Angular-dispersion type Fabry- Perot interferometer applied to - PowerPoint PPT Presentation

Angular-dispersion type Fabry- Perot interferometer applied to Ferroelectrics Jae-Hyeon Ko* 1 , Seiji Kojima 2 1 Department of Physics, Hallym University, Chuncheon-si, Gangwon-do, Korea 2 Institute of Materials Science, University of Tsukuba, Tsukuba, Ibaraki, Japan * e-mail address: hwangko@hallym.ac.kr

1. Brillouin spectroscopy � Light scattering spectroscopy can probe only the zone-center phonons Raman spectroscopy – optic phonons Sound velocity Elastic stiffness coefficient Brillouin spectroscopy – acoustic phonons

Two scattering events in solids � Sound velocity v = ∆ω/ Q, � Scattering vector Q=4 π n sin( θ /2) / λ Stokes Anti-Stokes

Fabry-Perot etalon – two plane parallel mirrors with a high reflectivity

Important factors of Fabry-Perot Interferometer • Transmittance Free Spectral Range (FSR) • Finesse • Contrast C = I MAX / I MIN

Tandem multi-pass Fabry-Perot interferometer � Brillouin scattering has been a powerful tool in examining acoustic properties of condensed matters. � The conventional scanning-type tandem multipass Fabry-Perot Interferometer is characterized by high contrast and resolution. It needs a long acquisition time for weak scatterers and is thus not appropriate for real time monitoring of transient acoustic properties.

Nonscanning angular dispersion-type Fabry- Perot interferometer (NSFPI) � DPSS532: a DPSS single-mode � CL1~CL4: lenses in the collimator laser (532 nm) � FL: focusing lens (f=100 mm) � SE: a solid etalon with FSR of 30GHz (Reflectivity=98.5%, Temperature CCD contro ller flatness= λ /100) Controller IS SE Slit � CCD1: for observing the scattering volume in the sample s � CCD2: highly sensitive CCD CL1 CL2 CL3 CL4 detector either of ST-6B (SBIG) FL with a pixel size of 23 x 27 µ m 2 or 140 of AP32E-2 (Apogee) with a pixel 120 m e S s n size of 6.8 x 6.8 µ m 2 s 100 S e 2 P n 3 i 80 F D 5 � IS: iris whose aperture size can 60 be varied between 10 ~ 2 mm 40 0 4 8 12 16 20 aperture size (mm) � Slit: to remove stray light

(1) Effect of pixel size of CCD on the spectra - Brillouin spectra of ethanol Ethanol (RT) ST-6 (299K) aperture 6 mm AP32E-2 (290K) finesse 98 (AP32E-2) 2000 finesse 108 (ST-6) • Owing to the higher resolution of AP32E-2 CCD 1500 Intensity (arb. units) detector, more reliable spectra could be collected than using ST-6. 1000 500 -10.0 -7.5 -5.0 -2.5 0.0 2.5 5.0 7.5 10.0 Brillouin Shift (GHz)

(2) Effect of the aperture size on the finesse - from the Brillouin spectra of ethanol 6 • Smaller aperture size 140 reduces the kinetic broadening, which is due to 120 Flatness (nm) the finite solid angle of the 4 Finesse ( F ) 100 lens CL1. • A smaller diameter of the 80 iris can make it possible to 2 use the local area, 60 particularly that of the central 40 region, of the solid etalon. 0 4 8 12 16 20 Aperture Size (mm) Flatness of the local region of − = the solid etalon is known to + 1 2 2 F (2/ M ) (1/ F ) R be much better than the = π − average flatness of λ /100, F R /(1 R ): reflectivity finesse ( :reflectivity) R R λ resulting in the improvement M / 2: flatness finesse ( /M: flatness) of the finesse.

Results(I) – a fused quartz glass a fused quartz glass tandem NSFPI FPI NSFPI V LA (m/s) 5861 (5) 5889 (28) Intensity (arb. units) V TA (m/s) 3718 (42) 3729 (51) LA LA L(C 11 ) (GPa) 75.6 (0.1) 76.3 (0.7) TA TA G(C 44 ) (GPa) 30.4 (0.7) 30.6 (0.8) Scanning multipass FPI K (GPa) 35.1 (1.1) 35.5 (1.8) E (GPa) 70.8 (4.8 ) 71.3 (7.4) -30 -20 -10 0 10 20 30 Brillouin Shift (GHz) • V LA , V TA : longitudinal and transverse acoustic sound velocities • L, G, K, E: longitudinal, shear, bulk, and Young ’ s moduli • C ij : elastic stiffness coefficients of isotropic materials

Results(II) – ADP (ammonium dihydrogen phosphate) single crystals [001]=Z [110]=X polarizer Incident light (532 nm) ADP [110]=Y � �� � �� analyzer = − q k k s i Scattered light The direction of the analyzer is along [001] � X(ZZ)Y: C 11 can be obtained. The direction of the analyzer is along [110] � X(ZX)Y: C 44 can be obtained.

(1) Results of ADP from NSFPI X(ZZ)Y X(ZX)Y LA Intensity (arb. unit) TA 0 -30 -20 -10 0 10 20 30 Brillouin Shift (GHz) • condition: an aperture of 10 mm diameter and a 10-s CCD-detector exposure time • One longitudinal acoustic (LA) mode and one transverse acoustic (TA) mode were observed at X(ZZ)Y and X(ZX)Y scattering geometries, respectively, which is consistent with the selection rule.

(2) Comparison of Brillouin spectra obtained from NSFPI and scanning tandem FPI scanning FPI X(ZZ)Y NSFPI Both measurements 1000 rescaled according to showed the same the wavelength of the result within 0.2 GHz Intensity (arb. unit) laser accuracy. 500 0 -30 -20 -10 0 10 20 30 Brillouin Shift (GHz) [Condition] • NSFPI: an aperture of 10 mm diameter and a 10-s CCD-detector exposure time • scanning FPI: 5 minutes acquisition time with a FSR of 70 GHz

(3) Calculation of elastic stiffness coefficients of ADP π θ 4 n ∆ ϖ = π ν ∆ = = LA LA e 2 qv sin 2 v λ B B LA π θ 4 n ∆ ϖ = π ν ∆ = = TA TA o 2 qv sin 2 v λ B B TA = ρ = ρ 2 2 C v , C v 11 LA 44 TA Brillouin Elastic Sound Remark Scattering Acoustic constant velocity Shift geometry mode (ref.) (x10 10 Pa) (m/s) (GHz) X(ZZ)Y 24.86 LA 6310 C 11 ~7.05 C 11 ~6.76 X(ZX)Y 8.89 TA 2190 C 44 ~0.86 C 44 ~0.87 * ref. [Acoustic fields and waves in solids] by B. A. Auld (John & Wiley, 1990)

Results(III) – TPGME (tri-propylene glycol monomethyl ether) 30 • The Brillouin spectra at 25 intermediate temperatures are characterized by the existence of Intensity (arb. units) 20 the broad central peak and the 393.15 K increase of the Brillouin linewidth. 15 x 1/3 10 • The Brillouin spectra at 249.7 K temperatures even below the glass 5 149.9 K transition point could be observed 0 by NSFPI. -15 -10 -5 0 5 10 15 Brillouin Shift (GHz)

Sound velocity and Brillouin linewidth of TPGME • The deviation of the sound velocity from the low-frequency Intensity (arb. units) T = 140 K 1.8 limiting value and the increase 3.0 of the central peak in addition to 1.6 Sound Velocity (km/s) the Brillouin linewidth indicate 2.5 FWHM (GHz) 1.4 -10 0 10 a coupling of some structural Brillouin Shift (GHz) 1.2 relaxation to the density supercooled solid 2.0 liquid (glass) fluctuation modes. 1.0 1.5 0.8 • The slope of sound velocity shows a clear change at the glass 0.6 1.0 transition temperature, about 0.4 170 K, at which the supercooled 150 200 250 300 350 400 Temperature (K) Tg liquid state changes into solid glassy state.

Conclusions � Quick and efficient measurements of Brillouin spectra of condensed matters could become possible by using a nonscanning FPI combined with an area detector such as CCD. Thanks to the high resolution and sensitivity in addition to the combination of a solid etalon and an iris, Brillouin spectra of solid samples could be successfully measured by NSFPI. � Brillouin spectra of quartz glass and ammonium dihydrogen phosphate were measured by both NSFPI and conventional scanning type FPI, and both results were in good consistency with each other and previous reports. � The improvement and modification of NSFPI will make it possible to achieve a real-time monitoring of the acoustic properties of condensed matters.

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