Abstract

We describe an ultrafast optical technique to quantitatively detect picosecond ultrasonic displacements of solid surfaces, thus giving access to the longitudinal strain pulse shape. Transient optical reflectance changes recorded at oblique optical incidence with a common-path interferometric configuration based on ultrafast ellipsometry monitor gigahertz coherent phonon pulses. We demonstrate for a tungsten film the quantitative extraction of the strain pulse shape free of distortions arising from the photoelastic effect, and analyze the results with the two-temperature model to obtain the value g3×1017Wm3K1 for the electron–phonon coupling constant. Analysis of the data also reveals a thermo-optic contribution.

© 2013 Optical Society of America

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  1. C. Thomsen, J. Strait, Z. Vardeny, H. J. Maris, J. Tauc, and J. J. Hauser, “Coherent phonon generation and detection by picosecond light pulses,” Phys. Rev. Lett. 53, 989–992 (1984).
    [CrossRef]
  2. C. Thomsen, H. T. Grahn, H. J. Maris, and J. Tauc, “Surface generation and detection of phonons by picosecond light pulses,” Phys. Rev. B 34, 4129–4138 (1986).
    [CrossRef]
  3. O. B. Wright and K. Kawashima, “Coherent phonon detection from ultrafast surface vibrations,” Phys. Rev. Lett. 69, 1668–1671 (1992).
    [CrossRef]
  4. G. Tas and H. J. Maris, “Electron diffusion in metals studied by picosecond ultrasonics,” Phys. Rev. B 49, 15046–15054 (1994).
    [CrossRef]
  5. O. B. Wright, “Ultrafast nonequilibrium stress generation in gold and silver,” Phys. Rev. B 49, 9985–9988 (1994).
    [CrossRef]
  6. B. Perrin, B. Bonello, J.-C. Jeannet, and E. Romatet, “Interferometric detection of hypersound waves in modulated structures,” Prog. Nat. Sci. S6, S444–S448 (1996).
  7. J. L. Hostetler, A. N. Smith, and P. M. Norris, “Thin-film thermal conductivity and thickness measurements using picosecond ultrasonics,” Microscale Thermophys. Eng. 1, 237–244 (1997).
    [CrossRef]
  8. C. J. K. Richardson, M. J. Ehrlich, and J. W. Wagner, “Interferometric detection of ultrafast thermoelastic transients in thin films: theory with supporting experiment,” J. Opt. Soc. Am. B 16, 1007–1015 (1999).
    [CrossRef]
  9. D. H. Hurley and O. B. Wright, “Detection of ultrafast phenomena by use of a modified Sagnac interferometer,” Opt. Lett. 24, 1305–1307 (1999).
    [CrossRef]
  10. C. K. Sun, J. C. Liang, and X. Y. Yu, “Coherent acoustic phonon oscillations in semiconductor multiple quantum wells with piezoelectric fields,” Phys. Rev. Lett. 84, 179–182 (2000).
    [CrossRef]
  11. A. Devos and C. Lerouge, “Evidence of laser-wavelength effect in picosecond ultrasonics: possible connection with interband transitions,” Phys. Rev. Lett. 86, 2669–2672 (2001).
    [CrossRef]
  12. O. B. Wright, B. Perrin, O. Matsuda, and V. E. Gusev, “Ultrafast carrier diffusion in gas probed with picosecond acoustic pulses,” Phys. Rev. B 64, 081202(R) (2001).
    [CrossRef]
  13. T. Saito, O. Matsuda, and O. B. Wright, “Picosecond acoustic phonon pulse generation in nickel and chromium,” Phys. Rev. B 67, 205421 (2003).
    [CrossRef]
  14. O. Matsuda, T. Tachizaki, T. Fukui, J. J. Baumberg, and O. B. Wright, “Acoustic phonon generation and detection in GaAs/Al0.3Ga0.7As quantum wells with picosecond laser pulses,” Phys. Rev. B 71, 115330 (2005).
    [CrossRef]
  15. A. Huynh, N. D. Lanzillotti-Kimura, B. Jusserand, B. Perrin, A. Fainstein, M. F. Pascual-Winter, E. Peronne, and A. Lemaître, “Subterahertz phonon dynamics in acoustic nanocavities,” Phys. Rev. Lett. 97, 115502 (2006).
    [CrossRef]
  16. A. V. Akimov, A. V. Scherbakov, D. R. Yakovlev, C. T. Foxon, and M. Bayer, “Ultrafast band-gap shift induced by a strain pulse in semiconductor heterostructures,” Phys. Rev. Lett. 97, 037401 (2006).
    [CrossRef]
  17. T. Dehoux, M. Perton, N. Chigarev, C. Rossignol, J. M. Rampnoux, and B. Audoin, “Effect of laser pulse duration in picosecond ultrasonics,” J. Appl. Phys. 100, 064318 (2006).
    [CrossRef]
  18. M. F. P. Winter, G. Rozas, A. Fainstein, B. Jusserand, B. Perrin, A. Huynh, P. O. Vaccaro, and S. Saravanan, “Selective optical generation of coherent acoustic nanocavity modes,” Phys. Rev. Lett. 98, 265501 (2007).
    [CrossRef]
  19. K.-H. Lin, C.-M. Lai, C.-C. Pan, J.-I. Chyi, J.-W. Shi, S.-Z. Sun, C.-F. Chang, and C.-K. Sun, “Spatial manipulation of nanoacoustic waves with nanoscale spot sizes,” Nature Nanotech. 2, 704–708 (2007).
    [CrossRef]
  20. C. Rossignol, N. Chigarev, M. Ducousso, B. Audoin, G. Forget, F. Guillemot, and M. C. Durrieu, “In vitro picosecond ultrasonic in a single cell,” Appl. Phys. Lett. 93, 123901 (2008).
    [CrossRef]
  21. O. Matsuda, O. B. Wright, D. H. Hurley, V. Gusev, and K. Shimizu, “Coherent shear phonon generation and detection with picosecond laser acoustics,” Phys. Rev. B 77, 224110 (2008).
    [CrossRef]
  22. O. B. Wright, B. Perrin, O. Matsuda, and V. E. Gusev, “Optical excitation and detection of picosecond acoustic pulses in liquid mercury,” Phys. Rev. B 78, 024303 (2008).
    [CrossRef]
  23. P. Babilotte, P. Ruello, G. Vaudel, T. Pezeril, D. Mounier, J. M. Breteau, and V. Gusev, “Picosecond acoustics in p-doped piezoelectric semiconductors,” Appl. Phys. Lett. 97, 174103 (2010).
    [CrossRef]
  24. H. Ogi, A. Yamamoto, K. Kondou, K. Nakano, K. Morita, N. Nakamura, T. Ono, and M. Hirao, “Significant softening of copper nanowires during electromigration studied by picosecond ultrasound spectroscopy,” Phys. Rev. B 82, 155436 (2010).
    [CrossRef]
  25. C. Klieber, E. Peronne, K. Katayama, J. Choi, M. Yamaguchi, T. Pezeril, and K. A. Nelson, “Narrow-band acoustic attenuation measurements in vitreous silica at frequencies between 20 and 400 GHz,” Appl. Phys. Lett. 98, 211908 (2011).
    [CrossRef]
  26. E. Pontecorvo, M. Ortolani, D. Polli, M. Ferretti, G. Ruocco, G. Cerullo, and T. Scopigno, “Visualizing coherent phonon propagation in the 100 GHz range: a broadband picosecond acoustics approach,” Appl. Phys. Lett. 98, 100901 (2011).
  27. Y.-C. Wen, K.-J. Wang, H.-H. Chang, J.-Y. Luo, C.-C. Shen, H.-L. Liu, C.-K. Sun, M.-J. Wang, and M.-K. Wu, “Gap opening and orbital modification of superconducting FeSe above the structural distortion,” Phys. Rev. Lett. 108, 267002 (2012).
    [CrossRef]
  28. J.-W. Kim, M. Vomir, and J.-Y. Bigot, “Ultrafast magnetoacoustics in nickel films,” Phys. Rev. Lett. 109, 166601 (2012).
    [CrossRef]
  29. N. Chigarev, C. Rossignol, and B. Audoin, “Surface displacement measured by beam distortion detection technique: application to picosecond ultrasonics,” Rev. Sci. Instrum. 77, 114901 (2006).
    [CrossRef]
  30. O. Matsuda and O. B. Wright, “Laser picosecond acoustics with oblique probe light incidence,” Rev. Sci. Instrum. 74, 895–897 (2003).
    [CrossRef]
  31. O. Matsuda, K. Aoki, T. Tachizaki, and O. Wright, “Direct measurement of ultrafast surface displacement in laser picosecond acoustics,” J. Phys. IV 125, 361–363 (2005).
    [CrossRef]
  32. R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, 1977).
  33. J. A. Bolger, A. E. Paul, and A. L. Smirl, “Ultrafast ellipsometry of coherent processes and exciton–exciton interactions in quantum wells at negative delays,” Phys. Rev. B 54, 11666–11671 (1996).
    [CrossRef]
  34. C. A. Bolme, S. D. McGrane, D. S. Moore, and D. J. Funk, “Single shot measurements of laser driven shock waves using ultrafast dynamic ellipsometry,” J. Appl. Phys. 102, 033513 (2007).
    [CrossRef]
  35. L. R. Watkins, “Interferometric ellipsometer,” Appl. Opt. 47, 2998–3001 (2008).
    [CrossRef]
  36. D. Mounier, E. Morozov, P. Ruello, J. M. Breteau, P. Picart, and V. Gusev, “Detection of shear picosecond acoustic pulses by transient femtosecond polarimetry,” Eur. J. Phys. Special Topics 153, 243–246 (2008).
    [CrossRef]
  37. C.-K. Min, D. G. Cahill, and S. Granick, “Time-resolved ellipsometry for studies of heat transfer at liquid/solid and gas/solid interfaces,” Rev. Sci. Instrum. 81, 074902 (2010).
    [CrossRef]
  38. O. Matsuda and O. B. Wright, “Reflection and transmission of light in multilayers perturbed by picosecond strain pulse propagation,” J. Opt. Soc. Am. B 19, 3028–3041 (2002).
    [CrossRef]
  39. A. A. Maradudin and D. L. Mills, “Scattering and absorption of electromagnetic radiation by a semi-infinite medium in the presence of surface roughness,” Phys. Rev. B 11, 1392–1415 (1975).
    [CrossRef]
  40. W is optically isotropic because it crystallizes in the cubic (bcc) phase. In addition, the elastic constants for tungsten single crystal are c11=502, c44=152, and c12=199  GPa [59], and coincidentally obey the relation c11−c12≃2c44, so that (independent of the film microstructure) the film is effectively elastically isotropic.
  41. O. B. Wright and K. Kawashima, “Ultrasonic detection from picosecond surface vibrations: application to interfacial layer detection,” Jpn. J. Appl. Phys. 32, 2452–2454 (1993).
    [CrossRef]
  42. The surface roughness contributes to the frequency-dependent ultrasonic absorption (see [22]), but we estimate its effect to be small over the frequency spectrum of the ultrasonic pulse associated with the first echo. The roughness of the W/crown-glass interface is ∼5  nm, and its effect can also be neglected.
  43. T. Tachizaki, T. Muroya, O. Matsuda, Y. Sugawara, D. H. Hurley, and O. B. Wright, “Scanning ultrafast sagnac interferometry for imaging two-dimensional surface wave propagation,” Rev. Sci. Instrum. 77, 043713 (2006).
    [CrossRef]
  44. D. R. Lide, ed., CRC Handbook of Chemistry and Physics, 85th ed. (CRC Press, 2004).
  45. M. Tomoda, O. Matsuda, and O. B. Wright, “Tomographic reconstruction of picosecond acoustic strain propagation,” Appl. Phys. Lett. 90, 041114 (2007).
    [CrossRef]
  46. Some residual photoelastic effect that was not cancelled is, however, still visible near t=0. This level of small remnant should not significantly affect the shape of the final extracted surface displacement variations.
  47. S. I. Anisimov, B. L. Kapeliovich, and T. L. Perel’man, “Emission of electrons from the surface of metals induced by ultrashort laser pulses,” Sov. Phys. JETP 39, 375–377 (1974).
  48. P. B. Corkum, F. Brunel, N. K. Sherman, and T. Srinivasan-Rao, “Thermal response of metals to ultrashort-pulse laser excitation,” Phys. Rev. Lett. 61, 2886–2889 (1988).
    [CrossRef]
  49. V. E. Gusev and O. B. Wright, “Ultrafast nonequilibrium dynamics of electrons in metals,” Phys. Rev. B 57, 2878–2888 (1998).
    [CrossRef]
  50. The simulation involves a nonlinear response: when the excitation energy flux is halved, for example, the maximum changes in Te and Tl are, respectively, 1.4% and 0.3% greater than the corresponding halved values. This nonlinear response is below the detection limit of the measurement here.
  51. R. T. Beyer and S. V. Letcher, Physical Ultrasonics (Academic, 1969), Chap. 10, pp. 325–358.
  52. H. Klein and O. Weis, “Absorption heat of GHz sound in polycrystalline metal films detected by multiple-beam interferometry and second-sound emission,” J. Low Temp. Phys. 94, 567–583 (1994).
    [CrossRef]
  53. We adopted b=4×102  m−1 GHz−2, which gives optimal agreement in the fitting of the surface displacement data, although other b differing by values of the same order also gave acceptable fits. On the other hand, a is more accurately obtained as a=(3.0±0.5)×105  m−1 for the chosen value of b. Our expression for bf2 is consistent with values of α found at 1 GHz in W (α=100–600  m−1, see [65–67]).
  54. S. Kashiwada, O. Matsuda, J. J. Baumberg, R. L. Voti, and O. B. Wright, “In situ monitoring of the growth of ice films by laser picosecond acoustics,” J. Appl. Phys. 100, 073506 (2006).
    [CrossRef]
  55. H. Hirori, T. Tachizaki, O. Matsuda, and O. B. Wright, “Electron dynamics in chromium probed with 20 fs optical pulses,” Phys. Rev. B 68, 113102 (2003).
    [CrossRef]
  56. Y. S. Touloukian, R. W. Powell, C. Y. Ho, and P. G. Klemens, eds., Thermal Conductivity—Metallic Elements and Alloys, Vol. 1 of Thermophysical Properties of Matter (IFI/Plenum, 1970).
  57. Y. S. Touloukian and E. H. Buyco, eds., Specific Heat—Metallic Elements and Alloys, Vol. 4 of Thermophysical Properties of Matter (IFI/Plenum, 1970).
  58. Z. Lin, L. V. Zhigilei, and V. Celli, “Electron–phonon coupling and electron heat capacity of metals under conditions of strong electron phonon nonequilibrium,” Phys. Rev. B 77, 075133 (2008).
    [CrossRef]
  59. B. A. Auld, Acoustic Fields and Waves in Solids, 2nd ed. (Krieger, 1990).
  60. As discussed in relation to Fig. 6, the permittivity at the probe light wavelength can be retrieved from the interferometric data. This fitted value for the probe light lies close to that of corresponding ellipsometry data, so we also adopted the ellipsometry data value for the pump light.
  61. J. G. Fujimoto, J. M. Liu, and E. P. Ippen, “Femtosecond laser interaction with metallic tungsten and nonequilibrium electron and lattice temperatures,” Phys. Rev. Lett. 53, 1837–1840 (1984).
    [CrossRef]
  62. S. D. Brorson, A. Kazeroonian, J. S. Moodera, D. W. Face, T. K. Cheng, E. P. Ippen, M. S. Dresselhaus, and G. Dresselhaus, “Femtosecond room-temperature measurement of the electron–phonon coupling constant λ in metallic superconductors,” Phys. Rev. Lett. 64, 2172–2175 (1990).
    [CrossRef]
  63. We used fitted values for the permittivity of the W film at the probe wavelength rather than from the literature, 5.3+16.2i (see [44]), or from ellipsometry measurement, 3.1+4.1i. These differences in permittivity may be attributable to impurities in the W film.
  64. The spectrum in strain, obtained by multiplication of that of the displacement by iω, shows significant noise above ∼30  GHz.
  65. C. K. Jones and J. A. Rayne, “Ultrasonic attenuation in tungsten and molybdenum up to 1  Gc/s,” Phys. Lett. 13, 282–283 (1964).
    [CrossRef]
  66. M. J. G. Lee, J. M. Perz, and J. Plotnick, “Electronic attenuation of longitudinal acoustic phonons in tungsten,” Phys. Rev. Lett. 48, 30–33 (1982).
    [CrossRef]
  67. G. D. Mansfeld, S. G. Alekseev, and I. M. Kotelyansky, “Acoustic HBAR spectroscopy of metal (W, Ti, Mo, Al) thin films,” in Ultrasonics Symposium, Vol. 1 (IEEE, 2001) pp. 415–418.

2012 (2)

Y.-C. Wen, K.-J. Wang, H.-H. Chang, J.-Y. Luo, C.-C. Shen, H.-L. Liu, C.-K. Sun, M.-J. Wang, and M.-K. Wu, “Gap opening and orbital modification of superconducting FeSe above the structural distortion,” Phys. Rev. Lett. 108, 267002 (2012).
[CrossRef]

J.-W. Kim, M. Vomir, and J.-Y. Bigot, “Ultrafast magnetoacoustics in nickel films,” Phys. Rev. Lett. 109, 166601 (2012).
[CrossRef]

2011 (2)

C. Klieber, E. Peronne, K. Katayama, J. Choi, M. Yamaguchi, T. Pezeril, and K. A. Nelson, “Narrow-band acoustic attenuation measurements in vitreous silica at frequencies between 20 and 400 GHz,” Appl. Phys. Lett. 98, 211908 (2011).
[CrossRef]

E. Pontecorvo, M. Ortolani, D. Polli, M. Ferretti, G. Ruocco, G. Cerullo, and T. Scopigno, “Visualizing coherent phonon propagation in the 100 GHz range: a broadband picosecond acoustics approach,” Appl. Phys. Lett. 98, 100901 (2011).

2010 (3)

P. Babilotte, P. Ruello, G. Vaudel, T. Pezeril, D. Mounier, J. M. Breteau, and V. Gusev, “Picosecond acoustics in p-doped piezoelectric semiconductors,” Appl. Phys. Lett. 97, 174103 (2010).
[CrossRef]

H. Ogi, A. Yamamoto, K. Kondou, K. Nakano, K. Morita, N. Nakamura, T. Ono, and M. Hirao, “Significant softening of copper nanowires during electromigration studied by picosecond ultrasound spectroscopy,” Phys. Rev. B 82, 155436 (2010).
[CrossRef]

C.-K. Min, D. G. Cahill, and S. Granick, “Time-resolved ellipsometry for studies of heat transfer at liquid/solid and gas/solid interfaces,” Rev. Sci. Instrum. 81, 074902 (2010).
[CrossRef]

2008 (6)

Z. Lin, L. V. Zhigilei, and V. Celli, “Electron–phonon coupling and electron heat capacity of metals under conditions of strong electron phonon nonequilibrium,” Phys. Rev. B 77, 075133 (2008).
[CrossRef]

C. Rossignol, N. Chigarev, M. Ducousso, B. Audoin, G. Forget, F. Guillemot, and M. C. Durrieu, “In vitro picosecond ultrasonic in a single cell,” Appl. Phys. Lett. 93, 123901 (2008).
[CrossRef]

O. Matsuda, O. B. Wright, D. H. Hurley, V. Gusev, and K. Shimizu, “Coherent shear phonon generation and detection with picosecond laser acoustics,” Phys. Rev. B 77, 224110 (2008).
[CrossRef]

O. B. Wright, B. Perrin, O. Matsuda, and V. E. Gusev, “Optical excitation and detection of picosecond acoustic pulses in liquid mercury,” Phys. Rev. B 78, 024303 (2008).
[CrossRef]

L. R. Watkins, “Interferometric ellipsometer,” Appl. Opt. 47, 2998–3001 (2008).
[CrossRef]

D. Mounier, E. Morozov, P. Ruello, J. M. Breteau, P. Picart, and V. Gusev, “Detection of shear picosecond acoustic pulses by transient femtosecond polarimetry,” Eur. J. Phys. Special Topics 153, 243–246 (2008).
[CrossRef]

2007 (4)

M. F. P. Winter, G. Rozas, A. Fainstein, B. Jusserand, B. Perrin, A. Huynh, P. O. Vaccaro, and S. Saravanan, “Selective optical generation of coherent acoustic nanocavity modes,” Phys. Rev. Lett. 98, 265501 (2007).
[CrossRef]

K.-H. Lin, C.-M. Lai, C.-C. Pan, J.-I. Chyi, J.-W. Shi, S.-Z. Sun, C.-F. Chang, and C.-K. Sun, “Spatial manipulation of nanoacoustic waves with nanoscale spot sizes,” Nature Nanotech. 2, 704–708 (2007).
[CrossRef]

C. A. Bolme, S. D. McGrane, D. S. Moore, and D. J. Funk, “Single shot measurements of laser driven shock waves using ultrafast dynamic ellipsometry,” J. Appl. Phys. 102, 033513 (2007).
[CrossRef]

M. Tomoda, O. Matsuda, and O. B. Wright, “Tomographic reconstruction of picosecond acoustic strain propagation,” Appl. Phys. Lett. 90, 041114 (2007).
[CrossRef]

2006 (6)

T. Tachizaki, T. Muroya, O. Matsuda, Y. Sugawara, D. H. Hurley, and O. B. Wright, “Scanning ultrafast sagnac interferometry for imaging two-dimensional surface wave propagation,” Rev. Sci. Instrum. 77, 043713 (2006).
[CrossRef]

S. Kashiwada, O. Matsuda, J. J. Baumberg, R. L. Voti, and O. B. Wright, “In situ monitoring of the growth of ice films by laser picosecond acoustics,” J. Appl. Phys. 100, 073506 (2006).
[CrossRef]

N. Chigarev, C. Rossignol, and B. Audoin, “Surface displacement measured by beam distortion detection technique: application to picosecond ultrasonics,” Rev. Sci. Instrum. 77, 114901 (2006).
[CrossRef]

A. Huynh, N. D. Lanzillotti-Kimura, B. Jusserand, B. Perrin, A. Fainstein, M. F. Pascual-Winter, E. Peronne, and A. Lemaître, “Subterahertz phonon dynamics in acoustic nanocavities,” Phys. Rev. Lett. 97, 115502 (2006).
[CrossRef]

A. V. Akimov, A. V. Scherbakov, D. R. Yakovlev, C. T. Foxon, and M. Bayer, “Ultrafast band-gap shift induced by a strain pulse in semiconductor heterostructures,” Phys. Rev. Lett. 97, 037401 (2006).
[CrossRef]

T. Dehoux, M. Perton, N. Chigarev, C. Rossignol, J. M. Rampnoux, and B. Audoin, “Effect of laser pulse duration in picosecond ultrasonics,” J. Appl. Phys. 100, 064318 (2006).
[CrossRef]

2005 (2)

O. Matsuda, T. Tachizaki, T. Fukui, J. J. Baumberg, and O. B. Wright, “Acoustic phonon generation and detection in GaAs/Al0.3Ga0.7As quantum wells with picosecond laser pulses,” Phys. Rev. B 71, 115330 (2005).
[CrossRef]

O. Matsuda, K. Aoki, T. Tachizaki, and O. Wright, “Direct measurement of ultrafast surface displacement in laser picosecond acoustics,” J. Phys. IV 125, 361–363 (2005).
[CrossRef]

2003 (3)

O. Matsuda and O. B. Wright, “Laser picosecond acoustics with oblique probe light incidence,” Rev. Sci. Instrum. 74, 895–897 (2003).
[CrossRef]

T. Saito, O. Matsuda, and O. B. Wright, “Picosecond acoustic phonon pulse generation in nickel and chromium,” Phys. Rev. B 67, 205421 (2003).
[CrossRef]

H. Hirori, T. Tachizaki, O. Matsuda, and O. B. Wright, “Electron dynamics in chromium probed with 20 fs optical pulses,” Phys. Rev. B 68, 113102 (2003).
[CrossRef]

2002 (1)

2001 (2)

A. Devos and C. Lerouge, “Evidence of laser-wavelength effect in picosecond ultrasonics: possible connection with interband transitions,” Phys. Rev. Lett. 86, 2669–2672 (2001).
[CrossRef]

O. B. Wright, B. Perrin, O. Matsuda, and V. E. Gusev, “Ultrafast carrier diffusion in gas probed with picosecond acoustic pulses,” Phys. Rev. B 64, 081202(R) (2001).
[CrossRef]

2000 (1)

C. K. Sun, J. C. Liang, and X. Y. Yu, “Coherent acoustic phonon oscillations in semiconductor multiple quantum wells with piezoelectric fields,” Phys. Rev. Lett. 84, 179–182 (2000).
[CrossRef]

1999 (2)

1998 (1)

V. E. Gusev and O. B. Wright, “Ultrafast nonequilibrium dynamics of electrons in metals,” Phys. Rev. B 57, 2878–2888 (1998).
[CrossRef]

1997 (1)

J. L. Hostetler, A. N. Smith, and P. M. Norris, “Thin-film thermal conductivity and thickness measurements using picosecond ultrasonics,” Microscale Thermophys. Eng. 1, 237–244 (1997).
[CrossRef]

1996 (2)

B. Perrin, B. Bonello, J.-C. Jeannet, and E. Romatet, “Interferometric detection of hypersound waves in modulated structures,” Prog. Nat. Sci. S6, S444–S448 (1996).

J. A. Bolger, A. E. Paul, and A. L. Smirl, “Ultrafast ellipsometry of coherent processes and exciton–exciton interactions in quantum wells at negative delays,” Phys. Rev. B 54, 11666–11671 (1996).
[CrossRef]

1994 (3)

G. Tas and H. J. Maris, “Electron diffusion in metals studied by picosecond ultrasonics,” Phys. Rev. B 49, 15046–15054 (1994).
[CrossRef]

O. B. Wright, “Ultrafast nonequilibrium stress generation in gold and silver,” Phys. Rev. B 49, 9985–9988 (1994).
[CrossRef]

H. Klein and O. Weis, “Absorption heat of GHz sound in polycrystalline metal films detected by multiple-beam interferometry and second-sound emission,” J. Low Temp. Phys. 94, 567–583 (1994).
[CrossRef]

1993 (1)

O. B. Wright and K. Kawashima, “Ultrasonic detection from picosecond surface vibrations: application to interfacial layer detection,” Jpn. J. Appl. Phys. 32, 2452–2454 (1993).
[CrossRef]

1992 (1)

O. B. Wright and K. Kawashima, “Coherent phonon detection from ultrafast surface vibrations,” Phys. Rev. Lett. 69, 1668–1671 (1992).
[CrossRef]

1990 (1)

S. D. Brorson, A. Kazeroonian, J. S. Moodera, D. W. Face, T. K. Cheng, E. P. Ippen, M. S. Dresselhaus, and G. Dresselhaus, “Femtosecond room-temperature measurement of the electron–phonon coupling constant λ in metallic superconductors,” Phys. Rev. Lett. 64, 2172–2175 (1990).
[CrossRef]

1988 (1)

P. B. Corkum, F. Brunel, N. K. Sherman, and T. Srinivasan-Rao, “Thermal response of metals to ultrashort-pulse laser excitation,” Phys. Rev. Lett. 61, 2886–2889 (1988).
[CrossRef]

1986 (1)

C. Thomsen, H. T. Grahn, H. J. Maris, and J. Tauc, “Surface generation and detection of phonons by picosecond light pulses,” Phys. Rev. B 34, 4129–4138 (1986).
[CrossRef]

1984 (2)

C. Thomsen, J. Strait, Z. Vardeny, H. J. Maris, J. Tauc, and J. J. Hauser, “Coherent phonon generation and detection by picosecond light pulses,” Phys. Rev. Lett. 53, 989–992 (1984).
[CrossRef]

J. G. Fujimoto, J. M. Liu, and E. P. Ippen, “Femtosecond laser interaction with metallic tungsten and nonequilibrium electron and lattice temperatures,” Phys. Rev. Lett. 53, 1837–1840 (1984).
[CrossRef]

1982 (1)

M. J. G. Lee, J. M. Perz, and J. Plotnick, “Electronic attenuation of longitudinal acoustic phonons in tungsten,” Phys. Rev. Lett. 48, 30–33 (1982).
[CrossRef]

1975 (1)

A. A. Maradudin and D. L. Mills, “Scattering and absorption of electromagnetic radiation by a semi-infinite medium in the presence of surface roughness,” Phys. Rev. B 11, 1392–1415 (1975).
[CrossRef]

1974 (1)

S. I. Anisimov, B. L. Kapeliovich, and T. L. Perel’man, “Emission of electrons from the surface of metals induced by ultrashort laser pulses,” Sov. Phys. JETP 39, 375–377 (1974).

1964 (1)

C. K. Jones and J. A. Rayne, “Ultrasonic attenuation in tungsten and molybdenum up to 1  Gc/s,” Phys. Lett. 13, 282–283 (1964).
[CrossRef]

Akimov, A. V.

A. V. Akimov, A. V. Scherbakov, D. R. Yakovlev, C. T. Foxon, and M. Bayer, “Ultrafast band-gap shift induced by a strain pulse in semiconductor heterostructures,” Phys. Rev. Lett. 97, 037401 (2006).
[CrossRef]

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G. D. Mansfeld, S. G. Alekseev, and I. M. Kotelyansky, “Acoustic HBAR spectroscopy of metal (W, Ti, Mo, Al) thin films,” in Ultrasonics Symposium, Vol. 1 (IEEE, 2001) pp. 415–418.

Anisimov, S. I.

S. I. Anisimov, B. L. Kapeliovich, and T. L. Perel’man, “Emission of electrons from the surface of metals induced by ultrashort laser pulses,” Sov. Phys. JETP 39, 375–377 (1974).

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O. Matsuda, K. Aoki, T. Tachizaki, and O. Wright, “Direct measurement of ultrafast surface displacement in laser picosecond acoustics,” J. Phys. IV 125, 361–363 (2005).
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C. Rossignol, N. Chigarev, M. Ducousso, B. Audoin, G. Forget, F. Guillemot, and M. C. Durrieu, “In vitro picosecond ultrasonic in a single cell,” Appl. Phys. Lett. 93, 123901 (2008).
[CrossRef]

T. Dehoux, M. Perton, N. Chigarev, C. Rossignol, J. M. Rampnoux, and B. Audoin, “Effect of laser pulse duration in picosecond ultrasonics,” J. Appl. Phys. 100, 064318 (2006).
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N. Chigarev, C. Rossignol, and B. Audoin, “Surface displacement measured by beam distortion detection technique: application to picosecond ultrasonics,” Rev. Sci. Instrum. 77, 114901 (2006).
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P. Babilotte, P. Ruello, G. Vaudel, T. Pezeril, D. Mounier, J. M. Breteau, and V. Gusev, “Picosecond acoustics in p-doped piezoelectric semiconductors,” Appl. Phys. Lett. 97, 174103 (2010).
[CrossRef]

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R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, 1977).

Baumberg, J. J.

S. Kashiwada, O. Matsuda, J. J. Baumberg, R. L. Voti, and O. B. Wright, “In situ monitoring of the growth of ice films by laser picosecond acoustics,” J. Appl. Phys. 100, 073506 (2006).
[CrossRef]

O. Matsuda, T. Tachizaki, T. Fukui, J. J. Baumberg, and O. B. Wright, “Acoustic phonon generation and detection in GaAs/Al0.3Ga0.7As quantum wells with picosecond laser pulses,” Phys. Rev. B 71, 115330 (2005).
[CrossRef]

Bayer, M.

A. V. Akimov, A. V. Scherbakov, D. R. Yakovlev, C. T. Foxon, and M. Bayer, “Ultrafast band-gap shift induced by a strain pulse in semiconductor heterostructures,” Phys. Rev. Lett. 97, 037401 (2006).
[CrossRef]

Beyer, R. T.

R. T. Beyer and S. V. Letcher, Physical Ultrasonics (Academic, 1969), Chap. 10, pp. 325–358.

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J.-W. Kim, M. Vomir, and J.-Y. Bigot, “Ultrafast magnetoacoustics in nickel films,” Phys. Rev. Lett. 109, 166601 (2012).
[CrossRef]

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J. A. Bolger, A. E. Paul, and A. L. Smirl, “Ultrafast ellipsometry of coherent processes and exciton–exciton interactions in quantum wells at negative delays,” Phys. Rev. B 54, 11666–11671 (1996).
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C. A. Bolme, S. D. McGrane, D. S. Moore, and D. J. Funk, “Single shot measurements of laser driven shock waves using ultrafast dynamic ellipsometry,” J. Appl. Phys. 102, 033513 (2007).
[CrossRef]

Bonello, B.

B. Perrin, B. Bonello, J.-C. Jeannet, and E. Romatet, “Interferometric detection of hypersound waves in modulated structures,” Prog. Nat. Sci. S6, S444–S448 (1996).

Breteau, J. M.

P. Babilotte, P. Ruello, G. Vaudel, T. Pezeril, D. Mounier, J. M. Breteau, and V. Gusev, “Picosecond acoustics in p-doped piezoelectric semiconductors,” Appl. Phys. Lett. 97, 174103 (2010).
[CrossRef]

D. Mounier, E. Morozov, P. Ruello, J. M. Breteau, P. Picart, and V. Gusev, “Detection of shear picosecond acoustic pulses by transient femtosecond polarimetry,” Eur. J. Phys. Special Topics 153, 243–246 (2008).
[CrossRef]

Brorson, S. D.

S. D. Brorson, A. Kazeroonian, J. S. Moodera, D. W. Face, T. K. Cheng, E. P. Ippen, M. S. Dresselhaus, and G. Dresselhaus, “Femtosecond room-temperature measurement of the electron–phonon coupling constant λ in metallic superconductors,” Phys. Rev. Lett. 64, 2172–2175 (1990).
[CrossRef]

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P. B. Corkum, F. Brunel, N. K. Sherman, and T. Srinivasan-Rao, “Thermal response of metals to ultrashort-pulse laser excitation,” Phys. Rev. Lett. 61, 2886–2889 (1988).
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C.-K. Min, D. G. Cahill, and S. Granick, “Time-resolved ellipsometry for studies of heat transfer at liquid/solid and gas/solid interfaces,” Rev. Sci. Instrum. 81, 074902 (2010).
[CrossRef]

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Z. Lin, L. V. Zhigilei, and V. Celli, “Electron–phonon coupling and electron heat capacity of metals under conditions of strong electron phonon nonequilibrium,” Phys. Rev. B 77, 075133 (2008).
[CrossRef]

Cerullo, G.

E. Pontecorvo, M. Ortolani, D. Polli, M. Ferretti, G. Ruocco, G. Cerullo, and T. Scopigno, “Visualizing coherent phonon propagation in the 100 GHz range: a broadband picosecond acoustics approach,” Appl. Phys. Lett. 98, 100901 (2011).

Chang, C.-F.

K.-H. Lin, C.-M. Lai, C.-C. Pan, J.-I. Chyi, J.-W. Shi, S.-Z. Sun, C.-F. Chang, and C.-K. Sun, “Spatial manipulation of nanoacoustic waves with nanoscale spot sizes,” Nature Nanotech. 2, 704–708 (2007).
[CrossRef]

Chang, H.-H.

Y.-C. Wen, K.-J. Wang, H.-H. Chang, J.-Y. Luo, C.-C. Shen, H.-L. Liu, C.-K. Sun, M.-J. Wang, and M.-K. Wu, “Gap opening and orbital modification of superconducting FeSe above the structural distortion,” Phys. Rev. Lett. 108, 267002 (2012).
[CrossRef]

Cheng, T. K.

S. D. Brorson, A. Kazeroonian, J. S. Moodera, D. W. Face, T. K. Cheng, E. P. Ippen, M. S. Dresselhaus, and G. Dresselhaus, “Femtosecond room-temperature measurement of the electron–phonon coupling constant λ in metallic superconductors,” Phys. Rev. Lett. 64, 2172–2175 (1990).
[CrossRef]

Chigarev, N.

C. Rossignol, N. Chigarev, M. Ducousso, B. Audoin, G. Forget, F. Guillemot, and M. C. Durrieu, “In vitro picosecond ultrasonic in a single cell,” Appl. Phys. Lett. 93, 123901 (2008).
[CrossRef]

T. Dehoux, M. Perton, N. Chigarev, C. Rossignol, J. M. Rampnoux, and B. Audoin, “Effect of laser pulse duration in picosecond ultrasonics,” J. Appl. Phys. 100, 064318 (2006).
[CrossRef]

N. Chigarev, C. Rossignol, and B. Audoin, “Surface displacement measured by beam distortion detection technique: application to picosecond ultrasonics,” Rev. Sci. Instrum. 77, 114901 (2006).
[CrossRef]

Choi, J.

C. Klieber, E. Peronne, K. Katayama, J. Choi, M. Yamaguchi, T. Pezeril, and K. A. Nelson, “Narrow-band acoustic attenuation measurements in vitreous silica at frequencies between 20 and 400 GHz,” Appl. Phys. Lett. 98, 211908 (2011).
[CrossRef]

Chyi, J.-I.

K.-H. Lin, C.-M. Lai, C.-C. Pan, J.-I. Chyi, J.-W. Shi, S.-Z. Sun, C.-F. Chang, and C.-K. Sun, “Spatial manipulation of nanoacoustic waves with nanoscale spot sizes,” Nature Nanotech. 2, 704–708 (2007).
[CrossRef]

Corkum, P. B.

P. B. Corkum, F. Brunel, N. K. Sherman, and T. Srinivasan-Rao, “Thermal response of metals to ultrashort-pulse laser excitation,” Phys. Rev. Lett. 61, 2886–2889 (1988).
[CrossRef]

Dehoux, T.

T. Dehoux, M. Perton, N. Chigarev, C. Rossignol, J. M. Rampnoux, and B. Audoin, “Effect of laser pulse duration in picosecond ultrasonics,” J. Appl. Phys. 100, 064318 (2006).
[CrossRef]

Devos, A.

A. Devos and C. Lerouge, “Evidence of laser-wavelength effect in picosecond ultrasonics: possible connection with interband transitions,” Phys. Rev. Lett. 86, 2669–2672 (2001).
[CrossRef]

Dresselhaus, G.

S. D. Brorson, A. Kazeroonian, J. S. Moodera, D. W. Face, T. K. Cheng, E. P. Ippen, M. S. Dresselhaus, and G. Dresselhaus, “Femtosecond room-temperature measurement of the electron–phonon coupling constant λ in metallic superconductors,” Phys. Rev. Lett. 64, 2172–2175 (1990).
[CrossRef]

Dresselhaus, M. S.

S. D. Brorson, A. Kazeroonian, J. S. Moodera, D. W. Face, T. K. Cheng, E. P. Ippen, M. S. Dresselhaus, and G. Dresselhaus, “Femtosecond room-temperature measurement of the electron–phonon coupling constant λ in metallic superconductors,” Phys. Rev. Lett. 64, 2172–2175 (1990).
[CrossRef]

Ducousso, M.

C. Rossignol, N. Chigarev, M. Ducousso, B. Audoin, G. Forget, F. Guillemot, and M. C. Durrieu, “In vitro picosecond ultrasonic in a single cell,” Appl. Phys. Lett. 93, 123901 (2008).
[CrossRef]

Durrieu, M. C.

C. Rossignol, N. Chigarev, M. Ducousso, B. Audoin, G. Forget, F. Guillemot, and M. C. Durrieu, “In vitro picosecond ultrasonic in a single cell,” Appl. Phys. Lett. 93, 123901 (2008).
[CrossRef]

Ehrlich, M. J.

Face, D. W.

S. D. Brorson, A. Kazeroonian, J. S. Moodera, D. W. Face, T. K. Cheng, E. P. Ippen, M. S. Dresselhaus, and G. Dresselhaus, “Femtosecond room-temperature measurement of the electron–phonon coupling constant λ in metallic superconductors,” Phys. Rev. Lett. 64, 2172–2175 (1990).
[CrossRef]

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M. F. P. Winter, G. Rozas, A. Fainstein, B. Jusserand, B. Perrin, A. Huynh, P. O. Vaccaro, and S. Saravanan, “Selective optical generation of coherent acoustic nanocavity modes,” Phys. Rev. Lett. 98, 265501 (2007).
[CrossRef]

A. Huynh, N. D. Lanzillotti-Kimura, B. Jusserand, B. Perrin, A. Fainstein, M. F. Pascual-Winter, E. Peronne, and A. Lemaître, “Subterahertz phonon dynamics in acoustic nanocavities,” Phys. Rev. Lett. 97, 115502 (2006).
[CrossRef]

Ferretti, M.

E. Pontecorvo, M. Ortolani, D. Polli, M. Ferretti, G. Ruocco, G. Cerullo, and T. Scopigno, “Visualizing coherent phonon propagation in the 100 GHz range: a broadband picosecond acoustics approach,” Appl. Phys. Lett. 98, 100901 (2011).

Forget, G.

C. Rossignol, N. Chigarev, M. Ducousso, B. Audoin, G. Forget, F. Guillemot, and M. C. Durrieu, “In vitro picosecond ultrasonic in a single cell,” Appl. Phys. Lett. 93, 123901 (2008).
[CrossRef]

Foxon, C. T.

A. V. Akimov, A. V. Scherbakov, D. R. Yakovlev, C. T. Foxon, and M. Bayer, “Ultrafast band-gap shift induced by a strain pulse in semiconductor heterostructures,” Phys. Rev. Lett. 97, 037401 (2006).
[CrossRef]

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J. G. Fujimoto, J. M. Liu, and E. P. Ippen, “Femtosecond laser interaction with metallic tungsten and nonequilibrium electron and lattice temperatures,” Phys. Rev. Lett. 53, 1837–1840 (1984).
[CrossRef]

Fukui, T.

O. Matsuda, T. Tachizaki, T. Fukui, J. J. Baumberg, and O. B. Wright, “Acoustic phonon generation and detection in GaAs/Al0.3Ga0.7As quantum wells with picosecond laser pulses,” Phys. Rev. B 71, 115330 (2005).
[CrossRef]

Funk, D. J.

C. A. Bolme, S. D. McGrane, D. S. Moore, and D. J. Funk, “Single shot measurements of laser driven shock waves using ultrafast dynamic ellipsometry,” J. Appl. Phys. 102, 033513 (2007).
[CrossRef]

Grahn, H. T.

C. Thomsen, H. T. Grahn, H. J. Maris, and J. Tauc, “Surface generation and detection of phonons by picosecond light pulses,” Phys. Rev. B 34, 4129–4138 (1986).
[CrossRef]

Granick, S.

C.-K. Min, D. G. Cahill, and S. Granick, “Time-resolved ellipsometry for studies of heat transfer at liquid/solid and gas/solid interfaces,” Rev. Sci. Instrum. 81, 074902 (2010).
[CrossRef]

Guillemot, F.

C. Rossignol, N. Chigarev, M. Ducousso, B. Audoin, G. Forget, F. Guillemot, and M. C. Durrieu, “In vitro picosecond ultrasonic in a single cell,” Appl. Phys. Lett. 93, 123901 (2008).
[CrossRef]

Gusev, V.

P. Babilotte, P. Ruello, G. Vaudel, T. Pezeril, D. Mounier, J. M. Breteau, and V. Gusev, “Picosecond acoustics in p-doped piezoelectric semiconductors,” Appl. Phys. Lett. 97, 174103 (2010).
[CrossRef]

O. Matsuda, O. B. Wright, D. H. Hurley, V. Gusev, and K. Shimizu, “Coherent shear phonon generation and detection with picosecond laser acoustics,” Phys. Rev. B 77, 224110 (2008).
[CrossRef]

D. Mounier, E. Morozov, P. Ruello, J. M. Breteau, P. Picart, and V. Gusev, “Detection of shear picosecond acoustic pulses by transient femtosecond polarimetry,” Eur. J. Phys. Special Topics 153, 243–246 (2008).
[CrossRef]

Gusev, V. E.

O. B. Wright, B. Perrin, O. Matsuda, and V. E. Gusev, “Optical excitation and detection of picosecond acoustic pulses in liquid mercury,” Phys. Rev. B 78, 024303 (2008).
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O. B. Wright, B. Perrin, O. Matsuda, and V. E. Gusev, “Ultrafast carrier diffusion in gas probed with picosecond acoustic pulses,” Phys. Rev. B 64, 081202(R) (2001).
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V. E. Gusev and O. B. Wright, “Ultrafast nonequilibrium dynamics of electrons in metals,” Phys. Rev. B 57, 2878–2888 (1998).
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C. Thomsen, J. Strait, Z. Vardeny, H. J. Maris, J. Tauc, and J. J. Hauser, “Coherent phonon generation and detection by picosecond light pulses,” Phys. Rev. Lett. 53, 989–992 (1984).
[CrossRef]

Hirao, M.

H. Ogi, A. Yamamoto, K. Kondou, K. Nakano, K. Morita, N. Nakamura, T. Ono, and M. Hirao, “Significant softening of copper nanowires during electromigration studied by picosecond ultrasound spectroscopy,” Phys. Rev. B 82, 155436 (2010).
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H. Hirori, T. Tachizaki, O. Matsuda, and O. B. Wright, “Electron dynamics in chromium probed with 20 fs optical pulses,” Phys. Rev. B 68, 113102 (2003).
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J. L. Hostetler, A. N. Smith, and P. M. Norris, “Thin-film thermal conductivity and thickness measurements using picosecond ultrasonics,” Microscale Thermophys. Eng. 1, 237–244 (1997).
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O. Matsuda, O. B. Wright, D. H. Hurley, V. Gusev, and K. Shimizu, “Coherent shear phonon generation and detection with picosecond laser acoustics,” Phys. Rev. B 77, 224110 (2008).
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T. Tachizaki, T. Muroya, O. Matsuda, Y. Sugawara, D. H. Hurley, and O. B. Wright, “Scanning ultrafast sagnac interferometry for imaging two-dimensional surface wave propagation,” Rev. Sci. Instrum. 77, 043713 (2006).
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D. H. Hurley and O. B. Wright, “Detection of ultrafast phenomena by use of a modified Sagnac interferometer,” Opt. Lett. 24, 1305–1307 (1999).
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M. F. P. Winter, G. Rozas, A. Fainstein, B. Jusserand, B. Perrin, A. Huynh, P. O. Vaccaro, and S. Saravanan, “Selective optical generation of coherent acoustic nanocavity modes,” Phys. Rev. Lett. 98, 265501 (2007).
[CrossRef]

A. Huynh, N. D. Lanzillotti-Kimura, B. Jusserand, B. Perrin, A. Fainstein, M. F. Pascual-Winter, E. Peronne, and A. Lemaître, “Subterahertz phonon dynamics in acoustic nanocavities,” Phys. Rev. Lett. 97, 115502 (2006).
[CrossRef]

Ippen, E. P.

S. D. Brorson, A. Kazeroonian, J. S. Moodera, D. W. Face, T. K. Cheng, E. P. Ippen, M. S. Dresselhaus, and G. Dresselhaus, “Femtosecond room-temperature measurement of the electron–phonon coupling constant λ in metallic superconductors,” Phys. Rev. Lett. 64, 2172–2175 (1990).
[CrossRef]

J. G. Fujimoto, J. M. Liu, and E. P. Ippen, “Femtosecond laser interaction with metallic tungsten and nonequilibrium electron and lattice temperatures,” Phys. Rev. Lett. 53, 1837–1840 (1984).
[CrossRef]

Jeannet, J.-C.

B. Perrin, B. Bonello, J.-C. Jeannet, and E. Romatet, “Interferometric detection of hypersound waves in modulated structures,” Prog. Nat. Sci. S6, S444–S448 (1996).

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M. F. P. Winter, G. Rozas, A. Fainstein, B. Jusserand, B. Perrin, A. Huynh, P. O. Vaccaro, and S. Saravanan, “Selective optical generation of coherent acoustic nanocavity modes,” Phys. Rev. Lett. 98, 265501 (2007).
[CrossRef]

A. Huynh, N. D. Lanzillotti-Kimura, B. Jusserand, B. Perrin, A. Fainstein, M. F. Pascual-Winter, E. Peronne, and A. Lemaître, “Subterahertz phonon dynamics in acoustic nanocavities,” Phys. Rev. Lett. 97, 115502 (2006).
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S. I. Anisimov, B. L. Kapeliovich, and T. L. Perel’man, “Emission of electrons from the surface of metals induced by ultrashort laser pulses,” Sov. Phys. JETP 39, 375–377 (1974).

Kashiwada, S.

S. Kashiwada, O. Matsuda, J. J. Baumberg, R. L. Voti, and O. B. Wright, “In situ monitoring of the growth of ice films by laser picosecond acoustics,” J. Appl. Phys. 100, 073506 (2006).
[CrossRef]

Katayama, K.

C. Klieber, E. Peronne, K. Katayama, J. Choi, M. Yamaguchi, T. Pezeril, and K. A. Nelson, “Narrow-band acoustic attenuation measurements in vitreous silica at frequencies between 20 and 400 GHz,” Appl. Phys. Lett. 98, 211908 (2011).
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S. D. Brorson, A. Kazeroonian, J. S. Moodera, D. W. Face, T. K. Cheng, E. P. Ippen, M. S. Dresselhaus, and G. Dresselhaus, “Femtosecond room-temperature measurement of the electron–phonon coupling constant λ in metallic superconductors,” Phys. Rev. Lett. 64, 2172–2175 (1990).
[CrossRef]

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J.-W. Kim, M. Vomir, and J.-Y. Bigot, “Ultrafast magnetoacoustics in nickel films,” Phys. Rev. Lett. 109, 166601 (2012).
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C. Klieber, E. Peronne, K. Katayama, J. Choi, M. Yamaguchi, T. Pezeril, and K. A. Nelson, “Narrow-band acoustic attenuation measurements in vitreous silica at frequencies between 20 and 400 GHz,” Appl. Phys. Lett. 98, 211908 (2011).
[CrossRef]

Kondou, K.

H. Ogi, A. Yamamoto, K. Kondou, K. Nakano, K. Morita, N. Nakamura, T. Ono, and M. Hirao, “Significant softening of copper nanowires during electromigration studied by picosecond ultrasound spectroscopy,” Phys. Rev. B 82, 155436 (2010).
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Kotelyansky, I. M.

G. D. Mansfeld, S. G. Alekseev, and I. M. Kotelyansky, “Acoustic HBAR spectroscopy of metal (W, Ti, Mo, Al) thin films,” in Ultrasonics Symposium, Vol. 1 (IEEE, 2001) pp. 415–418.

Lai, C.-M.

K.-H. Lin, C.-M. Lai, C.-C. Pan, J.-I. Chyi, J.-W. Shi, S.-Z. Sun, C.-F. Chang, and C.-K. Sun, “Spatial manipulation of nanoacoustic waves with nanoscale spot sizes,” Nature Nanotech. 2, 704–708 (2007).
[CrossRef]

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A. Huynh, N. D. Lanzillotti-Kimura, B. Jusserand, B. Perrin, A. Fainstein, M. F. Pascual-Winter, E. Peronne, and A. Lemaître, “Subterahertz phonon dynamics in acoustic nanocavities,” Phys. Rev. Lett. 97, 115502 (2006).
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A. Huynh, N. D. Lanzillotti-Kimura, B. Jusserand, B. Perrin, A. Fainstein, M. F. Pascual-Winter, E. Peronne, and A. Lemaître, “Subterahertz phonon dynamics in acoustic nanocavities,” Phys. Rev. Lett. 97, 115502 (2006).
[CrossRef]

Lerouge, C.

A. Devos and C. Lerouge, “Evidence of laser-wavelength effect in picosecond ultrasonics: possible connection with interband transitions,” Phys. Rev. Lett. 86, 2669–2672 (2001).
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R. T. Beyer and S. V. Letcher, Physical Ultrasonics (Academic, 1969), Chap. 10, pp. 325–358.

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C. K. Sun, J. C. Liang, and X. Y. Yu, “Coherent acoustic phonon oscillations in semiconductor multiple quantum wells with piezoelectric fields,” Phys. Rev. Lett. 84, 179–182 (2000).
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K.-H. Lin, C.-M. Lai, C.-C. Pan, J.-I. Chyi, J.-W. Shi, S.-Z. Sun, C.-F. Chang, and C.-K. Sun, “Spatial manipulation of nanoacoustic waves with nanoscale spot sizes,” Nature Nanotech. 2, 704–708 (2007).
[CrossRef]

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Z. Lin, L. V. Zhigilei, and V. Celli, “Electron–phonon coupling and electron heat capacity of metals under conditions of strong electron phonon nonequilibrium,” Phys. Rev. B 77, 075133 (2008).
[CrossRef]

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Y.-C. Wen, K.-J. Wang, H.-H. Chang, J.-Y. Luo, C.-C. Shen, H.-L. Liu, C.-K. Sun, M.-J. Wang, and M.-K. Wu, “Gap opening and orbital modification of superconducting FeSe above the structural distortion,” Phys. Rev. Lett. 108, 267002 (2012).
[CrossRef]

Liu, J. M.

J. G. Fujimoto, J. M. Liu, and E. P. Ippen, “Femtosecond laser interaction with metallic tungsten and nonequilibrium electron and lattice temperatures,” Phys. Rev. Lett. 53, 1837–1840 (1984).
[CrossRef]

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Y.-C. Wen, K.-J. Wang, H.-H. Chang, J.-Y. Luo, C.-C. Shen, H.-L. Liu, C.-K. Sun, M.-J. Wang, and M.-K. Wu, “Gap opening and orbital modification of superconducting FeSe above the structural distortion,” Phys. Rev. Lett. 108, 267002 (2012).
[CrossRef]

Mansfeld, G. D.

G. D. Mansfeld, S. G. Alekseev, and I. M. Kotelyansky, “Acoustic HBAR spectroscopy of metal (W, Ti, Mo, Al) thin films,” in Ultrasonics Symposium, Vol. 1 (IEEE, 2001) pp. 415–418.

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G. Tas and H. J. Maris, “Electron diffusion in metals studied by picosecond ultrasonics,” Phys. Rev. B 49, 15046–15054 (1994).
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C. Thomsen, H. T. Grahn, H. J. Maris, and J. Tauc, “Surface generation and detection of phonons by picosecond light pulses,” Phys. Rev. B 34, 4129–4138 (1986).
[CrossRef]

C. Thomsen, J. Strait, Z. Vardeny, H. J. Maris, J. Tauc, and J. J. Hauser, “Coherent phonon generation and detection by picosecond light pulses,” Phys. Rev. Lett. 53, 989–992 (1984).
[CrossRef]

Matsuda, O.

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[CrossRef]

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[CrossRef]

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[CrossRef]

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[CrossRef]

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[CrossRef]

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[CrossRef]

O. Matsuda and O. B. Wright, “Laser picosecond acoustics with oblique probe light incidence,” Rev. Sci. Instrum. 74, 895–897 (2003).
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Y.-C. Wen, K.-J. Wang, H.-H. Chang, J.-Y. Luo, C.-C. Shen, H.-L. Liu, C.-K. Sun, M.-J. Wang, and M.-K. Wu, “Gap opening and orbital modification of superconducting FeSe above the structural distortion,” Phys. Rev. Lett. 108, 267002 (2012).
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Other (15)

Some residual photoelastic effect that was not cancelled is, however, still visible near t=0. This level of small remnant should not significantly affect the shape of the final extracted surface displacement variations.

D. R. Lide, ed., CRC Handbook of Chemistry and Physics, 85th ed. (CRC Press, 2004).

The surface roughness contributes to the frequency-dependent ultrasonic absorption (see [22]), but we estimate its effect to be small over the frequency spectrum of the ultrasonic pulse associated with the first echo. The roughness of the W/crown-glass interface is ∼5  nm, and its effect can also be neglected.

Y. S. Touloukian, R. W. Powell, C. Y. Ho, and P. G. Klemens, eds., Thermal Conductivity—Metallic Elements and Alloys, Vol. 1 of Thermophysical Properties of Matter (IFI/Plenum, 1970).

Y. S. Touloukian and E. H. Buyco, eds., Specific Heat—Metallic Elements and Alloys, Vol. 4 of Thermophysical Properties of Matter (IFI/Plenum, 1970).

The simulation involves a nonlinear response: when the excitation energy flux is halved, for example, the maximum changes in Te and Tl are, respectively, 1.4% and 0.3% greater than the corresponding halved values. This nonlinear response is below the detection limit of the measurement here.

R. T. Beyer and S. V. Letcher, Physical Ultrasonics (Academic, 1969), Chap. 10, pp. 325–358.

We adopted b=4×102  m−1 GHz−2, which gives optimal agreement in the fitting of the surface displacement data, although other b differing by values of the same order also gave acceptable fits. On the other hand, a is more accurately obtained as a=(3.0±0.5)×105  m−1 for the chosen value of b. Our expression for bf2 is consistent with values of α found at 1 GHz in W (α=100–600  m−1, see [65–67]).

We used fitted values for the permittivity of the W film at the probe wavelength rather than from the literature, 5.3+16.2i (see [44]), or from ellipsometry measurement, 3.1+4.1i. These differences in permittivity may be attributable to impurities in the W film.

The spectrum in strain, obtained by multiplication of that of the displacement by iω, shows significant noise above ∼30  GHz.

G. D. Mansfeld, S. G. Alekseev, and I. M. Kotelyansky, “Acoustic HBAR spectroscopy of metal (W, Ti, Mo, Al) thin films,” in Ultrasonics Symposium, Vol. 1 (IEEE, 2001) pp. 415–418.

B. A. Auld, Acoustic Fields and Waves in Solids, 2nd ed. (Krieger, 1990).

As discussed in relation to Fig. 6, the permittivity at the probe light wavelength can be retrieved from the interferometric data. This fitted value for the probe light lies close to that of corresponding ellipsometry data, so we also adopted the ellipsometry data value for the pump light.

W is optically isotropic because it crystallizes in the cubic (bcc) phase. In addition, the elastic constants for tungsten single crystal are c11=502, c44=152, and c12=199  GPa [59], and coincidentally obey the relation c11−c12≃2c44, so that (independent of the film microstructure) the film is effectively elastically isotropic.

R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, 1977).

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Figures (8)

Fig. 1.
Fig. 1.

Schematic diagram showing the procedure for direct measurement of surface displacement. Expressions refer to the complex amplitude of the light, except I1 and I2, which refer to the intensity.

Fig. 2.
Fig. 2.

Schematic diagram of the interferometer setup. HWP, half-wave plate; QWP, quarter-wave plate; PBS, polarizing beam splitter; NPBS, nonpolarizing beam splitter; POL, polarizer; P.D., photodetector; and M, mirror.

Fig. 3.
Fig. 3.

(a)–(d) Oblique-incidence interferometric results for the W/crown-glass sample. (a) Real and (b) imaginary parts with s-polarized probe light. (c) Real and (d) imaginary parts with p-polarized probe light. (e) Result of direct displacement measurement.

Fig. 4.
Fig. 4.

Measured probe beam intensity variations for the W/crown-glass sample. (a) Oblique-incidence reflectivity change measurement with p-polarized probe light. (b) Use of an appropriate mixture of p- and s- polarized probe light in an interferometric setup cancels the photoelastic contribution. (c) Introduction of reference light with a π/2 phase retardation in this setup converts phase modulations from surface displacements into intensity variations. (d) A flip of polarity is observed by the use of reference light with a π phase shift compared to that used in (c). (e) Measured temporal derivative of the surface displacement.

Fig. 5.
Fig. 5.

(a) Experimental intensity variation from the interferometric setup with a π/2 phase retardation (solid line) and (b) corresponding theoretical variation (dashed line) for the W/crown-glass sample. Contributions to (b) are separately plotted as (c) the thermo-optic contribution, and (d) the surface displacement contribution.

Fig. 6.
Fig. 6.

First-echo experimental results (solid lines) and theory (dashed lines) for the W/crown-glass sample. (a) Real and (b) imaginary part of the relative reflectance change with s-polarized probe light. (c) Real and (d) imaginary parts with p-polarized probe light. (e) Surface displacement variation. (f) Temporal derivative of the surface displacement. For (b) and (d), the photoelastic (pe) and surface displacement (disp.) contributions are also shown, shifted for clarity. In (a)–(e), the thermo-optic background variations are subtracted.

Fig. 7.
Fig. 7.

Frequency spectrum for the first echo obtained experimentally (solid line) and theoretically (dashed line) from the surface displacement for the W/crown-glass sample.

Fig. 8.
Fig. 8.

(a) Combination of a quarter-wave plate (QWP) and a polarizer. (b) Axis definitions looking from downstream.

Tables (3)

Tables Icon

Table 1. Required Optical Components for Different Interferometric Measurementsa

Tables Icon

Table 2. Parameters Used for the Theoretical Simulation of the Tungsten Filma

Tables Icon

Table 3. Parameters Used for the Theoretical Simulations for Oblique-Incidence Interferometric Measurementsa

Equations (38)

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{2graddiv+k2ε(r,t)}E(r,t)=0,
E(r,t)=E(z,t)exp(ikxx),
{L(kx)+k2ε(z,t)}E(z,t)=0,
L(kx)(2z20ikxz02z2kx20ikxz0kx2).
ε(z,t)=εh(z)+Δε(z,t).
E0s={(exp(ikz)+rsexp(ikz))es(z<0)tsexp(ikz)es(z>0),
es=(010)
rs=kkk+k,ts=2kk+k
k=(k2kx2)1/2,k=(ε1k2kx2)1/2
E0p={exp(ikz)eip+rpexp(ikz)erp(z<0)tpexp(ikz)etp(z>0),
eip=1k(k0kx),erp=1k(k0kx),etp=1ε11/2k(k0kx)
rp=ε1kkε1k+k,tp=2ε11/2kε1k+k
E(z,t)=E0(z)+k2G(z,z)Δε(z,t)E(z,t)dzE0(z)+k2G(z,z)Δε(z,t)E0(z)dz
{L(kx)+k2εh(z)}G(z,z)=δ(zz)I,
Gxx(z,z)=ikkk2(ε1k+k)exp{i(kzkz)},Gxz(z,z)=ikkxk2(ε1k+k)exp{i(kzkz)},Gyy(z,z)=ik+kexp{i(kzkz)},Gzx(z,z)=ikkxk2(ε1k+k)exp{i(kzkz)},Gzz(z,z)=ikx2k2(ε1k+k)exp{i(kzkz)},
εpe(z,t)=(P12000P12000P11)ηzz(z,t),
εd(z,t)={(ε11)I(u0(t)<z<0)(1ε1)I(0<z<u0(t))0otherwise,
E(z,t)E0(z)+0k2G(z,z)εpe(z,t)E0(z)dz+k2u0(t)G(z,+0)(1ε1)E0(0).
E=(exp(ikz)+(rs+δrs)exp(ikz))es,
δrsrs=2iku0(t)+2ikP121ε10ηzz(z,t)exp(2ikz)dz.
E=exp(ikz)eip+(rp+δrp)exp(ikz)erp,
δrprp=2iku0(t)+2ik(P12k2P11kx2)k2ε12k2×0ηzz(z,t)exp(2ikz)dz.
δrsrs=iA+csB,δrprp=iA+cpB,
cs=2ikP121ε1,cp=2ik(P12k2P11kx2)k2ε12k2.
Eint=Esrs(1+iA+csB)+μEprp(1+iA+cpB),
Eint=(Esrs+μEprp)(1+iA),
I1|(Esrs+μEprp)|2,
I2|(Esrs+μEprp)(1+i+iA)|2=2|Esrs+μEprp|2(1+A).
η(z,t)=f(zvt)+f(z+vt),
uz(0,t)=+0{f(zvt)+f(z+vt)}dz.
uzt|z=0=2vf(vt).
ρ2uzt2=σzzz=c112uzz2(c11+2c12)βΔTz,
CeTet=z(κTez)g(TeTl)+S(z,t),ClTlt=g(TeTl),
α=a+bf2,
Δεij=PtoδijΔT+Pijklηkl.
E=(EXEY).
QWP45=12(1+i1+i1+i1+i).
EA=(cos(π4+ϕ)sin(π4+ϕ))QWP45E=i2(EXexp(+iϕ)+EYexp(iϕ)).

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