International
Tables for
Crystallography
Volume D
Physical properties of crystals
Edited by A. Authier

International Tables for Crystallography (2013). Vol. D, ch. 2.4, pp. 351-355

Section 2.4.6. Techniques of Brillouin spectroscopy

R. Vachera* and E. Courtensa

aLaboratoire des Verres, Université Montpellier 2, Case 069, Place Eugène Bataillon, 34095 Montpellier CEDEX, France
Correspondence e-mail:  rene.vacher@ldv.univ-montp2.fr

2.4.6. Techniques of Brillouin spectroscopy

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Brillouin spectroscopy with visible laser light requires observing frequency shifts falling typically in the range ∼1 to ∼100 GHz, or ∼0.03 to ∼3 cm−1. To achieve this with good resolution one mostly employs interferometry. For experiments at very small angles (near forward scattering), photocorrelation spectroscopy can also be used. If the observed frequency shifts are [\geq 1] cm−1, rough measurements of spectra can sometimes be obtained with modern grating instruments. Recently, it has also become possible to perform Brillouin scattering using other excitations, in particular neutrons or X-rays. In these cases, the coupling does not occur via the Pockels effect, and the frequency shifts that are observed are much larger. The following discussion is restricted to optical interferometry.

The most common interferometer that has been used for this purpose is the single-pass planar Fabry–Perot (Born & Wolf, 1993[link]). Upon illumination with monochromatic light, the frequency response of this instrument is given by the Airy function, which consists of a regular comb of maxima obtained as the optical path separating the mirrors is increased. Successive maxima are separated by [\lambda/2]. The ratio of the maxima separation to the width of a single peak is called the finesse F, which increases as the mirror reflectivity increases. The finesse is also limited by the planarity of the mirrors. A practical limit is [F\sim 100]. The resolving power of such an instrument is [{R}= 2{}\ell /\lambda], where [\ell] is the optical thickness. Values of R around [10{^6}] to [10{^7}] can be achieved. It is impractical to increase [\ell] above ∼5 cm because the luminosity of the instrument is proportional to [1/\ell]. If higher resolutions are required, one uses a spherical interferometer as described below.

A major limitation of the Fabry–Perot interferometer is its poor contrast, namely the ratio between the maximum and the minimum of the Airy function, which is typically ∼1000. This limits the use of this instrument to samples of very high optical quality, as otherwise the generally weak Brillouin signals are masked by the elastically scattered light. To avert this effect, several passes are made through the same instrument, thus elevating the Airy function to the corresponding power (Hariharan & Sen, 1961[link]; Sandercock, 1971[link]). Multiple-pass instruments with three, four or five passes are common. Another limitation of the standard Fabry–Perot interferometer is that the interference pattern is repeated at each order. Hence, if the spectrum has a broad spectral spread, the overlap of adjacent orders can greatly complicate the interpretation of measurements. In this case, tandem instruments can be of considerable help. They consist of two Fabry–Perot interferometers with combs of different periods placed in series (Chantrel, 1959[link]; Mach et al., 1963[link]). These are operated around a position where the peak transmission of the first interferometer coincides with that of the second one. The two Fabry–Perot interferometers are scanned simultaneously. With this setup, the successive orders are reduced to small ghosts and overlap is not a problem. A convenient commercial instrument has been designed by Sandercock (1982[link]).

To achieve higher resolutions, one uses the spherical Fabry–Perot interferometer (Connes, 1958[link]; Hercher, 1968[link]). This consists of two spherical mirrors placed in a near-confocal configuration. Their spacing [\ell] is scanned over a distance of the order of [\lambda]. The peculiarity of this instrument is that its luminosity increases with its resolution. One obvious drawback is that a change of resolving power, i.e. of [\ell], requires other mirrors. Of course, the single spherical Fabry–Perot interferometer suffers the same limitations regarding contrast and order overlap that were discussed above for the planar case. Multipassing the spherical Fabry–Perot interferometer is possible but not very convenient. It is preferable to use tandem instruments that combine a multipass planar instrument of low resolution followed by a spherical instrument of high resolution (Pine, 1972[link]; Vacher, 1972[link]). To analyse the linewidth of narrow phonon lines, the planar standard is adjusted dynamically to transmit the Brillouin line and the spherical interferometer is scanned across the line. With such a device, resolving powers of ∼[10{^8}] have been achieved. For the dynamical adjustment of this instrument one can use a reference signal near the frequency of the phonon line, which is derived by electro-optic modulation of the exciting laser (Sussner & Vacher, 1979[link]). In this case, not only the width of the phonon, but also its absolute frequency shift, can be determined with an accuracy of ∼1 MHz. It is obvious that to achieve this kind of resolution, the laser source itself must be appropriately stabilized.

In closing, it should be stressed that the practice of interferometry is still an art that requires suitable skills and training in spite of the availability of commercial instruments. The experimenter must take care of a large number of aspects relating to the optical setup, the collection and acceptance angles of the instruments, spurious reflections and spurious interferences, etc. A full list is too long to be given here. However, when properly executed, interferometry is a fine tool, the performance of which is unequalled in its frequency range.

References

Born, M. & Wolf, E. (1993). Principles of optics. Sixth corrected edition. Oxford: Pergamon Press. Reissued (1999) by Cambridge University Press.
Chantrel, H. (1959). Spectromètres interférentiels à un et deux étalons de Fabry–Perot. J. Rech. CNRS, 46, 17–33.
Connes, P. (1958). L'étalon de Fabry–Perot sphérique. J. Phys. Radium, 19, 262–269.
Hariharan, P. & Sen, J. (1961). Double-passed Fabry–Perot interfero­meter. J. Opt. Soc. Am. 51, 398–399.
Hercher, M. (1968). The spherical mirror Fabry–Perot interferometer. Appl. Opt. 7, 951–966.
Mach, J. E., McNutt, D. P., Roessler, F. L. & Chabbal, R. (1963). The PEPSIOS purely interferometric high-resolution scanning spectrometer. I. The pilot model. Appl. Opt. 2, 873–885.
Pine, A. S. (1972). Thermal Brillouin scattering in cadmium sulfide: velocity and attenuation of sound; acoustoelectric effects. Phys. Rev. B, 5, 2997–3003.
Sandercock, J. R. (1971). The design and use of a stabilised multipassed interferometer of high contrast ratio. In Light scattering in solids, edited by M. Balkanski, pp. 9–12. Paris: Flammarion.
Sandercock, J. R. (1982). Trends in Brillouin scattering: studies of opaque materials, supported films, and central modes. In Light scattering in solids III. Topics in appied physics, Vol. 51, edited by M. Cardona & G. Güntherodt, pp. 173–206. Berlin: Springer.
Sussner, H. & Vacher, R. (1979). High-precision measurements of Brillouin scattering frequencies. Appl. Opt. 18, 3815–3818.
Vacher, R. (1972). Contribution à l'étude de la dynamique du réseau cristallin par analyse du spectre de diffusion Brillouin. Doctoral Thesis, University of Montpellier II.








































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