Abstract

We present the design and experimental comparison of femtogram L3-nanobeam photonic crystal cavities for optomechanical studies. Two symmetric nanobeams are created by placing three air slots in a silicon photonic crystal slab where three holes are removed. The nanobeams’ mechanical frequencies are higher than 600 MHz with ultrasmall effective modal masses at approximately 20 femtograms. The optical quality factor (Q) is optimized up to 53,000. The optical and mechanical modes are dispersively coupled with a vacuum optomechanical coupling rate g0/2π exceeding 200 kHz. The anchor-loss-limited mechanical Q of the differential beam mode is evaluated to be greater than 10,000 for structures with ideally symmetric beams. The influence of variations on the air slot width and position is also investigated. The devices can be used as ultrasensitive sensors of mass, force, and displacement.

© 2012 OSA

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2012

E. Verhagen, S. Deléglise, S. Weis, A. Schliesser, and T. J. Kippenberg, “Quantum-coherent coupling of a mechanical oscillator to an optical cavity mode,” Nature 482(7383), 63–67 (2012).
[CrossRef] [PubMed]

G. Bahl, M. Tomes, F. Marquardt, and T. Carmon, “Observation of spontaneous Brillouin cooling,” Nat. Phys. 8(3), 203–207 (2012).
[CrossRef]

J. Zheng, Y. Li, M. S. Aras, A. Stein, K. L. Shepard, and C. W. Wong, “Parametric optomechanical oscillations in two-dimensional slot-type high-Q photonic crystal cavities,” Appl. Phys. Lett. 100(21), 211908 (2012).
[CrossRef]

X. Sun, J. Zheng, M. Poot, C. W. Wong, and H. X. Tang, “Femtogram doubly clamped nanomechanical resonators embedded in a high-Q two-dimensional photonic crystal nanocavity,” Nano Lett. 12(5), 2299–2305 (2012), doi:
[CrossRef] [PubMed]

M. Poot and H. S. J. van der Zant, “Mechanical systems in the quantum regime,” Phys. Rep. 511(5), 273–335 (2012).
[CrossRef]

2011

E. Gavartin, R. Braive, I. Sagnes, O. Arcizet, A. Beveratos, T. J. Kippenberg, and I. Robert-Philip, “Optomechanical coupling in a two-dimensional photonic crystal defect cavity,” Phys. Rev. Lett. 106(20), 203902 (2011).
[CrossRef] [PubMed]

M. Bagheri, M. Poot, M. Li, W. P. H. Pernice, and H. X. Tang, “Dynamic manipulation of nanomechanical resonators in the high-amplitude regime and non-volatile mechanical memory operation,” Nat. Nanotechnol. 6(11), 726–732 (2011).
[CrossRef] [PubMed]

V. Fiore, Y. Yang, M. C. Kuzyk, R. Barbour, L. Tian, and H. Wang, “Storing optical information as a mechanical excitation in a silica optomechanical resonator,” Phys. Rev. Lett. 107(13), 133601 (2011).
[CrossRef] [PubMed]

A. H. Safavi-Naeini, T. P. Mayer Alegre, J. Chan, M. Eichenfield, M. Winger, Q. Lin, J. T. Hill, D. E. Chang, and O. Painter, “Electromagnetically induced transparency and slow light with optomechanics,” Nature 472(7341), 69–73 (2011).
[CrossRef] [PubMed]

J. Chan, T. P. M. Alegre, A. H. Safavi-Naeini, J. T. Hill, A. Krause, S. Gröblacher, M. Aspelmeyer, and O. Painter, “Laser cooling of a nanomechanical oscillator into its quantum ground state,” Nature 478(7367), 89–92 (2011).
[CrossRef] [PubMed]

J. D. Teufel, T. Donner, D. Li, J. W. Harlow, M. S. Allman, K. Cicak, A. J. Sirois, J. D. Whittaker, K. W. Lehnert, and R. W. Simmonds, “Sideband cooling of micromechanical motion to the quantum ground state,” Nature 475(7356), 359–363 (2011).
[CrossRef] [PubMed]

2010

J. C. Sankey, C. Yang, B. M. Zwickl, A. M. Jayich, and J. G. E. Harris, “Strong and tunable nonlinear optomechanical coupling in a low-loss system,” Nat. Phys. 6(9), 707–712 (2010).
[CrossRef]

A. D. O’Connell, M. Hofheinz, M. Ansmann, R. C. Bialczak, M. Lenander, E. Lucero, M. Neeley, D. Sank, H. Wang, M. Weides, J. Wenner, J. M. Martinis, and A. N. Cleland, “Quantum ground state and single-phonon control of a mechanical resonator,” Nature 464(7289), 697–703 (2010).
[CrossRef] [PubMed]

S. Weis, R. Rivière, S. Deléglise, E. Gavartin, O. Arcizet, A. Schliesser, and T. J. Kippenberg, “Optomechanically induced transparency,” Science 330(6010), 1520–1523 (2010).
[CrossRef] [PubMed]

D. Van Thourhout and J. Roels, “Optomechanical device actuation through the optical gradient force,” Nat. Photonics 4(4), 211–217 (2010).
[CrossRef]

G. Anetsberger, E. Gavartin, O. Arcizet, Q. P. Unterreithmeier, E. M. Weig, M. L. Gorodetsky, J. P. Kotthaus, and T. J. Kippenberg, “Measuring nanomechanical motion with an imprecision far below the standard quantum limit,” Phys. Rev. A 82, 061804(R) (2010).

P. Colman, C. Husko, S. Combrie, I. Sagnes, C. W. Wong, and A. De Rossi, “Temporal solitons and pulse compression in photonic crystal waveguides,” Nat. Photonics 4(12), 862–868 (2010).
[CrossRef]

A. H. Safavi-Naeini, T. P. M. Alegre, M. Winger, and O. Painter, “Optomechanics in an ultrahigh-Q two-dimensional photonic crystal cavity,” Appl. Phys. Lett. 97(18), 181106 (2010).
[CrossRef]

J. Gao, J. F. McMillan, M.-C. Wu, J. Zheng, S. Assefa, and C. W. Wong, “Demonstration of an air-slot mode-gap confined photonic crystal slab nanocavity with ultrasmall mode volumes,” Appl. Phys. Lett. 96(5), 051123 (2010).
[CrossRef]

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181(3), 687–702 (2010).
[CrossRef]

J. F. McMillan, M. Yu, D.-L. Kwong, and C. W. Wong, “Observation of four-wave mixing in slow-light silicon photonic crystal waveguides,” Opt. Express 18(15), 15484–15497 (2010).
[CrossRef] [PubMed]

Y. Li, J. Zheng, J. Gao, J. Shu, M. S. Aras, and C. W. Wong, “Design of dispersive optomechanical coupling and cooling in ultrahigh-Q/V slot-type photonic crystal cavities,” Opt. Express 18(23), 23844–23856 (2010).
[CrossRef] [PubMed]

2009

Y. Takahashi, Y. Tanaka, H. Hagino, T. Sugiya, Y. Sato, T. Asano, and S. Noda, “Design and demonstration of high-Q photonic heterostructure nanocavities suitable for integration,” Opt. Express 17(20), 18093–18102 (2009).
[CrossRef] [PubMed]

M. Eichenfield, J. Chan, A. H. Safavi-Naeini, K. J. Vahala, and O. Painter, “Modeling dispersive coupling and losses of localized optical and mechanical modes in optomechanical crystals,” Opt. Express 17(22), 20078–20098 (2009).
[CrossRef] [PubMed]

X. Yang, M. Yu, D.-L. Kwong, and C. W. Wong, “All-optical analog to electromagnetically induced transparency in multiple coupled photonic crystal cavities,” Phys. Rev. Lett. 102(17), 173902 (2009).
[CrossRef] [PubMed]

G. S. Wiederhecker, L. Chen, A. Gondarenko, and M. Lipson, “Controlling photonic structures using optical forces,” Nature 462(7273), 633–636 (2009).
[CrossRef] [PubMed]

M. Eichenfield, R. Camacho, J. Chan, K. J. Vahala, and O. Painter, “A picogram- and nanometre-scale photonic-crystal optomechanical cavity,” Nature 459(7246), 550–555 (2009).
[CrossRef] [PubMed]

A. K. Naik, M. S. Hanay, W. K. Hiebert, X. L. Feng, and M. L. Roukes, “Towards single-molecule nanomechanical mass spectrometry,” Nat. Nanotechnol. 4(7), 445–450 (2009).
[CrossRef] [PubMed]

I. Favero and K. Karrai, “Optomechanics of deformable optical devices,” Nat. Photonics 3(4), 201–205 (2009).
[CrossRef]

Y.-S. Park and H. Wang, “Resolved-sideband and cryogenic cooling of an optomechanical resonator,” Nat. Phys. 5(7), 489–493 (2009).
[CrossRef]

S. Gröblacher, J. B. Hertzberg, M. R. Vanner, G. D. Cole, S. Gigan, K. C. Schwab, and M. Aspelmeyer, “Demonstration of an ultracold micro-optomechanical oscillator in a cryogenic cavity,” Nat. Phys. 5(7), 485–488 (2009).
[CrossRef]

2008

A. Schliesser, R. Rivière, G. Anetsberger, O. Arcizet, and T. J. Kippenberg, “Resolved-sideband cooling of a micromechanical oscillator,” Nat. Phys. 4(5), 415–419 (2008).
[CrossRef]

T. J. Kippenberg and K. J. Vahala, “Cavity optomechanics: back-action at the mesoscale,” Science 321(5893), 1172–1176 (2008).
[CrossRef] [PubMed]

F. Marquardt, “Optomechanics: push towards the quantum limit,” Nat. Phys. 4(7), 513–514 (2008).
[CrossRef]

C. A. Regal, J. D. Teufel, and K. W. Lehnert, “Measuring nanomechanical motion with a resonant microwave cavity interferometer,” Nat. Phys. 4(7), 555–560 (2008).
[CrossRef]

J. F. McMillan, M. Yu, D.-L. Kwong, and C. W. Wong, “Observations of spontaneous Raman scattering in silicon slow-light photonic crystal waveguides,” Appl. Phys. Lett. 93(25), 251105 (2008).
[CrossRef]

I. Fushman, D. Englund, A. Faraon, N. Stoltz, P. Petroff, and J. Vuckovic, “Controlled phase shifts with a single quantum dot,” Science 320(5877), 769–772 (2008).
[CrossRef] [PubMed]

M. Li, W. H. P. Pernice, C. Xiong, T. Baehr-Jones, M. Hochberg, and H. X. Tang, “Harnessing optical forces in integrated photonic circuits,” Nature 456(7221), 480–484 (2008).
[CrossRef] [PubMed]

G. Anetsberger, R. Rivière, A. Schliesser, O. Arcizet, and T. J. Kippenberg, “Ultralow-dissipation optomechanical resonators on a chip,” Nat. Photonics 2(10), 627–633 (2008).
[CrossRef]

2007

M. Li, H. X. Tang, and M. L. Roukes, “Ultra-sensitive NEMS-based cantilevers for sensing, scanned probe and very high-frequency applications,” Nat. Nanotechnol. 2(2), 114–120 (2007).
[CrossRef] [PubMed]

2006

M. Notomi, H. Taniyama, S. Mitsugi, and E. Kuramochi, “Optomechanical wavelength and energy conversion in high- Q double-layer cavities of photonic crystal slabs,” Phys. Rev. Lett. 97(2), 023903 (2006).
[CrossRef] [PubMed]

G. Khitrova, H. M. Gibbs, M. Kira, S. W. Koch, and A. Scherer, “Vacuum Rabi splitting in semiconductors,” Nat. Phys. 2(2), 81–90 (2006).
[CrossRef]

T. Asano, B.-S. Song, and S. Noda, “Analysis of the experimental Q factors (~ 1 million) of photonic crystal nanocavities,” Opt. Express 14(5), 1996–2002 (2006).
[CrossRef] [PubMed]

2005

2004

C. W. Wong, P. T. Rakich, S. G. Johnson, M. Qi, H. I. Smith, E. P. Ippen, L. C. Kimerling, Y. Jeon, G. Barbastathis, and S.-G. Kim, “Strain-tunable silicon photonic band gap microcavities in optical waveguides,” Appl. Phys. Lett. 84(8), 1242–1244 (2004).
[CrossRef]

B.-S. Song, T. Asano, Y. Akahane, Y. Tanaka, and S. Noda, “Transmission and reflection characteristics of in-plane hetero-photonic crystals,” Appl. Phys. Lett. 85(20), 4591–4593 (2004).
[CrossRef]

I. Wilson-Rae, P. Zoller, and A. Imamoğlu, “Laser cooling of a nanomechanical resonator mode to its quantum ground state,” Phys. Rev. Lett. 92(7), 075507 (2004).
[CrossRef] [PubMed]

2003

U. Basu and A. K. Chopra, “Perfectly matched layers for time-harmonic elastodynamics of unbounded domains: theory and finite-element implementation,” Comput. Methods Appl. Mech. Eng. 192(11-12), 1337–1375 (2003).
[CrossRef]

2002

S. G. Johnson, M. Ibanescu, M. A. Skorobogatiy, O. Weisberg, J. D. Joannopoulos, and Y. Fink, “Perturbation theory for Maxwell’s equations with shifting material boundaries,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 65(6), 066611 (2002).
[CrossRef] [PubMed]

K. Srinivasan and O. Painter, “Momentum space design of high-Q photonic crystal optical cavities,” Opt. Express 10(15), 670–684 (2002).
[CrossRef] [PubMed]

2001

2000

K. Y. Yasumura, T. D. Stowe, E. M. Chow, T. Pfafman, T. W. Kenny, B. C. Stipe, and D. Rugar, “Quality factors in micron- and submicron-thick cantilevers,” J. Microelectromech. Syst. 9(1), 117–125 (2000).
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Supplementary Material (2)

» Media 1: MOV (650 KB)     
» Media 2: MOV (819 KB)     

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Figures (8)

Fig. 1
Fig. 1

Geometry of the L3-nanobeam cavity. (a) Overview of the device. (b) Zoom-in of the beam region. a is the lattice constant of the triangular PhC; sx1, sx2, and sx3 are the hole offsets in the x direction; sy is the hole offset in the y direction; wb1 and wb2 are beam widths; was1, was2, and was3 are slot widths. (c) Scanning electron micrograph of a fabricated beam-cavity.

Fig. 2
Fig. 2

(a) TE-like bands of a PhC slab with a triangular lattice of air holes where lattice constant a = 430 nm, hole radius r = 0.29a, refractive index of silicon nsi = 3.48, and silicon slab thickness h = 220 nm. (b) TE-like y-odd waveguide band for the slotted W1.35 waveguide with wwg = 1.35× 3 a , (was, wb) = (60 nm, 80 nm) (red solid line) and (was, wb) = (60 nm, 60 nm) (red dashed line). Red circles indicate the bandedges. (c) Waveguide bandedge frequency versus the waveguide width wwg. The gray regions indicate the PhC slab mode continua. The inset illustrates the geometry. (d),(e) Field distribution of Ey at the bandedge as indicated by the upper and lower red circles in (b), respectively. (f) Ey intensity profile along the y direction, i.e., perpendicular to the slots. The solid line is obtained from (d) and the dashed from (e), cut from center of the hot optical spots.

Fig. 3
Fig. 3

(a) Band structure of the TE-like y-odd band for the “mirror” waveguide with hole radius rwg = 160 nm. (b) Waveguide bandedge frequency versus the waveguide hole radius rwg. The inset illustrates the geometry.

Fig. 4
Fig. 4

Optimization process for the cavity with (was, wb) = (60 nm, 80 nm) by tuning hole positions of sx1, sx2, sx3, and sy respectively in series, as shown in panels (a) to (d). For an air slot length Ls of 1.8a, the maximum optical Q of 1.95 × 104 is achieved with (sx1, sx2, sx3, sy) = (−0.18a, −0.06a, 0.22a, −0.15a) [Design 1]. With a similar optimization process, cavities with (was, wb) = (60 nm, 60 nm) achieve a higher optical Q of 5.22 × 104 with (Ls, sx1, sx2, sx3, sy) = (1.9a, −0.3a, −0.02a, 0.1a, 0) [Design 2]. Solid lines indicate the optical Q, while the dashed lines indicate the normalized resonant frequency. The red dot in Panel (d) indicates the measured unloaded optical Q of the nanobeam cavity based on Design 1 from experiments.

Fig. 5
Fig. 5

(a)−(c) Modal distribution of the Ey field. (d)−(f) Corresponding spatial Fourier transformation (FT) for cavities with increasing optical Q. (a) and (d) correspond to (Ls, sx1) = (1.8a, −0.18a) in Fig. 4(a) with an optical Q of 7.3 × 103. (b) and (e) correspond to the optimized geometry Design 1. (c) and (f) correspond to the optimized geometry Design 2.

Fig. 6
Fig. 6

(a) Top view of the meshed structure used in the finite-element analysis. Fixed boundary conditions are applied outside the PMLs. The top and bottom surfaces are set as free boundaries. (b),(c) Normalized displacement field intensity (log scale) for the differential and common mode of Design 1, respectively. The insets are zoom-ins of the localized beam motion showing the displacements in linear scale. (d),(e) Corresponding von Mises stress field (log scale). (f) Radiating longitudinal elastic wave excited by the differential beam motion (Media 1). (g) Radiating transverse wave excited by the common beam motion (Media 2). In (f) and (g), the displacement fields (linear scale) are overlaid with structural deformation.

Fig. 7
Fig. 7

(a) Transfer function obtained by forced frequency−response analysis. The phase, the transfer intensity, and its Lorentzian fit are plotted in blue dashed line, blue square markers, and red solid line, respectively. (b) Mechanical frequency fm and quality factor Qm versus the beam width for both the differential and common mode. Design 2 with wb = 60 nm is used here.

Fig. 8
Fig. 8

(a) Mechanical frequency fm and quality factor Qm versus the center-slot displacement sc. Design 1 corresponds to the structure with sc = 0. Mode 1 originates from the differential mode, while Mode 2 originates from the common mode. (b)–(e) Zooms of the displacement fields of the nanobeams with sc = 0.25 nm (b,c) and sc = 3.0 nm (d,e).

Tables (1)

Tables Icon

Table 1 Optomechanical properties of the L3-nanobeam cavities. Design 1 and Design 2 refer to the two structures obtained in optical Q optimization for different beam geometries.

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