Abstract

We describe the strong optomechanical dynamical interactions in ultrahigh-Q/V slot-type photonic crystal cavities. The dispersive coupling is based on mode-gap photonic crystal cavities with light localization in an air mode with 0.02(λ/n)3 modal volumes while preserving optical cavity Q up to 5 × 106. The mechanical mode is modeled to have fundamental resonance Ωm/2π of 460 MHz and a quality factor Qm estimated at 12,000. For this slot-type optomechanical cavity, the dispersive coupling gom is numerically computed at up to 940 GHz/nm (Lom of 202 nm) for the fundamental optomechanical mode. Dynamical parametric oscillations for both cooling and amplification, in the resolved and unresolved sideband limit, are examined numerically, along with the displacement spectral density and cooling rates for various operating parameters.

© 2010 OSA

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2010

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

Q. Lin, J. Rosenberg, D. Chang, R. Camacho, M. Eichenfield, K. J. Vahala, and O. Painter, “Coherent mixing of mechanical excitations in nano-optomechanical structures,” Nat. Photonics 4(4), 236–242 (2010).
[CrossRef]

S. Mohammadi, A. A. Eftekhar, A. Khelif, and A. Adibi, “Simultaneous two-dimensional phononic and photonic band gaps in opto-mechanical crystal slabs,” Opt. Express 18(9), 9164–9172 (2010).
[CrossRef] [PubMed]

I. W. Frank, P. B. Deotare, M. W. McCutcheon, and M. Lončar, “Programmable photonic crystal nanobeam cavities,” Opt. Express 18(8), 8705–8712 (2010).
[CrossRef] [PubMed]

Y.-G. Roh, T. Tanabe, A. Shinya, H. Taniyama, E. Kuramochi, S. Matsuo, T. Sato, and M. Notomi, “Strong optomechanical interaction in a bilayer photonic crystal,” Phys. Rev. B 81, 121101 (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]

Y.-G. Roh, T. Tanabe, A. Shinya, H. Taniyama, E. Kuramochi, S. Matsuo, T. Sato, and M. Notomi, “Strong Optomechanical interaction in a bilayer photonic crystal,” Phys. Rev. B 81(12), 121101 (2010).
[CrossRef]

2009

A. Di Falco, L. O’Faolain, and T. F. Krauss, “Chemical sensing in slotted photonic crystal heterostructure cavities,” Appl. Phys. Lett. 94(6), 063503 (2009).
[CrossRef]

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]

T. H. Metcalf, B. B. Pate, D. M. Photiadis, and B. H. Houston, “Thermoelastic damping in micromechanical resonators,” Appl. Phys. Lett. 95(6), 061903 (2009).
[CrossRef]

D. J. Wilson, C. A. Regal, S. B. Papp, and H. J. Kimble, “Cavity optomechanics with stoichiometric SiN films,” Phys. Rev. Lett. 103(20), 207204 (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]

Q. Lin, J. Rosenberg, X. Jiang, K. J. Vahala, and O. Painter, “Mechanical oscillation and cooling actuated by the optical gradient force,” Phys. Rev. Lett. 103(10), 103601 (2009).
[CrossRef] [PubMed]

G. Anetsberger, O. Arcizet, Q. P. Unterreithmeier, R. Rivière, A. Schliesser, E. M. Weig, J. P. Kotthaus, and T. J. Kippenberg, “Near-field cavity optomechanics with nanomechanical oscillators,” Nat. Phys. 5(12), 909–914 (2009).
[CrossRef]

M. Li, W. H. P. Pernice, and H. X. Tang, “Tunable bipolar optical interactions between guided lightwaves,” Nat. Photonics 3(8), 464–468 (2009).
[CrossRef]

M. Li, W. H. P. Pernice, and H. X. Tang, “Reactive cavity optical force on microdisk-coupled nanomechanical beam waveguides,” Phys. Rev. Lett. 103(22), 223901 (2009).
[CrossRef]

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

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, 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]

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

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

F. Marquardt and S. M. Girvin, “Optomechanics,” Physics 2, 40 (2009).
[CrossRef]

2008

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

M. Li, W. H. 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]

J. D. Thompson, B. M. Zwickl, A. M. Jayich, and S. M. Florian Marquardt, “Girvin, and J. G. E. Harris, “Strong dispersive coupling of a high-finesse cavity to a micromechanical membrane,” Nature 452, 06715 (2008).

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

M. Hossein-Zadeh and K. J. Vahala, “Photonic RF Down-Converter based on Optomechanical Oscillation,” IEEE Photon. Technol. Lett. 20(4), 234–236 (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]

H. Taniyama, M. Notomi, E. Kuramochi, T. Yamamoto, Y. Yoshikawa, Y. Torii, and T. Kuga, “Strong radiation force induced in two-dimensional photonical crystal slab cavities,” Phys. Rev. B 78(16), 165129 (2008).
[CrossRef]

2007

F. Riboli, P. Bettotti, and L. Pavesi, “Band gap characterization and slow light effects in one dimensional photonic crystals based on silicon slot-waveguides,” Opt. Express 15(19), 11769–11775 (2007).
[CrossRef] [PubMed]

S. Xiao, M. H. Khan, H. Shen, and M. Qi, “Compact silicon microring resonators with ultra-low propagation loss in the C band,” Opt. Express 15(22), 14467–14475 (2007).
[CrossRef] [PubMed]

T. J. Kippenberg and K. J. Vahala, “Cavity opto-mechanics,” Opt. Express 15(25), 17172–17205 (2007).
[CrossRef] [PubMed]

M. Eichenfield, C. Michael, R. Perahia, and O. Painter, “Actuation of Micro-Optomechanical Systems Via Cavity Enhanced Optical Dipole Forces,” Nat. Photonics 1(7), 416–422 (2007).
[CrossRef]

P. T. Rakich, M. A. Popović, M. Soljačić, and E. P. Ippen, “Trapping, corralling and spectral bonding of optical resonances through optically induced potentials,” Nat. Photonics 1(11), 658–665 (2007).
[CrossRef]

R. Ma, A. Schliesser, P. Del’haye, A. Dabirian, G. Anetsberger, and T. J. Kippenberg, “Radiation-pressure-driven vibrational modes in ultrahigh-Q silica microspheres,” Opt. Lett. 32(15), 2200–2202 (2007).
[CrossRef] [PubMed]

F. Marquardt, J. P. Chen, A. A. Clerk, and S. M. Girvin, “Quantum theory of cavity-assisted sideband cooling of mechanical motion,” Phys. Rev. Lett. 99(9), 093902 (2007).
[CrossRef] [PubMed]

2006

D. Kleckner and D. Bouwmeester, “Sub-kelvin optical cooling of a micromechanical resonator,” Nature 444(7115), 75–78 (2006).
[CrossRef] [PubMed]

O. Arcizet, P. F. Cohadon, T. Briant, M. Pinard, and A. Heidmann, “Radiation-pressure cooling and optomechanical instability of a micromirror,” Nature 444(7115), 71–74 (2006).
[CrossRef] [PubMed]

S. Gigan, H. R. Böhm, M. Paternostro, F. Blaser, G. Langer, J. B. Hertzberg, K. C. Schwab, D. Bäuerle, M. Aspelmeyer, and A. Zeilinger, “Self-cooling of a micromirror by radiation pressure,” Nature 444(7115), 67–70 (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]

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

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

2005

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

J. T. Robinson, C. Manolatou, L. Chen, and M. Lipson, “Ultrasmall mode volumes in dielectric optical microcavities,” Phys. Rev. Lett. 95(14), 143901 (2005).
[CrossRef] [PubMed]

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Appl. Phys. Lett.

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Nat. Photonics

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Nat. Phys.

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Opt. Lett.

Photonics Nanostruct. Fundam. Appl.

C. Jamois, R. B. Wehrspohn, L. C. Andreani, C. Herrmann, O. Hess, and U. Gosele, ““Silicon-based two-dimensional photonic crystal waveguides,” Photonics Nanostruct. Fundam. Appl. 1(1), 1–13 (2003).
[CrossRef]

Phys. Lett. A

V. B. Braginsky, S. E. Strigin, and S. P. Vyatchanin, “Parametric Oscillatory instability in Fabri-Perot Interferometer,” Phys. Lett. A 287(5-6), 331–338 (2001).
[CrossRef]

Phys. Rev.

C. Zener, “Internal Friction in Solids. I. Theory of Internal Friction in Reeds,” Phys. Rev. 52(3), 230–235 (1937).
[CrossRef]

Phys. Rev. A

C. K. Law, “Interaction between a moving mirror and radiation pressure: A Hamiltonian formulation,” Phys. Rev. A 51(3), 2537–2541 (1995).
[CrossRef] [PubMed]

S. Mancini and P. Tombesi, “Quantum noise reduction by radiation pressure,” Phys. Rev. A 49(5), 4055–4065 (1994).
[CrossRef] [PubMed]

Phys. Rev. B

Y.-G. Roh, T. Tanabe, A. Shinya, H. Taniyama, E. Kuramochi, S. Matsuo, T. Sato, and M. Notomi, “Strong Optomechanical interaction in a bilayer photonic crystal,” Phys. Rev. B 81(12), 121101 (2010).
[CrossRef]

Y.-G. Roh, T. Tanabe, A. Shinya, H. Taniyama, E. Kuramochi, S. Matsuo, T. Sato, and M. Notomi, “Strong optomechanical interaction in a bilayer photonic crystal,” Phys. Rev. B 81, 121101 (2010).
[CrossRef]

H. Taniyama, M. Notomi, E. Kuramochi, T. Yamamoto, Y. Yoshikawa, Y. Torii, and T. Kuga, “Strong radiation force induced in two-dimensional photonical crystal slab cavities,” Phys. Rev. B 78(16), 165129 (2008).
[CrossRef]

Phys. Rev. E Stat. Nonlin. Soft Matter Phys.

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 Pt 2), 066611 (2002).
[CrossRef] [PubMed]

Phys. Rev. Lett.

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

J. T. Robinson, C. Manolatou, L. Chen, and M. Lipson, “Ultrasmall mode volumes in dielectric optical microcavities,” Phys. Rev. Lett. 95(14), 143901 (2005).
[CrossRef] [PubMed]

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]

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(3), 033901 (2005).
[CrossRef] [PubMed]

F. Marquardt, J. P. Chen, A. A. Clerk, and S. M. Girvin, “Quantum theory of cavity-assisted sideband cooling of mechanical motion,” Phys. Rev. Lett. 99(9), 093902 (2007).
[CrossRef] [PubMed]

T. Carmon, H. Rokhsari, L. Yang, T. J. Kippenberg, and K. J. Vahala, “Temporal behavior of radiation-pressure-induced vibrations of an optical microcavity phonon mode,” Phys. Rev. Lett. 94(22), 223902 (2005).
[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]

D. J. Wilson, C. A. Regal, S. B. Papp, and H. J. Kimble, “Cavity optomechanics with stoichiometric SiN films,” Phys. Rev. Lett. 103(20), 207204 (2009).
[CrossRef]

M. Li, W. H. P. Pernice, and H. X. Tang, “Reactive cavity optical force on microdisk-coupled nanomechanical beam waveguides,” Phys. Rev. Lett. 103(22), 223901 (2009).
[CrossRef]

Q. Lin, J. Rosenberg, X. Jiang, K. J. Vahala, and O. Painter, “Mechanical oscillation and cooling actuated by the optical gradient force,” Phys. Rev. Lett. 103(10), 103601 (2009).
[CrossRef] [PubMed]

Physics

F. Marquardt and S. M. Girvin, “Optomechanics,” Physics 2, 40 (2009).
[CrossRef]

Science

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

S. Chu, “Laser manipulation of atoms and particles,” Science 253(5022), 861–866 (1991).
[CrossRef] [PubMed]

Other

P. Meystre and M. Sargent III, “Mechanical Effects of Light,” in Elements of Quantum Optics (Springer, 2007), Chapter 6.

V. B. Braginsky, Measurement of Weak Forces in Physics Experiments (University of Chicago Press, Chicago, 1977).

A. H. Safavi-Naeini, T. P. Mayer Alegre, M. Winger, and O. Painter, “Optomechanics in an ultrahigh-Q slotted 2D photonic crystal cavity,” arXiv: 1006.3964.

C. Cohen-Tannoudji, B. Din, and F. Laloe, Quantum Mechanics (Hermann, Paris, 1977), Vol. 1, Chap. 2; Vol. 2, Chaps. 11 and 13.

H. A. Haus, Waves and Fields in Optoelectronics (Prentice-Hall 1984).

Stephen D. Senturia, Microsystem Design (Springer 2000).

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Figures (7)

Fig. 1
Fig. 1

(a) Photonic band structure of slotted PhCWG with s = 80nm. The blue dashed lines show the three modes in the slotted PhCWG. (b) H-field and energy distribution of waveguide modes I, II and III. (c) E-field and energy distribution of the first (above) and the second (below) cavity modes.

Fig. 2
Fig. 2

Illustration of air-slot mode-gap optomechanical silicon cavity, fabricated with electron-beam lithography [60,61]. The holes shifts are shown with dA = 0.0286a (red), dB = 0.019a (blue) and dC = 0.0095a (green), where a is the crystal lattice constant, for increasing the intrinsic cavity Q.

Fig. 3
Fig. 3

Mechanical displacement profile of the first eight mechanical modes. Modes in color (a, c, h) are allowed by parity considerations to couple to the optical modes; modes in grayscale (b, d, e, f, g) are forbidden by parity for sizable optomechanical coupling.

Fig. 4
Fig. 4

(a) Computed optomechanical coupling rates of the fundamental optical mode with first (black solid squares) and second (red open circles) allowed mechanical modes, computed for the different slot gaps s. The inset panel is the corresponding coupling length. (b) Computed optomechanical coupling rates of the second optical mode coupled with first (black solid squares) and second (red open circles) allowed mechanical modes.

Fig. 5
Fig. 5

(a) Time-domain cavity amplitude a (solid blue line) and displacement x (dashed green line) of the first optical and first mechanical modes, with gom of 940 GHz/nm, Ωm /2π of 470 MHz, Qm of 12,400, κ/2π of 425 GHz, and (1/τex )/2π of 38 MHz. (b) Time-domain cavity amplitude for normalized detunings Δτ at −1, −0.25, 0, 0.25 and 1 (top to bottom).

Fig. 6
Fig. 6

(a-c) Two-dimensional surface plots of the first optical – first mechanical mode linewidth (a) mechanical frequency (b) and effective temperature (c), for varying detunings and optical Q factors. A fixed pump power of 1pW is used, along with an effective mass of 200fg and a 300K bath temperature. The dashed white line denotes the condition for Ωm = κ. (d-f) Example first optical – first mechanical mode linewidths (d), frequency shift (e) and effective temperature (f) with two input powers (P) and varying laser-cavity detuning. Otherwise indicated, the conditions are identical to panel (a), and with optical Q chosen at 5 × 105.

Fig. 7
Fig. 7

(a) Displacement spectral density of the first mechanical mode, with optical detuning from the first optical mode. With the input power increasing from 0 to 9.5uW, in addition to an observed optical stiffening, the amplitude decreases with a larger linewidth for a decrease in the effective temperature. The detuning Δτ is fixed at −0.25, for an optical Q of 5 × 105, meff of 200fg, at 300K bath temperature. (b) Displacement spectral density of the first and second allowed mechanical modes with different detunings. The scale bar is in dB with units of m2/Hz (pump powers P1 of 0.1uW and P2 of 50uW used respectively in the modeling).

Equations (2)

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L O M 1 = 1 2 d A ( q ( r ) n ^ ) [ Δ ε 12 ( r ) | E | | ( 0 ) ( r ) | 2 Δ ( ε 12 1 ( r ) ) | D ( 0 ) ( r ) | 2 ] d V ε ( r ) | E ( r ) | 2 ,
d a d t = i Δ ( x ) a ( 1 2 τ 0 + 1 2 τ e x ) a + i 1 τ e x s , d 2 x d t 2 + Ω m 2 Q m d x d t + Ω m 2 x = F O M ( t ) m e f f + F L ( t ) m e f f = g O M ω 0 | a | 2 m e f f + F L ( t ) m e f f ,

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