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Electro-optical properties of
crystals
Magneto-optical effect in gases
Miroslav Šulc
Technical University of Liberec
Departement of Physics
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
Optical properties of Crystals II
Outline
2
Electro-optic coefficients
• Applied electric field E changes optical indicatrix and impermitivity tensor η of


investigated materials.
   0
• If the intensity of electric field is small, it is possible to express this tensor η as a Taylor
expansion
ij E   ij   rijk Ek   sijkl Ek El
kl
• Coefficients rijk (linear Pockels coefficients) are the first derivation of impermitivity tensor
for zero electric field
rijk  ij Ek
• These coefficients characterize electro-optical properties of crystals ADP, KDP, LiNbO3,
LiTaO3, CdTe, PZN-PT, PMN-PT. It requires inversion asymmetry
sijkl  12  2ij Ek E j
Optical properties of Crystals II
k
• Kerr effect, described by coefficients sijkl , is observable in crystals with central symmetry,
liquids and gases
3
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
0
0
0
0
r5 1
r2 2
 r2 2
r2 2
0
r5 1
0
0
r1 3
r1 3
r3 3
0
0
0
Optical properties of Crystals II
• 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.
4
Elektrooptický jev
Optical properties of Crystals II
• 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
5
kde
Elektrooptický jev
Optical properties of Crystals II
• Elektrooptický tenzor pro některé isotropní a
anizotropní (uniaxiální) materiály. Nesymetrie
koeficientů značí
GaAs, GaP,
kubická soustava
LiNbO3 a LiTaO3
hexagonalní soustava
ADP, KDP
tetragonální soustava
6
Optical properties of Crystals II
• Some
electrooptical
materials
7
ADP – Fosfid dihydrogen amoný, KDP – Fosfid dihydrogen draselný
Optical properties of Crystals II
• Nejednodušší případ – intenzita elektrického pole
E působí ve směru optické osy z a směr šíření
pole je ve směru osy x
8
Crystal LiNbO3
E=0
E
• 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
L  d 31EL
Optical properties of Crystals II
ne E   ne  12 ne3r33E
n0 E   no  12 no3 r13 E
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Šíření optické vlny krystalem
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.
Optical properties of Crystals II
• Uniaxiální krystaly vykazují při šíření dvojlom a tenzor
permitivity lze vyjádřit
10
• 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
Optical properties of Crystals II
Šíření optické vlny krystalem
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Important applications
modulating the power of a laser beam, for example for laser printing or data recording,
telecommunications, data transmission
V
V
Properties of ideal electro-optic
material:
• large change in refractive index
per volt.
• high optical quality and
transmission
• low dielectric constant (low
capacitance).
A transverse electro-optic phase modulator.
• low dielectric loss tangent (no
dielectric heating due to a highfrequency electric field), and no
distortions in modulator output
from piezoelectric resonances.

I  I 0 1  cos Q 
2
Optical properties of Crystals II
  
12
An amplitude modulator in its simplest form
Elektrooptický modulátor
EO
EO
Elektro-optický fázový modulátor, změny n < 1.6 x 10-3 [ 2 ]
Optical properties of Crystals II
Elektrooptický modulátor
14
Mach-Zehenderův interferometr využitý jako elektrooptický modulátor [ 2 ]
• 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
r
1
2 2  y
U out
U A
U p p n 3 L
Optical properties of Crystals II
ELECTRO-OPTICAL COEFFICIENTS MEASUREMENT
15
Compensation of piezoelectric induced displacement
2n  1  d i
ri  r 
n3
Optical properties of Crystals II
• 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 MachZehnder interferometer arrangement
16
Measurement of electro-optical coefficients of crystal LiNbO3 in
pm/V and r33= 30,4±0,4 pm/V.
35
30
25
r33
20
15
r13
10
5
0
0,1
1
frekvence [kHz]
10
Optical properties of Crystals II
elektro-optické koeficienty [pm/V]
• 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
EO Coefficients [pm/V]
wide temperature range
17
The temperature characteristic
40
12
11
35
9
30
8
25
7
20
6
160
150
200
250
teplota [K]
300
350
180
200
220
240
260
280
300
320
teplota [K]
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
340
Optical properties of Crystals II
r33 [pm/V]
r13 [pm/V]
10
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Vacuum Magnetic Birefringence
• 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
Optical properties of Crystals II
in vacuum and gases
19
Birefringence
• 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 magneticfield-induced birefringence at gases, also known as a
Cotton-Mouton, in air, in nitrogen, helium and finely in
vacuum
Optical properties of Crystals II
• 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
20
• 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
Optical properties of Crystals II
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)
21
• Electro-optical modulator EOM ~ 30 MHz
Half-wave plate, turning
around with ω, rotates
electric field with 2 ω
Electro-optical modulator for
phase modulation
B
Optical properties of Crystals II
Half-wave plate vs. EOM
B
E
E
Standard
frequency:
up to
300 Hz
30
MHz
22
The best orientation of the each
successive component in set up is at
45 degree relative to its previous
element
• 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 GlanThomson 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.
Optical properties of Crystals II
VMB with EOM -experimental set-up
23
Detection in experiment with EOM
𝐼=
𝐼0
(1
2
+ 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 ) sin 𝑚𝜔𝑡
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.
Optical properties of Crystals II
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
24
Optical properties of Crystals II
Laboratory test
New laboratory set-up was build in
universities laboratories to solve stability
problems
50 MHz electrooptical modulator
from Quantum
Technologies
25
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
Deep modulation 99,5 % , perfect sinusoidal
signal (agreement 0.99998), half-wave voltage
125,57 V
• modulator works
properly
• it has very good
stability
Optical properties of Crystals II
Electro-optical modulator
26
The EO modulator was calibrated
Detected intensity I depends on
amplitude of phase modulation T0
(≈ applied voltage) by equation
𝐼=
𝐼0
(1
2
Optical properties of Crystals II
Calibration curve
+ sin(𝑇𝑜 sin 𝜔𝑡))
We measure the first harmonic
signal, so correlation with Bessel
functions J1 was checked
• 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
27
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%
Optical properties of Crystals II
Method was checked by Soleil-Babinet
compensator measurement
28
Run in CERN SM18 test hall, August -September 2012
The base element of the set-up
was stabilized 1mW He-Ne laser
(Melles Griot)
The new beam expanders were
used for precision collimation of
laser beam inside the LHC
magnet pipe
Glan-Thompson
prisms (CVI
Melles Griot) were
used for
polarization of
light. They
provides
extinction ratio
1:10000.
HAMATSU
photodiode detector
with preamplifier with
optical fiber input
was used for light
detection
Optical properties of Crystals II
• Cotton- Mouton constant at nitrogen was measured
• The new components were used
29
• 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
Optical properties of Crystals II
Set-up for the measurement of the Gas
Magnetic Birefringence with electro-optic
modulator
30
Photos of real experiment September 2012
Optical properties of Crystals II
31
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 CottonMouton 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
Optical properties of Crystals II
32
This result is in good
agreement with
published values !!!!
Expected OSQAR VMB sensitivity
•
•
•
•
•
𝜹 ·𝝀
∆𝒏 =
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
Optical properties of Crystals II
• Birefringence δ sensitivity of our set-up is extending to 10-4
rad now
33