Technical University of Liberec

Departement of Physics

Miroslav Šulc

Electro-optical properties of

crystals

Magneto-optical effect in gases

Outline

Electro-optical effects

• Electro-optical coefficients

• Applications of electro-optical effects

• Measurement of electro-optical coefficients

Vacuum Magnetic Birefringence - measurement in gases and vacuum

Nano-optics

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Electro-optic coefficients • Applied electric field E changes optical indicatrix and impermitivity tensor η of

investigated materials.

• If the intensity of electric field is small, it is possible to express this tensor η as a Taylor expansion

• Coefficients rijk (linear Pockels coefficients) are the first derivation of impermitivity tensor for zero electric field

• These coefficients characterize electro-optical properties of crystals ADP, KDP, LiNbO3, LiTaO3, CdTe, PZN-PT, PMN-PT. It requires inversion asymmetry

• Kerr effect, described by coefficients sijkl , is observable in crystals with central symmetry, liquids and gases

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kl

lkijkl

k

kijkijij EEsErE

kijijk Er

jkijijkl EEs 221

0

• The impermitivity tensor is symmetrical, it has 6 independent coefficients with indexes ij. They can be replaced by one index

• λ ( ij~λ: 11~1, 22~2, 33~3, 23~4, 13~5, 12~6).

• This is why 6x3 matrix can express Pockels tensor rijk.

For example - LiNbO3 crystal

• Crystals LiNbO3 is an uniaxial rhombohedral crystal with point-group symmetry 3m. It has only r13, r33, r22, r15 non-zero electro-optical coefficients

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00

00

00

00

0

0

22

51

51

33

1322

1322

r

r

r

r

rr

rr

Elektrooptický jev • Obecný elektrooptický tenzor – při působení

elektrického pole, rij-elektrooptický koeficient, kde pro indexy i= 4-6 jde o rotace budící vlny vzhledem k optické ose krystalu

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kde

Elektrooptický jev

• Elektrooptický tenzor pro některé isotropní a anizotropní (uniaxiální) materiály. Nesymetrie koeficientů značí

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LiNbO3 a LiTaO3

hexagonalní soustava

ADP, KDP

tetragonální soustava

GaAs, GaP,

kubická soustava

• Some electro-optical materials

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ADP – Fosfid dihydrogen amoný, KDP – Fosfid dihydrogen draselný

• Nejednodušší případ – intenzita elektrického pole E působí ve směru optické osy z a směr šíření pole je ve směru osy x

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Crystal LiNbO3

• Applied electric field E=(0,0,E) along optical axis z, perpendicular to laser beam. The values of the principal refractive indices with field E are ne(E) and no(E)

• The change of refractive index causes the optical phase shift of light wave in the sample. The electric field in optical axis direction induces also a change of the sample length ΔL along the path of the laser beam due to piezoelectric effect. It is proportional to piezoelectric coefficient d31

ErnnEn oo 13

3

21

0

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ErnnEn eee 33

3

21

ELdL 31

E E=0

Šíření optické vlny krystalem

• Uniaxiální krystaly vykazují při šíření dvojlom a tenzor permitivity lze vyjádřit

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V každém směru se mohou šířit dvě vlny, lišící se

polarizací a indexem lomu- řádná vlna – index lomu

nO nezávisí na směru šíření, směr intenzity E je kolmý

k optické ose krystalu a ke směru šíření, mimořádná

vlna – kde index lomu ne závisí na úhlu Q mezi

směrem šíření a optickou osou krystalu.

Šíření optické vlny krystalem

• Rozdíl indexů nO a ne je velký až - 0,08. Obě vlny se

šíří nezávisle ve vlnovodné oblasti.

• Pokud je optická osa krystalu kolmá k podložce

šíří se vlna TE v libovolném směru s řádným

indexem nO. A vlna TM s mimořádným indexem ne

• Pokud je optická osa krystalu v rovině vlnovodu

pak se vlna TM šíří jako řádná a vlna TE jako

mimořádná a indexy lomu závisí na velikosti úhlu

mezi směrem šíření a podložkou

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Important applications modulating the power of a laser beam, for example for laser printing or data recording, telecommunications, data transmission

Properties of ideal electro-optic material:

• large change in refractive index per volt.

• high optical quality and transmission

• low dielectric constant (low capacitance).

• low dielectric loss tangent (no dielectric heating due to a high-frequency electric field), and no distortions in modulator output from piezoelectric resonances.

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A transverse electro-optic phase modulator.

An amplitude modulator in its simplest form Q

cos1

20II

V

V

Elektro-optický fázový modulátor, změny n < 1.6 x 10-3 [ 2 ]

EO

EO

Elektrooptický modulátor

Mach-Zehenderův interferometr využitý jako elektrooptický modulátor [ 2 ]

Elektrooptický modulátor

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ELECTRO-OPTICAL COEFFICIENTS MEASUREMENT

• Measurement of phase change in Mach-Zehnder interferometer arrangment

• Light polarization and direction of electric field determine measured coefficients Important to separate Pockels and inverse piezoelectic effect

L

y

nUU

Ur

pp

out

A

3

221

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Compensation of piezoelectric induced displacement

• The second crystal, made from the same material as sample crystal, but with another length is used with mirror placed on the top of this crystal

• If there is applied the same electric field on investigated sample (light is passing through it) and on compensating crystal (light is reflected from this one), we can fully compensate piezoelectric effect

• This compensation can be made both in Michelson and Mach-Zehnder interferometer arrangement

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3

12

n

dnrr i

i

Measurement of electro-optical coefficients of crystal LiNbO3 in

wide temperature range • Undoped crystal LiNbO3, of

congruent composition (48,5%Li, 51,5% Nb)

• Bulk shape 36x3x2 mm3 • This crystal was investigated in

transversal configuration. Applied electric field E=(0,0,E) was along optical axis z

• Point grup, symmetry 3m. Only coefficient r13, r33, r22, r15

• Correction for piezoelectric effect (d31 = –0,85·10-12 C/N) was take in account (–0,2·pm/V).

• Resulting values are r13= 9,7±0,2 pm/V and r33= 30,4±0,4 pm/V.

0,1 1 10

0

5

10

15

20

25

30

35

r33

r13

ele

ktr

o-o

ptické

ko

eficie

nty

[p

m/V

]

frekvence [kHz] Op

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EO

Coeffic

ients

[pm

/V]

The temperature characteristic

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seems to be constant for both coefficients. It seems that electro-optical coefficient r33 became lower with decrease of the temperature, coefficients r13 is constant

150 200 250 300 350

6

7

8

9

10

11

12

r 13 [

pm

/V]

teplota [K]

160 180 200 220 240 260 280 300 320 340

20

25

30

35

40

r 33 [pm

/V]

teplota [K]

Vacuum Magnetic Birefringence in vacuum and gases

• Precise method want to measure the ultrafine Vacuum Magnetic Birefringence

• The change of the light velocity in a background magnetic field is given by QED prediction

• expected value by QED is Δn ≈ 3.6 10-22 in 9.5 T field

• axion presence can partially modify this birefringence

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Birefringence • Anisotropy of refractive index, the birefringence δ shown

by the vacuum (or gas) after the light has propagated along an optical path L is

δ = 2π Δn (L/ λ)sin2θ and Δn = CCMλ0B2

• the initially linearly polarized light beam acquires in magnetic field ellipticity

• the predicted VMB effect is very weak so subsequent steps must be done

• VMB experiment starts from measurement of magnetic-field-induced birefringence at gases, also known as a Cotton-Mouton, in air, in nitrogen, helium and finely in vacuum

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VMB modulation detection techniques

Variation of relative directions of electric and magnetic field is needed (or magnetic field pulses….)

Magnetic filed rotation

• Field Modulation at 1-1000 mHz (PVLAS …)

Electric filed rotation

• Half-wave plate ~300 Hz (OSQAR 2007)

• Electro-optical modulator EOM ~ 30 MHz

• Noise limitation coming mostly from the shot noise of the photodetector. Signal must be modulated for Signal/Noise optimization.

• The modulation techniques are sensitive with dedicated filtering techniques

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B B

Half-wave plate vs. EOM

Half-wave plate, turning around with ω, rotates electric field with 2 ω

Electro-optical modulator for phase modulation

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E E

Standard

frequency:

up to

300 Hz 30

MHz

VMB with EOM -experimental set-up

• The set of possible configurations of polarized elements was investigated. Calculus with Jones symbolic matrixes was done.

• Laser beam increases degree of polarization by passing Glan-Thomson polarizer prism

• The beam then goes through the electro-optical modulator

• than propagate trough magnetic field where the light acquires an ellipticity from induced anisotropy

• The polarization of the beam is

finally analyzed by an analyzer.

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The best orientation of the each successive component in set up is at 45 degree relative to its previous element

Detection in experiment with EOM

The detected intensity I has both constant and time-variable parts, described for amplitude of modulator induced phase shift To > 0.1 rad by equation

𝐼 =𝐼0

2(1 + 𝛿 sin 𝑇)

where δ is very small birefringence of the investigated sample, and sin T can be expressed by odd Bessel functions J

sin 𝑇 = 2 𝐽𝑚(𝑇𝑜) sin𝑚𝜔𝑡

𝑚=𝑜𝑑𝑑

The measured sample birefringence is

𝛿 = 𝑈𝑚

2𝑈 𝐽1

where U is detected constant voltage and Um is amplitude of alternating voltage of measured signal.

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Laboratory test

New laboratory set-up was build in universities laboratories to solve stability problems

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50 MHz electro-

optical modulator

from Quantum

Technologies

Electro-optical modulator 50 MHz electro-optical modulator from Quantum Technologies

• We check working condition, influence of environment

• We change our set-up from phase modulation to intensity modulation and intensity modulation was measured

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• modulator works

properly

• it has very good

stability

Deep modulation 99,5 % , perfect sinusoidal

signal (agreement 0.99998), half-wave voltage

125,57 V

Calibration curve

The EO modulator was calibrated

Detected intensity I depends on amplitude of phase modulation T0 (≈ applied voltage) by equation

𝐼 =𝐼0

2(1 + sin(𝑇𝑜 sin𝜔𝑡))

We measure the first harmonic signal, so correlation with Bessel functions J1 was checked

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• Good agreement with prediction was achieved

• Due a technical limits of our EOM (maximal applied voltage), it

is not be able to work at the maximum of Bessel function (highest

signal)

• We work at phase shift amplitude about 1 rad

Method was checked by Soleil-Babinet compensator measurement

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Perfect agreement between adjusted value at S-B

compensator and measured values

Pearson product-moment correlation coefficient

0.99998

expected sensitivity 10-4 rad, with accuracy ~5%

Run in CERN SM18 test hall, August -September 2012

• Cotton- Mouton constant at nitrogen was measured

• The new components were used

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The base element of the set-up

was stabilized 1mW He-Ne laser

(Melles Griot)

Glan-Thompson

prisms (CVI

Melles Griot) were

used for

polarization of

light. They

provides

extinction ratio

1:10000.

The new beam expanders were

used for precision collimation of

laser beam inside the LHC

magnet pipe

HAMATSU

photodiode detector

with preamplifier with

optical fiber input

was used for light

detection

Set-up for the measurement of the Gas Magnetic Birefringence with electro-optic modulator

• AC modulation signal is built up by wave function generator

• System response was analysed by 100 kHz Lock-in amplifier Stanford Research 830 DSP

• New DAQ had took data

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Photos of real experiment September 2012

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The Cotton-Mouton effect in N2

Results of the measured optical retardance δ has been found to increase with the square of magnetic field The constant of the Cotton-Mouton effect for N2 at 1 bar is found to be equal to

-3.6∙10-7 rad T-2m-1 The difference in refractive indices is

Δn ≈ (2.28∙±0.16)∙10-13 for N2 at atmospheric pressure in 1 T field

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This result is in good

agreement with

published values !!!!

Expected OSQAR VMB sensitivity

• Birefringence δ sensitivity of our set-up is extending to 10-4 rad now

∆𝒏 = 𝜹 · 𝝀

𝟐𝝅𝑳

• For He-Ne laser λ= 632.8 nm, and LHC magnet L=14.3 m, the difference Δn ≈ 6 ∙10-14 can be measurable

• Our previous experiments were made without resonant cavities

• Sensitivity can be significantly increased by an application of high finesse cavities

• It can improve sensitivity by a factor 103 - 105

• We are still far from QED prediction, but we are approaching

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