Abstract

Silicon-on-insulator (SOI) provides an important material system for photonic-electronic integration. Further integration of mechanical devices in SOI is hampered by incompatible under-etch or release steps required to prevent leakage of mechanical energy into the substrate. The purpose of this work is to demonstrate co-integration of nanomechanical structures on the surface of SOI. Silicon fin waveguides are used to generate co-localized and interacting optical and mechanical resonances. Radiation pressure interaction from laser driving is demonstrated. Our work enables co-integration of electronic, photonic, and phononic degrees of freedom on a single platform.

© 2017 Optical Society of America

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References

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2016 (1)

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[Crossref]

2015 (1)

B. Bahr, R. Marathe, and D. Weinstein, J. Microelectromech. Syst. 24, 1520 (2015).
[Crossref]

2014 (2)

S. M. Meenehan, J. D. Cohen, S. Gröblacher, J. T. Hill, A. H. Safavi-Naeini, M. Aspelmeyer, and O. Painter, Phys. Rev. A 90, 011803 (2014).
[Crossref]

M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt, Rev. Mod. Phys. 86, 1391 (2014).
[Crossref]

2013 (1)

2009 (2)

L.-D. Haret, T. Tanabe, E. Kuramochi, and M. Notomi, Opt. Express 17, 21108 (2009).
[Crossref]

M. Eichenfield, J. Chan, R. M. Camacho, K. J. Vahala, and O. Painter, Nature 462, 78 (2009).
[Crossref]

2008 (1)

M. Li, W. H. P. Pernice, C. Xiong, T. Baehr-Jones, M. Hochberg, and H. X. Tang, Nature 456, 480 (2008).
[Crossref]

2006 (1)

R. Soref, IEEE J. Sel. Top. Quantum Electron. 12, 1678 (2006).
[Crossref]

2000 (1)

K. Yasumura, T. Stowe, E. Chow, T. Pfafman, T. Kenny, B. Stipe, and D. Rugar, J. Microelectromech. Syst. 9, 117 (2000).
[Crossref]

1971 (1)

I. Mason, R. de la Rue, R. Schmidt, E. Ash, and P. Lagasse, Electron. Lett. 7, 395 (1971).
[Crossref]

1969 (1)

E. Ash, R. De La Rue, and R. Humphryes, IEEE Trans. Microw. Theory Tech. 17, 882 (1969).
[Crossref]

Ash, E.

I. Mason, R. de la Rue, R. Schmidt, E. Ash, and P. Lagasse, Electron. Lett. 7, 395 (1971).
[Crossref]

E. Ash, R. De La Rue, and R. Humphryes, IEEE Trans. Microw. Theory Tech. 17, 882 (1969).
[Crossref]

Aspelmeyer, M.

S. M. Meenehan, J. D. Cohen, S. Gröblacher, J. T. Hill, A. H. Safavi-Naeini, M. Aspelmeyer, and O. Painter, Phys. Rev. A 90, 011803 (2014).
[Crossref]

M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt, Rev. Mod. Phys. 86, 1391 (2014).
[Crossref]

Baehr-Jones, T.

M. Li, W. H. P. Pernice, C. Xiong, T. Baehr-Jones, M. Hochberg, and H. X. Tang, Nature 456, 480 (2008).
[Crossref]

Bahr, B.

B. Bahr, R. Marathe, and D. Weinstein, J. Microelectromech. Syst. 24, 1520 (2015).
[Crossref]

Bulk, R. F.

K. Y. Hashimoto and R. F. Bulk, Acoustic Wave Filters for Communications, 1st ed. (Artech House, 2015).

Camacho, R. M.

M. Eichenfield, J. Chan, R. M. Camacho, K. J. Vahala, and O. Painter, Nature 462, 78 (2009).
[Crossref]

Chan, J.

M. Eichenfield, J. Chan, R. M. Camacho, K. J. Vahala, and O. Painter, Nature 462, 78 (2009).
[Crossref]

Chow, E.

K. Yasumura, T. Stowe, E. Chow, T. Pfafman, T. Kenny, B. Stipe, and D. Rugar, J. Microelectromech. Syst. 9, 117 (2000).
[Crossref]

Cleland, A. N.

A. N. Cleland, Foundations of Nanomechanics (Springer-Verlag, 2003).

Cohen, J. D.

S. M. Meenehan, J. D. Cohen, S. Gröblacher, J. T. Hill, A. H. Safavi-Naeini, M. Aspelmeyer, and O. Painter, Phys. Rev. A 90, 011803 (2014).
[Crossref]

de la Rue, R.

I. Mason, R. de la Rue, R. Schmidt, E. Ash, and P. Lagasse, Electron. Lett. 7, 395 (1971).
[Crossref]

E. Ash, R. De La Rue, and R. Humphryes, IEEE Trans. Microw. Theory Tech. 17, 882 (1969).
[Crossref]

Eggleton, B. J.

Eichenfield, M.

M. Eichenfield, J. Chan, R. M. Camacho, K. J. Vahala, and O. Painter, Nature 462, 78 (2009).
[Crossref]

Gröblacher, S.

S. M. Meenehan, J. D. Cohen, S. Gröblacher, J. T. Hill, A. H. Safavi-Naeini, M. Aspelmeyer, and O. Painter, Phys. Rev. A 90, 011803 (2014).
[Crossref]

Haret, L.-D.

Hashimoto, K. Y.

K. Y. Hashimoto and R. F. Bulk, Acoustic Wave Filters for Communications, 1st ed. (Artech House, 2015).

Hill, J. T.

C. J. Sarabalis, J. T. Hill, and A. H. Safavi-Naeini, APL Photon. 1, 071301 (2016).
[Crossref]

S. M. Meenehan, J. D. Cohen, S. Gröblacher, J. T. Hill, A. H. Safavi-Naeini, M. Aspelmeyer, and O. Painter, Phys. Rev. A 90, 011803 (2014).
[Crossref]

Hochberg, M.

M. Li, W. H. P. Pernice, C. Xiong, T. Baehr-Jones, M. Hochberg, and H. X. Tang, Nature 456, 480 (2008).
[Crossref]

Humphryes, R.

E. Ash, R. De La Rue, and R. Humphryes, IEEE Trans. Microw. Theory Tech. 17, 882 (1969).
[Crossref]

Kenny, T.

K. Yasumura, T. Stowe, E. Chow, T. Pfafman, T. Kenny, B. Stipe, and D. Rugar, J. Microelectromech. Syst. 9, 117 (2000).
[Crossref]

Kippenberg, T. J.

M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt, Rev. Mod. Phys. 86, 1391 (2014).
[Crossref]

Kuramochi, E.

Lagasse, P.

I. Mason, R. de la Rue, R. Schmidt, E. Ash, and P. Lagasse, Electron. Lett. 7, 395 (1971).
[Crossref]

Li, M.

M. Li, W. H. P. Pernice, C. Xiong, T. Baehr-Jones, M. Hochberg, and H. X. Tang, Nature 456, 480 (2008).
[Crossref]

Marathe, R.

B. Bahr, R. Marathe, and D. Weinstein, J. Microelectromech. Syst. 24, 1520 (2015).
[Crossref]

Marquardt, F.

M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt, Rev. Mod. Phys. 86, 1391 (2014).
[Crossref]

Mason, I.

I. Mason, R. de la Rue, R. Schmidt, E. Ash, and P. Lagasse, Electron. Lett. 7, 395 (1971).
[Crossref]

Meenehan, S. M.

S. M. Meenehan, J. D. Cohen, S. Gröblacher, J. T. Hill, A. H. Safavi-Naeini, M. Aspelmeyer, and O. Painter, Phys. Rev. A 90, 011803 (2014).
[Crossref]

Notomi, M.

Painter, O.

S. M. Meenehan, J. D. Cohen, S. Gröblacher, J. T. Hill, A. H. Safavi-Naeini, M. Aspelmeyer, and O. Painter, Phys. Rev. A 90, 011803 (2014).
[Crossref]

M. Eichenfield, J. Chan, R. M. Camacho, K. J. Vahala, and O. Painter, Nature 462, 78 (2009).
[Crossref]

A. H. Safavi-Naeini and O. Painter, Cavity Optomechanics, M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt, eds., Quantum Science and Technology (Springer, 2014), pp. 195–231.

Pant, R.

Pernice, W. H. P.

M. Li, W. H. P. Pernice, C. Xiong, T. Baehr-Jones, M. Hochberg, and H. X. Tang, Nature 456, 480 (2008).
[Crossref]

Pfafman, T.

K. Yasumura, T. Stowe, E. Chow, T. Pfafman, T. Kenny, B. Stipe, and D. Rugar, J. Microelectromech. Syst. 9, 117 (2000).
[Crossref]

Poulton, C. G.

Rugar, D.

K. Yasumura, T. Stowe, E. Chow, T. Pfafman, T. Kenny, B. Stipe, and D. Rugar, J. Microelectromech. Syst. 9, 117 (2000).
[Crossref]

Safavi-Naeini, A. H.

C. J. Sarabalis, J. T. Hill, and A. H. Safavi-Naeini, APL Photon. 1, 071301 (2016).
[Crossref]

S. M. Meenehan, J. D. Cohen, S. Gröblacher, J. T. Hill, A. H. Safavi-Naeini, M. Aspelmeyer, and O. Painter, Phys. Rev. A 90, 011803 (2014).
[Crossref]

A. H. Safavi-Naeini and O. Painter, Cavity Optomechanics, M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt, eds., Quantum Science and Technology (Springer, 2014), pp. 195–231.

Sarabalis, C. J.

C. J. Sarabalis, J. T. Hill, and A. H. Safavi-Naeini, APL Photon. 1, 071301 (2016).
[Crossref]

Schmidt, R.

I. Mason, R. de la Rue, R. Schmidt, E. Ash, and P. Lagasse, Electron. Lett. 7, 395 (1971).
[Crossref]

Soref, R.

R. Soref, IEEE J. Sel. Top. Quantum Electron. 12, 1678 (2006).
[Crossref]

Stipe, B.

K. Yasumura, T. Stowe, E. Chow, T. Pfafman, T. Kenny, B. Stipe, and D. Rugar, J. Microelectromech. Syst. 9, 117 (2000).
[Crossref]

Stowe, T.

K. Yasumura, T. Stowe, E. Chow, T. Pfafman, T. Kenny, B. Stipe, and D. Rugar, J. Microelectromech. Syst. 9, 117 (2000).
[Crossref]

Tanabe, T.

Tang, H. X.

M. Li, W. H. P. Pernice, C. Xiong, T. Baehr-Jones, M. Hochberg, and H. X. Tang, Nature 456, 480 (2008).
[Crossref]

Vahala, K. J.

M. Eichenfield, J. Chan, R. M. Camacho, K. J. Vahala, and O. Painter, Nature 462, 78 (2009).
[Crossref]

Weinstein, D.

B. Bahr, R. Marathe, and D. Weinstein, J. Microelectromech. Syst. 24, 1520 (2015).
[Crossref]

Xiong, C.

M. Li, W. H. P. Pernice, C. Xiong, T. Baehr-Jones, M. Hochberg, and H. X. Tang, Nature 456, 480 (2008).
[Crossref]

Yasumura, K.

K. Yasumura, T. Stowe, E. Chow, T. Pfafman, T. Kenny, B. Stipe, and D. Rugar, J. Microelectromech. Syst. 9, 117 (2000).
[Crossref]

Adv. Opt. Photon. (1)

APL Photon. (1)

C. J. Sarabalis, J. T. Hill, and A. H. Safavi-Naeini, APL Photon. 1, 071301 (2016).
[Crossref]

Electron. Lett. (1)

I. Mason, R. de la Rue, R. Schmidt, E. Ash, and P. Lagasse, Electron. Lett. 7, 395 (1971).
[Crossref]

IEEE J. Sel. Top. Quantum Electron. (1)

R. Soref, IEEE J. Sel. Top. Quantum Electron. 12, 1678 (2006).
[Crossref]

IEEE Trans. Microw. Theory Tech. (1)

E. Ash, R. De La Rue, and R. Humphryes, IEEE Trans. Microw. Theory Tech. 17, 882 (1969).
[Crossref]

J. Microelectromech. Syst. (2)

B. Bahr, R. Marathe, and D. Weinstein, J. Microelectromech. Syst. 24, 1520 (2015).
[Crossref]

K. Yasumura, T. Stowe, E. Chow, T. Pfafman, T. Kenny, B. Stipe, and D. Rugar, J. Microelectromech. Syst. 9, 117 (2000).
[Crossref]

Nature (2)

M. Li, W. H. P. Pernice, C. Xiong, T. Baehr-Jones, M. Hochberg, and H. X. Tang, Nature 456, 480 (2008).
[Crossref]

M. Eichenfield, J. Chan, R. M. Camacho, K. J. Vahala, and O. Painter, Nature 462, 78 (2009).
[Crossref]

Opt. Express (1)

Phys. Rev. A (1)

S. M. Meenehan, J. D. Cohen, S. Gröblacher, J. T. Hill, A. H. Safavi-Naeini, M. Aspelmeyer, and O. Painter, Phys. Rev. A 90, 011803 (2014).
[Crossref]

Rev. Mod. Phys. (1)

M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt, Rev. Mod. Phys. 86, 1391 (2014).
[Crossref]

Other (4)

K. Y. Hashimoto and R. F. Bulk, Acoustic Wave Filters for Communications, 1st ed. (Artech House, 2015).

COMSOL AB, Stockholm, COMSOL v. 5.0, https://www.comsol.com/ .

A. H. Safavi-Naeini and O. Painter, Cavity Optomechanics, M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt, eds., Quantum Science and Technology (Springer, 2014), pp. 195–231.

A. N. Cleland, Foundations of Nanomechanics (Springer-Verlag, 2003).

Supplementary Material (1)

NameDescription
» Supplement 1       Supplement 1

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Figures (3)

Fig. 1.
Fig. 1. (a) Dispersion diagram for guided waves in silicon fins with dimensions h=340  nm and w=100  nm on an oxide substrate. (b) Mechanical frequencies for the E-B model of a fin (solid line) and a fin on glass (dashed line) are compared. E-B model starts to break down for small values of h/w, and there is a deviation from linearity in the full solution. Additionally, the fins on the oxide generally have lower frequency due to the “softer” clamping boundary condition. Simulated radiation limited quality factors (dot-dashed line) for the fins are overlaid with Qm measurements (stars). Corresponding solutions are marked with a red circle on (a) and (b).
Fig. 2.
Fig. 2. (a) SEM of the fabricated structure composed of two fins surrounding a wide beam and forming a photonic crystal cavity. The unit cell of the photonic crystal is shown with the geometric parameters defined. (b) Modulating the width of the fins leads to localized mechanical resonances with modes labeled f0 to f3 (these are only the even modes; odd modes are optically dark). (c) TE optical bands of a symmetric fin cavity unit cell have a 17-THz bandgap. Same variation that leads to trapped phonons (b) causes optical resonances to be trapped in the central region. Transverse component of the electric field for one such mode (TE00) is overlaid in the SEM in (a, d). Measurement scheme: cleaved fibers are aligned to TE grating couplers. Optical transmission spectra are recorded on an output channel and intensity fluctuations induced by the mechanics are read out upon reflection. (e) Optical transmission spectrum for the fin cavity reported here (black) is plotted for comparison alongside the transmission of a through waveguide (red, higher ηgc than measured for the cavity—see Supplement 1). In the inset, a narrower scan of the TE00 mode is shown. Detected RF power spectral density for the laser tuned to the slope of the cavity resonance transmission for optical modes TE00 and TE01 are shown in (f) and (g), respectively.
Fig. 3.
Fig. 3. (a) Optical mechanical spring effect is fit to determine the optomechanical coupling rate for TE00 and f0 modes. (b) Resulting g0,nk (black) between TE00 and four mechanical modes of the 65 nm fin are fit (as described in the text) and seen to agree well with simulated coupling rates (red). (c) Same as (b) but for optical mode TE01.

Equations (3)

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ΩEρwh2.
Hint=k,ng0,nk(b^k+b^k)a^na^n,
dΩk=2(g0,nk|α|)2Δ(ΔΩk)2+κt24,

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