Abstract

We use ultrashort optical pulses to excite and detect vibrations of single silica spheres with a diameter of 5μm placed at the surface of an acoustically mismatched substrate. In addition to the photoelastic detection of picosecond longitudinal acoustic pulses propagating inside the bulk, we detect gigahertz acoustic resonances of the sphere through probe beam defocusing. The mode frequencies are in close accord with those calculated from the elastic vibrations of a free sphere. We also record a resonant enhancement in the amplitude of specific modes of two touching spheres.

© 2009 Optical Society of America

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  1. J. Wang, Z. Ren, and C. T. C. Nguyen, IEEE Trans. Ultrason. Ferroelectr. Freq. Control 51, 1607 (2004).
    [CrossRef]
  2. A. Gaidarzhy, M. Imboden, P. Mohanty, J. Rankin, and B. W. Sheldon, Appl. Phys. Lett. 91, 203503 (2007).
    [CrossRef]
  3. D. H. Hurley and K. L. Telschow, Phys. Rev. B 66, 153301 (2002).
    [CrossRef]
  4. D. M. Profunser, O. B. Wright, and O. Matsuda, Phys. Rev. Lett. 97, 055502 (2006).
    [CrossRef] [PubMed]
  5. H. S. Lim, M. H. Kuok, S. C. Ng, and Z. K. Wang, Appl. Phys. Lett. 84, 4182 (2004).
    [CrossRef]
  6. S. Ishikawa, N. Nakaso, N. Takeda, T. Mihara, Y. Tsukahara, and K. Yamanaka, Appl. Phys. Lett. 83, 4649 (2003).
    [CrossRef]
  7. J. Tian, H. Ogi, and M. Hirao, J. Appl. Phys. 95, 8366 (2004).
    [CrossRef]
  8. D. Clorennec and D. Royer, Appl. Phys. Lett. 85, 2435 (2004).
    [CrossRef]
  9. D. B. Murray and L. Saviot, Physica E (Amsterdam) 26, 417 (2005).
    [CrossRef]
  10. R. Ma, A. Schliesser, P. Del'Haye, A. Dabirian, G. Anetsberger, and T. J. Kippenberg, Opt. Lett. 32, 2200 (2007).
    [CrossRef] [PubMed]
  11. J. E. Mark, The Polymer Data Handbook (Oxford U. Press, 1999).
  12. D. Lide, CRC Handbook of Chemistry and Physics (CRC Press, 1999).
  13. C. Luo, F. Meng, X. Liu, and Y. Guo, Microelectron. J. 37, 5 (2006).
    [CrossRef]
  14. M. Grimsditch, Phys. Rev. B 31, 6818 (1985).
    [CrossRef]
  15. Z. Lin, L. V. Zhigilei, and V. Celli, Phys. Rev. B 77, 075133 (2008).
    [CrossRef]
  16. C. Thomsen, H. T. Grahn, H. J. Maris, and J. Tauc, Phys. Rev. B 34, 4129 (1986).
    [CrossRef]
  17. H. Lamb, Proc. London Math. Soc. S1-13, 189 (1881).
    [CrossRef]
  18. M. D. M. Peri and C. Cetinkaya, J. Colloid Interface Sci. 288, 432 (2005).
    [CrossRef]
  19. Y. Satô and T. Usami, Geophys. Mag. 31, 15 (1962).
  20. Y. Shui, D. Royer, E. Dieulesaint, and Z. Sun, in IEEE Symposium Proceedings (1988), p. 343.
  21. N. V. Chigarev, C. Rossignol, and B. Audoin, Rev. Sci. Instrum. 77, 114901 (2006).
    [CrossRef]
  22. A. C. Hladky-Hennion, A. Devos, and M. d. Billy, J. Acoust. Soc. Am. 116, 117 (2004).
    [CrossRef]
  23. W. S. Capinski and H. J. Maris, Rev. Sci. Instrum. 67, 2720 (1996).
    [CrossRef]

2008

Z. Lin, L. V. Zhigilei, and V. Celli, Phys. Rev. B 77, 075133 (2008).
[CrossRef]

2007

A. Gaidarzhy, M. Imboden, P. Mohanty, J. Rankin, and B. W. Sheldon, Appl. Phys. Lett. 91, 203503 (2007).
[CrossRef]

R. Ma, A. Schliesser, P. Del'Haye, A. Dabirian, G. Anetsberger, and T. J. Kippenberg, Opt. Lett. 32, 2200 (2007).
[CrossRef] [PubMed]

2006

D. M. Profunser, O. B. Wright, and O. Matsuda, Phys. Rev. Lett. 97, 055502 (2006).
[CrossRef] [PubMed]

C. Luo, F. Meng, X. Liu, and Y. Guo, Microelectron. J. 37, 5 (2006).
[CrossRef]

N. V. Chigarev, C. Rossignol, and B. Audoin, Rev. Sci. Instrum. 77, 114901 (2006).
[CrossRef]

2005

M. D. M. Peri and C. Cetinkaya, J. Colloid Interface Sci. 288, 432 (2005).
[CrossRef]

D. B. Murray and L. Saviot, Physica E (Amsterdam) 26, 417 (2005).
[CrossRef]

2004

J. Wang, Z. Ren, and C. T. C. Nguyen, IEEE Trans. Ultrason. Ferroelectr. Freq. Control 51, 1607 (2004).
[CrossRef]

J. Tian, H. Ogi, and M. Hirao, J. Appl. Phys. 95, 8366 (2004).
[CrossRef]

D. Clorennec and D. Royer, Appl. Phys. Lett. 85, 2435 (2004).
[CrossRef]

H. S. Lim, M. H. Kuok, S. C. Ng, and Z. K. Wang, Appl. Phys. Lett. 84, 4182 (2004).
[CrossRef]

A. C. Hladky-Hennion, A. Devos, and M. d. Billy, J. Acoust. Soc. Am. 116, 117 (2004).
[CrossRef]

2003

S. Ishikawa, N. Nakaso, N. Takeda, T. Mihara, Y. Tsukahara, and K. Yamanaka, Appl. Phys. Lett. 83, 4649 (2003).
[CrossRef]

2002

D. H. Hurley and K. L. Telschow, Phys. Rev. B 66, 153301 (2002).
[CrossRef]

1996

W. S. Capinski and H. J. Maris, Rev. Sci. Instrum. 67, 2720 (1996).
[CrossRef]

1986

C. Thomsen, H. T. Grahn, H. J. Maris, and J. Tauc, Phys. Rev. B 34, 4129 (1986).
[CrossRef]

1985

M. Grimsditch, Phys. Rev. B 31, 6818 (1985).
[CrossRef]

1962

Y. Satô and T. Usami, Geophys. Mag. 31, 15 (1962).

1881

H. Lamb, Proc. London Math. Soc. S1-13, 189 (1881).
[CrossRef]

Anetsberger, G.

Audoin, B.

N. V. Chigarev, C. Rossignol, and B. Audoin, Rev. Sci. Instrum. 77, 114901 (2006).
[CrossRef]

Billy, M. d.

A. C. Hladky-Hennion, A. Devos, and M. d. Billy, J. Acoust. Soc. Am. 116, 117 (2004).
[CrossRef]

Capinski, W. S.

W. S. Capinski and H. J. Maris, Rev. Sci. Instrum. 67, 2720 (1996).
[CrossRef]

Celli, V.

Z. Lin, L. V. Zhigilei, and V. Celli, Phys. Rev. B 77, 075133 (2008).
[CrossRef]

Cetinkaya, C.

M. D. M. Peri and C. Cetinkaya, J. Colloid Interface Sci. 288, 432 (2005).
[CrossRef]

Chigarev, N. V.

N. V. Chigarev, C. Rossignol, and B. Audoin, Rev. Sci. Instrum. 77, 114901 (2006).
[CrossRef]

Clorennec, D.

D. Clorennec and D. Royer, Appl. Phys. Lett. 85, 2435 (2004).
[CrossRef]

Dabirian, A.

Del'Haye, P.

Devos, A.

A. C. Hladky-Hennion, A. Devos, and M. d. Billy, J. Acoust. Soc. Am. 116, 117 (2004).
[CrossRef]

Dieulesaint, E.

Y. Shui, D. Royer, E. Dieulesaint, and Z. Sun, in IEEE Symposium Proceedings (1988), p. 343.

Gaidarzhy, A.

A. Gaidarzhy, M. Imboden, P. Mohanty, J. Rankin, and B. W. Sheldon, Appl. Phys. Lett. 91, 203503 (2007).
[CrossRef]

Grahn, H. T.

C. Thomsen, H. T. Grahn, H. J. Maris, and J. Tauc, Phys. Rev. B 34, 4129 (1986).
[CrossRef]

Grimsditch, M.

M. Grimsditch, Phys. Rev. B 31, 6818 (1985).
[CrossRef]

Guo, Y.

C. Luo, F. Meng, X. Liu, and Y. Guo, Microelectron. J. 37, 5 (2006).
[CrossRef]

Hirao, M.

J. Tian, H. Ogi, and M. Hirao, J. Appl. Phys. 95, 8366 (2004).
[CrossRef]

Hladky-Hennion, A. C.

A. C. Hladky-Hennion, A. Devos, and M. d. Billy, J. Acoust. Soc. Am. 116, 117 (2004).
[CrossRef]

Hurley, D. H.

D. H. Hurley and K. L. Telschow, Phys. Rev. B 66, 153301 (2002).
[CrossRef]

Imboden, M.

A. Gaidarzhy, M. Imboden, P. Mohanty, J. Rankin, and B. W. Sheldon, Appl. Phys. Lett. 91, 203503 (2007).
[CrossRef]

Ishikawa, S.

S. Ishikawa, N. Nakaso, N. Takeda, T. Mihara, Y. Tsukahara, and K. Yamanaka, Appl. Phys. Lett. 83, 4649 (2003).
[CrossRef]

Kippenberg, T. J.

Kuok, M. H.

H. S. Lim, M. H. Kuok, S. C. Ng, and Z. K. Wang, Appl. Phys. Lett. 84, 4182 (2004).
[CrossRef]

Lamb, H.

H. Lamb, Proc. London Math. Soc. S1-13, 189 (1881).
[CrossRef]

Lide, D.

D. Lide, CRC Handbook of Chemistry and Physics (CRC Press, 1999).

Lim, H. S.

H. S. Lim, M. H. Kuok, S. C. Ng, and Z. K. Wang, Appl. Phys. Lett. 84, 4182 (2004).
[CrossRef]

Lin, Z.

Z. Lin, L. V. Zhigilei, and V. Celli, Phys. Rev. B 77, 075133 (2008).
[CrossRef]

Liu, X.

C. Luo, F. Meng, X. Liu, and Y. Guo, Microelectron. J. 37, 5 (2006).
[CrossRef]

Luo, C.

C. Luo, F. Meng, X. Liu, and Y. Guo, Microelectron. J. 37, 5 (2006).
[CrossRef]

Ma, R.

Maris, H. J.

W. S. Capinski and H. J. Maris, Rev. Sci. Instrum. 67, 2720 (1996).
[CrossRef]

C. Thomsen, H. T. Grahn, H. J. Maris, and J. Tauc, Phys. Rev. B 34, 4129 (1986).
[CrossRef]

Mark, J. E.

J. E. Mark, The Polymer Data Handbook (Oxford U. Press, 1999).

Matsuda, O.

D. M. Profunser, O. B. Wright, and O. Matsuda, Phys. Rev. Lett. 97, 055502 (2006).
[CrossRef] [PubMed]

Meng, F.

C. Luo, F. Meng, X. Liu, and Y. Guo, Microelectron. J. 37, 5 (2006).
[CrossRef]

Mihara, T.

S. Ishikawa, N. Nakaso, N. Takeda, T. Mihara, Y. Tsukahara, and K. Yamanaka, Appl. Phys. Lett. 83, 4649 (2003).
[CrossRef]

Mohanty, P.

A. Gaidarzhy, M. Imboden, P. Mohanty, J. Rankin, and B. W. Sheldon, Appl. Phys. Lett. 91, 203503 (2007).
[CrossRef]

Murray, D. B.

D. B. Murray and L. Saviot, Physica E (Amsterdam) 26, 417 (2005).
[CrossRef]

Nakaso, N.

S. Ishikawa, N. Nakaso, N. Takeda, T. Mihara, Y. Tsukahara, and K. Yamanaka, Appl. Phys. Lett. 83, 4649 (2003).
[CrossRef]

Ng, S. C.

H. S. Lim, M. H. Kuok, S. C. Ng, and Z. K. Wang, Appl. Phys. Lett. 84, 4182 (2004).
[CrossRef]

Nguyen, C. T. C.

J. Wang, Z. Ren, and C. T. C. Nguyen, IEEE Trans. Ultrason. Ferroelectr. Freq. Control 51, 1607 (2004).
[CrossRef]

Ogi, H.

J. Tian, H. Ogi, and M. Hirao, J. Appl. Phys. 95, 8366 (2004).
[CrossRef]

Peri, M. D. M.

M. D. M. Peri and C. Cetinkaya, J. Colloid Interface Sci. 288, 432 (2005).
[CrossRef]

Profunser, D. M.

D. M. Profunser, O. B. Wright, and O. Matsuda, Phys. Rev. Lett. 97, 055502 (2006).
[CrossRef] [PubMed]

Rankin, J.

A. Gaidarzhy, M. Imboden, P. Mohanty, J. Rankin, and B. W. Sheldon, Appl. Phys. Lett. 91, 203503 (2007).
[CrossRef]

Ren, Z.

J. Wang, Z. Ren, and C. T. C. Nguyen, IEEE Trans. Ultrason. Ferroelectr. Freq. Control 51, 1607 (2004).
[CrossRef]

Rossignol, C.

N. V. Chigarev, C. Rossignol, and B. Audoin, Rev. Sci. Instrum. 77, 114901 (2006).
[CrossRef]

Royer, D.

D. Clorennec and D. Royer, Appl. Phys. Lett. 85, 2435 (2004).
[CrossRef]

Y. Shui, D. Royer, E. Dieulesaint, and Z. Sun, in IEEE Symposium Proceedings (1988), p. 343.

Satô, Y.

Y. Satô and T. Usami, Geophys. Mag. 31, 15 (1962).

Saviot, L.

D. B. Murray and L. Saviot, Physica E (Amsterdam) 26, 417 (2005).
[CrossRef]

Schliesser, A.

Sheldon, B. W.

A. Gaidarzhy, M. Imboden, P. Mohanty, J. Rankin, and B. W. Sheldon, Appl. Phys. Lett. 91, 203503 (2007).
[CrossRef]

Shui, Y.

Y. Shui, D. Royer, E. Dieulesaint, and Z. Sun, in IEEE Symposium Proceedings (1988), p. 343.

Sun, Z.

Y. Shui, D. Royer, E. Dieulesaint, and Z. Sun, in IEEE Symposium Proceedings (1988), p. 343.

Takeda, N.

S. Ishikawa, N. Nakaso, N. Takeda, T. Mihara, Y. Tsukahara, and K. Yamanaka, Appl. Phys. Lett. 83, 4649 (2003).
[CrossRef]

Tauc, J.

C. Thomsen, H. T. Grahn, H. J. Maris, and J. Tauc, Phys. Rev. B 34, 4129 (1986).
[CrossRef]

Telschow, K. L.

D. H. Hurley and K. L. Telschow, Phys. Rev. B 66, 153301 (2002).
[CrossRef]

Thomsen, C.

C. Thomsen, H. T. Grahn, H. J. Maris, and J. Tauc, Phys. Rev. B 34, 4129 (1986).
[CrossRef]

Tian, J.

J. Tian, H. Ogi, and M. Hirao, J. Appl. Phys. 95, 8366 (2004).
[CrossRef]

Tsukahara, Y.

S. Ishikawa, N. Nakaso, N. Takeda, T. Mihara, Y. Tsukahara, and K. Yamanaka, Appl. Phys. Lett. 83, 4649 (2003).
[CrossRef]

Usami, T.

Y. Satô and T. Usami, Geophys. Mag. 31, 15 (1962).

Wang, J.

J. Wang, Z. Ren, and C. T. C. Nguyen, IEEE Trans. Ultrason. Ferroelectr. Freq. Control 51, 1607 (2004).
[CrossRef]

Wang, Z. K.

H. S. Lim, M. H. Kuok, S. C. Ng, and Z. K. Wang, Appl. Phys. Lett. 84, 4182 (2004).
[CrossRef]

Wright, O. B.

D. M. Profunser, O. B. Wright, and O. Matsuda, Phys. Rev. Lett. 97, 055502 (2006).
[CrossRef] [PubMed]

Yamanaka, K.

S. Ishikawa, N. Nakaso, N. Takeda, T. Mihara, Y. Tsukahara, and K. Yamanaka, Appl. Phys. Lett. 83, 4649 (2003).
[CrossRef]

Zhigilei, L. V.

Z. Lin, L. V. Zhigilei, and V. Celli, Phys. Rev. B 77, 075133 (2008).
[CrossRef]

Appl. Phys. Lett.

A. Gaidarzhy, M. Imboden, P. Mohanty, J. Rankin, and B. W. Sheldon, Appl. Phys. Lett. 91, 203503 (2007).
[CrossRef]

H. S. Lim, M. H. Kuok, S. C. Ng, and Z. K. Wang, Appl. Phys. Lett. 84, 4182 (2004).
[CrossRef]

S. Ishikawa, N. Nakaso, N. Takeda, T. Mihara, Y. Tsukahara, and K. Yamanaka, Appl. Phys. Lett. 83, 4649 (2003).
[CrossRef]

D. Clorennec and D. Royer, Appl. Phys. Lett. 85, 2435 (2004).
[CrossRef]

Geophys. Mag.

Y. Satô and T. Usami, Geophys. Mag. 31, 15 (1962).

IEEE Trans. Ultrason. Ferroelectr. Freq. Control

J. Wang, Z. Ren, and C. T. C. Nguyen, IEEE Trans. Ultrason. Ferroelectr. Freq. Control 51, 1607 (2004).
[CrossRef]

J. Acoust. Soc. Am.

A. C. Hladky-Hennion, A. Devos, and M. d. Billy, J. Acoust. Soc. Am. 116, 117 (2004).
[CrossRef]

J. Appl. Phys.

J. Tian, H. Ogi, and M. Hirao, J. Appl. Phys. 95, 8366 (2004).
[CrossRef]

J. Colloid Interface Sci.

M. D. M. Peri and C. Cetinkaya, J. Colloid Interface Sci. 288, 432 (2005).
[CrossRef]

Microelectron. J.

C. Luo, F. Meng, X. Liu, and Y. Guo, Microelectron. J. 37, 5 (2006).
[CrossRef]

Opt. Lett.

Phys. Rev. B

M. Grimsditch, Phys. Rev. B 31, 6818 (1985).
[CrossRef]

Z. Lin, L. V. Zhigilei, and V. Celli, Phys. Rev. B 77, 075133 (2008).
[CrossRef]

C. Thomsen, H. T. Grahn, H. J. Maris, and J. Tauc, Phys. Rev. B 34, 4129 (1986).
[CrossRef]

D. H. Hurley and K. L. Telschow, Phys. Rev. B 66, 153301 (2002).
[CrossRef]

Phys. Rev. Lett.

D. M. Profunser, O. B. Wright, and O. Matsuda, Phys. Rev. Lett. 97, 055502 (2006).
[CrossRef] [PubMed]

Physica E (Amsterdam)

D. B. Murray and L. Saviot, Physica E (Amsterdam) 26, 417 (2005).
[CrossRef]

Proc. London Math. Soc.

H. Lamb, Proc. London Math. Soc. S1-13, 189 (1881).
[CrossRef]

Rev. Sci. Instrum.

N. V. Chigarev, C. Rossignol, and B. Audoin, Rev. Sci. Instrum. 77, 114901 (2006).
[CrossRef]

W. S. Capinski and H. J. Maris, Rev. Sci. Instrum. 67, 2720 (1996).
[CrossRef]

Other

Y. Shui, D. Royer, E. Dieulesaint, and Z. Sun, in IEEE Symposium Proceedings (1988), p. 343.

J. E. Mark, The Polymer Data Handbook (Oxford U. Press, 1999).

D. Lide, CRC Handbook of Chemistry and Physics (CRC Press, 1999).

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Figures (3)

Fig. 1
Fig. 1

(a) Sample and setup (DM, dichroic mirror; PBS, polarizing beam splitter). Inset, SEM. (b) Normalized angular frequency ω D / 2 v T 2 versus l.

Fig. 2
Fig. 2

(a) δ R / R 0 for two different single spheres. Downward arrow, second set of acoustic pulses. Inset, zoom-in on the first set of acoustic pulses (upward arrows). (b) Amplitude and phase of Fourier spectra related to (a). Arrows, observed resonances. (c) δ R / R 0 for two different paired spheres (displaced). (b) Amplitude of Fourier spectra related to (c).

Fig. 3
Fig. 3

Left, radial deformation of the sphere due to mode (0,4). Right, fixed-ϕ cross-section (side-view). Dotted line, initial position of the surface.

Equations (1)

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u l n ( r , θ ) = A l n [ j l ( ξ l n r ) r + l ( l + 1 ) j l ( η l n r ) r ] P l ( cos   θ ) ,

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