Brillouin Scattering in Cubic Crystals

G. B. Benedek; K. Fritsch

doi:10.1103/PhysRev.149.647

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Brillouin Scattering in Cubic Crystals

G. B. Benedek and K. Fritsch^*

Department of Physics, Spectroscopy Laboratory, and Center for Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts

^*Now at Department of Physics, The Catholic University of America, Washington, D. C.

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Phys. Rev. 149, 647 – Published 16 September, 1966

DOI: https://doi.org/10.1103/PhysRev.149.647

Abstract

Using a helium-neon laser light source and a high-resolution grating spectrograph we have studied, at room temperature, the Brillouin spectrum of light scattered from three alkali halide crystals: KCl, RbCl, and KI. By suitable orientation of the crystal axes relative to the incident beam we have obtained the frequency and the velocity of thermally excited phonons of ∼3000 Å wavelength in longitudinal and "mixed" acoustic phonon branches as a function of the direction of propagation in the [110] plane. From these data we have determined for each crystal, entirely in the absence of acoustic excitation, the elastic constants $C_{11}$ , $C_{12}$ , and $C_{44}$ for microwave (8-15 kMc/sec) sound waves with an accuracy from 0.25% to 4%. The elastic constants so determined are in very good agreement with investigations made in the ultrasonic region using externally generated sound waves of frequency ∼10 Mc/sec. This agreement indicates the absence of dispersion in the sound-wave velocity over three orders of magnitude change in the sound-wave frequency. We also present the theory for the scattering of light from thermally excited sound waves in a cubic crystal. This theory predicts the intensity, polarization, and spectral distribution of the scattered light as a function of the incident and scattered directions in the crystal. By treating the phonons quantum-mechanically at temperatures comparable to the scattering phonon frequency, we have also obtained expressions for the temperatures dependence of the scattering valid at very low temperature. The theory is in quite good agreement with our measurements of the relative intensity of the scattering from phonons in the longitudinal and "mixed" acoustic modes.

References (44)

L. Brillouin, Compt. Rend. 158, 1331 (1914)
L. Brillouin, Ann. Phys. (Paris) 17, 88 (1922)
G. Benedek, J. B. Lastovka, K. Fritsch, and T. Greytak, J. Opt. Soc. Am. 54, 1284 (1964)
R. Y. Chiao and B. P. Stoicheff, J. Opt. Soc. Am. 54, 1286 (1964)
Lord Rayleigh, Phil. Mag. 41, 107 (1871) ibid.41, 274 (1871) ibid.41, 447 (1871) ibid.47, 375 (1899)
M. Von Smoluchowski, Ann. Physik 25, 205 (1908)
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Omitted endnote
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[c1] L. Brillouin, Compt. Rend. 158, 1331 (1914)

[c2] L. Brillouin, Ann. Phys. (Paris) 17, 88 (1922)

[c3] G. Benedek, J. B. Lastovka, K. Fritsch, and T. Greytak, J. Opt. Soc. Am. 54, 1284 (1964)

[c4] R. Y. Chiao and B. P. Stoicheff, J. Opt. Soc. Am. 54, 1286 (1964)

[c5] Lord Rayleigh, Phil. Mag. 41, 107 (1871) ibid.41, 274 (1871) ibid.41, 447 (1871) ibid.47, 375 (1899)

[c6] M. Von Smoluchowski, Ann. Physik 25, 205 (1908)

[c7] A. Einstein, Ann. Physik 38, 1275 (1910)

[c8] P. Debye, Ann. Physik 39, 789 (1912)

[c9] R. W. James, The Optical Principles of the Diffraction of X-Rays (G. Bell and Sons, Ltd., London, 1958)

[c10] B. N. Brockhouse and A. T. Stewart, Rev. Mod. Phys. 30, 236 (1958)

[c11] E. Gross, Nature, 126, 201 (1930) ibid.126, 400 (1930) ibid.126, 603 (1930) ibid.129, 722 (1932)

[c12] E. H. L. Meyer and W. Ramm, Physik. Z. 33, 270 (1932) ibid.35, 111, 756 (1934)

[c13] P. Debye and F. W. Sears, Proc. Natl. Acad. Sci. 18, 409 (1932)

[c14] C. V. Raman and N. Nath, Proc. Indian Acad. Sci. A2, 406 (1935) ibid.A2, 413 (1935) ibid.A3, 75 (1936) ibid.A3, 119 (1936) ibid.A3, 459 (1936)

[c15] L. Bergmann, Ultrasonics and their Scientific and Technical Applications (John Wiley & Sons, Inc., New York, 1938)

[c16] L. Landau and G. Placzek, Physik Z. Sowjetunion 5, 172 (1934)

[c17] L. Landau and E. M. Lifshitz, Electrodynamics of Continuous Media (Addison-Wesley Publishing Company, Inc., Reading, Massachusetts, 1960), pp. 393 ff

[c18] R. Pecora, J. Chem. Phys. 40, 1604 (1964)

[c19] R. D. Mountain, Rev. Mod. Phys. 38, 205 (1966)

[c20] I. Fabelinskii, Usp. Fiz. Nauk 63, 355 (1957)

[c21] D. H. Rank, E. R. Shull, and D. W. Axford, Nature 164, 67 (1949)

[c22] R. S. Krishnan, Proc. Indian Acad. Sci. A41, 91 (1955)

[c23] D. I. Mash, V. S. Starunov, and I. Fabelinskii, Zh. Eksperim. i Teor. Fiz. 47, 783 (1964) [English transl.: Soviet Phys.—JETP 20, 523 (1965)]

[c24] R. Y. Chiao and P. Fleury, Physics of Quantum Electronics, edited by P. Kelley, B. Lax, and P. E. Tannenwald (McGraw-Hill Book Publishers, Inc., New York, 1966)

[c25] G. Benedek and T. Greytak, Proc. IEEE 53, 1623 (1965)

[c26] H. Z. Cummins, N. Knable, and Y. Yeh, Phys. Rev. Letters 12, 150 (1964)

[c27] S. S. Alpert, Y. Yeh, and E. Lipworth, Phys. Rev. Letters 14, 486 (1965)

[c28] D. A. Jennings and H. Takuma, Appl. Phys. Letters 5, 241 (1964)

[c29] J. B. Lastovka and G. B. Benedek, Physics of Quantum Electronics, edited by P. Kelley, B. Lax, and P. E. Tannenwald (McGraw-Hill Book Publishers, Inc., New York, 1966)

[c30] N. C. Ford, Jr., and G. B. Benedek, Phys. Rev. Letters 15, 694 (1965)

[c31] K. Fritsch, M.S. thesis, M.I.T., 1965 (unpublished)

[c32] K. Fritsch and G. Benedek, Bull. Am. Phys. Soc. 10, 109 (1965)

[c33] Omitted endnote

[c34] J. F. Nye, Physical Properties of Crystals, Oxford (Clarendon Press, Oxford, England, 1957), pp. 243 ff

[c35] M. Born and K. Huang, Dynamical Theory of Crystal Lattices (Clarendon Press, Oxford, England, 1954), pp. 373 ff

[c36] J. DeLauney, Solid State Physics, edited by F. Seitz and D. Turnbull (Academic Press Inc., New York, 1956), Vol. 2

[c37] M. Born and E. Wolf, Principles of Optics (The Macmillan Company, New York, 1964), 2nd ed., pp. 435 ff

[c38] Tschunko, J. Opt. Soc. Am. 55, 1 (1965)

[c39] Landolt-Börnstein, Zahlenwerte und Funktionen ans Physik-Chemie-Astronomie-Geophysik-Technik (Springer-Verlag, Berlin, 1962), 6th ed., Vol. II, Part A, Chap. 8

[c40] A. A. Maradudin, E. W. Montroll, and G. Weiss, Theory of Lattice Dynamics in the Harmonic Approximation (Academic Press Inc., New York, 1963)

[c41] S. Haussühl, Z. Phys. 159, 223 (1960)

[c42] P. Jacquinot, Rept. Progr. Phys. 23, 267 (1960)

[c43] E. Burstein and P. L. Smith, Phys. Rev. 74, 229, 1880 (1948)

[c44] F. Pockels, Lehrbuch der Kristalloptik (Teubner, Leipzig, 1906), p. 467

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Brillouin Scattering in Cubic Crystals

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