FARADAY ROTATION EFFECT

Jaydeep Sanjay BelapureM.Sc. II,

Dept. of Physics, University of Pune

Under the guidance of

Joydeep BagchiVSP-2007, IUCAA

INTRODUCTION

• Michael Faraday (England) :

In 1845 Discoveredthe First effect connecting Magnetismand Light,

“The Faraday Rotation Effect”.

Faraday Rotation Effect

• The incident Plane of linearlypolarized light Rotates by an angle when it passes through the medium.

“Magnetic Birefringence”

Rotation Angle

• The faraday rotation ‘θ’ is proportional to Magnetic field and the length traversed.

( )R Ld n n zπθλ

= − ( )R Ln n B− ∝

VBzθ =

3 2

2 2 2 20

4( )NeV

m cπ ωω ω

=−

Where,

V = Verdet constantnR = Refractive Index for

Right Circular lightnR = Refractive Index for

Left Circular lightωo = Resonance frequencyN = Number density of

electrons

EXPERIMENTAL SETUP

LASERSOLENOID

ANALYSERPHOTODIODE

AMPLIFIER

CURRENT SOURCE

POLARIZER

Solenoid

zpL.

z2 1

• L: 15 cm • r1 : 0.88 cm• r2 : 1.87 cm

• 160 turns/layer• 10 layers

0 2 12 2 2 22 1

2iN z zBL z r z r

µ = − + +

Finite length (shell) :

2 2 2 22 2 2 1 2 20

2 12 2 2 22 1 2 1 1 1 1 1

ln ln2( )

z r r z r riNB z zr r L z r r z r rµ + + + +

= −− + + + +

Finite Thickness :

( ).L

V B z dzθ = ∫

Magnetic Field along the solenoid length.We consider a shell of average radius r = 1.38 cm, with same total current

Central Magnetic field as a function of current

Observation Method

Malus’s Curve NO Magnetic field

Faraday Rotation

MagneticField OFF

Magneticfield ON

New Observation Method

α

ImaxImax

α – θ

θ rotation

Sin2

(α)

Cos2(α ) Cos2(α - θ )

Sin2(α - θ )

Without Magnetic Field With Magnetic Field

1tan yx

α − =

1tan rot

rot

yx

θ α − = −

Observations

• We use the New Method to Measure“Faraday Rotation Angle”

• WITH –• Different Magnet fields• Materials: Lead silicate glass, Water, Benzene• Laser sourses : Red (650 nm), Green (543 nm)

Faraday Rotation Measured for Lead Silicate Glass

Wavelength Dependance of Rotation angle

Red Laser

Green Laser

V

V

3 2

2 2 2 20

4( )Ne Bz

m cπ ωθω ω

= −

Faraday Rotation Measured for Water

Green Laser

Red Laser

V

V

3 2

2 2 2 20

4( )Ne Bz

m cπ ωθω ω

= −

Wavelength Dependence of Rotation angle

Comparing Verdet Constants

Lead silicate GlassGreen Laser

Red Laser

WaterGreen

Red

Benzene (Red)

Wavelength Dependence of Verdetconstant

Astrophysical Application of Faraday Rotation Effect

int( ) ( )obs λ λΨ = Ψ +∆Ψ3

2int 2 4( ) ( ) ( ) ( )

2

L

obs ee o

e n l B l dlm c

λ λ λπ

Ψ = Ψ +

∫

Rotation Measure (RM) (rad/m2)Plotting Y= C + X*RM

Radio Jet CGCG049-033• GMRT• 1.3GHz• Resolution: 11 arc sec

The largest and highlycollimated radio jet~400kpc large

• VLA• 1.4GHz• Resolution =

45 arc sec

• Max Planck 100m• 8.4GHz• Resolution =

84 arc sec

Acknowledgement

I wish to thank my guide Prof Bagchi, Prof K Subramanian, Dr Joe Jacob, Viral andall my VSP friends during my stay at IUCAA. ☺

☺