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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2009

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

2008

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

2007

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]

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

2006

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

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

2005

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

2003

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

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

2001

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

1997

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.

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.

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

J. Microelectromech. Syst.

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

J. Vac. Sci. Technol. B

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

Mech. Syst. Signal Process.

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

Opt. Express

Opt. Laser Eng.

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

Opt. Lett.

Phys. Rev. Lett.

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

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

Rev. Sci. Instrum.

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

Science

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

Small

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

Other

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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