Design Of Dispersive Optomechanical Coupling And Cooling . PDF

14d ago
1.97 MB
13 Pages

Design of dispersive optomechanical couplingand cooling in ultrahigh-Q/V slot-type photoniccrystal cavitiesYing Li,* Jiangjun Zheng, Jie Gao, Jing Shu, Mehmet Sirin Aras, and Chee Wei WongOptical Nanostructures Laboratory, Center for Integrated Science and Engineering, Solid-State Science andEngineering, and Mechanical Engineering, Columbia University, New York, New York 10027, USA*[email protected]: We describe the strong optomechanical dynamical interactions inultrahigh-Q/V slot-type photonic crystal cavities. The dispersive coupling isbased on mode-gap photonic crystal cavities with light localization in an airmode with 0.02(λ/n)3 modal volumes while preserving optical cavity Q upto 5 106. The mechanical mode is modeled to have fundamental resonanceΩm/2π of 460 MHz and a quality factor Qm estimated at 12,000. For thisslot-type optomechanical cavity, the dispersive coupling gom is numericallycomputed at up to 940 GHz/nm (Lom of 202 nm) for the fundamentaloptomechanical mode. Dynamical parametric oscillations for both coolingand amplification, in the resolved and unresolved sideband limit, areexamined numerically, along with the displacement spectral density andcooling rates for various operating parameters. 2010 Optical Society of AmericaOCIS codes: (230.5298) Photonic crystals; (230.5750) Resonators; (220.4880) Optomechanics;(230.4685) Optical microelectromechanical devices.References and links1. Meystre, and M. Sargent III, “Mechanical Effects of Light,” in Elements of Quantum Optics (Springer, 2007),Chapter 6.S. Chu, “Laser manipulation of atoms and particles,” Science 253(5022), 861–866 (1991).F. Marquardt, and S. M. Girvin, “Optomechanics,” Physics 2, 40 (2009).T. J. Kippenberg, and K. J. Vahala, “Cavity opto-mechanics,” Opt. Express 15(25), 17172–17205 (2007).T. J. Kippenberg, and K. J. Vahala, “Cavity optomechanics: back-action at the mesoscale,” Science 321(5893),1172–1176 (2008).I. Favero, and K. Karrai, “Optomechanics of deformable optical cavities,” Nat. Photonics 3(4), 201–205 (2009).D. Van Thourhout, and J. Roels, “Optomechanical Device actuation through the optical gradient force,” Nat.Photonics 4(4), 211–217 (2010).C. K. Law, “Interaction between a moving mirror and radiation pressure: A Hamiltonian formulation,” Phys.Rev. A 51(3), 2537–2541 (1995).S. Mancini, and P. Tombesi, “Quantum noise reduction by radiation pressure,” Phys. Rev. A 49(5), 4055–4065(1994).I. Wilson-Rae, P. Zoller, and A. Imamoğlu, “Laser cooling of a nanomechanical resonator mode to its quantumground state,” Phys. Rev. Lett. 92(7), 075507 (2004).T. J. Kippenberg, H. Rokhsari, T. Carmon, A. Scherer, and K. J. Vahala, “Analysis of radiation-pressure inducedmechanical oscillation of an optical microcavity,” Phys. Rev. Lett. 95(3), 033901 (2005).H. Rokhsari, T. J. Kippenberg, T. Carmon, and K. J. Vahala, “Radiation-pressure-driven micro-mechanicaloscillator,” Opt. Express 13(14), 5293–5301 (2005).T. Carmon, H. Rokhsari, L. Yang, T. J. Kippenberg, and K. J. Vahala, “Temporal behavior of radiation-pressureinduced vibrations of an optical microcavity phonon mode,” Phys. Rev. Lett. 94(22), 223902 (2005).D. Kleckner, and D. Bouwmeester, “Sub-kelvin optical cooling of a micromechanical resonator,” Nature444(7115), 75–78 (2006).O. Arcizet, P. F. Cohadon, T. Briant, M. Pinard, and A. Heidmann, “Radiation-pressure cooling andoptomechanical instability of a micromirror,” Nature 444(7115), 71–74 (2006).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).M. Eichenfield, C. Michael, R. Perahia, and O. Painter, “Actuation of Micro-Optomechanical Systems ViaCavity Enhanced Optical Dipole Forces,” Nat. Photonics 1(7), 416–422 (2007).#133205 - 15.00 USD(C) 2010 OSAReceived 10 Aug 2010; revised 10 Oct 2010; accepted 14 Oct 2010; published 28 Oct 20108 November 2010 / Vol. 18, No. 23 / OPTICS EXPRESS 23844

18. P. T. Rakich, M. A. Popović, M. Soljačić, and E. P. Ippen, “Trapping, corralling and spectral bonding of opticalresonances through optically induced potentials,” Nat. Photonics 1(11), 658–665 (2007).19. R. Ma, A. Schliesser, P. Del’haye, A. Dabirian, G. Anetsberger, and T. J. Kippenberg, “Radiation-pressuredriven vibrational modes in ultrahigh-Q silica microspheres,” Opt. Lett. 32(15), 2200–2202 (2007).20. F. Marquardt, J. P. Chen, A. A. Clerk, and S. M. Girvin, “Quantum theory of cavity-assisted sideband cooling ofmechanical motion,” Phys. Rev. Lett. 99(9), 093902 (2007).21. J. D. Thompson, B. M. Zwickl, A. M. Jayich, and S. M. Florian Marquardt, “Girvin, and J. G. E. Harris, “Strongdispersive coupling of a high-finesse cavity to a micromechanical membrane,” Nature 452, 06715 (2008).22. A. Schliesser, R. Riviere, G. Anetsberger, O. Arcizet, and I. J. Kippenberg, “Resolved-sideband cooling of amicromechanical oscillator,” Nat. Phys. 4(5), 415–419 (2008).23. M. Hossein-Zadeh, and K. J. Vahala, “Photonic RF Down-Converter based on Optomechanical Oscillation,”IEEE Photon. Technol. Lett. 20(4), 234–236 (2008).24. Y.-S. Park, and H. Wang, “Resolved-sideband and cryogenic cooling of an optomechanical resonator,” Nat.Phys. 5(7), 489–493 (2009).25. Q. Lin, J. Rosenberg, X. Jiang, K. J. Vahala, and O. Painter, “Mechanical oscillation and cooling actuated by theoptical gradient force,” Phys. Rev. Lett. 103(10), 103601 (2009).26. 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).27. 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-phononcontrol of a mechanical resonator,” Nature 464(7289), 697–703 (2010).28. Q. Lin, J. Rosenberg, D. Chang, R. Camacho, M. Eichenfield, K. J. Vahala, and O. Painter, “Coherent mixing ofmechanical excitations in nano-optomechanical structures,” Nat. Photonics 4(4), 236–242 (2010).29. V. B. Braginsky, Measurement of Weak Forces in Physics Experiments (University of Chicago Press, Chicago,1977).30. V. B. Braginsky, S. E. Strigin, and S. P. Vyatchanin, “Parametric Oscillatory instability in Fabri-PerotInterferometer,” Phys. Lett. A 287(5-6), 331–338 (2001).31. A. Schliesser, P. Del’Haye, N. Nooshi, K. J. Vahala, and T. J. Kippenberg, “Radiation pressure cooling of amicromechanical oscillator using dynamical backaction,” Phys. Rev. Lett. 97(24), 243905 (2006).32. 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).33. M. L. Povinelli, M. Lončar, M. Ibanescu, E. J. Smythe, S. G. Johnson, F. Capasso, and J. D. Joannopoulos,“Evanescent-wave bonding between optical waveguides,” Opt. Lett. 30(22), 3042–3044 (2005).34. M. Li, W. H. Pernice, C. Xiong, T. Baehr-Jones, M. Hochberg, and H. X. Tang, “Harnessing optical forces inintegrated photonic circuits,” Nature 456(7221), 480–484 (2008).35. M. Li, W. H. P. Pernice, and H. X. Tang, “Tunable bipolar optical interactions between guided lightwaves,” Nat.Photonics 3(8), 464–468 (2009).36. M. Li, W. H. P. Pernice, and H. X. Tang, “Reactive cavity optical force on microdisk-coupled nanomechanicalbeam waveguides,” Phys. Rev. Lett. 103(22), 223901 (2009).37. G. S. Wiederhecker, L. Chen, A. Gondarenko, and M. Lipson, “Controlling photonic structures using opticalforces,” Nature 462(7273), 633–636 (2009).38. A. H. Safavi-Naeini, T. P. Mayer Alegre, M. Winger, and O. Painter, “Optomechanics in an ultrahigh-Q slotted2D photonic crystal cavity,” arXiv: 1006.3964.39. M. Notomi, H. Taniyama, S. Mitsugi, and E. Kuramochi, “Optomechanical wavelength and energy conversion inhigh- double-layer cavities of photonic crystal slabs,” Phys. Rev. Lett. 97(2), 023903 (2006).40. H. Taniyama, M. Notomi, E. Kuramochi, T. Yamamoto, Y. Yoshikawa, Y. Torii, and T. Kuga, “Strong radiationforce induced in two-dimensional photonical crystal slab cavities,” Phys. Rev. B 78(16), 165129 (2008).41. J. Chan, M. Eichenfield, R. Camacho, and O. Painter, “Optical and mechanical design of a “zipper” photoniccrystal optomechanical cavity,” Opt. Express 17(5), 3802–3817 (2009).42. M. Eichenfield, J. Chan, A. H. Safavi-Naeini, K. J. Vahala, and O. Painter, “Modeling dispersive coupling andlosses of localized optical and mechanical modes in optomechanical crystals,” Opt. Express 17(22), 20078–20098 (2009).43. M. Eichenfield, J. Chan, R. M. Camacho, K. J. Vahala, and O. Painter, “Optomechanical crystals,” Nature462(7269), 78–82 (2009).44. S. Mohammadi, A. A. Eftekhar, A. Khelif, and A. Adibi, “Simultaneous two-dimensional phononic and photonicband gaps in opto-mechanical crystal slabs,” Opt. Express 18(9), 9164–9172 (2010).45. B.-S. Song, S. Noda, T. Asano, and Y. Akahane, “Ultra-high-Q photonic double-heterostructure nanocavity,”Nat. Mater. 4(3), 207–210 (2005).46. E. Kuramochi, M. Notomi, S. Mitsugi, A. Shinya, T. Tanabe, and T. Watanabe, “Ultra-high-Q photonic crystalnanocavities realized by the local width modulation of a line defect,” Appl. Phys. Lett. 88(4), 041112 (2006).47. T. Yamamoto, M. Notomi, H. Taniyama, E. Kuramochi, Y. Yoshikawa, Y. Torii, and T. Kuga, “Design of ahigh-Q air-slot cavity based on a width-modulated line-defect in a photonic crystal slab,” Opt. Express 16(18),13809–13817 (2008).48. M. Eichenfield, R. Camacho, J. Chan, K. J. Vahala, and O. Painter, “A picogram- and nanometre-scale photoniccrystal optomechanical cavity,” Nature 459(7246), 550–555 (2009).49. I. W. Frank, P. B. Deotare, M. W. McCutcheon, and M. Lončar, “Programmable photonic crystal nanobeamcavities,” Opt. Express 18(8), 8705–8712 (2010).#133205 - 15.00 USD(C) 2010 OSAReceived 10 Aug 2010; revised 10 Oct 2010; accepted 14 Oct 2010; published 28 Oct 20108 November 2010 / Vol. 18, No. 23 / OPTICS EXPRESS 23845

50. Y.-G. Roh, T. Tanabe, A. Shinya, H. Taniyama, E. Kuramochi, S. Matsuo, T. Sato, and M. Notomi, “Strongoptomechanical interaction in a bilayer photonic crystal,” Phys. Rev. B 81, 121101 (2010).51. J. Gao, J. F. McMillan, M.-C. Wu, J. Zheng, S. Assefa, and C. W. Wong, “Demonstration of an air-slot modegap confined photonic crystal slab nanocavity with ultrasmall mode volumes,” Appl. Phys. Lett. 96(5), 051123(2010).52. F. Riboli, P. Bettotti, and L. Pavesi, “Band gap characterization and slow light effects in one dimensionalphotonic crystals based on silicon slot-waveguides,” Opt. Express 15(19), 11769–11775 (2007).53. Y.-G. Roh, T. Tanabe, A. Shinya, H. Taniyama, E. Kuramochi, S. Matsuo, T. Sato, and M. Notomi, “StrongOptomechanical interaction in a bilayer photonic crystal,” Phys. Rev. B 81(12), 121101 (2010).54. A. Di Falco, L. O’Faolain, and T. F. Krauss, “Chemical sensing in slotted photonic crystal heterostructurecavities,” Appl. Phys. Lett. 94(6), 063503 (2009).55. 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).56. J. T. Robinson, C. Manolatou, L. Chen, and M. Lipson, “Ultrasmall mode volumes in dielectric opticalmicrocavities,” Phys. Rev. Lett. 95(14), 143901 (2005).57. S. G. Johnson, M. Ibanescu, M. A. Skorobogatiy, O. Weisberg, J. D. Joannopoulos, and Y. Fink, “Perturbationtheory for Maxwell’s equations with shifting material boundaries,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.65(6 Pt 2), 066611 (2002).58. 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), 1242–1246 (2004).59. C. Jamois, R. B. Wehrspohn, L. C. Andreani, C. Herrmann, O. Hess, and U. Gosele, ““Silicon-based twodimensional photonic crystal waveguides,” Photonics Nanostruct. Fundam. Appl. 1(1), 1–13 (2003).60. T. Baehr-Jones, M. Hochberg, C. Walker, and A. Scherer, “High-Q optical resonators in silicon-on-insulatorbased slot waveguides,” Appl. Phys. Lett. 86(8), 081101 (2005).61. S. Xiao, M. H. Khan, H. Shen, and M. Qi, “Compact silicon microring resonators with ultra-low propagation lossin the C band,” Opt. Express 15(22), 14467–14475 (2007).62. Stephen D. Senturia, Microsystem Design (Springer 2000).63. C. Zener, “Internal Friction in Solids. I. Theory of Internal Friction in Reeds,” Phys. Rev. 52(3), 230–235 (1937).64. T. H. Metcalf, B. B. Pate, D. M. Photiadis, and B. H. Houston, “Thermoelastic damping in micromechanicalresonators,” Appl. Phys. Lett. 95(6), 061903 (2009).65. C. Cohen-Tannoudji, B. Din, and F. Laloe, Quantum Mechanics (Hermann, Paris, 1977), Vol. 1, Chap. 2; Vol. 2,Chaps. 11 and 13.66. Haus H A, Waves and Fields in Optoelectronics (Prentice-Hall 1984).1. IntroductionIt is well-known that light has mechanical effects [1] and its radiation forces can be used tomanipulate small atoms and particles [2]. Nowadays, the effects of optical forces in variousmechanical and optical structures and systems have attracted intense and increasing interestfor investigation [3]. Especially, the field of cavity optomechanics develops very fast [4–7],with recent studies covering a vast span of fundamental physics and derived applications[8–28]. In this field, the optomechanical coupling between the supported mechanical andoptical cavity modes are of key importance due to its direct relevance to the generated opticalforces, and one main goal of the developed techniques is to cool the targeted mechanicalmode to its quantum mechanical ground state [10,20,24,27]. Several classes of cavityoptomechanical systems have been explored. One of the initial efforts examines macroscopicmovable mirrors in the Laser Interferometer Gravitational Wave Observatory (LIGO) project[29,30]. Based on the micro- and nano-fabrication techniques, optomechanical resonators suchas mirror coated AFM-cantilevers [14], movable micromirrors [15,16], vibrating microtoroids[11,31], and nano-membranes [21,32] have been examined recently. Radiation-pressuredynamic backaction could be observed in these geometries. In addition, another class ofoptomechanical devices utilizes optical gradient forces [33–38] based on near-field effects.Compared to radiation-pressure based optomechanical cavities, these devices can achievewavelength-scale effective optomechanical coupling lengths due to the strong transverseevanescent-field coupling between the adjacent cavity elements [25,26,33–35,18,38].Photonic crystal membranes can be very good candidate platform with great design flexibility[39–44], with photonic crystal cavities offering an ultrahigh optical quality factor with a smallvolume [45–47]. The internal optical intensity is very high and sensitive to the geometricalchanges. However,

Design of dispersive optomechanical coupling and cooling in ultrahigh-Q/V slot-type photonic crystal cavities . Ying Li,* Jiangjun Zheng, Jie Gao, Jing Shu, Mehmet Sirin Aras, and Chee Wei Wong