Abstract

We present the design of a double-slot photonic crystal cavity as an optomechanical device which contains a nanomechanical resonator with an effective mass as small as 6.91 fg. The optical Q-factor is optimized to 2 × 105. Using phononic crystals, the mechanical vibration is confined in a small volume to form a mechanical mode of 4 GHz with a high mechanical Q-factor and a femtogram effective mass. The localized mechanical mode overlaps with the optical field and strengthens the optomechanical coupling with a vacuum optomechanical coupling rate g0/2π exceeding 600 kHz. Considering fabrication imperfections, structures with deviation from ideal design are studied. The symmetry breakage of the structures and the displacement fields makes the mechanical effective masses reduced and close to 4 fg. The devices can be used in ultrasensitive sensing of mass, force and displacement.

© 2015 Optical Society of America

1. Introduction

Optomechanical coupling, the interaction of optical and mechanical degrees of freedom, has led to a variety of applications including quantum ground-state cooling [1–4 ], optical information conversion [5–8 ] and highly sensitive detection [9–12 ]. Nanomechanical resonators have been widely used in ultrasensitive measurements involving mass [13,14 ], force [15,16 ] and displacement [17,18 ]. Because of their small masses, high resonant frequencies and high mechanical Q-factors, nanomechanical resonators usually have high sensitivity especially in resonant mass sensing [19,20 ]. It is desirable to obtain an optomechanical system combining high-Q optical cavities and high-Q nanomechanical resonators with small mechanical mass, and strong optomechanical coupling [21,22 ].

In this paper, we present the design of a double-slot photonic crystal (PhC) cavity which consists of a 1D phononic crystal (PnC) nanobeam and two 2D triangular lattice PhC slabs on both sides. The optical mode is concentrated in the two slots with a high optical Q-factor. And the mechanical vibration is confined in a small volume in the center of the nanobeam by the 1D phononic crystals and overlapped with the optical field well. This strengthens the optomechanical coupling and forms a mechanical mode with a high mechanical Q-factor and a femtogram effective mass. The mechanical effective mass is only 6.91 fg and the vacuum optomechanical coupling rate g0/2π is 654.53 kHz. The influence of fabrication imperfections is analyzed by considering three kinds of imperfect cavities. The symmetry breakage of the structures and the displacement fields makes the effective masses smaller and close to 4 fg.

2. Optical design

When an air-slot is embedded into a W1 line-defect PhC cavity, light will be confined in the slot because of the tangential component of the electric field (E) continuous across the boundary of two different dielectrics [23]. This kind of cavities can provide high optical Q-factors and ultrasmall mode volumes [24,25 ]. The tight optical confinement in the air-slot PhC cavities, which define the nanomechanical resonators, allows better overlap between optical and mechanical modes, enhancing optomechanical coupling greatly [26–28 ]. We begin with the basic double-slot PhC waveguide as shown in Fig. 1(a) which is used to construct the double-slot PhC cavity later.

 figure: Fig. 1

Fig. 1 (a) Geometry of the double-slot PhC waveguide. A unit cell is indicated by dashed white lines. (b) TE-like optical band diagram of (a). Three waveguide modes in the bandgap are shown. The light and dark gray shades represent the continua of the guided and radiant modes respectively. (c) The normalized Ey field of the three waveguide modes at the bandedge (kx = 0.5 × 2π/a) indicated by circles with corresponding colors in (b). (d) The bandedge frequencies of the waveguide modes versus a of unit cells. When a decreases, hy of unit cells increases linearly at the same time. The leftmost and rightmost frequencies in the diagram correspond to the normal and defect unit cells. The horizontal dashed red line shows that the bandedge frequency of Mode C in the defect unit cell is between Mode B and C of the normal unit cell.

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The band structure of the TE-like waveguide modes is calculated by 3D finite-difference time-domain (FDTD) method as shown in Fig. 1(b). The geometric parameters are (a, r, w, hx, hy, s, t) = (444, 120, 400, 271, 236, 60, 220) nm where a is the lattice constant of the 2D PhC slabs and the 1D PnC nanobeam, r is the radius of the air holes, w is the width of the nanobeam between the two PhC slabs, hx and hy are the x- and y-directional widths of the rectangular holes respectively, s is the width of the slots and t is the thickness of the slabs with a refractive index of 3.46 (we consider silicon as their material). In practice, a rectangle hole in design will become a rounded rectangle after the etching process [29], so we consider rounded rectangle holes in the nanobeam with fillet radiuses of 40 nm. The distance between the slots and the nearest holes in the 2D PhC slabs is 0.45×3a. These geometric parameters are chosen to yield a quasi-complete optical bandgap near 1550 nm, providing optical confinement in the waveguide direction. Similar to the single-slot PhC waveguide [25], there are three waveguide modes in the bandgap with the normalized Ey field shown in Fig. 1(c). Although all of the three optical waveguide modes can be used to form optical cavity modes, their interaction with the mechanical vibration is quite different. In contrast to the others, Mode C exhibits better overlap with the mechanical vibration of the nanobeam, leading to a larger optomechanical coupling rate. Therefore, Mode C is used to form the optical cavity mode in our design.

In order to introduce defects and realize light confinement in the x direction, the period along x-direction of the central unit cell is locally modulated to create defect mode in the bandgap [30, 31 ]. The light confinement in the y and z direction is provided by the 2D photonic crystals and total internal reflection of the slabs, respectively [32]. Figure 1(d) shows the bandedge frequencies of the waveguide modes versus a of unit cells. When a decreases, hy of unit cells increases linearly at the same time. Based on the band structure calculation, the period of the central unit cell is decreased to introduce defect unit cell while keeping the bandedge frequency of Mode C [indicated by the horizontal dashed red line in Fig. 1(d)] between Mode B and C of the normal unit cells. The hy of the rectangle hole in the central unit cell is increased at the same time to introduce confinement of the mechanical vibration. The geometric parameters are (a, r, w, hx, hy, s, t)defect = (431, 120, 400, 271, 320, 60, 220) nm and (a, r, w, hx, hy, s, t)normal = (444, 120, 400, 271, 236, 60, 220) nm respectively. Between the defect and normal unit cells, two transitional unit cells whose a and hy vary linearly are used to form a multistep double-heterostructure optical cavity [30] as shown in Fig. 2(a) . These transitional unit cells can reduce optical scattering losses which result from effective mode index mismatching and mode profile mismatching [33]. There are two reasons for using non-terminated air-slots. From the point of optical modes, the confinement of light in the waveguide direction is not due to the band-gap effect [22,34 ] but the mode-gap effect [24,25 ] which can realize a high optical Q-factor for air-slot PhC cavities easily. From the point of mechanical modes, the non-terminated slots block the mechanical energy leakage into the side PhC slabs [35]. 3D FDTD method is used to simulate the optical cavity and optimize its Q-factor. The optimized structure yields an optical mode with a simulated radiation-limited optical Q-factor of 2.37 × 105 at 1551.73 nm. The normalized Ey field of the optical mode is shown in Fig. 2(b).

 figure: Fig. 2

Fig. 2 (a) Geometry of the double-slot PhC multistep double-heterostructure cavity. The defect, transitional and normal unit cells are indicated. The two slots are labeled as “Slot1” and “Slot2.” (b) The normalized Ey field of the optical mode.

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3. Mechanical design

In the optical design, photonic crystal structure provides optical bandgap for optical confinement. Similarly, the periodic rectangular holes in the nanobeam work as 1D phononic crystals [29,35,36 ] with acoustic bandgap to inhibit the propagation of elastic waves. The dissipation of mechanical resonators results from clamping losses, viscous losses, material-induced losses and so on [37]. Among these loss mechanisms, the clamping losses due to the radiation of elastic waves into the substrate through the supporting parts are usually the major loss for mechanical resonators in vacuum. In proposed device, the non-terminated slots block the mechanical energy leakage into the side PhC slabs, and the 1D phononic crystals can suppress the radiation of elastic waves in the waveguide direction. Moreover, the mechanical vibration is confined in a small volume and sufficiently overlaps with the optical mode, enhancing the optomechanical coupling significantly. The effective mass of mechanical mode is small due to its small mode volume, which is very important for applications of ultrasensitive sensing [20].

In this work, we focus on the flexural mechanical mode of the nanobeam, since it usually has a small effective mass and strong optomechanical coupling [29]. The material parameters of silicon for simulation are the Young’s modulus E of 170 GPa and the density ρ of 2329 kg/m3. Figure 3(a) shows the normalized displacement field of the flexural mechanical mode of a normal unit cell simulated using 3D finite-element-method (FEM). The in-plane acoustic band structure of the 1D phononic crystals in the nanobeam is shown in Fig. 3(b). There is a series of acoustic bands which can be classified into two types according to their displacement symmetry [29,36 ]. An acoustic quasi-bandgap for the bands of y- and z-symmetric displacement fields [red bands in Fig. 3(b)] is indicated with gray shade in Fig. 3(b). Near the point of kx = 0, the displacement pattern of the flexural mechanical mode has been shown in Fig. 3(a). Because the hy of the defect unit cell is larger than the normal unit cells, the flexural mechanical mode frequency of the defect unit cell is lower than the normal unit cells and falls into their bandgap as shown in Fig. 3(c). As a consequence, the flexural mechanical mode of the defect unit cell is confined in the center of the nanobeam. The two blue bands across the acoustic quasi-bandgap of the normal unit cells can couple and hybridize with the flexural mechanical mode of the defect unit cell when fabrication imperfections break the structural symmetries. The normalized displacement fields of these two blue bands at the same frequency with the flexural mechanical mode of the defect unit cell (indicated with blue filled circles) are shown to the right of the band diagram in Fig. 3(b).

 figure: Fig. 3

Fig. 3 (a) The normalized displacement field of the flexural mechanical mode at kx = 0 [indicated by a red circle in (b)] for a normal unit cell. (b) In-plane acoustic band diagram of the 1D phononic crystals in the nanobeam. Modes of y- and z-symmetries (red bands), and modes of other symmetries (blue bands) are shown. The gray shade represents the acoustic quasi-complete bandgap for the red bands. The normalized displacement fields of the two blue bands across the bandgap at the same frequency with the flexural mechanical mode of the defect unit cell (indicated with blue filled circles) are shown to the right of the band diagram. (c) The frequency fm of the flexural mechanical mode at kx = 0 and the bandgap versus a and hy of unit cells. The leftmost and rightmost frequencies in the diagram correspond to the normal and defect unit cells. The horizontal dashed red line shows that the frequency at kx = 0 of the flexural mechanical mode in the defect unit cell falls in the bandgap of the normal unit cells.

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The normalized displacement field Q(x, y, z) of the localized flexural mechanical mode is simulated and shown in Fig. 4(a) . In the simulation, both ends of the nanobeam are clamped on the substrate and mechanical PMLs surround the substrate to absorb the elastic waves leaking from the localized mechanical mode. The clamping-loss-limited mechanical Q-factor is calculated with the method in [22]. Since the frequency of the acoustic bandgap varies with hy of unit cells, there is a strong dependence of the mechanical Q-factor on the hy of the normal unit cells as shown in Fig. 4(b). When the hy of the normal unit cells is 236 nm, the simulated clamping-loss-limited mechanical Q-factor is the highest of 3.70 × 107 at 4.07 GHz. As a part of the mechanical mode penetrates into the transitional and normal unit cells, the increase of hy of the transitional and normal unit cells will decrease the stiffness of the mechanical mode, leading to the decrease of the mechanical frequency. In order to obtain a mechanical resonator with small effective mass, the rails of the central defect unit cell should be as narrow as possible. However, it is limited by the fabrication capability. We choose hy = 360 nm for the central defect unit cell, corresponding to 40-nm-width rails. The effective mass is simulated to be meff = 6.91 fg with the definition of meff=dVρ|Q|2/max(|Q|2). In the optical design, only two transitional unit cells and linearly tapered variations are used between the defect and normal unit cells. This makes the mechanical mode strongly confined in a small volume to obtain an ultrasmall effective mass. Although the optical scattering losses resulting from effective mode index mismatching and mode profile mismatching are reduced due to the transitional parts, they are still the main losses of the optical cavity. When more transitional unit cells and quadratically tapered variations are used, the optical mode yields a Gaussian-type field attenuation profile [29]. This will improve the optical Q-factor further. However more transitional unit cells will increase the mode volume of the mechanical mode at the same time, leading to a larger effective mass.

 figure: Fig. 4

Fig. 4 (a) The normalized displacement field of the flexural mechanical mode confined in the center of the nanobeam. Close-up view of the flexural mechanical mode is also shown. (b) The simulated clamping-loss-limited mechanical Q-factor Qm and frequency fm as a function of the hy of the normal unit cells.

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4. Optomechanical coupling and influence of structural asymmetry

When the optical and mechanical modes spatially co-localized in the center of the device, the coupling between them happens. The coupling strength is characterized by the dispersive optomechanical coupling rate which means the resonant wavelength shift of the optical mode versus the displacement of the mechanical mode, noted as gom = dωo/dx, where ωo is the optical angular frequency and x is the amplitude of the mechanical displacement [37]. The coupling strength between a photon and a phonon can be characterized by the vacuum optomechanical coupling rate with the definition of g0 = gomxzpf, where xzpf=/2meffωm is zero-point fluctuation of the mechanical mode with the mechanical angular frequency ωm = 2πfm [37]. The g0/2π of the optimized structure is simulated to be 654.53 kHz. In other to enhance optomechanical coupling, the mechanical mode should be sufficiently overlapped with the optical field. Just like the designs in [27] and [36], the vacuum optomechanical coupling rates are simulated to be 800 and 770 kHz respectively. However limited by the optical diffraction, the cavity volumes cannot be reduced further and so are the effective masses. Their effective masses are 20 pg and 127 fg respectively. Another design aiming at ultrasmall effective masses is embedding double nanomechanical beams in a L3 PhC cavity [21]. It achieves a g0/2π of 200 kHz and a meff of 25 fg. However, the optical Q-factor is simulated to be only 1.95 × 104 due to strong optical scattering losses. The design presented here yields a g0/2π of 650 kHz and an optical Q-factor larger than 2 × 105. The effective mass is only 6.91 fg, smaller than one third of the value for the reported design of nanomechanical beams in a L3 PhC cavity.

In the above design, we assume that the structure is symmetric across the x-z-plane, which means the two slots are exactly the same and have the same distance to the center. As the width of the slots is only a few tens of nanometers, small deviation from the design will change the performance greatly. In fabrication process, it is hard to obtain two identical slots due to unavoidable fabrication imperfections. It is necessary to study the effect of fabrication imperfections. Three kinds of imperfect cavities are considered: enlarging Slot2’s width by 5 nm and 10 nm (ESW5nm and ESW10nm), shifting Slot2’s position by 5 nm and −5 nm along y direction (SSP5nm and SSP-5nm), and shifting the rectangular hole of the central defect unit cell by −2.5 nm along y direction (SRP-2.5nm). Except of these variations, the other structural parameters maintain unchanged. Figure 5 shows the schematics of these cavities with the widths of the two slots and the two rails of the central defect unit cell. Table 1 shows the optical and mechanical properties of the ideal design and the imperfect cavities. Figure 6 shows the displacement fields of their mechanical modes. For the cavities with larger Slot2’s width, the resonant wavelength of the optical mode shifts to blueside since the effective mode index of the waveguide becomes lower [24]. The optical Q-factor decreases compared with the ideal design. Moreover, the larger slot width will make the corresponding rails narrower, leading to symmetry breakage in structure. Therefore, the displacement field of the mechanical mode is no longer symmetric as shown in Figs. 6(b) and 6(c). Asymmetric structure allows the localized mechanical mode to couple and hybridize with the two blue bands across the acoustic quasi-bandgap of the normal unit cells [indicated with blue filled circles in Fig. 3(b)]. The clamping-loss-limited mechanical Q-factor decreases due to the radiation of elastic waves of the localized mechanical mode into the substrate through these two blue bands. In our design, the high mechanical Q-factor is due to the confinement of elastic waves in the phononic crystals. It is different from the destructive interference of elastic waves [21,22,38 ], which significantly depends on the symmetric structures. Even though the width difference of the two slots is as large as 10 nm (the width difference of the two rails in a unit cell is 5 nm), the clamping losses can be suppressed effectively and a simulated clamping-loss-limited mechanical Q-factor larger than 105 is obtained. As the symmetry breakage of the displacement field and the smaller width of the rails on one side, the effective mass of the mechanical mode becomes smaller, helpful for ultrasensitive sensing. For the cavity with Slot2 shifted by 5 nm along y direction, the rails on the same side become narrower and the resulting optical and mechanical properties are similar to the ESW cavities. But the cavity with Slot2 shifted by −5 nm has wider rails, and the reduction of the effective mass due to the symmetry breakage of the displacement field is counteracted. The properties of the SRP-2.5nm cavity are similar to the ESW cavities. In our design, the deviation from symmetric structure due to fabrication imperfections doesn’t degenerate the optical and mechanical properties to an unacceptable degree. The single-photon cooperativities, a figure of merit of optomechanical devices, larger than 10−3 can still be obtained [37]. On the contrary, the mechanical effective mass even benefits from the symmetry breakage and decreases to around 4 fg. Therefore, it is notable that the proposed device structure has large tolerance of fabrication imperfections to some extent.

 figure: Fig. 5

Fig. 5 Schematics of the ideal design and imperfect cavities. The widths of the two slots and the two rails of the central defect unit cell are shown with red and blue arrows respectively. The variations in structures of the imperfect cavities are exaggerated for clarity.

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Tables Icon

Table 1. Optical and mechanical properties of the ideal design and imperfect cavities

 figure: Fig. 6

Fig. 6 The normalized displacement fields of the flexural mechanical modes of the ideal design and imperfect cavities. (a) Ideal design. (b) ESW5nm. (c) ESW10nm. (d) SSP5nm. (e) SSP-5nm. (f) SRP-2.5nm. The corresponding effective masses are also shown.

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4. Conclusions

We have designed and numerically studied a double-slot PhC optomechanical cavity which consists of a 1D PnC nanobeam and two 2D triangular lattice PhC slabs. The optical characteristic is studied by 3D FDTD method and an optimized optical mode with a radiation-limited Q-factor of 2.37 × 105 near 1550 nm is obtained. 3D FEM is used to simulate the flexural mechanical mode of the nanobeam. Through suppressing the propagation of elastic waves into the substrate by the phononic crystals, the structure yields a clamping-loss-limited mechanical Q-factor beyond 107 at 4 GHz. The phononic crystals confine the mechanical vibration in a small volume in the center of the nanobeam, producing a good optomechanical overlap and a small effective mass. The effective mass of the flexural mechanical mode is only 6.91 fg. Considering the fabrication imperfections, three kinds of imperfect cavities are studied. Asymmetric displacement fields due to the symmetry breakage in structures reduce the effective masses to around 4 fg. These on-chip integrated optomechanical devices combining high-Q optical cavities and low damping high frequency nanomechanical resonators with effective masses of a few femtograms are promising in optomechanical applications and ultrasensitive sensing.

Acknowledgments

This work was partly supported by the Major State Basic Research Development Program of China (Grant No. 2013CB933303 and 2013CB632104), the National Natural Science Foundation of China (Grant No. 61335002 and 61177049), and the Program for New Century Excellent Talents in Ministry of Education of China (Grant No. NCET-12-0218).

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References

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  1. 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]
  2. A. Schliesser, P. Del’Haye, N. Nooshi, K. J. Vahala, and T. J. Kippenberg, “Radiation pressure cooling of a micromechanical oscillator using dynamical backaction,” Phys. Rev. Lett. 97(24), 243905 (2006).
    [Crossref] [PubMed]
  3. 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]
  4. Y. Park and H. Wang, “Resolved-sideband and cryogenic cooling of an optomechanical resonator,” Nat. Phys. 5(7), 489–493 (2009).
    [Crossref]
  5. R. W. Andrews, R. W. Peterson, T. P. Purdy, K. Cicak, R. W. Simmonds, C. A. Regal, and K. W. Lehnert, “Bidirectional and efficient conversion between microwave and optical light,” Nat. Phys. 10(4), 321–326 (2014).
    [Crossref]
  6. Y. Wang and A. A. Clerk, “Using dark modes for high-fidelity optomechanical quantum state transfer,” New J. Phys. 14(10), 105010 (2012).
    [Crossref]
  7. J. T. Hill, A. H. Safavi-Naeini, J. Chan, and O. Painter, “Coherent optical wavelength conversion via cavity optomechanics,” Nat. Commun. 3, 1196 (2012).
    [Crossref] [PubMed]
  8. C. Dong, V. Fiore, M. C. Kuzyk, L. Tian, and H. Wang, “Optical wavelength conversion via optomechanical coupling in a silica resonator,” Ann. Phys. 527(1–2), 100–106 (2015).
    [Crossref]
  9. A. H. Safavi-Naeini, J. Chan, J. T. Hill, T. P. M. Alegre, A. Krause, and O. Painter, “Observation of quantum motion of a nanomechanical resonator,” Phys. Rev. Lett. 108(3), 033602 (2012).
    [Crossref] [PubMed]
  10. 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 below the standard quantum limit,” Phys. Rev. A 82(6), 061804 (2010).
    [Crossref]
  11. A. G. Krause, M. Winger, T. D. Blasius, Q. Lin, and O. Painter, “A high-resolution microchip optomechanical accelerometer,” Nat. Photonics 6(11), 768–772 (2012).
    [Crossref]
  12. S. Forstner, E. Sheridan, J. Knittel, C. L. Humphreys, G. A. Brawley, H. Rubinsztein-Dunlop, and W. P. Bowen, “Ultrasensitive optomechanical magnetometry,” Adv. Mater. 26(36), 6348–6353 (2014).
    [Crossref] [PubMed]
  13. Y. T. Yang, C. Callegari, X. L. Feng, K. L. Ekinci, and M. L. Roukes, “Zeptogram-scale nanomechanical mass sensing,” Nano Lett. 6(4), 583–586 (2006).
    [Crossref] [PubMed]
  14. H. Y. Chiu, P. Hung, H. W. C. Postma, and M. Bockrath, “Atomic-scale mass sensing using carbon nanotube resonators,” Nano Lett. 8(12), 4342–4346 (2008).
    [Crossref] [PubMed]
  15. E. Gavartin, P. Verlot, and T. J. Kippenberg, “A hybrid on-chip optomechanical transducer for ultrasensitive force measurements,” Nat. Nanotechnol. 7(8), 509–514 (2012).
    [Crossref] [PubMed]
  16. J. Moser, J. Güttinger, A. Eichler, M. J. Esplandiu, D. E. Liu, M. I. Dykman, and A. Bachtold, “Ultrasensitive force detection with a nanotube mechanical resonator,” Nat. Nanotechnol. 8(7), 493–496 (2013).
    [Crossref] [PubMed]
  17. J. D. Teufel, T. Donner, M. A. Castellanos-Beltran, J. W. Harlow, and K. W. Lehnert, “Nanomechanical motion measured with an imprecision below that at the standard quantum limit,” Nat. Nanotechnol. 4(12), 820–823 (2009).
    [Crossref] [PubMed]
  18. O. Basarir, S. Bramhavar, and K. L. Ekinci, “Motion transduction in nanoelectromechanical systems (NEMS) arrays using near-field optomechanical coupling,” Nano Lett. 12(2), 534–539 (2012).
    [Crossref] [PubMed]
  19. 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]
  20. K. L. Ekinci, Y. T. Yang, and M. L. Roukes, “Ultimate limits to inertial mass sensing based upon nanoelectromechanical systems,” J. Appl. Phys. 95(5), 2682 (2004).
    [Crossref]
  21. 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).
    [Crossref] [PubMed]
  22. J. Zheng, X. Sun, Y. Li, M. Poot, A. Dadgar, N. N. Shi, W. H. P. Pernice, H. X. Tang, and C. W. Wong, “Femtogram dispersive L3-nanobeam optomechanical cavities: design and experimental comparison,” Opt. Express 20(24), 26486–26498 (2012).
    [Crossref] [PubMed]
  23. V. R. Almeida, Q. Xu, C. A. Barrios, and M. Lipson, “Guiding and confining light in void nanostructure,” Opt. Lett. 29(11), 1209–1211 (2004).
    [Crossref] [PubMed]
  24. T. Yamamoto, M. Notomi, H. Taniyama, E. Kuramochi, Y. Yoshikawa, Y. Torii, and T. Kuga, “Design of a high-Q air-slot cavity based on a width-modulated line-defect in a photonic crystal slab,” Opt. Express 16(18), 13809–13817 (2008).
    [Crossref] [PubMed]
  25. J. Gao, J. F. McMillan, M. 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]
  26. J. Chan, M. Eichenfield, R. Camacho, and O. Painter, “Optical and mechanical design of a “zipper” photonic crystal optomechanical cavity,” Opt. Express 17(5), 3802–3817 (2009).
    [Crossref] [PubMed]
  27. 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]
  28. 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]
  29. M. Eichenfield, J. Chan, R. M. Camacho, K. J. Vahala, and O. Painter, “Optomechanical crystals,” Nature 462(7269), 78–82 (2009).
    [Crossref] [PubMed]
  30. B. Song, S. Noda, T. Asano, and Y. Akahane, “Ultra-high-Q photonic double-heterostructure nanocavity,” Nat. Mater. 4(3), 207–210 (2005).
    [Crossref]
  31. E. Kuramochi, M. Notomi, S. Mitsugi, A. Shinya, T. Tanabe, and T. Watanabe, “Ultrahigh-Q photonic crystal nanocavities realized by the local width modulation of a line defect,” Appl. Phys. Lett. 88(4), 041112 (2006).
    [Crossref]
  32. Y. Akahane, T. Asano, B. S. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425(6961), 944–947 (2003).
    [Crossref] [PubMed]
  33. P. Lalanne, C. Sauvan, and J. P. Hugonin, “Photon confinement in photonic crystal nanocavities,” Laser Photonics Rev. 2(6), 514–526 (2008).
    [Crossref]
  34. C. Schriever, C. Bohley, and J. Schilling, “Designing the quality factor of infiltrated photonic wire slot microcavities,” Opt. Express 18(24), 25217–25224 (2010).
    [Crossref] [PubMed]
  35. J. Gomis-Bresco, D. Navarro-Urrios, M. Oudich, S. El-Jallal, A. Griol, D. Puerto, E. Chavez, Y. Pennec, B. Djafari-Rouhani, F. Alzina, A. Martínez, and C. M. S. Torres, “A one-dimensional optomechanical crystal with a complete phononic band gap,” Nat. Commun. 5, 4452 (2014).
    [Crossref] [PubMed]
  36. J. Chan, A. H. Safavi-Naeini, J. T. Hill, S. Meenehan, and O. Painter, “Optimized optomechanical crystal cavity with acoustic radiation shield,” Appl. Phys. Lett. 101(8), 081115 (2012).
    [Crossref]
  37. M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt, “Cavity optomechanics,” Rev. Mod. Phys. 86(4), 1391–1452 (2014).
    [Crossref]
  38. M. Zhang, G. Luiz, S. Shah, G. Wiederhecker, and M. Lipson, “Eliminating anchor loss in optomechanical resonators using elastic wave interference,” Appl. Phys. Lett. 105(5), 051904 (2014).
    [Crossref]

2015 (1)

C. Dong, V. Fiore, M. C. Kuzyk, L. Tian, and H. Wang, “Optical wavelength conversion via optomechanical coupling in a silica resonator,” Ann. Phys. 527(1–2), 100–106 (2015).
[Crossref]

2014 (5)

R. W. Andrews, R. W. Peterson, T. P. Purdy, K. Cicak, R. W. Simmonds, C. A. Regal, and K. W. Lehnert, “Bidirectional and efficient conversion between microwave and optical light,” Nat. Phys. 10(4), 321–326 (2014).
[Crossref]

S. Forstner, E. Sheridan, J. Knittel, C. L. Humphreys, G. A. Brawley, H. Rubinsztein-Dunlop, and W. P. Bowen, “Ultrasensitive optomechanical magnetometry,” Adv. Mater. 26(36), 6348–6353 (2014).
[Crossref] [PubMed]

J. Gomis-Bresco, D. Navarro-Urrios, M. Oudich, S. El-Jallal, A. Griol, D. Puerto, E. Chavez, Y. Pennec, B. Djafari-Rouhani, F. Alzina, A. Martínez, and C. M. S. Torres, “A one-dimensional optomechanical crystal with a complete phononic band gap,” Nat. Commun. 5, 4452 (2014).
[Crossref] [PubMed]

M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt, “Cavity optomechanics,” Rev. Mod. Phys. 86(4), 1391–1452 (2014).
[Crossref]

M. Zhang, G. Luiz, S. Shah, G. Wiederhecker, and M. Lipson, “Eliminating anchor loss in optomechanical resonators using elastic wave interference,” Appl. Phys. Lett. 105(5), 051904 (2014).
[Crossref]

2013 (1)

J. Moser, J. Güttinger, A. Eichler, M. J. Esplandiu, D. E. Liu, M. I. Dykman, and A. Bachtold, “Ultrasensitive force detection with a nanotube mechanical resonator,” Nat. Nanotechnol. 8(7), 493–496 (2013).
[Crossref] [PubMed]

2012 (9)

O. Basarir, S. Bramhavar, and K. L. Ekinci, “Motion transduction in nanoelectromechanical systems (NEMS) arrays using near-field optomechanical coupling,” Nano Lett. 12(2), 534–539 (2012).
[Crossref] [PubMed]

A. G. Krause, M. Winger, T. D. Blasius, Q. Lin, and O. Painter, “A high-resolution microchip optomechanical accelerometer,” Nat. Photonics 6(11), 768–772 (2012).
[Crossref]

Y. Wang and A. A. Clerk, “Using dark modes for high-fidelity optomechanical quantum state transfer,” New J. Phys. 14(10), 105010 (2012).
[Crossref]

J. T. Hill, A. H. Safavi-Naeini, J. Chan, and O. Painter, “Coherent optical wavelength conversion via cavity optomechanics,” Nat. Commun. 3, 1196 (2012).
[Crossref] [PubMed]

A. H. Safavi-Naeini, J. Chan, J. T. Hill, T. P. M. Alegre, A. Krause, and O. Painter, “Observation of quantum motion of a nanomechanical resonator,” Phys. Rev. Lett. 108(3), 033602 (2012).
[Crossref] [PubMed]

J. Chan, A. H. Safavi-Naeini, J. T. Hill, S. Meenehan, and O. Painter, “Optimized optomechanical crystal cavity with acoustic radiation shield,” Appl. Phys. Lett. 101(8), 081115 (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).
[Crossref] [PubMed]

J. Zheng, X. Sun, Y. Li, M. Poot, A. Dadgar, N. N. Shi, W. H. P. Pernice, H. X. Tang, and C. W. Wong, “Femtogram dispersive L3-nanobeam optomechanical cavities: design and experimental comparison,” Opt. Express 20(24), 26486–26498 (2012).
[Crossref] [PubMed]

E. Gavartin, P. Verlot, and T. J. Kippenberg, “A hybrid on-chip optomechanical transducer for ultrasensitive force measurements,” Nat. Nanotechnol. 7(8), 509–514 (2012).
[Crossref] [PubMed]

2011 (1)

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]

2010 (5)

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 below the standard quantum limit,” Phys. Rev. A 82(6), 061804 (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]

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]

C. Schriever, C. Bohley, and J. Schilling, “Designing the quality factor of infiltrated photonic wire slot microcavities,” Opt. Express 18(24), 25217–25224 (2010).
[Crossref] [PubMed]

J. Gao, J. F. McMillan, M. 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]

2009 (4)

J. Chan, M. Eichenfield, R. Camacho, and O. Painter, “Optical and mechanical design of a “zipper” photonic crystal optomechanical cavity,” Opt. Express 17(5), 3802–3817 (2009).
[Crossref] [PubMed]

M. Eichenfield, J. Chan, R. M. Camacho, K. J. Vahala, and O. Painter, “Optomechanical crystals,” Nature 462(7269), 78–82 (2009).
[Crossref] [PubMed]

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

J. D. Teufel, T. Donner, M. A. Castellanos-Beltran, J. W. Harlow, and K. W. Lehnert, “Nanomechanical motion measured with an imprecision below that at the standard quantum limit,” Nat. Nanotechnol. 4(12), 820–823 (2009).
[Crossref] [PubMed]

2008 (4)

H. Y. Chiu, P. Hung, H. W. C. Postma, and M. Bockrath, “Atomic-scale mass sensing using carbon nanotube resonators,” Nano Lett. 8(12), 4342–4346 (2008).
[Crossref] [PubMed]

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. Yamamoto, M. Notomi, H. Taniyama, E. Kuramochi, Y. Yoshikawa, Y. Torii, and T. Kuga, “Design of a high-Q air-slot cavity based on a width-modulated line-defect in a photonic crystal slab,” Opt. Express 16(18), 13809–13817 (2008).
[Crossref] [PubMed]

P. Lalanne, C. Sauvan, and J. P. Hugonin, “Photon confinement in photonic crystal nanocavities,” Laser Photonics Rev. 2(6), 514–526 (2008).
[Crossref]

2007 (1)

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 (3)

Y. T. Yang, C. Callegari, X. L. Feng, K. L. Ekinci, and M. L. Roukes, “Zeptogram-scale nanomechanical mass sensing,” Nano Lett. 6(4), 583–586 (2006).
[Crossref] [PubMed]

A. Schliesser, P. Del’Haye, N. Nooshi, K. J. Vahala, and T. J. Kippenberg, “Radiation pressure cooling of a micromechanical oscillator using dynamical backaction,” Phys. Rev. Lett. 97(24), 243905 (2006).
[Crossref] [PubMed]

E. Kuramochi, M. Notomi, S. Mitsugi, A. Shinya, T. Tanabe, and T. Watanabe, “Ultrahigh-Q photonic crystal nanocavities realized by the local width modulation of a line defect,” Appl. Phys. Lett. 88(4), 041112 (2006).
[Crossref]

2005 (1)

B. Song, S. Noda, T. Asano, and Y. Akahane, “Ultra-high-Q photonic double-heterostructure nanocavity,” Nat. Mater. 4(3), 207–210 (2005).
[Crossref]

2004 (2)

V. R. Almeida, Q. Xu, C. A. Barrios, and M. Lipson, “Guiding and confining light in void nanostructure,” Opt. Lett. 29(11), 1209–1211 (2004).
[Crossref] [PubMed]

K. L. Ekinci, Y. T. Yang, and M. L. Roukes, “Ultimate limits to inertial mass sensing based upon nanoelectromechanical systems,” J. Appl. Phys. 95(5), 2682 (2004).
[Crossref]

2003 (1)

Y. Akahane, T. Asano, B. S. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425(6961), 944–947 (2003).
[Crossref] [PubMed]

Akahane, Y.

B. Song, S. Noda, T. Asano, and Y. Akahane, “Ultra-high-Q photonic double-heterostructure nanocavity,” Nat. Mater. 4(3), 207–210 (2005).
[Crossref]

Y. Akahane, T. Asano, B. S. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425(6961), 944–947 (2003).
[Crossref] [PubMed]

Alegre, T. P. M.

A. H. Safavi-Naeini, J. Chan, J. T. Hill, T. P. M. Alegre, A. Krause, and O. Painter, “Observation of quantum motion of a nanomechanical resonator,” Phys. Rev. Lett. 108(3), 033602 (2012).
[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]

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]

Almeida, V. R.

Alzina, F.

J. Gomis-Bresco, D. Navarro-Urrios, M. Oudich, S. El-Jallal, A. Griol, D. Puerto, E. Chavez, Y. Pennec, B. Djafari-Rouhani, F. Alzina, A. Martínez, and C. M. S. Torres, “A one-dimensional optomechanical crystal with a complete phononic band gap,” Nat. Commun. 5, 4452 (2014).
[Crossref] [PubMed]

Andrews, R. W.

R. W. Andrews, R. W. Peterson, T. P. Purdy, K. Cicak, R. W. Simmonds, C. A. Regal, and K. W. Lehnert, “Bidirectional and efficient conversion between microwave and optical light,” Nat. Phys. 10(4), 321–326 (2014).
[Crossref]

Anetsberger, G.

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 below the standard quantum limit,” Phys. Rev. A 82(6), 061804 (2010).
[Crossref]

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]

Aras, M. S.

Arcizet, O.

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 below the standard quantum limit,” Phys. Rev. A 82(6), 061804 (2010).
[Crossref]

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]

Asano, T.

B. Song, S. Noda, T. Asano, and Y. Akahane, “Ultra-high-Q photonic double-heterostructure nanocavity,” Nat. Mater. 4(3), 207–210 (2005).
[Crossref]

Y. Akahane, T. Asano, B. S. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425(6961), 944–947 (2003).
[Crossref] [PubMed]

Aspelmeyer, M.

M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt, “Cavity optomechanics,” Rev. Mod. Phys. 86(4), 1391–1452 (2014).
[Crossref]

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]

Assefa, S.

J. Gao, J. F. McMillan, M. 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]

Bachtold, A.

J. Moser, J. Güttinger, A. Eichler, M. J. Esplandiu, D. E. Liu, M. I. Dykman, and A. Bachtold, “Ultrasensitive force detection with a nanotube mechanical resonator,” Nat. Nanotechnol. 8(7), 493–496 (2013).
[Crossref] [PubMed]

Barrios, C. A.

Basarir, O.

O. Basarir, S. Bramhavar, and K. L. Ekinci, “Motion transduction in nanoelectromechanical systems (NEMS) arrays using near-field optomechanical coupling,” Nano Lett. 12(2), 534–539 (2012).
[Crossref] [PubMed]

Blasius, T. D.

A. G. Krause, M. Winger, T. D. Blasius, Q. Lin, and O. Painter, “A high-resolution microchip optomechanical accelerometer,” Nat. Photonics 6(11), 768–772 (2012).
[Crossref]

Bockrath, M.

H. Y. Chiu, P. Hung, H. W. C. Postma, and M. Bockrath, “Atomic-scale mass sensing using carbon nanotube resonators,” Nano Lett. 8(12), 4342–4346 (2008).
[Crossref] [PubMed]

Bohley, C.

Bowen, W. P.

S. Forstner, E. Sheridan, J. Knittel, C. L. Humphreys, G. A. Brawley, H. Rubinsztein-Dunlop, and W. P. Bowen, “Ultrasensitive optomechanical magnetometry,” Adv. Mater. 26(36), 6348–6353 (2014).
[Crossref] [PubMed]

Bramhavar, S.

O. Basarir, S. Bramhavar, and K. L. Ekinci, “Motion transduction in nanoelectromechanical systems (NEMS) arrays using near-field optomechanical coupling,” Nano Lett. 12(2), 534–539 (2012).
[Crossref] [PubMed]

Brawley, G. A.

S. Forstner, E. Sheridan, J. Knittel, C. L. Humphreys, G. A. Brawley, H. Rubinsztein-Dunlop, and W. P. Bowen, “Ultrasensitive optomechanical magnetometry,” Adv. Mater. 26(36), 6348–6353 (2014).
[Crossref] [PubMed]

Callegari, C.

Y. T. Yang, C. Callegari, X. L. Feng, K. L. Ekinci, and M. L. Roukes, “Zeptogram-scale nanomechanical mass sensing,” Nano Lett. 6(4), 583–586 (2006).
[Crossref] [PubMed]

Camacho, R.

Camacho, R. M.

M. Eichenfield, J. Chan, R. M. Camacho, K. J. Vahala, and O. Painter, “Optomechanical crystals,” Nature 462(7269), 78–82 (2009).
[Crossref] [PubMed]

Castellanos-Beltran, M. A.

J. D. Teufel, T. Donner, M. A. Castellanos-Beltran, J. W. Harlow, and K. W. Lehnert, “Nanomechanical motion measured with an imprecision below that at the standard quantum limit,” Nat. Nanotechnol. 4(12), 820–823 (2009).
[Crossref] [PubMed]

Chan, J.

A. H. Safavi-Naeini, J. Chan, J. T. Hill, T. P. M. Alegre, A. Krause, and O. Painter, “Observation of quantum motion of a nanomechanical resonator,” Phys. Rev. Lett. 108(3), 033602 (2012).
[Crossref] [PubMed]

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Purdy, T. P.

R. W. Andrews, R. W. Peterson, T. P. Purdy, K. Cicak, R. W. Simmonds, C. A. Regal, and K. W. Lehnert, “Bidirectional and efficient conversion between microwave and optical light,” Nat. Phys. 10(4), 321–326 (2014).
[Crossref]

Regal, C. A.

R. W. Andrews, R. W. Peterson, T. P. Purdy, K. Cicak, R. W. Simmonds, C. A. Regal, and K. W. Lehnert, “Bidirectional and efficient conversion between microwave and optical light,” Nat. Phys. 10(4), 321–326 (2014).
[Crossref]

Rivière, R.

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]

Roukes, M. L.

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]

Y. T. Yang, C. Callegari, X. L. Feng, K. L. Ekinci, and M. L. Roukes, “Zeptogram-scale nanomechanical mass sensing,” Nano Lett. 6(4), 583–586 (2006).
[Crossref] [PubMed]

K. L. Ekinci, Y. T. Yang, and M. L. Roukes, “Ultimate limits to inertial mass sensing based upon nanoelectromechanical systems,” J. Appl. Phys. 95(5), 2682 (2004).
[Crossref]

Rubinsztein-Dunlop, H.

S. Forstner, E. Sheridan, J. Knittel, C. L. Humphreys, G. A. Brawley, H. Rubinsztein-Dunlop, and W. P. Bowen, “Ultrasensitive optomechanical magnetometry,” Adv. Mater. 26(36), 6348–6353 (2014).
[Crossref] [PubMed]

Safavi-Naeini, A. H.

A. H. Safavi-Naeini, J. Chan, J. T. Hill, T. P. M. Alegre, A. Krause, and O. Painter, “Observation of quantum motion of a nanomechanical resonator,” Phys. Rev. Lett. 108(3), 033602 (2012).
[Crossref] [PubMed]

J. T. Hill, A. H. Safavi-Naeini, J. Chan, and O. Painter, “Coherent optical wavelength conversion via cavity optomechanics,” Nat. Commun. 3, 1196 (2012).
[Crossref] [PubMed]

J. Chan, A. H. Safavi-Naeini, J. T. Hill, S. Meenehan, and O. Painter, “Optimized optomechanical crystal cavity with acoustic radiation shield,” Appl. Phys. Lett. 101(8), 081115 (2012).
[Crossref]

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]

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]

Sauvan, C.

P. Lalanne, C. Sauvan, and J. P. Hugonin, “Photon confinement in photonic crystal nanocavities,” Laser Photonics Rev. 2(6), 514–526 (2008).
[Crossref]

Schilling, J.

Schliesser, A.

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]

A. Schliesser, P. Del’Haye, N. Nooshi, K. J. Vahala, and T. J. Kippenberg, “Radiation pressure cooling of a micromechanical oscillator using dynamical backaction,” Phys. Rev. Lett. 97(24), 243905 (2006).
[Crossref] [PubMed]

Schriever, C.

Shah, S.

M. Zhang, G. Luiz, S. Shah, G. Wiederhecker, and M. Lipson, “Eliminating anchor loss in optomechanical resonators using elastic wave interference,” Appl. Phys. Lett. 105(5), 051904 (2014).
[Crossref]

Sheridan, E.

S. Forstner, E. Sheridan, J. Knittel, C. L. Humphreys, G. A. Brawley, H. Rubinsztein-Dunlop, and W. P. Bowen, “Ultrasensitive optomechanical magnetometry,” Adv. Mater. 26(36), 6348–6353 (2014).
[Crossref] [PubMed]

Shi, N. N.

Shinya, A.

E. Kuramochi, M. Notomi, S. Mitsugi, A. Shinya, T. Tanabe, and T. Watanabe, “Ultrahigh-Q photonic crystal nanocavities realized by the local width modulation of a line defect,” Appl. Phys. Lett. 88(4), 041112 (2006).
[Crossref]

Shu, J.

Simmonds, R. W.

R. W. Andrews, R. W. Peterson, T. P. Purdy, K. Cicak, R. W. Simmonds, C. A. Regal, and K. W. Lehnert, “Bidirectional and efficient conversion between microwave and optical light,” Nat. Phys. 10(4), 321–326 (2014).
[Crossref]

Song, B.

B. Song, S. Noda, T. Asano, and Y. Akahane, “Ultra-high-Q photonic double-heterostructure nanocavity,” Nat. Mater. 4(3), 207–210 (2005).
[Crossref]

Song, B. S.

Y. Akahane, T. Asano, B. S. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425(6961), 944–947 (2003).
[Crossref] [PubMed]

Sun, X.

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).
[Crossref] [PubMed]

J. Zheng, X. Sun, Y. Li, M. Poot, A. Dadgar, N. N. Shi, W. H. P. Pernice, H. X. Tang, and C. W. Wong, “Femtogram dispersive L3-nanobeam optomechanical cavities: design and experimental comparison,” Opt. Express 20(24), 26486–26498 (2012).
[Crossref] [PubMed]

Tanabe, T.

E. Kuramochi, M. Notomi, S. Mitsugi, A. Shinya, T. Tanabe, and T. Watanabe, “Ultrahigh-Q photonic crystal nanocavities realized by the local width modulation of a line defect,” Appl. Phys. Lett. 88(4), 041112 (2006).
[Crossref]

Tang, H. X.

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).
[Crossref] [PubMed]

J. Zheng, X. Sun, Y. Li, M. Poot, A. Dadgar, N. N. Shi, W. H. P. Pernice, H. X. Tang, and C. W. Wong, “Femtogram dispersive L3-nanobeam optomechanical cavities: design and experimental comparison,” Opt. Express 20(24), 26486–26498 (2012).
[Crossref] [PubMed]

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]

Taniyama, H.

Teufel, J. D.

J. D. Teufel, T. Donner, M. A. Castellanos-Beltran, J. W. Harlow, and K. W. Lehnert, “Nanomechanical motion measured with an imprecision below that at the standard quantum limit,” Nat. Nanotechnol. 4(12), 820–823 (2009).
[Crossref] [PubMed]

Tian, L.

C. Dong, V. Fiore, M. C. Kuzyk, L. Tian, and H. Wang, “Optical wavelength conversion via optomechanical coupling in a silica resonator,” Ann. Phys. 527(1–2), 100–106 (2015).
[Crossref]

Torii, Y.

Torres, C. M. S.

J. Gomis-Bresco, D. Navarro-Urrios, M. Oudich, S. El-Jallal, A. Griol, D. Puerto, E. Chavez, Y. Pennec, B. Djafari-Rouhani, F. Alzina, A. Martínez, and C. M. S. Torres, “A one-dimensional optomechanical crystal with a complete phononic band gap,” Nat. Commun. 5, 4452 (2014).
[Crossref] [PubMed]

Unterreithmeier, Q. P.

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 below the standard quantum limit,” Phys. Rev. A 82(6), 061804 (2010).
[Crossref]

Vahala, K. J.

M. Eichenfield, J. Chan, R. M. Camacho, K. J. Vahala, and O. Painter, “Optomechanical crystals,” Nature 462(7269), 78–82 (2009).
[Crossref] [PubMed]

A. Schliesser, P. Del’Haye, N. Nooshi, K. J. Vahala, and T. J. Kippenberg, “Radiation pressure cooling of a micromechanical oscillator using dynamical backaction,” Phys. Rev. Lett. 97(24), 243905 (2006).
[Crossref] [PubMed]

Verlot, P.

E. Gavartin, P. Verlot, and T. J. Kippenberg, “A hybrid on-chip optomechanical transducer for ultrasensitive force measurements,” Nat. Nanotechnol. 7(8), 509–514 (2012).
[Crossref] [PubMed]

Wang, H.

C. Dong, V. Fiore, M. C. Kuzyk, L. Tian, and H. Wang, “Optical wavelength conversion via optomechanical coupling in a silica resonator,” Ann. Phys. 527(1–2), 100–106 (2015).
[Crossref]

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

Wang, Y.

Y. Wang and A. A. Clerk, “Using dark modes for high-fidelity optomechanical quantum state transfer,” New J. Phys. 14(10), 105010 (2012).
[Crossref]

Watanabe, T.

E. Kuramochi, M. Notomi, S. Mitsugi, A. Shinya, T. Tanabe, and T. Watanabe, “Ultrahigh-Q photonic crystal nanocavities realized by the local width modulation of a line defect,” Appl. Phys. Lett. 88(4), 041112 (2006).
[Crossref]

Weig, E. M.

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 below the standard quantum limit,” Phys. Rev. A 82(6), 061804 (2010).
[Crossref]

Wiederhecker, G.

M. Zhang, G. Luiz, S. Shah, G. Wiederhecker, and M. Lipson, “Eliminating anchor loss in optomechanical resonators using elastic wave interference,” Appl. Phys. Lett. 105(5), 051904 (2014).
[Crossref]

Winger, M.

A. G. Krause, M. Winger, T. D. Blasius, Q. Lin, and O. Painter, “A high-resolution microchip optomechanical accelerometer,” Nat. Photonics 6(11), 768–772 (2012).
[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]

Wong, C. W.

J. Zheng, X. Sun, Y. Li, M. Poot, A. Dadgar, N. N. Shi, W. H. P. Pernice, H. X. Tang, and C. W. Wong, “Femtogram dispersive L3-nanobeam optomechanical cavities: design and experimental comparison,” Opt. Express 20(24), 26486–26498 (2012).
[Crossref] [PubMed]

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).
[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]

J. Gao, J. F. McMillan, M. 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]

Wu, M.

J. Gao, J. F. McMillan, M. 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]

Xu, Q.

Yamamoto, T.

Yang, Y. T.

Y. T. Yang, C. Callegari, X. L. Feng, K. L. Ekinci, and M. L. Roukes, “Zeptogram-scale nanomechanical mass sensing,” Nano Lett. 6(4), 583–586 (2006).
[Crossref] [PubMed]

K. L. Ekinci, Y. T. Yang, and M. L. Roukes, “Ultimate limits to inertial mass sensing based upon nanoelectromechanical systems,” J. Appl. Phys. 95(5), 2682 (2004).
[Crossref]

Yoshikawa, Y.

Zhang, M.

M. Zhang, G. Luiz, S. Shah, G. Wiederhecker, and M. Lipson, “Eliminating anchor loss in optomechanical resonators using elastic wave interference,” Appl. Phys. Lett. 105(5), 051904 (2014).
[Crossref]

Zheng, J.

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).
[Crossref] [PubMed]

J. Zheng, X. Sun, Y. Li, M. Poot, A. Dadgar, N. N. Shi, W. H. P. Pernice, H. X. Tang, and C. W. Wong, “Femtogram dispersive L3-nanobeam optomechanical cavities: design and experimental comparison,” Opt. Express 20(24), 26486–26498 (2012).
[Crossref] [PubMed]

J. Gao, J. F. McMillan, M. 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]

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]

Adv. Mater. (1)

S. Forstner, E. Sheridan, J. Knittel, C. L. Humphreys, G. A. Brawley, H. Rubinsztein-Dunlop, and W. P. Bowen, “Ultrasensitive optomechanical magnetometry,” Adv. Mater. 26(36), 6348–6353 (2014).
[Crossref] [PubMed]

Ann. Phys. (1)

C. Dong, V. Fiore, M. C. Kuzyk, L. Tian, and H. Wang, “Optical wavelength conversion via optomechanical coupling in a silica resonator,” Ann. Phys. 527(1–2), 100–106 (2015).
[Crossref]

Appl. Phys. Lett. (5)

J. Gao, J. F. McMillan, M. 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. 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]

E. Kuramochi, M. Notomi, S. Mitsugi, A. Shinya, T. Tanabe, and T. Watanabe, “Ultrahigh-Q photonic crystal nanocavities realized by the local width modulation of a line defect,” Appl. Phys. Lett. 88(4), 041112 (2006).
[Crossref]

J. Chan, A. H. Safavi-Naeini, J. T. Hill, S. Meenehan, and O. Painter, “Optimized optomechanical crystal cavity with acoustic radiation shield,” Appl. Phys. Lett. 101(8), 081115 (2012).
[Crossref]

M. Zhang, G. Luiz, S. Shah, G. Wiederhecker, and M. Lipson, “Eliminating anchor loss in optomechanical resonators using elastic wave interference,” Appl. Phys. Lett. 105(5), 051904 (2014).
[Crossref]

J. Appl. Phys. (1)

K. L. Ekinci, Y. T. Yang, and M. L. Roukes, “Ultimate limits to inertial mass sensing based upon nanoelectromechanical systems,” J. Appl. Phys. 95(5), 2682 (2004).
[Crossref]

Laser Photonics Rev. (1)

P. Lalanne, C. Sauvan, and J. P. Hugonin, “Photon confinement in photonic crystal nanocavities,” Laser Photonics Rev. 2(6), 514–526 (2008).
[Crossref]

Nano Lett. (4)

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).
[Crossref] [PubMed]

Y. T. Yang, C. Callegari, X. L. Feng, K. L. Ekinci, and M. L. Roukes, “Zeptogram-scale nanomechanical mass sensing,” Nano Lett. 6(4), 583–586 (2006).
[Crossref] [PubMed]

H. Y. Chiu, P. Hung, H. W. C. Postma, and M. Bockrath, “Atomic-scale mass sensing using carbon nanotube resonators,” Nano Lett. 8(12), 4342–4346 (2008).
[Crossref] [PubMed]

O. Basarir, S. Bramhavar, and K. L. Ekinci, “Motion transduction in nanoelectromechanical systems (NEMS) arrays using near-field optomechanical coupling,” Nano Lett. 12(2), 534–539 (2012).
[Crossref] [PubMed]

Nat. Commun. (2)

J. T. Hill, A. H. Safavi-Naeini, J. Chan, and O. Painter, “Coherent optical wavelength conversion via cavity optomechanics,” Nat. Commun. 3, 1196 (2012).
[Crossref] [PubMed]

J. Gomis-Bresco, D. Navarro-Urrios, M. Oudich, S. El-Jallal, A. Griol, D. Puerto, E. Chavez, Y. Pennec, B. Djafari-Rouhani, F. Alzina, A. Martínez, and C. M. S. Torres, “A one-dimensional optomechanical crystal with a complete phononic band gap,” Nat. Commun. 5, 4452 (2014).
[Crossref] [PubMed]

Nat. Mater. (1)

B. Song, S. Noda, T. Asano, and Y. Akahane, “Ultra-high-Q photonic double-heterostructure nanocavity,” Nat. Mater. 4(3), 207–210 (2005).
[Crossref]

Nat. Nanotechnol. (4)

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]

E. Gavartin, P. Verlot, and T. J. Kippenberg, “A hybrid on-chip optomechanical transducer for ultrasensitive force measurements,” Nat. Nanotechnol. 7(8), 509–514 (2012).
[Crossref] [PubMed]

J. Moser, J. Güttinger, A. Eichler, M. J. Esplandiu, D. E. Liu, M. I. Dykman, and A. Bachtold, “Ultrasensitive force detection with a nanotube mechanical resonator,” Nat. Nanotechnol. 8(7), 493–496 (2013).
[Crossref] [PubMed]

J. D. Teufel, T. Donner, M. A. Castellanos-Beltran, J. W. Harlow, and K. W. Lehnert, “Nanomechanical motion measured with an imprecision below that at the standard quantum limit,” Nat. Nanotechnol. 4(12), 820–823 (2009).
[Crossref] [PubMed]

Nat. Photonics (1)

A. G. Krause, M. Winger, T. D. Blasius, Q. Lin, and O. Painter, “A high-resolution microchip optomechanical accelerometer,” Nat. Photonics 6(11), 768–772 (2012).
[Crossref]

Nat. Phys. (3)

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]

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

R. W. Andrews, R. W. Peterson, T. P. Purdy, K. Cicak, R. W. Simmonds, C. A. Regal, and K. W. Lehnert, “Bidirectional and efficient conversion between microwave and optical light,” Nat. Phys. 10(4), 321–326 (2014).
[Crossref]

Nature (3)

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]

M. Eichenfield, J. Chan, R. M. Camacho, K. J. Vahala, and O. Painter, “Optomechanical crystals,” Nature 462(7269), 78–82 (2009).
[Crossref] [PubMed]

Y. Akahane, T. Asano, B. S. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425(6961), 944–947 (2003).
[Crossref] [PubMed]

New J. Phys. (1)

Y. Wang and A. A. Clerk, “Using dark modes for high-fidelity optomechanical quantum state transfer,” New J. Phys. 14(10), 105010 (2012).
[Crossref]

Opt. Express (5)

Opt. Lett. (1)

Phys. Rev. A (1)

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 below the standard quantum limit,” Phys. Rev. A 82(6), 061804 (2010).
[Crossref]

Phys. Rev. Lett. (2)

A. Schliesser, P. Del’Haye, N. Nooshi, K. J. Vahala, and T. J. Kippenberg, “Radiation pressure cooling of a micromechanical oscillator using dynamical backaction,” Phys. Rev. Lett. 97(24), 243905 (2006).
[Crossref] [PubMed]

A. H. Safavi-Naeini, J. Chan, J. T. Hill, T. P. M. Alegre, A. Krause, and O. Painter, “Observation of quantum motion of a nanomechanical resonator,” Phys. Rev. Lett. 108(3), 033602 (2012).
[Crossref] [PubMed]

Rev. Mod. Phys. (1)

M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt, “Cavity optomechanics,” Rev. Mod. Phys. 86(4), 1391–1452 (2014).
[Crossref]

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Figures (6)

Fig. 1
Fig. 1 (a) Geometry of the double-slot PhC waveguide. A unit cell is indicated by dashed white lines. (b) TE-like optical band diagram of (a). Three waveguide modes in the bandgap are shown. The light and dark gray shades represent the continua of the guided and radiant modes respectively. (c) The normalized Ey field of the three waveguide modes at the bandedge (kx = 0.5 × 2π/a) indicated by circles with corresponding colors in (b). (d) The bandedge frequencies of the waveguide modes versus a of unit cells. When a decreases, hy of unit cells increases linearly at the same time. The leftmost and rightmost frequencies in the diagram correspond to the normal and defect unit cells. The horizontal dashed red line shows that the bandedge frequency of Mode C in the defect unit cell is between Mode B and C of the normal unit cell.
Fig. 2
Fig. 2 (a) Geometry of the double-slot PhC multistep double-heterostructure cavity. The defect, transitional and normal unit cells are indicated. The two slots are labeled as “Slot1” and “Slot2.” (b) The normalized Ey field of the optical mode.
Fig. 3
Fig. 3 (a) The normalized displacement field of the flexural mechanical mode at kx = 0 [indicated by a red circle in (b)] for a normal unit cell. (b) In-plane acoustic band diagram of the 1D phononic crystals in the nanobeam. Modes of y- and z-symmetries (red bands), and modes of other symmetries (blue bands) are shown. The gray shade represents the acoustic quasi-complete bandgap for the red bands. The normalized displacement fields of the two blue bands across the bandgap at the same frequency with the flexural mechanical mode of the defect unit cell (indicated with blue filled circles) are shown to the right of the band diagram. (c) The frequency fm of the flexural mechanical mode at kx = 0 and the bandgap versus a and hy of unit cells. The leftmost and rightmost frequencies in the diagram correspond to the normal and defect unit cells. The horizontal dashed red line shows that the frequency at kx = 0 of the flexural mechanical mode in the defect unit cell falls in the bandgap of the normal unit cells.
Fig. 4
Fig. 4 (a) The normalized displacement field of the flexural mechanical mode confined in the center of the nanobeam. Close-up view of the flexural mechanical mode is also shown. (b) The simulated clamping-loss-limited mechanical Q-factor Qm and frequency fm as a function of the hy of the normal unit cells.
Fig. 5
Fig. 5 Schematics of the ideal design and imperfect cavities. The widths of the two slots and the two rails of the central defect unit cell are shown with red and blue arrows respectively. The variations in structures of the imperfect cavities are exaggerated for clarity.
Fig. 6
Fig. 6 The normalized displacement fields of the flexural mechanical modes of the ideal design and imperfect cavities. (a) Ideal design. (b) ESW5nm. (c) ESW10nm. (d) SSP5nm. (e) SSP-5nm. (f) SRP-2.5nm. The corresponding effective masses are also shown.

Tables (1)

Tables Icon

Table 1 Optical and mechanical properties of the ideal design and imperfect cavities

Metrics