Abstract

Interferometric imaging of normal mode dynamics in electromechanical resonators, oscillating in the rf regime, is demonstrated by synchronous imaging with a pulsed nanosecond laser. Profiles of mechanical modes in suspended thin film structures and their equilibrium profiles are measured through all-optical Fabry–Perot reflectance fits to the temporal traces. As a proof of principle, the mode patterns of a microdrum silicon resonator are visualized, and the extracted vibration modes and equilibrium profile show good agreement with numerical estimations.

© 2010 Optical Society of America

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    [Crossref] [PubMed]
  2. M. Roukes, Phys. World 14, 25 (2001).
  3. K. L. Ekinci and M. L. Roukes, Rev. Sci. Instrum. 76, 061101 (2005).
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  5. D. Garcia-Sanchez, A. San Paulo, M. J. Esplandiu, F. Perez-Murano, L. Forr, A. Aguasca, and A. Bachtold, Phys. Rev. Lett. 99, 085501 (2007).
    [Crossref] [PubMed]
  6. B. Ilic, S. Krylov, L. M. Bellan, and H. G. Craighead, J. Appl. Phys. 101, 044308 (2007).
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  7. J. V. Knuuttila, P. T. Tikka, and M. M. Salomaa, Opt. Lett. 25, 613 (2000).
    [Crossref]
  8. S. Petitgrand, R. Yahiaoui, K. Danaie, A. Bosseboeuf, and J. P. Gilles, Opt. Laser Eng. 36, 77 (2001).
    [Crossref]
  9. G. G. Fattinger and P. T. Tikka, Appl. Phys. Lett. 79, 290 (2001).
    [Crossref]
  10. H. Martinussen, A. Aksnes, and H. E. Engan, Opt. Express 15, 11370 (2007).
    [Crossref] [PubMed]
  11. K. Kokkonen and M. Kaivola, Appl. Phys. Lett. 92, 063502 (2008).
    [Crossref]
  12. C. Rembe and R. S. Muller, J. Microelectromech. Syst. 11, 479 (2002).
    [Crossref]
  13. P. Castellini, M. Martarelli, and E. P. Tomasini, Mech. Syst. Signal Process. 20, 1265 (2006).
    [Crossref]
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    [Crossref]
  15. M. Zalalutdinov, K. L. Aubin, M. Pandey, A. T. Zehnder, R. H. Rand, H. G. Craighead, J. M. Parpia, and B. H. Houston, Appl. Phys. Lett. 83, 3281 (2003).
    [Crossref]
  16. D. R. Southworth, H. G. Craighead, and J. M. Parpia, Appl. Phys. Lett. 94, 213506 (2009).
    [Crossref]
  17. M. Bass, Handbook of Optics (McGraw-Hill, 1995).
  18. K. J. Bathe, Automatic Dynamic Incremental Nonlinear Analysis (ADINA R&D, Inc., 2005).

2009 (1)

D. R. Southworth, H. G. Craighead, and J. M. Parpia, Appl. Phys. Lett. 94, 213506 (2009).
[Crossref]

2008 (1)

K. Kokkonen and M. Kaivola, Appl. Phys. Lett. 92, 063502 (2008).
[Crossref]

2007 (3)

H. Martinussen, A. Aksnes, and H. E. Engan, Opt. Express 15, 11370 (2007).
[Crossref] [PubMed]

D. Garcia-Sanchez, A. San Paulo, M. J. Esplandiu, F. Perez-Murano, L. Forr, A. Aguasca, and A. Bachtold, Phys. Rev. Lett. 99, 085501 (2007).
[Crossref] [PubMed]

B. Ilic, S. Krylov, L. M. Bellan, and H. G. Craighead, J. Appl. Phys. 101, 044308 (2007).
[Crossref]

2006 (2)

C. Ke and H. D. Espinosa, Small 2, 1484 (2006).
[Crossref] [PubMed]

P. Castellini, M. Martarelli, and E. P. Tomasini, Mech. Syst. Signal Process. 20, 1265 (2006).
[Crossref]

2005 (1)

K. L. Ekinci and M. L. Roukes, Rev. Sci. Instrum. 76, 061101 (2005).
[Crossref]

2003 (1)

M. Zalalutdinov, K. L. Aubin, M. Pandey, A. T. Zehnder, R. H. Rand, H. G. Craighead, J. M. Parpia, and B. H. Houston, Appl. Phys. Lett. 83, 3281 (2003).
[Crossref]

2002 (1)

C. Rembe and R. S. Muller, J. Microelectromech. Syst. 11, 479 (2002).
[Crossref]

2001 (3)

M. Roukes, Phys. World 14, 25 (2001).

S. Petitgrand, R. Yahiaoui, K. Danaie, A. Bosseboeuf, and J. P. Gilles, Opt. Laser Eng. 36, 77 (2001).
[Crossref]

G. G. Fattinger and P. T. Tikka, Appl. Phys. Lett. 79, 290 (2001).
[Crossref]

2000 (2)

1997 (1)

D. W. Carr and H. G. Craighead, J. Vac. Sci. Technol. B 15, 2760 (1997).
[Crossref]

Aguasca, A.

D. Garcia-Sanchez, A. San Paulo, M. J. Esplandiu, F. Perez-Murano, L. Forr, A. Aguasca, and A. Bachtold, Phys. Rev. Lett. 99, 085501 (2007).
[Crossref] [PubMed]

Aksnes, A.

Aubin, K. L.

M. Zalalutdinov, K. L. Aubin, M. Pandey, A. T. Zehnder, R. H. Rand, H. G. Craighead, J. M. Parpia, and B. H. Houston, Appl. Phys. Lett. 83, 3281 (2003).
[Crossref]

Bachtold, A.

D. Garcia-Sanchez, A. San Paulo, M. J. Esplandiu, F. Perez-Murano, L. Forr, A. Aguasca, and A. Bachtold, Phys. Rev. Lett. 99, 085501 (2007).
[Crossref] [PubMed]

Bass, M.

M. Bass, Handbook of Optics (McGraw-Hill, 1995).

Bathe, K. J.

K. J. Bathe, Automatic Dynamic Incremental Nonlinear Analysis (ADINA R&D, Inc., 2005).

Bellan, L. M.

B. Ilic, S. Krylov, L. M. Bellan, and H. G. Craighead, J. Appl. Phys. 101, 044308 (2007).
[Crossref]

Bosseboeuf, A.

S. Petitgrand, R. Yahiaoui, K. Danaie, A. Bosseboeuf, and J. P. Gilles, Opt. Laser Eng. 36, 77 (2001).
[Crossref]

Carr, D. W.

D. W. Carr and H. G. Craighead, J. Vac. Sci. Technol. B 15, 2760 (1997).
[Crossref]

Castellini, P.

P. Castellini, M. Martarelli, and E. P. Tomasini, Mech. Syst. Signal Process. 20, 1265 (2006).
[Crossref]

Craighead, H. G.

D. R. Southworth, H. G. Craighead, and J. M. Parpia, Appl. Phys. Lett. 94, 213506 (2009).
[Crossref]

B. Ilic, S. Krylov, L. M. Bellan, and H. G. Craighead, J. Appl. Phys. 101, 044308 (2007).
[Crossref]

M. Zalalutdinov, K. L. Aubin, M. Pandey, A. T. Zehnder, R. H. Rand, H. G. Craighead, J. M. Parpia, and B. H. Houston, Appl. Phys. Lett. 83, 3281 (2003).
[Crossref]

H. G. Craighead, Science 290, 1532 (2000).
[Crossref] [PubMed]

D. W. Carr and H. G. Craighead, J. Vac. Sci. Technol. B 15, 2760 (1997).
[Crossref]

Danaie, K.

S. Petitgrand, R. Yahiaoui, K. Danaie, A. Bosseboeuf, and J. P. Gilles, Opt. Laser Eng. 36, 77 (2001).
[Crossref]

Ekinci, K. L.

K. L. Ekinci and M. L. Roukes, Rev. Sci. Instrum. 76, 061101 (2005).
[Crossref]

Engan, H. E.

Espinosa, H. D.

C. Ke and H. D. Espinosa, Small 2, 1484 (2006).
[Crossref] [PubMed]

Esplandiu, M. J.

D. Garcia-Sanchez, A. San Paulo, M. J. Esplandiu, F. Perez-Murano, L. Forr, A. Aguasca, and A. Bachtold, Phys. Rev. Lett. 99, 085501 (2007).
[Crossref] [PubMed]

Fattinger, G. G.

G. G. Fattinger and P. T. Tikka, Appl. Phys. Lett. 79, 290 (2001).
[Crossref]

Forr, L.

D. Garcia-Sanchez, A. San Paulo, M. J. Esplandiu, F. Perez-Murano, L. Forr, A. Aguasca, and A. Bachtold, Phys. Rev. Lett. 99, 085501 (2007).
[Crossref] [PubMed]

Garcia-Sanchez, D.

D. Garcia-Sanchez, A. San Paulo, M. J. Esplandiu, F. Perez-Murano, L. Forr, A. Aguasca, and A. Bachtold, Phys. Rev. Lett. 99, 085501 (2007).
[Crossref] [PubMed]

Gilles, J. P.

S. Petitgrand, R. Yahiaoui, K. Danaie, A. Bosseboeuf, and J. P. Gilles, Opt. Laser Eng. 36, 77 (2001).
[Crossref]

Houston, B. H.

M. Zalalutdinov, K. L. Aubin, M. Pandey, A. T. Zehnder, R. H. Rand, H. G. Craighead, J. M. Parpia, and B. H. Houston, Appl. Phys. Lett. 83, 3281 (2003).
[Crossref]

Ilic, B.

B. Ilic, S. Krylov, L. M. Bellan, and H. G. Craighead, J. Appl. Phys. 101, 044308 (2007).
[Crossref]

Kaivola, M.

K. Kokkonen and M. Kaivola, Appl. Phys. Lett. 92, 063502 (2008).
[Crossref]

Ke, C.

C. Ke and H. D. Espinosa, Small 2, 1484 (2006).
[Crossref] [PubMed]

Knuuttila, J. V.

Kokkonen, K.

K. Kokkonen and M. Kaivola, Appl. Phys. Lett. 92, 063502 (2008).
[Crossref]

Krylov, S.

B. Ilic, S. Krylov, L. M. Bellan, and H. G. Craighead, J. Appl. Phys. 101, 044308 (2007).
[Crossref]

Martarelli, M.

P. Castellini, M. Martarelli, and E. P. Tomasini, Mech. Syst. Signal Process. 20, 1265 (2006).
[Crossref]

Martinussen, H.

Muller, R. S.

C. Rembe and R. S. Muller, J. Microelectromech. Syst. 11, 479 (2002).
[Crossref]

Pandey, M.

M. Zalalutdinov, K. L. Aubin, M. Pandey, A. T. Zehnder, R. H. Rand, H. G. Craighead, J. M. Parpia, and B. H. Houston, Appl. Phys. Lett. 83, 3281 (2003).
[Crossref]

Parpia, J. M.

D. R. Southworth, H. G. Craighead, and J. M. Parpia, Appl. Phys. Lett. 94, 213506 (2009).
[Crossref]

M. Zalalutdinov, K. L. Aubin, M. Pandey, A. T. Zehnder, R. H. Rand, H. G. Craighead, J. M. Parpia, and B. H. Houston, Appl. Phys. Lett. 83, 3281 (2003).
[Crossref]

Perez-Murano, F.

D. Garcia-Sanchez, A. San Paulo, M. J. Esplandiu, F. Perez-Murano, L. Forr, A. Aguasca, and A. Bachtold, Phys. Rev. Lett. 99, 085501 (2007).
[Crossref] [PubMed]

Petitgrand, S.

S. Petitgrand, R. Yahiaoui, K. Danaie, A. Bosseboeuf, and J. P. Gilles, Opt. Laser Eng. 36, 77 (2001).
[Crossref]

Rand, R. H.

M. Zalalutdinov, K. L. Aubin, M. Pandey, A. T. Zehnder, R. H. Rand, H. G. Craighead, J. M. Parpia, and B. H. Houston, Appl. Phys. Lett. 83, 3281 (2003).
[Crossref]

Rembe, C.

C. Rembe and R. S. Muller, J. Microelectromech. Syst. 11, 479 (2002).
[Crossref]

Roukes, M.

M. Roukes, Phys. World 14, 25 (2001).

Roukes, M. L.

K. L. Ekinci and M. L. Roukes, Rev. Sci. Instrum. 76, 061101 (2005).
[Crossref]

Salomaa, M. M.

San Paulo, A.

D. Garcia-Sanchez, A. San Paulo, M. J. Esplandiu, F. Perez-Murano, L. Forr, A. Aguasca, and A. Bachtold, Phys. Rev. Lett. 99, 085501 (2007).
[Crossref] [PubMed]

Southworth, D. R.

D. R. Southworth, H. G. Craighead, and J. M. Parpia, Appl. Phys. Lett. 94, 213506 (2009).
[Crossref]

Tikka, P. T.

G. G. Fattinger and P. T. Tikka, Appl. Phys. Lett. 79, 290 (2001).
[Crossref]

J. V. Knuuttila, P. T. Tikka, and M. M. Salomaa, Opt. Lett. 25, 613 (2000).
[Crossref]

Tomasini, E. P.

P. Castellini, M. Martarelli, and E. P. Tomasini, Mech. Syst. Signal Process. 20, 1265 (2006).
[Crossref]

Yahiaoui, R.

S. Petitgrand, R. Yahiaoui, K. Danaie, A. Bosseboeuf, and J. P. Gilles, Opt. Laser Eng. 36, 77 (2001).
[Crossref]

Zalalutdinov, M.

M. Zalalutdinov, K. L. Aubin, M. Pandey, A. T. Zehnder, R. H. Rand, H. G. Craighead, J. M. Parpia, and B. H. Houston, Appl. Phys. Lett. 83, 3281 (2003).
[Crossref]

Zehnder, A. T.

M. Zalalutdinov, K. L. Aubin, M. Pandey, A. T. Zehnder, R. H. Rand, H. G. Craighead, J. M. Parpia, and B. H. Houston, Appl. Phys. Lett. 83, 3281 (2003).
[Crossref]

Appl. Phys. Lett. (4)

G. G. Fattinger and P. T. Tikka, Appl. Phys. Lett. 79, 290 (2001).
[Crossref]

K. Kokkonen and M. Kaivola, Appl. Phys. Lett. 92, 063502 (2008).
[Crossref]

M. Zalalutdinov, K. L. Aubin, M. Pandey, A. T. Zehnder, R. H. Rand, H. G. Craighead, J. M. Parpia, and B. H. Houston, Appl. Phys. Lett. 83, 3281 (2003).
[Crossref]

D. R. Southworth, H. G. Craighead, and J. M. Parpia, Appl. Phys. Lett. 94, 213506 (2009).
[Crossref]

J. Appl. Phys. (1)

B. Ilic, S. Krylov, L. M. Bellan, and H. G. Craighead, J. Appl. Phys. 101, 044308 (2007).
[Crossref]

J. Microelectromech. Syst. (1)

C. Rembe and R. S. Muller, J. Microelectromech. Syst. 11, 479 (2002).
[Crossref]

J. Vac. Sci. Technol. B (1)

D. W. Carr and H. G. Craighead, J. Vac. Sci. Technol. B 15, 2760 (1997).
[Crossref]

Mech. Syst. Signal Process. (1)

P. Castellini, M. Martarelli, and E. P. Tomasini, Mech. Syst. Signal Process. 20, 1265 (2006).
[Crossref]

Opt. Express (1)

Opt. Laser Eng. (1)

S. Petitgrand, R. Yahiaoui, K. Danaie, A. Bosseboeuf, and J. P. Gilles, Opt. Laser Eng. 36, 77 (2001).
[Crossref]

Opt. Lett. (1)

Phys. Rev. Lett. (1)

D. Garcia-Sanchez, A. San Paulo, M. J. Esplandiu, F. Perez-Murano, L. Forr, A. Aguasca, and A. Bachtold, Phys. Rev. Lett. 99, 085501 (2007).
[Crossref] [PubMed]

Phys. World (1)

M. Roukes, Phys. World 14, 25 (2001).

Rev. Sci. Instrum. (1)

K. L. Ekinci and M. L. Roukes, Rev. Sci. Instrum. 76, 061101 (2005).
[Crossref]

Science (1)

H. G. Craighead, Science 290, 1532 (2000).
[Crossref] [PubMed]

Small (1)

C. Ke and H. D. Espinosa, Small 2, 1484 (2006).
[Crossref] [PubMed]

Other (2)

M. Bass, Handbook of Optics (McGraw-Hill, 1995).

K. J. Bathe, Automatic Dynamic Incremental Nonlinear Analysis (ADINA R&D, Inc., 2005).

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Figures (3)

Fig. 1
Fig. 1

Experimental setup to study electromechanical resonators. (a) Frequency-domain arm, consisting of a sweeping rf network analyzer and a cw optical return loop. (b) Time-domain synchronous imaging arm. (c) Typical temporal traces of electrical drive (50% duty) and imaging beam pulses (10% duty).

Fig. 2
Fig. 2

Drum resonator modes. (a) FDS spectrum. (b), (c) Synchronous imaging within a single cycle for: (b) fundamental mode (0,1), f 0 = 9.2 MHz and (c) second symmetric mode (0,2), f 0 = 25.5 MHz . All interference images are subtracted from the full contrast reference image of the drum (bottom left) and normalized.

Fig. 3
Fig. 3

(a) Cross-section geometry used in the analysis. (b), (c) Mode profiles [estimated along the dashed line in the inset of (a)] for the first (0,1) and second (0,2) modes, respectively. (d) Equilibrium profile ( d 0 ) estimated from the first mode fit. Hollow circles indicate numerical profile estimations. Error bars in the data indicate fit boundaries within a 95% confidence level around the average values.

Equations (2)

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( a b ) = M tot ( 1 n s ) ,
I diff ( x , t ) = R { x , d 1 ( t ) } R { x , d 0 }

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