Abstract

Plasmomechanical systems are an emerging class of devices that hold great promise for manipulating light-matter interactions with high speed and subdiffraction spatial resolution. However, realizing their potential requires developing active plasmomechanical systems that can localize their functionality to the level of an individual subwavelength plasmonic resonator. Here, we present an active, electrically tunable plasmomechanical system that uses a localized-gap plasmonic resonator to mediate optical, thermal, and mechanical interactions within a subwavelength footprint. Our device enables facile electromechanical modulation of localized plasmons, selective subdiffraction transduction of nanomechanical motion, and functions as a plasmomechanical oscillator that can be injection-locked to, and thus amplify, weak external stimuli. These functionalities benefit applications in nanomechanical sensing, spatial light modulators, and reconfigurable metasurfaces.

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References

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2017 (1)

R. De Alba, T. S. Abhilash, R. H. Rand, H. G. Craighead, and J. M. Parpia, “Low-power photothermal self-oscillation of bimetallic nanowires,” Nano Lett. 17, 3995–4002 (2017).
[Crossref]

2016 (6)

Y. Zhao, A. A. E. Saleh, and J. A. Dionne, “Enantioselective optical trapping of chiral nanoparticles with plasmonic tweezers,” ACS Photon. 3, 304–309 (2016).
[Crossref]

B. J. Roxworthy and V. A. Aksyuk, “Nanomechanical motion transduction with a scalable localized gap plasmon architecture,” Nat. Commun. 7, 13746 (2016).
[Crossref]

J. Y. Ou, E. Plum, J. Zhang, and N. I. Zheludev, “Giant nonlinearity of an optically reconfigurable plasmonic metamaterial,” Adv. Mater. 28, 729–733 (2016).
[Crossref]

H. Zhu, F. Yi, and E. Cubukcu, “Plasmonic metamaterial absorber for broadband manipulation of mechanical resonances,” Nat. Photonics 10, 709–714 (2016).
[Crossref]

B. Dong, X. Chen, F. Zhou, C. Wang, H. F. Zhang, and C. Sun, “Gigahertz all-optical modulation using reconfigurable nanophotonic metamolecules,” Nano Lett. 16, 7690–7695 (2016).
[Crossref]

N. I. Zheludev and E. Plum, “Reconfigurable nanomechanical photonic metamaterials,” Nat. Nanotechnol. 11, 16–22 (2016).
[Crossref]

2015 (4)

J. B. Khurgin, “How to deal with the loss in plasmonics and metamaterials,” Nat. Nanotechnol. 10, 2–6 (2015).
[Crossref]

B. S. Dennis, M. I. Haftel, D. A. Czaplewski, D. Lopez, G. Blumberg, and V. A. Aksyuk, “Compact nanomechanical plasmonic phase modulators,” Nat. Photonics 9, 267–273 (2015).
[Crossref]

M. Wang, C. Zhao, X. Miao, Y. Zhao, J. Rufo, Y. J. Liu, T. J. Huang, and Y. Zheng, “Plasmofluidics: merging light and fluids at the micro-/nanoscale,” Small 11, 4423–4444 (2015).
[Crossref]

Y. Y. Liu, J. Stehlik, M. J. Gullans, J. M. Taylor, and J. R. Petta, “Injection locking of a semiconductor double-quantum-dot micromaser,” Phys. Rev. A 92, 053802 (2015).
[Crossref]

2014 (5)

X. Luan, Y. Huang, Y. Li, J. F. McMillan, J. Zheng, S.-W. Huang, P.-C. Hsieh, T. Gu, D. Wang, A. Hati, D. A. Howe, G. Wen, M. Yu, G. Lo, D.-L. Kwong, and C. W. Wong, “An integrated low phase noise radiation-pressure-driven optomechanical oscillator chipset,” Sci. Rep. 4, 6842 (2014).
[Crossref]

T.-Z. Shen, S.-H. Hong, and J.-K. Song, “Electro-optical switching of graphene oxide liquid crystals with an extremely large Kerr coefficient,” Nat. Mater. 13, 394–399 (2014).
[Crossref]

M. Wu, A. C. Hryciw, C. Healey, D. P. Lake, H. Jayakumar, M. R. Freeman, J. P. Davis, and P. E. Barclay, “Dissipative and dispersive optomechanics in a nanocavity torque sensor,” Phys. Rev. X 4, 021052 (2014).
[Crossref]

K. Y. Fong, M. Poot, X. Han, and H. X. Tang, “Phase noise of self-sustained optomechanical oscillators,” Phys. Rev. A 90, 023825 (2014).
[Crossref]

M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt, “Cavity optomechanics,” Rev. Mod. Phys. 86, 1391–1452 (2014).
[Crossref]

2013 (6)

M. Bagheri, M. Poot, L. Fan, F. Marquardt, and H. X. Tang, “Photonic cavity synchronization of nanomechanical oscillators,” Phys. Rev. Lett. 111, 213902 (2013).
[Crossref]

M. Maldovan, “Sound and heat revolutions in phononics,” Nature 503, 209–217 (2013).
[Crossref]

S. V. Boriskina, H. Ghasemi, and G. Chen, “Plasmonic materials for energy: from physics to applications,” Mater. Today 16(10), 375–386 (2013).
[Crossref]

M. S. Tame, K. R. McEnery, Ş. K. Özdemir, J. Lee, S. A. Maier, and M. S. Kim, “Quantum plasmonics,” Nat. Phys. 9, 329–340 (2013).
[Crossref]

R. Thijssen, E. Verhagen, T. J. Kippenberg, and A. Polman, “Plasmon nanomechanical coupling for nanoscale transduction,” Nano Lett. 13, 3293–3297 (2013).
[Crossref]

B. D. Hauer, C. Doolin, K. S. D. Beach, and J. P. Davis, “A general procedure for thermomechanical calibration of nano/micro-mechanical resonators,” Ann. Phys. 339, 181–207 (2013).
[Crossref]

2012 (6)

D. Antonio, D. H. Zanette, and D. López, “Frequency stabilization in nonlinear micromechanical oscillators,” Nat. Commun. 3, 806 (2012).
[Crossref]

M. Zhang, G. S. Wiederhecker, S. Manipatruni, A. Barnard, P. McEuen, and M. Lipson, “Synchronization of micromechanical oscillators using light,” Phys. Rev. Lett. 109, 233906 (2012).
[Crossref]

M. Kauranen and A. V. Zayats, “Nonlinear plasmonics,” Nat. Photonics 6, 737–748 (2012).
[Crossref]

B. J. Roxworthy, K. D. Ko, A. Kumar, K. H. Fung, E. K. C. Chow, G. L. Liu, N. X. Fang, and K. C. Toussaint, “Application of plasmonic bowtie nanoantenna arrays for optical trapping, stacking, and sorting,” Nano Lett. 12, 796–801 (2012).
[Crossref]

J. B. Khurgin, M. W. Pruessner, T. H. Stievater, and W. S. Rabinovich, “Optically pumped coherent mechanical oscillators: the laser rate equation theory and experimental verification,” New J. Phys. 14, 105022 (2012).
[Crossref]

J. B. Khurgin, M. W. Pruessner, T. H. Stievater, and W. S. Rabinovich, “Laser-rate-equation description of optomechanical oscillators,” Phys. Rev. Lett. 108, 223904 (2012).
[Crossref]

2011 (4)

S. Zaitsev, A. K. Pandey, O. Shtempluck, and E. Buks, “Forced and self-excited oscillations of an optomechanical cavity,” Phys. Rev. E 84, 046605 (2011).
[Crossref]

M. I. Stockman, “Nanoplasmonics: past, present, and glimpse into future,” Opt. Express 19, 22029–22106 (2011).
[Crossref]

L. G. Villanueva, R. B. Karabalin, M. H. Matheny, E. Kenig, M. C. Cross, and M. L. Roukes, “A nanoscale parametric feedback oscillator,” Nano Lett. 11, 5054–5059 (2011).
[Crossref]

W. L. Diaz-Merced, R. M. Candey, N. Brickhouse, M. Schneps, J. C. Mannone, S. Brewster, and K. Kolenberg, “Sonification of astronomical data,” Proc. Int. Astron. Union 7, 133–136 (2011).
[Crossref]

2010 (3)

S. Knünz, M. Herrmann, V. Batteiger, G. Saathoff, T. W. Hänsch, K. Vahala, and T. Udem, “Injection locking of a trapped-ion phonon laser,” Phys. Rev. Lett. 105, 013004 (2010).
[Crossref]

M. Hossein-Zadeh and K. J. Vahala, “An optomechanical oscillator on a silicon chip,” IEEE J. Sel. Top. Quantum Electron. 16, 276–287 (2010).
[Crossref]

V. A. Fedotov, N. Papasimakis, E. Plum, A. Bitzer, M. Walther, P. Kuo, D. P. Tsai, and N. I. Zheludev, “Spectral collapse in ensembles of metamolecules,” Phys. Rev. Lett. 104, 223901 (2010).
[Crossref]

2009 (2)

M. Li, W. H. P. Pernice, and H. X. Tang, “Reactive cavity optical force on microdisk-coupled nanomechanical beam waveguides,” Phys. Rev. Lett. 103, 223901 (2009).
[Crossref]

Y. Liu, E. N. Mills, and R. J. Composto, “Tuning optical properties of gold nanorods in polymer films through thermal reshaping,” J. Mater. Chem. 19, 2704–2709 (2009).
[Crossref]

2008 (2)

C. Metzger, M. Ludwig, C. Neuenhahn, A. Ortlieb, I. Favero, K. Karrai, and F. Marquardt, “Self-Induced oscillations in an optomechanical system driven by bolometric backaction,” Phys. Rev. Lett. 101, 133903 (2008).
[Crossref]

J. N. Anker, W. P. Hall, O. Lyandres, N. C. Shah, J. Zhao, and R. P. Van Duyne, “Biosensing with plasmonic nanosensors,” Nat. Mater. 7, 442–453 (2008).
[Crossref]

2007 (1)

T. Søndergaard and S. Bozhevolnyi, “Slow-plasmon resonant nanostructures: scattering and field enhancements,” Phys. Rev. B 75, 073402 (2007).
[Crossref]

2006 (1)

M. Hossein-Zadeh, H. Rokhsari, A. Hajimiri, and K. Vahala, “Characterization of a radiation-pressure-driven micromechanical oscillator,” Phys. Rev. A 74, 023813 (2006).
[Crossref]

2005 (3)

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

T. J. Kippenberg, H. Rokhsari, T. Carmon, A. Scherer, and K. J. Vahala, “Analysis of radiation-pressure induced mechanical oscillation of an optical microcavity,” Phys. Rev. Lett. 95, 033901 (2005).
[Crossref]

H. Rokhsari, T. J. Kippenberg, T. Carmon, and K. J. Vahala, “Radiation-pressure-driven micro-mechanical oscillator,” Opt. Express 13, 5293–5301 (2005).
[Crossref]

2004 (1)

C. Metzger and K. Karrai, “Cavity cooling of a microlever,” Nature 432, 1002–1005 (2004).
[Crossref]

2003 (2)

E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, “A hybridization model for the plasmon response of complex nanostructures,” Science 302, 419–422 (2003).
[Crossref]

D. J. Bergman and M. I. Stockman, “Surface plasmon amplification by stimulated emission of radiation: quantum generation of coherent surface plasmons in nanosystems,” Phys. Rev. Lett. 90, 027402 (2003).
[Crossref]

2001 (1)

M. Zalalutdinov, A. Zehnder, A. Olkhovets, S. Turner, L. Sekaric, B. Ilic, D. Czaplewski, J. M. Parpia, and H. G. Craighead, “Autoparametric optical drive for micromechanical oscillators,” Appl. Phys. Lett. 79, 695–697 (2001).
[Crossref]

2000 (1)

L. Koster, H. Gerth, and H. Haase, “Thermal modes and their application to turbogenerator rotors,” Electron. Eng. 82, 135–144 (2000).
[Crossref]

1946 (1)

R. Adler, “A study of locking phenomena in oscillators,” Proc. IRE 34, 351–357 (1946).
[Crossref]

Abhilash, T. S.

R. De Alba, T. S. Abhilash, R. H. Rand, H. G. Craighead, and J. M. Parpia, “Low-power photothermal self-oscillation of bimetallic nanowires,” Nano Lett. 17, 3995–4002 (2017).
[Crossref]

Adler, R.

R. Adler, “A study of locking phenomena in oscillators,” Proc. IRE 34, 351–357 (1946).
[Crossref]

Aksyuk, V. A.

B. J. Roxworthy and V. A. Aksyuk, “Nanomechanical motion transduction with a scalable localized gap plasmon architecture,” Nat. Commun. 7, 13746 (2016).
[Crossref]

B. S. Dennis, M. I. Haftel, D. A. Czaplewski, D. Lopez, G. Blumberg, and V. A. Aksyuk, “Compact nanomechanical plasmonic phase modulators,” Nat. Photonics 9, 267–273 (2015).
[Crossref]

Anker, J. N.

J. N. Anker, W. P. Hall, O. Lyandres, N. C. Shah, J. Zhao, and R. P. Van Duyne, “Biosensing with plasmonic nanosensors,” Nat. Mater. 7, 442–453 (2008).
[Crossref]

Antonio, D.

D. Antonio, D. H. Zanette, and D. López, “Frequency stabilization in nonlinear micromechanical oscillators,” Nat. Commun. 3, 806 (2012).
[Crossref]

Aspelmeyer, M.

M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt, “Cavity optomechanics,” Rev. Mod. Phys. 86, 1391–1452 (2014).
[Crossref]

Bagheri, M.

M. Bagheri, M. Poot, L. Fan, F. Marquardt, and H. X. Tang, “Photonic cavity synchronization of nanomechanical oscillators,” Phys. Rev. Lett. 111, 213902 (2013).
[Crossref]

Barclay, P. E.

M. Wu, A. C. Hryciw, C. Healey, D. P. Lake, H. Jayakumar, M. R. Freeman, J. P. Davis, and P. E. Barclay, “Dissipative and dispersive optomechanics in a nanocavity torque sensor,” Phys. Rev. X 4, 021052 (2014).
[Crossref]

Barnard, A.

M. Zhang, G. S. Wiederhecker, S. Manipatruni, A. Barnard, P. McEuen, and M. Lipson, “Synchronization of micromechanical oscillators using light,” Phys. Rev. Lett. 109, 233906 (2012).
[Crossref]

Batteiger, V.

S. Knünz, M. Herrmann, V. Batteiger, G. Saathoff, T. W. Hänsch, K. Vahala, and T. Udem, “Injection locking of a trapped-ion phonon laser,” Phys. Rev. Lett. 105, 013004 (2010).
[Crossref]

Beach, K. S. D.

B. D. Hauer, C. Doolin, K. S. D. Beach, and J. P. Davis, “A general procedure for thermomechanical calibration of nano/micro-mechanical resonators,” Ann. Phys. 339, 181–207 (2013).
[Crossref]

Bergman, D. J.

D. J. Bergman and M. I. Stockman, “Surface plasmon amplification by stimulated emission of radiation: quantum generation of coherent surface plasmons in nanosystems,” Phys. Rev. Lett. 90, 027402 (2003).
[Crossref]

Bitzer, A.

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[Crossref]

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Sonification of injection locking data, https://doi.org/10.6084/m9.figshare.5771151 .

Supplementary Material (3)

NameDescription
» Dataset 1       Sonification of injection locking data.
» Supplement 1       Supplemental document
» Visualization 1       Electro-optical switching of an individual localized gap plasmon resonator with 2.75 V.

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Figures (8)

Fig. 1.
Fig. 1. (a) Illustration of the device architecture. The inset shows a side view of the device structural layers and elements. The red color represents the 3rd-order localized gap plasmon mode. The white lines represent the actuator electric field. (b) A line scan of an atomic force micrograph (gray dashed line, inset) of a 4 μm cantilever with an integrated LGPR on the same chip as the devices studied in this work. The total gap size is the sum of the nominal 20 nm sacrificial layer thickness and the upward deflection due to residual stress; the profile is corrected for the 130  nm lead thickness. The red lines are fits that indicate the upward deflection of the structure due to tilt at the gold-coated base (linear) and the curved shape of the free cantilever (parabolic). Regions of expected dispersive and reactive optomechanical coupling, based on simulation data, are indicated by the shaded region.
Fig. 2.
Fig. 2. Finite element calculations of (a) the reflectance of the LGP resonance as a function of gap, where the arrows illustrate the direction of change of the reflectance dip with decreasing gap in the different coupling regimes. (b) The extracted LGP wavelength (right panel) with an exponential fit and the calculated dispersive optomechanical coupling constant (left panel).
Fig. 3.
Fig. 3. Optical modulation with LGPRs. (a) The experimental setup for modulation and transduction in ambient conditions. The components are: (P)BS, (polarizing) beam splitter; P, polarizer; PD, photodiode; VNA, vector network analyzer; DUT, device under test. (b) The experimentally measured spectral reflectance of a single LGPR as a function of applied voltage with Lorentzian fits; the inset shows the measured amplitude modulation of the electrically actuated LGPR. The reflectance spectra are normalized relative to the laser reference spectrum measured by focusing the broadband probe laser on the gold pad through the cantilever but displaced from the LGPR 1  μm. Reference measurements are taken within 1 s of each spectrum measurement to minimize the effects of laser spectrum drift. (c) The experimentally measured LGP wavelengths and (d) the relative shift of the LGP resonance as a function of voltage; uncertainties are derived from Lorentzian fits.
Fig. 4.
Fig. 4. (a) Normalized magnitude of electrostatically driven motion transduced, in ambient air conditions, by a dispersive (left panels) and reactive (right panels) LGPR, measured with different probe laser detuning δλ. Black lines correspond to a best fit of two Lorentzian functions added coherently; inset cartoons depict the shape of the flexural mechanical modes. The change in the relative strength of the resonances between the left and right panels indicate selective mode transduction. The dispersive case illustrates that the LGPR motion is described by a coherent superposition of the displacement from two flexural modes: the modal displacements are cancelling each other out at the LGPR position near the 20 MHz excitation frequency. (b) The motion phase near the second-order flexural mode resonance. Dispersive coupling produces the opposite phase at different signs of detuning, indicating a change in the sign of the reflectance derivative sign[xR] with detuning. Reactively coupled devices produce the same phase (sign[xR]) regardless of detuning.
Fig. 5.
Fig. 5. Scanning electron micrographs and measured motion signals for electrostatically actuated 500 nm wide cantilevers with (a) 2 μm length and (b) 1.5 μm length. The (90×75×40)  nm3 LGPR, embedded on the underside of the cantilever, forms a visible “bulb” through the thickness that protrudes from the top of the silicon nitride. (c) The reflectance spectrum from the LGPR showing the m=1 LGP mode.
Fig. 6.
Fig. 6. (a) Experimental setup for vacuum conditions. The components are: VA—variable attenuator, FPC—fiber polarization controller, and ESA—electronic spectrum analyzer. (b) The mechanical amplitude spectral density, plotted on a logarithmic scale, for optical pump powers in different regimes of below threshold (black, gray), above threshold (dark red), and saturated (gold). There exists an apparently chaotic regime [36] for pumping near saturation (red curve, 1500 μW), whereby the amplitude and frequency fluctuate rapidly. In this case, the apparent broadened linewidth is a result of rapid frequency variation during the instrument averaging. The reduction in the noise floor with increasing pump power is a result of decreased imprecision noise. The inset shows the reflectance spectrum of the LGPR with negative and positive experimental wavelength detunings marked with blue and red lines, respectively. (c) The mechanical oscillation amplitude of the LGPR on a logarithmic scale as function of pump power for negative (blue dots) and positive (red dots) wavelength detuning; the inset shows corresponding mechanical linewidths and their uncertainties determined from Lorentzian fits. The shaded gray region indicates the measurement resolution limit.
Fig. 7.
Fig. 7. Calculated plasmomechanical absorbance gain landscape (red-yellow: excitation, blue: cooling) with experimental measurement points for negative (white dot) and positive (black dot) wavelength detuning; gap value and uncertainty are from the AFM measurements. The solid black line indicates the zero-gain contour and the dotted line indicates the expected gap of the device.
Fig. 8.
Fig. 8. (a) Log-scale contour plot of the motion power spectral density of the plasmomechanical oscillator (free-running frequency f0) for varying injection frequency fin at an injection amplitude of xin25  pm. The oscillator is locked to the input RF tone and follows fin over the interval fL. (b) Line cuts of the motion power spectra for unlocked (black curves, fin marked by the * symbol) and locked (red, gray, blue, and green curves) operation, plotted on a log scale. Numerical annotations represent the distortion sideband order up to a value of ±3. Additional sidebands appearing at the top of the locking range (green curve) are distinct from the distortion sidebands outside the locking range predicted by Eq. (2), and are likely the result of intermodulation between the applied actuated displacement and the oscillator. (c) The total observed locking range (red) [i.e., central rectangular band in (a)] and the Adler theory prediction fL=ωm/2π  xin/xfree (black); these quantities agree at low injection amplitude. The predicted values correspond to the average ratio of the injection displacement to the free-running displacement xin/xfree measured at far-detuned fin, ranging from 3800 kHz to 3825 kHz; uncertainties are one standard deviation of the values from multiple detunings. (d) The ratio of the total observed range to the theoretical predictions from Adler’s theory, which shows a linear relationship converging to unity for weak injected signals, for which the Adler theory is valid.

Equations (3)

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P0mth  cp|gA|gBωm2+τt2Qmωm,
fp=fin+(p+1)δf1(fL/2δf)2  ,
fL=ωm2π1Qmxinjxfree=ωm2πxinxfree,

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