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Probing near-normally propagating bulk acoustic waves using pseudo-reflection geometry Brillouin spectroscopy
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Figures

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FIG. 1.

Brillouin scattering geometries: (a) pseudo-reflection and (b) 180°-backscattering. The wavevectors of the probed acoustic wave, external (internal) incident light, and external (internal) scattered light are q, ( ), and ( ), respectively. The propagation directions of the acoustic wave, external (internal) incident light, and external (internal) scattered light are defined relative to the surface normal by angles α, θ i i ), and θ s s ), respectively. All angles are between 0 and π/2.

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FIG. 2.

Dependence of α PR on θ m and refractive index for (a) θ d = 3° and (b) θ d = 5°. Here, θ d ⩽ θ m ⩽ (π/2 − θ d ) ensures that both θ i and θ s lie between 0 and π/2.

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FIG. 3.

Dependence of error in the sound velocity on angle of propagation within the (001)-plane of GaP. The dashed (solid) curve corresponds to the calculated error in the velocity of the slow transverse (longitudinal) mode. Calculations were determined using equations (3.1), (3.2), and (3.3) in ref. 24 together with the sample parameters therein. Since the velocity of the fast transverse mode is independent of propagation direction within this crystal plane, the expected error is zero.

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FIG. 4.

Brillouin spectra of (a) fused quartz, (b) (100)-oriented GaP, (c) deionized water, and (d) a 58 % porous silicon film for different values of θ m . Peaks due to transverse (T) and longitudinal (L) bulk acoustic modes were observed. The Rayleigh peak at ∼0 GHz was shuttered to prevent photomultiplier saturation. The arrow indicates the base of this peak which is outside the shuttered region. In the case of water, the spectrum collected at θ m = 63° was smoothed using 3-point adjacent-averaging. For clarity, only the Stokes portions of the GaP spectra are shown. The inset is a close-up of the longitudinal and transverse mode peaks collected from GaP at θ m = 0°. For all spectra shown, the collected scattered light was unpolarized.

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FIG. 5.

Acoustic wave frequency versus k m for (a) fused quartz, (b) GaP, (c) water, and (d) 50 % (diamonds) and 58 % (circles) porous silicon. Filled (open) symbols: experimental longitudinal (transverse) mode data; dashed lines: best fits of Eq. (18) . The shown fits include the data collected using the 180°-backscattering geometry. Fits with and without 180°-backscattering geometry data had adjusted R 2 values greater than 0.99. The vertical error bars are smaller than the symbols, while the horizontal error bars correspond to the experimental random error obtained from Eq. (23) using the refractive index values obtained using alternate methods.

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FIG. 6.

Acoustic wave frequency versus q PR for fused quartz. Filled (open) symbols: experimental longitudinal (transverse) mode data; dashed lines: dispersion curves deduced from obtained V L and V T values. The refractive index used to compute the q PR values was that obtained from the fit of Eq. (18) to the corresponding ν versus k m data shown in Fig. 5(a) . The vertical error bars are smaller than the symbols.

Tables

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Table I.

Refractive index and bulk acoustic velocities for fused quartz, GaP, water, and porous silicon (π-Si) determined using pseudo-reflection Brillouin spectroscopy. Values in parentheses correspond to fits done using both the pseudo-reflection and 180°-backscattering geometry data. Previously published values of these parameters are also given. Note: The n alt values for porous silicon were deduced from gravimetrically-determined porosities using the two-component Bruggeman effective medium model. The corresponding ( ) value were obtained using n alt with earlier 180°-backscattering Brillouin measurements done on similar samples.

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Table II.

Ranges of k m and corresponding q PR probed in fused quartz, GaP, water and porous silicon films. The q PR values were deduced from the refractive indices obtained through fits of Eq. (18) to the ν versus k m data shown in Fig. 5 .

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/content/aip/journal/adva/2/3/10.1063/1.4749255
2012-08-27
2014-04-19

Abstract

Pseudo-reflection geometry Brillouin spectroscopy can be used to probe acoustic wave dispersion approximately along the surface normal of a material system while avoiding the difficulties associated with specularly reflected light encountered in an ideal reflection configuration. As an example of its application, we show analytically that it can be used to determine both the refractive index and bulk acoustic mode velocities of optically-isotropic non-metallic materials and confirm the utility of the approach via a series of experiments on fused quartz, gallium phosphide, water, and porous silicon films.

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Scitation: Probing near-normally propagating bulk acoustic waves using pseudo-reflection geometry Brillouin spectroscopy
http://aip.metastore.ingenta.com/content/aip/journal/adva/2/3/10.1063/1.4749255
10.1063/1.4749255
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