Abstract

Sensitive displacement detection has emerged as a significant technological challenge in mechanical resonators with nanometer-scale dimensions. A novel nanomechanical displacement detection scheme based upon the scattering of focused evanescent fields is proposed. The sensitivity of the proposed approach is studied using diffraction theory of evanescent waves. Diffraction theory results are compared with numerical simulations.

© 2007 Optical Society of America

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References

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  1. K. L. Ekinci and M. L. Roukes, Rev. Sci. Instrum. 76, 061101 (2005).
    [Crossref]
  2. H. G. Craighead, Science 290, 1532 (2000).
    [Crossref] [PubMed]
  3. T. Kouh, D. Karabacak, D. H. Kim, and K. L. Ekinci, Appl. Phys. Lett. 86, 013106 (2005).
    [Crossref]
  4. D. Karabacak, T. Kouh, C. C. Huang, and K. L. Ekinci, Appl. Phys. Lett. 88, 193122 (2006).
    [Crossref]
  5. S. B. Ippolito, B. B. Goldberg, and M. S. Ünlü, Appl. Phys. Lett. 78, 4071 (2001).
    [Crossref]
  6. M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 1999).
  7. P. S. Carney and J. C. Schotland, Opt. Lett. 26, 1072 (2001).
    [Crossref]
  8. T. D. Visser, H. Blok, and D. Lenstra, IEEE J. Quantum Electron. 35, 240 (1999).
    [Crossref]
  9. D. Karabacak, T. Kouh, and K. L. Ekinci, J. Appl. Phys. 98, 124309 (2005).
    [Crossref]

2006 (1)

D. Karabacak, T. Kouh, C. C. Huang, and K. L. Ekinci, Appl. Phys. Lett. 88, 193122 (2006).
[Crossref]

2005 (3)

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

D. Karabacak, T. Kouh, and K. L. Ekinci, J. Appl. Phys. 98, 124309 (2005).
[Crossref]

T. Kouh, D. Karabacak, D. H. Kim, and K. L. Ekinci, Appl. Phys. Lett. 86, 013106 (2005).
[Crossref]

2001 (2)

P. S. Carney and J. C. Schotland, Opt. Lett. 26, 1072 (2001).
[Crossref]

S. B. Ippolito, B. B. Goldberg, and M. S. Ünlü, Appl. Phys. Lett. 78, 4071 (2001).
[Crossref]

2000 (1)

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

1999 (2)

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 1999).

T. D. Visser, H. Blok, and D. Lenstra, IEEE J. Quantum Electron. 35, 240 (1999).
[Crossref]

Blok, H.

T. D. Visser, H. Blok, and D. Lenstra, IEEE J. Quantum Electron. 35, 240 (1999).
[Crossref]

Born, M.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 1999).

Carney, P. S.

Craighead, H. G.

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

Ekinci, K. L.

D. Karabacak, T. Kouh, C. C. Huang, and K. L. Ekinci, Appl. Phys. Lett. 88, 193122 (2006).
[Crossref]

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

T. Kouh, D. Karabacak, D. H. Kim, and K. L. Ekinci, Appl. Phys. Lett. 86, 013106 (2005).
[Crossref]

D. Karabacak, T. Kouh, and K. L. Ekinci, J. Appl. Phys. 98, 124309 (2005).
[Crossref]

Goldberg, B. B.

S. B. Ippolito, B. B. Goldberg, and M. S. Ünlü, Appl. Phys. Lett. 78, 4071 (2001).
[Crossref]

Huang, C. C.

D. Karabacak, T. Kouh, C. C. Huang, and K. L. Ekinci, Appl. Phys. Lett. 88, 193122 (2006).
[Crossref]

Ippolito, S. B.

S. B. Ippolito, B. B. Goldberg, and M. S. Ünlü, Appl. Phys. Lett. 78, 4071 (2001).
[Crossref]

Karabacak, D.

D. Karabacak, T. Kouh, C. C. Huang, and K. L. Ekinci, Appl. Phys. Lett. 88, 193122 (2006).
[Crossref]

T. Kouh, D. Karabacak, D. H. Kim, and K. L. Ekinci, Appl. Phys. Lett. 86, 013106 (2005).
[Crossref]

D. Karabacak, T. Kouh, and K. L. Ekinci, J. Appl. Phys. 98, 124309 (2005).
[Crossref]

Kim, D. H.

T. Kouh, D. Karabacak, D. H. Kim, and K. L. Ekinci, Appl. Phys. Lett. 86, 013106 (2005).
[Crossref]

Kouh, T.

D. Karabacak, T. Kouh, C. C. Huang, and K. L. Ekinci, Appl. Phys. Lett. 88, 193122 (2006).
[Crossref]

T. Kouh, D. Karabacak, D. H. Kim, and K. L. Ekinci, Appl. Phys. Lett. 86, 013106 (2005).
[Crossref]

D. Karabacak, T. Kouh, and K. L. Ekinci, J. Appl. Phys. 98, 124309 (2005).
[Crossref]

Lenstra, D.

T. D. Visser, H. Blok, and D. Lenstra, IEEE J. Quantum Electron. 35, 240 (1999).
[Crossref]

Roukes, M. L.

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

Schotland, J. C.

Ünlü, M. S.

S. B. Ippolito, B. B. Goldberg, and M. S. Ünlü, Appl. Phys. Lett. 78, 4071 (2001).
[Crossref]

Visser, T. D.

T. D. Visser, H. Blok, and D. Lenstra, IEEE J. Quantum Electron. 35, 240 (1999).
[Crossref]

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 1999).

Appl. Phys. Lett. (3)

T. Kouh, D. Karabacak, D. H. Kim, and K. L. Ekinci, Appl. Phys. Lett. 86, 013106 (2005).
[Crossref]

D. Karabacak, T. Kouh, C. C. Huang, and K. L. Ekinci, Appl. Phys. Lett. 88, 193122 (2006).
[Crossref]

S. B. Ippolito, B. B. Goldberg, and M. S. Ünlü, Appl. Phys. Lett. 78, 4071 (2001).
[Crossref]

IEEE J. Quantum Electron. (1)

T. D. Visser, H. Blok, and D. Lenstra, IEEE J. Quantum Electron. 35, 240 (1999).
[Crossref]

J. Appl. Phys. (1)

D. Karabacak, T. Kouh, and K. L. Ekinci, J. Appl. Phys. 98, 124309 (2005).
[Crossref]

Opt. Lett. (1)

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]

Other (1)

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 1999).

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Figures (3)

Fig. 1
Fig. 1

Cross-sectional ( x z plane) view of the proposed detection. Here, an infinitely long strip of width w is suspended by Δ and oscillates with amplitude δ Δ above a substrate of refractive index n. The device is illuminated by the evanescent field E i in the direction of k i formed by the total internal reflection of the incoming wave in the direction of k s . This scheme can be realized by illuminating a typical doubly clamped nanomechanical resonator through an index-matched NAIL attached to the backside of the sample, as shown in the inset.

Fig. 2
Fig. 2

Normalized distribution of the intensity (the squared magnitude of the electric field) as a function of angle in the plane normal to the longitudinal axis of the strip of width w = 50 nm . The plots are for different strip heights as indicated. The incident field in vacuum is taken to be of unit amplitude at the Si interface with wavelength λ = 1.3 μ m and a wave vector of ( 2.2 k 0 , 0 , 2.0 i k 0 ) . The dashed curves indicate the results of numerical simulation, and the solid curves the outcome of Eq. (5). In the top panel the incident field is TE-polarized, and in the bottom panel it is TM-polarized. The curves were normalized to the peak height of the analytic result at 100 nm and then scaled by a factor N indicated by the curve for display purposes.

Fig. 3
Fig. 3

Normalized dynamic signal in the scattered field due to a focus superposition of evanescent waves with a FWHM spot size of 250 nm centered on the strip, at height Δ = 100 nm , due to an oscillation of amplitude δ Δ = 0.5 nm , for both TE and TM polarization of the incident field.

Equations (5)

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E ( r ) = 1 4 π A d 2 r [ E i ( r ) × × G ( r , r ) G ( r , r ) × × E i ( r ) ] n .
G ( r , r ) = i 2 π d 2 k e i k ( r r ) 1 k z [ D ( k ) + e 2 i k z z R ( k ) ] ,
D ( k ) = u ̂ te ( k ) u ̂ te ( k ) + u ̂ tm ( k ) u ̂ tm ( k ) ,
R ( k ) = u ̂ te ( k ) r te u ̂ te ( k ̃ ) + u ̂ tm ( k ) r tm u ̂ tm ( k ̃ ) ,
E te tm ( r ) = i e i k 0 r 2 r δ ( k y k i y ) sin [ ( k x k i x ) w 2 ] ( k x k i x ) 2 e i ( k z k i z ) Δ E 0 × [ u ̂ te tm ( k ) × ( k + k i ) + e 2 i k z Δ r te tm u ̂ te tm ( k ̃ ) × ( k ̃ + k i ) ] n .

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