Skip to main content
SpringerLink
Log in

Surface Acoustic Waves on Nonlinear Substrates

  • Chapter
Nonlinear Waves in Solid State Physics

Part of the book series: NATO ASI Series ((NSSB,volume 247))

Abstract

All elastic media are nonlinear to a greater or lesser extent. In this chapter we examine some of the consequences of this nonlinearity on the propagation of surface acoustic waves of sagittal and predominantly shear horizontal polarizations across planar and periodically corrugated solid surfaces. These consequences can involve changes in the frequency of the surface acoustic wave, such as occur in the acoustical rectification of a surface acoustic wave, in harmonic generation, and in nonlinear mixing of surface acoustic waves. The nonlinearity can also affect a surface acoustic wave in ways that involve no change in its frequency. It can give rise to nonlinear surface acoustic waves, and to associated surface acoustic solitary waves. Although both kinds of consequences of elastic nonlinearity for surface acoustic waves will be considered in this chapter, the emphasis will be on effects that involve no change in the frequency of the wave. In addition, in the calculations described in this chapter we will confine ourselves primarily to non-piezoelectric materials. However, their extension to piezoelectric media will be indicated briefly.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
eBook
USD 16.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. V. I. Karpman and E. M. Krushkal’, Zh. Eksp. Teor. Fiz. 55, 530 (1968) [Soviet Physics — JETP 28, 277 (1969)].

    Google Scholar 

  2. D. F. Parker, Physica 16D, 385 (1985).

    ADS  Google Scholar 

  3. D. F. Nelson, Electric, Optic & Acoustic Interactions in Dielectrics (Wiley, New York, 1979).

    Google Scholar 

  4. G. Leibfried and W. Ludwig, Z. Phys. 160, 80 (1960).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  5. A. A. Maradudin, in Physics of Phonons, T. Paszkiewicz ed. (Springer, New York, 1987).

    Google Scholar 

  6. H. F. Tiersten, J. Appl. Phys. 40, 770 (1969).

    Article  ADS  Google Scholar 

  7. S. V. Bogdanov, M. D. Levin, and I. B. Yakovkin, Akust. Zhur. 15, 12 (1969).

    Google Scholar 

  8. A. I. Murdoch, J. Mech. Phys. Solids 24, 137 (1976).

    Article  ADS  MATH  Google Scholar 

  9. G. W. Farnell, in Acoustic Surface Waves, A. A. Oliner ed. (Springer, New York, 1978), p. 13.

    Chapter  Google Scholar 

  10. V. R. Velasco and F. Garcia-Moliner, Physica Scripta 20, 111, (1979).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  11. B. Djafari-Rouhani, L. Dobrzynski, V. R. Velasco and F. Garcia-Moliner, Surf. Sci. 110, 129 (1981).

    Article  ADS  Google Scholar 

  12. L. Dobrzynski and B. Djafari-Rouhani, in Vibrations at Surfaces, R. Caudano, J. M. Gilles, and A. A. Lucas eds. (Plenum, New York, 1982), p. 1.

    Chapter  Google Scholar 

  13. A. A. Maradudin, in Nonequilibrium Phonon Dynamics, W. E. Bron ed. (Plenum, New York, 1985), p. 395.

    Google Scholar 

  14. D. C. Gazis, R. Herman, and R. F. Wallis, Phys. Rev. 119, 533, (1960).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  15. G. R. Gerhart, J. Acoust. Soc. Am. 60, 1085 (1976).

    Article  ADS  Google Scholar 

  16. K. Jassby and D. Saltoun, Mater. Eval. 40, 198 (1982).

    Google Scholar 

  17. M. Hayes and R. S. Rivlin, Arch. Rat. Mech. Anal. 8, 15 (1961).

    Article  MathSciNet  MATH  Google Scholar 

  18. Y. Iwashimizu and O. Kobori, J. Acoust. Soc. Am. 64, 910 (1978).

    Article  ADS  MATH  Google Scholar 

  19. A. Tverdokhlebov, J. Acoust. Soc. Am. 73, 2006 (1983).

    Article  ADS  MATH  Google Scholar 

  20. P. P. Delsanto and A. V. Clark, Jr., J. Acoust. Soc. Am. 81, 952 (1987).

    Article  ADS  Google Scholar 

  21. G. T. Mase and G. C. Johnson, J. Appl. Mech. 54, 127 (1987).

    Article  ADS  MATH  Google Scholar 

  22. A. J. C. Ladd and W. G. Hoover, Preprint.

    Google Scholar 

  23. J. Lothe and D. M. Barnett, J. Appl. Phys. 47, 428 (1976).

    Article  ADS  Google Scholar 

  24. B. A. Auld, Acoustic Fields and Waves in Solids, vol. II (Wiley, New York, 1973).

    Google Scholar 

  25. H. F. Tiersten, J. Acoust. Soc. Am. 64, 832 (1978).

    Article  ADS  MATH  Google Scholar 

  26. H. F. Tiersten and B. K. Sinha, J. Appl. Phys. 49, 87 (1978).

    Article  ADS  Google Scholar 

  27. D. Husson, J. Appl. Phys. 57, 1562 (1985).

    Article  ADS  Google Scholar 

  28. R. N. Thurston and K. Brugger, Phys. Rev. 133, A1604 (1964).

    Article  ADS  Google Scholar 

  29. Landolt-Börnstein New Series, Group III, vol. 11, K.-H. Hellwege ed. (Springer, Berlin, 1979); vol. 18, K.-H. Hellwege and O. Madelung eds. (Springer, Berlin, 1984).

    Google Scholar 

  30. For a review see: F. Nizzoli and G. I. Stegeman, in Surface Excitations, V. M. Agrano-vich and R. Loudon eds. (North-Holland, Amsterdam, 1985). For a detailed discussion see M. Planat, Propagation nonlinéaire des ondes acoustiques dans les solides, thesis, Université de Franche-Comté (1984).

    Google Scholar 

  31. H. F. Tiersten and J. C. Baumhauer, J. Appl. Phys. 58, 1867 (1985).

    Article  ADS  Google Scholar 

  32. R. Normandin, M. Fukui, and G. I. Stegeman, J. Appl. Phys. 50, 81 (1979).

    Article  ADS  Google Scholar 

  33. P. O. LÏ•pen, J. Appl. Phys. 39, 5400 (1968).

    Article  ADS  Google Scholar 

  34. J. W. Gibson and P. Meijer, J. Appl. Phys. 45, 3288 (1974).

    Article  ADS  Google Scholar 

  35. A. Alippi, A. Palma, L. Palmieri, and G. Socino, J. Appl. Phys. 48, 2182 (1977).

    Article  ADS  Google Scholar 

  36. M. Toda, Theory of Nonlinear Lattices (Springer, Berlin, 1981).

    Book  MATH  Google Scholar 

  37. G. B. Whitham, Linear and Nonlinear Waves (Wiley, New York, 1974).

    MATH  Google Scholar 

  38. H. C. Yuen and B. M. Lake, Phys. Fluids 18, 956 (1975) and references therein.

    Article  ADS  MATH  Google Scholar 

  39. T. Taniuti and N. Yajima, J. Math. Phys. 10, 1369 (1969).

    Article  MathSciNet  ADS  Google Scholar 

  40. N. Kalyanasundaram, Int. J. Engng. Sci. 19, 279 (1981).

    Article  MATH  Google Scholar 

  41. N. Kalyanasundaram, Int. J. Engng. Sci. 19, 435 (1981).

    Article  Google Scholar 

  42. N. Kalyanasundaram, R. Ravindran, and P. Prasad, J. Acoust. Soc. Am. 72, 488 (1982).

    Article  ADS  MATH  Google Scholar 

  43. R. W. Lardner, Int. J. Engng. Sci. 21, 1331 (1983).

    Article  MathSciNet  MATH  Google Scholar 

  44. R. W. Lardner, J. Appl. Phys. 55, 3251 (1984).

    Article  ADS  Google Scholar 

  45. M. Planat, J. Appl. Phys. 57, 4911 (1985).

    Article  ADS  Google Scholar 

  46. T. Sakuma and Y. Kawanami, Phys. Rev. B29, 869 (1984).

    ADS  Google Scholar 

  47. T. Sakuma and Y. Kawanami, Phys. Rev. B29, 880 (1984).

    ADS  Google Scholar 

  48. T. Sakuma and T. Miyazaki, Phys. Rev. B33, 1036 (1986).

    ADS  Google Scholar 

  49. T. Sakuma and O. Saito, Phys. Rev. B35, 1294 (1987).

    ADS  Google Scholar 

  50. V. I. Nayanov, Pis’ma Zh. Eksp. Teor. Fiz. 44, 245 (1986) [JETP Letters 44, 314 (1986)].

    Google Scholar 

  51. D. Royer and E. Dieulesaint, J. Acoust. Soc. Am. 76, 1438 (1984).

    Article  ADS  Google Scholar 

  52. V. I. Karpman, Non-Linear Waves in Dispersive Media, (Pergamon, Oxford, 1974) [Russ. edition: Nauka, Moscow, 1973].

    Google Scholar 

  53. V. E. Zakharov and A. B. Shabat, Zh. Eksp. Teor. Fiz. 61, 118 (1971) [Soviet Physics — JETP 34, 62 (1972)].

    Google Scholar 

  54. A. D. Boardman, G. S. Cooper, A. A. Maradudin, and T. P. Shen, Phys. Rev. B34, 8273 (1986).

    ADS  Google Scholar 

  55. R. C. Hollinger and G. R. Barsch, J. Phys. Chem. Solids 37, 845 (1976).

    Article  ADS  Google Scholar 

  56. L. M. Brekhovskikh, Akust. Zhur. 5, 288 (1959) [Soviet Physics — Acoustics 5, 288 (1960)].

    MathSciNet  Google Scholar 

  57. F. Rischbieter, Acustica 16, 75 (1965).

    Google Scholar 

  58. P. V. H. Sabine, Electronics Lett. 6, 149 (1970).

    Article  Google Scholar 

  59. B. A. Auld, J. J. Gagnepain, and M. Tan, Electronics Lett. 12, 650 (1976).

    Article  Google Scholar 

  60. Yu. V. Gulyaev and V. P. Plessky, Zh. Tekh. Fiz. 48, 447 (1978) [Soviet Physics — Technical Physics 23, 266 (1978)].

    Google Scholar 

  61. N. E. Glass and A. A. Maradudin, Electronics Lett. 17, 773, (1981).

    Article  ADS  Google Scholar 

  62. N. E. Glass, R. Loudon, and A. A. Maradudin, Phys. Rev. B24, 6843 (1981).

    ADS  Google Scholar 

  63. N. E. Glass and A. A. Maradudin, J. Appl. Phys. 54, 796 (1983).

    Article  ADS  Google Scholar 

  64. H. F. Tiersten, J. T. Song, and D. V. Shick, J. Appl. Phys. 62, 1154 (1987).

    Article  ADS  Google Scholar 

  65. B. Hillebrands and G. I. Stegeman, unpublished work.

    Google Scholar 

  66. For a review and introduction, see also Ref. 5.

    Google Scholar 

  67. G. A. Maugin, Nonlinear Electromechanical Effects and Applications (World Scientific, Singapore, 1985).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Physics and Institute for Surface and Interface Science, University of California, Irvine, CA, 92717, USA

    A. A. Maradudin & A. P. Mayer

Authors
  1. A. A. Maradudin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. P. Mayer
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. University of Salford, Salford, UK

    A. D. Boardman  & T. Twardowski  & 

  2. University of Rome, Rome, Italy

    M. Bertolotti

Rights and permissions

Reprints and permissions

Copyright information

© 1990 Plenum Press, New York

About this chapter

Cite this chapter

Maradudin, A.A., Mayer, A.P. (1990). Surface Acoustic Waves on Nonlinear Substrates. In: Boardman, A.D., Bertolotti, M., Twardowski, T. (eds) Nonlinear Waves in Solid State Physics. NATO ASI Series, vol 247. Springer, Boston, MA. https://doi.org/10.1007/978-1-4684-5898-5_4

Download citation

  • DOI: https://doi.org/10.1007/978-1-4684-5898-5_4

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4684-5900-5

  • Online ISBN: 978-1-4684-5898-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation