Phase Sensitive Faraday Rotation in TERBIUM GALLIUM GARNET crystalTERBIUM GALLIUM GARNET crystal and various Diamagnetic liquid

Samples

Supervisor: Dr. Saadat Anwar Siddiqi

Presented by: Aysha Aftab

Co-Supervisor: Dr. Muhammad Sabieh Anwar

Presented by: Aysha Aftab

Roll. No. 0702

M.Phil (2007‐2009)7/30/2010 1

O tliOutlines

Magneto optics Magneto optics Polarization of light

J C l l Jones Calculus Faraday Rotation

L k i A lifi PSD Lock-in Amplifier ; PSD Why PSD in Faraday rotation?

S h i f h i Schematic of the experiment. Results Determination of V using higher harmonics. References

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Magneto Optics

Historical background

1813 Morrichini 1814 Faraday 1814 Faraday 1826 S. H. Christie 1834 Faraday 1834 Faraday 1844 “ Magnetic force and light were

proved to have relation to each other”.p

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Magneto Optics (cont…)

Magnetic medium

Optical radiation

Interactionor

Optically inactive medium placed inmedium placed in Magnetic field

Faraday rotationFaraday rotation Kerr effect

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Polarization of light

• Orientation of E field remains

1.Linear polarization• Orientation of E field remains constant, magnitude and sign varies.

Unpolarized light

varies.

• Plane of oscillation, containing , gE and K

• Electromagnetic wave with E field oscillating parallel to y axis.

Linearly polarized7/30/2010 5

Linear polarization (cont…)

)cos()( tkzEitzE

Horizontally polarized light propagating inz direction

)cos(),( tkzEitzE oxx

),( tzEx

Vertically polarized at phase difference ε,

)cos(),( tkzEjtzE oyy7/30/2010 6

Li l i ti ( t )Linear polarization (cont…)

Superposition of the two

)cos()cos(),(

tkzEjtkzEitzE oyox

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2. Circular polarization

•Two orthogonal waves have equal amplitudes.

• Relative phase shift of o90Relative phase shift of

•Direction of E is time varying, magnitude remains

90

constant.

a) Right Circularly polarized light• relative phase difference of • rotating clockwise

) g y p gm290o

rotating clockwise

)]sin()cos([ tkzjtkziEE o

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2. Circular polarization (cont..)

Ri ht i lRight circular• Left circularly polarized, phase shift of m290o • rotating anti clockwise

)]sin()cos([ tkzjtkziEE

)]sin()cos([ tkzjtkziEE o 7/30/2010 9

2 Ci l l i ti ( t )2. Circular polarization (cont..)

Left circular• Linearly polarized is sum of R.C.P and L C PL.C.P

)cos(2),( tkziEtzE o

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Jones calculus R. Clark Jones in 1941 For perfectly polarized light

)cos()cos(),(

tkzEjtkzEitzE oyox

iox

E

EtzE ),( y

ioyeE

)(

For linearly polarized light

cos

),( tzE x

sin

),(

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Jones calculus (cont…)

Incident Jones vector is related to transmitted jones vector through matrix J

iEEvector through matrix, JtE

JEE it JEE

For beam passing through a series of optical elementsp g g p

EJJJJE int EJJJJE 123...

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Faraday rotation

Linearly polarized monochromatic light while y p gtransmitting through an optically inactive material, under the influence of an axial magnetic field, is rotated b l θby an angle θ.

Is non-reciprocal.

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F d t ti ( t ) For uniform B field

Faraday rotation (cont…) For uniform B field

VBd

d For non uniform B field

dzzBV0

).(0Where,

d= length of the sampleV= material parameter called Verdet constant, is a function of wave length of light. of the order of micro rad /G cm.7/30/2010 14

Faraday rotation (cont…)

Induced circular birefringence

nlnrn

birefringence

nlr

The plane of polarization of pplane-polarized light gets rotatedg g

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Phase Sensitive Detection (PSD)

kHz20at sin wavenV10V

• Amplifier

1MHB d idth1000QHznV 4 noiseinput

V10nV1010001MHzBandwidth 1000Q

oV mV4noise

o

V

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Ph S iti D t ti ( t )Phase Sensitive Detection (cont…)

Band pass filter1000Q kHz50at

)1000)(nV4(500

Q

noiseVV89

PSD

Hz 0.125 widthBand V4.1 noiseV

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Lock in Amplifier A lock-in amplifier amplifies a small frequencyLock in Amplifier

band around a certain reference frequency. A lock-in can be used toMeasure sinusoidal voltage amplitudes and

phasephaseMeasure noise around a certain frequency. Consists of

Signal channelgReference channelPSD : Heart of lock in amplifierPSD : Heart of lock-in amplifier

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L k i A lifi ( t )Lock in Amplifier (cont…)

Lock in amplifier, block diagram

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L k i A lifi ( t )Lock in Amplifier (cont…)MixerMixer

)sin( tAVin

)sin( tBVref

)]2cos()[cos(2

tABVo 2

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L k i A lifi ( t )Lock in Amplifier (cont…)Low pass filterLow pass filter

)(ABV )cos(2

Vo

Noise close and closer to the reference frequency is removed

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is removed.

Why PSD in Faraday rotation?

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Wh PSD in Farada rotation? (cont )Why PSD in Faraday rotation? (cont…)

Noise and signal amplitude asa function of frequency.

Modulating the signal to a region of low noise.

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Schematic of the experiment

• Light source• Source of magnetic field• Detecting devices• Detecting devices

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Schematic of the experiment (cont )

Light source

Schematic of the experiment (cont…)

Light source Laser

(A)( )

(B) He-Ne gas laser (C) AlGaN diode laser7/30/2010 25

S h ti f th i t ( t )Schematic of the experiment (cont…)

Linear polarizerMalus’s law

Source of magnetic field• Dc sourcelarge, expansive, bulky water cooled electromagnets.

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Schematic of the experiment (cont )Schematic of the experiment (cont…)

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S h ti f th i t ( t )• Ac source

Schematic of the experiment (cont…)Ac source

Low magnetic field is required.Signal of interest can be extracted successfullySignal of interest can be extracted successfully through PSD.Solenoid Helmholtz coil

Helmholtz coilSolenoid, Helmholtz coil.

Two identical coils with separation equalto their common radius.

)( 64

N4

...)1( 66

44 xcxcBB o

In superpositioni

aNB o

23)54(

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Schematic of the experiment (cont )Schematic of the experiment (cont…)

Magnetic lines of force of our Helmholtz coil drawn in Vizimag7/30/2010 29

Schematic of the experiment (cont )Schematic of the experiment (cont…)

Helmholtz coil7/30/2010 30

S h ti f th i t ( t ) Parameters of coil

Schematic of the experiment (cont…)Parameters of coil

• 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 cm• L=7 mH

Connected a capacitor of 0 97µF to resonate the coil0.97µF to resonate the coil at 1.22 kHz to maximize the current and hence Bthe current and hence B

LCf 1f

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Resonance in HelmholtzSchematic of the experiment (cont…)

G t Resonance in Helmholtz coil

Gauss meter

38QT 107.6 3 iB

38Q 7/30/2010 32

S h ti f th i t ( t )Schematic of the experiment (cont…)

Magnetic field varies linearly with the current applied

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Magnetic field varies linearly with the current applied.

Schematic of the experiment (cont…)

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Setup for the experimentSetup for the experiment

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Working principleJones vector of horizontally polarized light traveling in

Working principle

z direction

1 )(exp

01

tkziAE oo

For rotated polarized light, after sample

)(expsincos

tkziAE oo

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Working principle (cont )After analyzer

)()(

Working principle (cont…)

)(exp)sin()cos()cos()cos(

tkziAE oo

I t it d bIntensity measured by photodiode

* EEI)(cos

.22

oAEEI

)(cos o

oAI )21(

2

2

tII )sin(20

7/30/2010 37dcac ii 2

Resistance measurement throughResistance measurement through Lock-in Amplifier

Vs

ca R

VV

R BV

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Using optical chopper with Lock inUsing optical chopper with Lock-in Amplifier

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Res ltsTGG at 405 nmResults

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TGG at 405 nm

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TGG at 633 nm

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CS2 at 405 nm

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CS at 633 nmCS2 at 633 nm

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Methanol at 405 nmMethanol at 405 nm

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Methanol at 633 nm

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Water at 405 nm

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Water at 633 nm

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Isopropanol at 405 nm

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Isopropanol at 633 nm

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Determination of V using higherharmonicsharmonics

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Summary

sample Wave length Verdet constant

Summary

sample Wave length(nm)

Verdet constant(rad/G cm)

TGG 633 (0 146±0 003)×10-3TGG 633 (0.146±0.003)×10-3

TGG 405 (1.70±0.02)×10-3

CS2 633 (0.97±0.07)×10-5

CS2 405 (0.50±0.01)×10-4CS2 405 (0.50±0.01) 10Methanol 633 (0.24±0.02)×10-5

Methanol 405 (1.20±0.05)×10-5

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Summary (cont…)

sample Wave length(nm)

Verdet constant(rad/G cm)( ) ( ad/G c )

Water 633 (0.30±0.02)×10-5

W t 405 (1 50±0 08)×10 5Water 405 (1.50±0.08)×10-5

Isopropanol 633 (3.55±0.02)×10-6

Isopropanol 405 (2.2±0.06)×10-5

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ReferencesReferences1. Aloke Jain, Jayant Kumar, Fumin Zhou and Lian Li, “ A simple experiment for determining Verdet constant usingalternating magnetic fields” Am. J. Phys. 67, 714-717 (1999) .

2. Eugene Hetch and A. R. Ganesan, “Optics", 4th edition, Pearson Education Inc India 2008Pearson 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).

4. Frank J. Loeffier, “A Faraday rotation experiment for the Undergraduate physics laboratory", Am. J. Phys.

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Undergraduate physics laboratory , Am. J. Phys. 51, 661-663 (1983).

R fReference5. K. Turvey, “Determination of Verdet constant from combined ac and dc measurents, "Am. J. Phys. 64, 1561-1567 (1993).

6. http://www.enzim.hu/~siza/cddemo/edemo0.htm

7. Lock-in amplifier, user Manual, Stanford Research System, SR 510, http://www.thinksrs.com.

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