sincos1
)( wtkzi
AtE 



  

45
11،‫فروری‬11 24
)(
sincos2
),( wtkzi
eAtzE 


 
 


25. Working Principle (cont…)
Intensity after the beam splitter



 



 
212
AIA
Intensity after the beam splitter
*
.EEI 



 



 212IB
)cos(,, tVVI AacAdcA 
V
Adc
Aac
V
V
,
,
2

Using differential detection Using differential detection
)cos(2 2
tAII BA  
acac VV

11،‫فروری‬11 25
BdcAdc VV ,, 44


26. ResultsResults
11،‫فروری‬11 26
Single ended

27. ResultsResults
11،‫فروری‬11 27
Differential detection

28. ResultsResults
Sample Method Verdet Constant
TGG Single ended detection 3.80 0.02 10‐4 rad/G‐
cm
TGG Differential detection 3.892 0.024 10‐4 
rad/G‐cm
11،‫فروری‬11 28

29. Birefringence
•Anisotropic crystal
•Different refractive indices in•Different refractive indices in
different directions Mechanical model depicting a
negatively charged shell bound
to a positive nucleus by pairs of
spring having different stiffness
Wave Plates
•Objects made from birefringent crystals used
to introduce predetermined phase shift in to introduce predetermined phase shift in
incident light beams.
•The emerging beams has a phase difference of
|)(|
2
ennd  



11،‫فروری‬11 29

30. Quarter Wave Plate
•Introduces phase shift of 
90•Introduces phase shift of
•Converts linearly polarized light into
circular or elliptical polarized light
90

90
A quarter wave plate converts linearly
polarized light into circular polarized light
11،‫فروری‬11 30

31. Schematic of the experimentSchematic of the experiment
11،‫فروری‬11 31

32. Working Principle
•A system consisting of a polarizer, a quarter wave plate
d l i d b
Working Principle
and an analyzer is represented by
123 TTTH 
where
Th t i b l d d d d tThe matrix can be solved and reduced to
11،‫فروری‬11 32

33. Working Principle(cont )Working Principle(cont…)
Transmitted intensity of the system is
 )22sin(2sin2222 
By solving and manipulating
 cos
2
)22sin(2sin
)(sinsin)(cos[cos 2222 
II
1 
 2sin4sin
2
sin2cos)2sincos2(cos1[
2
1
),( 222 
I
By substituting  IyIyx  ,,2cos

 
4sin)
2
(sin)
2
()2sincos2(cos4)
2
(4 242222 

y
yx
y
yx
At 
 45
)2coscos1(
2
1
  II
11،‫فروری‬11 33

34. Working Principle(cont )
nmxy 
Working Principle(cont…)
Equation of a straight line
 cos
2
1
Im
In
1
In
2

11،‫فروری‬11 34

35. Results

 10

 0 
 20

 30

 45
 40
11،‫فروری‬11 35

36. Results (cont )Results (cont…)

 10 
 20
 0

 30 
 40

 45
11،‫فروری‬11 36

37. ReferencesReferences
1. Aloke Jain, Jayant Kumar, Fumin Zhou and Lian Li, “ A
simple experiment for determining Verdet constant usingsimple experiment for determining Verdet constant using
alternating magnetic fields” Am. J. Phys. 67, 714‐717 (1999) .
E H t h d A R G “O ti " th diti 2. Eugene Hetch and A. R. Ganesan, “Optics", 4th edition,
Pearson Education, Inc, India, 2008.
3. Frank L. Pedrotti and Peter Bandettini, “Faraday rotation
in the undergraduate advanced laboratory",
Am. J. Phys. 58, 542‐544 (1990).Am. J. Phys. 58, 542 544 (1990).
4. Frank J. Loeffier, “A Faraday rotation experiment for the
Undergraduate ph sics laborator " Am J Ph s
2/11/2011 37
Undergraduate physics laboratory , Am. J. Phys.
51, 661‐663 (1983).

38. R f
5 “Birefringence of cellophane tape: Jones representation
References
5. Birefringence of cellophane tape: Jones representation
and experimental analysis”, A. Belendez, E. Fernandez,
J. Frances, C. Neipp, European Journal of Physics 31, 551 (2010).
6. V K Valev, J Wouters and T Verbiest, “Differential detection
for measurements of Faraday rotation by means of ac magnetic
fields”, European Journal of Physics. 29, 1099‐1104(2008).
7 http://www enzim hu/~siza/cddemo/edemo0 htm7. http://www.enzim.hu/ siza/cddemo/edemo0.htm
11،‫فروری‬11 38

39. 11،‫فروری‬11 39