Abstract
Various phenomena have been observed when a bounded acoustic beam is incident from a liquid onto the surface of a solid at or near the Rayleigh angle. These phenomena include: a shift of the reflected beam from the position predicted by geometrical acoustics, a null or minimum of intensity within the reflected beam, a 180° phase reversal of the field on either side of the null, a weak trailing field on only one side of the reflected beam and a frequency of least reflection when the solid is lossy. By carefully examining the reflection coefficient for angles in the vicinity of the Rayleight angle, and by taking into account the angular spectrum of plane waves that comprise a bounded beam, a model of the reflection process is developed that explains all of the observed phenomena. This model shows that the various critical-reflection effects result from the interference between a geometrically reflected field and the field of a leaky Rayleigh wave, which is excited by the incident beam. Moreover, this model resolves the conflict between various explanations made for these phenomena in the past; in particular, it is found that Schoch's classical description of a laterally displaced reflected beam is valid only for beams having a large width.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
F. Goos, H. Haenchen: Ann. Physik1 (6), 333 (1947)
A. Schoch: Ergeb. Exakt. Naturwiss.23, 127 (1950)
H.K.V. Lotsch: Optik32, 116, 189, 299 and 553 (1970–71)
A. Schoch: Acustics2, 18 (1952)
R.F. Smith: Lateral displacement of an ultrasonic beam upon reflection from a solid immersed in a liquid. Tech. Rept. No. 6, Univ. of Tennessee, Knoxville, Tenn. (1968)
O.I. Diachok, W.G. Mayer: IEEE Trans.SU-16, 219 (1969)
O.I. Diachok, W.G. Mayer: J. Acoust. Soc. Am.47, 155 (1970)
F.L. Becker, R.L. Richardson: InResearch Techniques in Nondestructive Testing, ed. by R. S. Sharpe, (Academic Press, London 1970) Ch. 4
F.L. Becker, R.L. Richardson: J. Acoust. Soc. Am.51, 1609 (1971)
F.L. Becker: J. Appl. Phys.42, 199 (1971)
J.H. Smith: Energy redistribution in an ultrasonic beam reflected at a liquid-solid interface, Rept. No. Y-1798, Union Carbide Corp., Nuclear Div., Oak Ridge, Tenn. (1971)
W.G. Neubauer: J. Appl. Phys.44, 48 (1973)
G. Mott: J. Acoust. Soc. Am.50, 819 (1971)
V.M. Merkulova: Sov. Phys. Acoustics15, 404 (1970)
L.M. Brekhovskikh:Waves in Lavered Media (Academic Press, New York 1960) Section 8, p. 100
T. Tamir, H.L. Berton: J. Opt. Soc. Am.61, 1397 (1971)
—:Waves in Lavered Media (Academic Press, New York 1960), Ref. [15], Section 4.2, p. 30
W.M. Ewing, W.C. Jardetzky, F. Press:Elastic Waves in Layered Media (McGraw-Hill, New York 1957), Chapter 3, p. 14
— Ref. [15], Section 4.6, p. 38
I.A. Viktorov:Rayleigh and Lamb Waves (Plenum Press, New York 1967) Sec. I.6, p. 46
T. Tamir: Leaky-wave antennas, inAntenna Theory, Pt. 2 ed. by R. E. Collin and F. J. Zucker, (McGraw-Hill, New York 1959) Chapter 20, p. 259
T. Tamir: Optik38, 271 (1973)
R.J. Hallermeier, O.I. Diachok: J. Appl. Phys.41, 4763 (1970)
Handbook of Mathematical Functions, ed. by M. Abramowitz I.A. Stegun, (Dover Publ., New York 1965), Chapter 7, p. 297
Author information
Authors and Affiliations
Additional information
This work was supported by the U.S. Army Electronics Command under Contract No. DAAB07-71-C-0328 and by the National Science Foundation under Grant No. GK-34729.
Rights and permissions
About this article
Cite this article
Bertoni, H.L., Tamir, T. Unified theory of Rayleigh-angle phenomena for acoustic beams at liquid-solid interfaces. Appl. Phys. 2, 157–172 (1973). https://doi.org/10.1007/BF00884205
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF00884205