Electro-optical properties of crystals Magneto-optical effect in gases Miroslav Šulc Technical University of Liberec Departement of Physics
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 2
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 ij E ij rijk Ek k kl s ijkl E k E Coefficients r ijk (linear Pockels coefficients) are the first derivation of impermitivity tensor for zero electric field r ijk ij E k 0 l These coefficients characterize electro-optical properties of crystals ADP, KDP, LiNbO 3, LiTaO 3, CdTe, PZN-PT, PMN-PT. It requires inversion asymmetry s ijkl 1 2 2 ij E k E j Kerr effect, described by coefficients s ijkl, is observable in crystals with central symmetry, liquids and gases 3
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 - LiNbO 3 crystal Crystals LiNbO 3 is an uniaxial rhombohedral crystal with point-group symmetry 3m. It has only r 13, r 33, r 22, r 15 non-zero electro-optical coefficients 0 0 0 0 r r 51 22 r r r 22 0 51 0 0 22 r r r 13 13 33 0 0 0 4
Elektrooptický jev Obecný elektrooptický tenzor při působení elektrického pole, r ij -elektrooptický koeficient, kde pro indexy i= 4-6 jde o rotace budící vlny vzhledem k optické ose krystalu kde 5
Elektrooptický jev Elektrooptický tenzor pro některé isotropní a anizotropní (uniaxiální) materiály. Nesymetrie koeficientů značí GaAs, GaP, kubická soustava LiNbO 3 a LiTaO 3 hexagonalní soustava ADP, KDP tetragonální soustava 6
Some electrooptical materials 7 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 8
Crystal LiNbO 3 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 n e (E) and n o (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 d 31 E E=0 E n E n0 n 3 e ne 1 2 ne r33 n r 1 3 o 2 o 13 E E L d31el 9
Šíření optické vlny krystalem Uniaxiální krystaly vykazují při šíření dvojlom a tenzor permitivity lze vyjádřit V každém směru se mohou šířit dvě vlny, lišící se polarizací a indexem lomu- řádná vlna index lomu n O nezávisí na směru šíření, směr intenzity E je kolmý k optické ose krystalu a ke směru šíření, mimořádná vlna kde index lomu n e závisí na úhlu Q mezi směrem šíření a optickou osou krystalu. 10
Šíření optické vlny krystalem Rozdíl indexů n O a n e 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 n O. A vlna TM s mimořádným indexem n e 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 11
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 highfrequency electric field), and no distortions in modulator output from piezoelectric resonances. V V A transverse electro-optic phase modulator. I I 0 2 1 cos Q An amplitude modulator in its simplest form 12
Elektrooptický modulátor EO EO Elektro-optický fázový modulátor, změny n < 1.6 x 10-3 [ 2 ]
Elektrooptický modulátor Mach-Zehenderův interferometr využitý jako elektrooptický modulátor [ 2 ] 14
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 r 1 2 2 y U out 3 U U n L A p p 15
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 r i r 2 n 1 n 3 d i 16
EO Coefficients [pm/v] elektro-optické koeficienty [pm/v] Optical properties of Crystals II Measurement of electro-optical coefficients of crystal LiNbO 3 in wide temperature range Undoped crystal LiNbO 3, of congruent composition (48,5%Li, 51,5% Nb) Bulk shape 36x3x2 mm 3 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 r 13, r 33, r 22, r 15 Correction for piezoelectric effect (d 31 = 0,85 10-12 C/N) was take in account ( 0,2 pm/v). Resulting values are r 13 = 9,7±0,2 pm/v and r 33 = 30,4±0,4 pm/v. 35 30 25 20 15 10 5 r 33 0 0,1 1 10 r 13 frekvence [khz] 17
r 13 [pm/v] r 33 [pm/v] The temperature characteristic 12 40 11 35 10 9 30 8 25 7 6 150 200 250 300 350 teplota [K] 20 160 180 200 220 240 260 280 300 320 340 teplota [K] seems to be constant for both coefficients. It seems that electro-optical coefficient r 33 became lower with decrease of the temperature, coefficients r 13 is constant 18
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 19
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 = C CM λ 0 B 2 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 20
VMB modulation detection techniques 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 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 21
Half-wave plate vs. EOM Half-wave plate, turning around with ω, rotates electric field with 2 ω B E Electro-optical modulator for phase modulation E B Standard frequency: up to 300 Hz 30 MHz 22
VMB with EOM -experimental set-up 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 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. 23
Detection in experiment with EOM The detected intensity I has both constant and time-variable parts, described for amplitude of modulator induced phase shift T o > 0.1 rad by equation I = I 0 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 J m (T o ) sin mωt m=odd The measured sample birefringence is U m δ = 2U J 1 where U is detected constant voltage and U m is amplitude of alternating voltage of measured signal. 24
Laboratory test New laboratory set-up was build in universities laboratories to solve stability problems 50 MHz electrooptical modulator from Quantum Technologies 25
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 Deep modulation 99,5 %, perfect sinusoidal signal (agreement 0.99998), half-wave voltage 125,57 V modulator works properly it has very good stability 26
Calibration curve The EO modulator was calibrated Detected intensity I depends on amplitude of phase modulation T 0 ( applied voltage) by equation I = I 0 2 (1 + sin(t o sin ωt)) We measure the first harmonic signal, so correlation with Bessel functions J 1 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
Method was checked by Soleil-Babinet compensator measurement 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% 28
Run in CERN SM18 test hall, August -September 2012 Cotton- Mouton constant at nitrogen was measured The new components were used 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 29
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 30
Photos of real experiment September 2012 31
The Cotton-Mouton effect in N 2 32 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 N 2 at 1 bar is found to be equal to -3.6 10-7 rad T -2 m -1 The difference in refractive indices is Δn (2.28 ±0.16) 10-13 for N 2 at atmospheric pressure in 1 T field 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 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 10 3-10 5 We are still far from QED prediction, but we are approaching 33