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 Kojima2

1Department of Physics, Hallym University, Chuncheon-si,

Gangwon-do, Korea

2Institute 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 Brillouin spectroscopy – acoustic phonons Sound velocity Elastic stiffness coefficient

Two scattering events in solids

Sound velocity v = ∆ω/Q, Scattering vector Q=4πn 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 = IMAX / IMIN

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

laser (532 nm)

SE: a solid etalon with FSR of

30GHz (Reflectivity=98.5%, flatness=λ/100)

CCD1:

for

• bserving

the scattering volume in the sample

CCD2:

highly sensitive CCD detector either of ST-6B (SBIG) with a pixel size of 23 x 27 µm2 or

• f AP32E-2 (Apogee) with a pixel

size of 6.8 x 6.8 µm2

IS: iris whose aperture size can

be varied between 10 ~ 2 mm

Slit: to remove stray light

D P S S 5 3 2 n m

Temperature Controller

FL

s

CL1 CL2 CL3 CL4 Slit IS SE CCD contro ller

4 8 12 16 20 40 60 80 100 120 140

F i n e s s e aperture size (mm)

CL1~CL4: lenses in the collimator FL: focusing lens (f=100 mm)

(1) Effect of pixel size of CCD on the spectra

• Brillouin spectra of ethanol
• 10.0
• 7.5
• 5.0
• 2.5

0.0 2.5 5.0 7.5 10.0 500 1000 1500 2000

Ethanol (RT) aperture 6 mm finesse 98 (AP32E-2) finesse 108 (ST-6) Intensity (arb. units) Brillouin Shift (GHz) ST-6 (299K) AP32E-2 (290K)

• Owing to the higher

resolution of AP32E-2 CCD detector, more reliable spectra could be collected than using ST-6.

(2) Effect of the aperture size on the finesse

• from the Brillouin spectra of ethanol
• Smaller aperture size

reduces the kinetic broadening, which is due to the finite solid angle of the lens CL1.

• A smaller diameter of the

iris can make it possible to use the local area, particularly that of the central region, of the solid etalon. Flatness of the local region of the solid etalon is known to be much better than the average flatness of λ/100, resulting in the improvement

• f the finesse.

4 8 12 16 20 40 60 80 100 120 140

Flatness (nm) Finesse (F) Aperture Size (mm) 2 4 6

1 2 2

(2/ ) (1/ ) /(1 ): reflectivity finesse ( :reflectivity) / 2: flatness finesse ( /M: flatness)

R R

F R R π λ

− =

+ = − F M F R M

a fused quartz glass

• 30
• 20
• 10

10 20 30 TA LA TA LA

Scanning multipass FPI NSFPI

Intensity (arb. units) Brillouin Shift (GHz)

tandem FPI NSFPI

VLA (m/s) 5861 (5) 5889 (28) VTA (m/s) 3718 (42) 3729 (51) L(C11) (GPa) 75.6 (0.1) 76.3 (0.7) G(C44) (GPa) 30.4 (0.7) 30.6 (0.8) K (GPa) 35.1 (1.1) 35.5 (1.8) E (GPa) 70.8 (4.8 ) 71.3 (7.4)

Results(I) – a fused quartz glass

• VLA, VTA: longitudinal and transverse acoustic sound velocities
• L, G, K, E: longitudinal, shear, bulk, and Young’s moduli
• Cij: elastic stiffness coefficients of isotropic materials

Results(II) – ADP (ammonium dihydrogen phosphate) single crystals

[001]=Z [110]=Y [110]=X

ADP

polarizer Incident light (532 nm)

s i

q k k = −

• analyzer

Scattered light The direction of the analyzer is along [001] X(ZZ)Y: C11 can be obtained. The direction of the analyzer is along [110] X(ZX)Y: C44 can be obtained.

• 30
• 20
• 10

10 20 30

TA LA

Intensity (arb. unit) Brillouin Shift (GHz)

X(ZZ)Y X(ZX)Y

• 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
• bserved at X(ZZ)Y and X(ZX)Y scattering geometries, respectively, which is

consistent with the selection rule.

(1) Results of ADP from NSFPI

• 30
• 20
• 10

10 20 30 500 1000

rescaled according to the wavelength of the laser

X(ZZ)Y

Intensity (arb. unit) Brillouin Shift (GHz) scanning FPI NSFPI

(2) Comparison of Brillouin spectra obtained from NSFPI and scanning tandem FPI

[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

Both measurements showed the same result within 0.2 GHz accuracy.

(3) Calculation of elastic stiffness coefficients

• f ADP

2 2 11 44

4 2 sin 2 4 2 sin 2 ,

LA LA e B B LA TA TA

• B

B TA LA TA

n qv v n qv v C v C v π θ ϖ π ν λ π θ ϖ π ν λ ρ ρ ∆ = ∆ = = ∆ = ∆ = = = =

Scattering geometry Brillouin Shift (GHz) Acoustic mode Sound velocity (m/s) Elastic constant (x1010 Pa) Remark (ref.) X(ZZ)Y 24.86 LA 6310 C11~7.05 C11~6.76 X(ZX)Y 8.89 TA 2190 C44~0.86 C44~0.87

* ref. [Acoustic fields and waves in solids] by B. A. Auld (John & Wiley, 1990)

Results(III) – TPGME (tri-propylene glycol monomethyl ether)

• 15
• 10
• 5

5 10 15 5 10 15 20 25 30

x 1/3 149.9 K 249.7 K 393.15 K

Intensity (arb. units) Brillouin Shift (GHz)

• The

Brillouin spectra at intermediate temperatures are characterized by the existence of the broad central peak and the increase of the Brillouin linewidth.

• The

Brillouin spectra at temperatures even below the glass transition point could be observed by NSFPI.

Sound velocity and Brillouin linewidth of TPGME

150 200 250 300 350 400 1.0 1.5 2.0 2.5 3.0 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8

• 10

10

supercooled liquid solid (glass)

FWHM (GHz)

Tg

Sound Velocity (km/s) Temperature (K)

Brillouin Shift (GHz) Intensity (arb. units) T = 140 K

• The deviation of the sound

velocity from the low-frequency limiting value and the increase

• f the central peak in addition to

the Brillouin linewidth indicate a coupling of some structural relaxation to the density fluctuation modes.

• The slope of sound velocity

shows a clear change at the glass transition temperature, about 170 K, at which the supercooled 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.

References

• 1. D. Walton, J. J. Vanderwal, H. Xia, and P. Zhao, Rev. Sci. Instrum. 67,

2727 (1996).

• 2. S. Itoh, T. Yamana, and S. Kojima, Jpn. J. Appl. Phys. 35, 2879 (1996).
• 3. H. Xia, H. E. Jackson, K. J. Chen, X. K. Zhang, and D. Walton, Phys.
• Rev. B 54, 17805 (1996).
• 4. J.-H. Ko, Z. Chao, S. Itoh, and S. Kojima, Jpn. J. Appl. Phys. 40,

3575 (2001); J.-H. Ko, and S. Kojima, J. Kor. Phys. Soc. 39, 702 (2001).

• 5. K. J. Koski, J. Muller, H. D. Hochheimer, J. L. Yarger, Rev. Sci. Instrum.

73, 1235 (2002).

• 6. M. Sinha, J. E. Mark, H. E. Jackson, D. Walton, J. Chem. Phys. 117,

2968 (2002).

• 7. J.-H. Ko, and S. Kojima, Rev. Sci. Instrum. 73, 4390 (2002).
• 8. Y. Ike, and S. Kojima, J. Kor. Phys. Soc. 46, 90 (2005).