OSA's Digital Library

Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 18, Iss. 14 — Jul. 5, 2010
  • pp: 14926–14943

Design of optomechanical cavities and waveguides on a simultaneous bandgap phononic-photonic crystal slab

Amir H. Safavi-Naeini and Oskar Painter  »View Author Affiliations


Optics Express, Vol. 18, Issue 14, pp. 14926-14943 (2010)
http://dx.doi.org/10.1364/OE.18.014926


View Full Text Article

Acrobat PDF (3165 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

In this paper we study and design quasi-2D optomechanical crystals, waveguides, and resonant cavities formed from patterned slabs. Two-dimensional periodicity allows for in-plane pseudo-bandgaps in frequency where resonant optical and mechanical excitations localized to the slab are forbidden. By tailoring the unit cell geometry, we show that it is possible to have a slab crystal with simultaneous optical and mechanical pseudo-bandgaps, and for which optical waveguiding is not compromised. We then use these crystals to design optomechanical cavities in which strongly interacting, co-localized photonic-phononic resonances occur. A resonant cavity structure formed by perturbing a ``linear defect' waveguide of optical and acoustic waves in a silicon optomechanical crystal slab is shown to support an optical resonance at wavelength λ0 ≈ 1.5 μm and a mechanical resonance of frequency ωm/2π ≈ 9.5 GHz. These resonances, due to the simultaneous pseudo-bandgap of the waveguide structure, are simulated to have optical and mechanical radiation-limited Q-factors greater than 107. The optomechanical coupling of the optical and acousticresonances in this cavity due to radiation pressure is also studied, with a quantum conversion rate, corresponding to the scattering rate of a single cavity photon via a single cavity phonon, calculated to be g/2π = 292 kHz.

© 2010 Optical Society of America

OCIS Codes
(230.1040) Optical devices : Acousto-optical devices
(230.5298) Optical devices : Photonic crystals

ToC Category:
Photonic Crystals

History
Original Manuscript: March 29, 2010
Revised Manuscript: June 22, 2010
Manuscript Accepted: June 24, 2010
Published: June 29, 2010

Citation
Amir H. Safavi-Naeini and Oskar Painter, "Design of optomechanical cavities and waveguides on a simultaneous bandgap phononic-photonic crystal slab," Opt. Express 18, 14926-14943 (2010)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-14-14926


Sort:  Author  |  Year  |  Journal  |  Reset

References

  1. T. J. Kippenberg and K. J. Vahala, “Cavity optomechanics: Back-action at the mesoscale,” Science 321, 1172–1176 (2008). [CrossRef]
  2. I. Favero and K. Karrai, “Optomechanics of deformable optical cavities,” Nat. Photonics 3, 201–205 (2009). [CrossRef]
  3. J. Chan, M. Eichenfield, R. Camacho, and O. Painter, “Optical and mechanical design of a “zipper” photonic crystal optomechanical cavity,” Opt. Express 17, 3802–3817 (2009). [CrossRef]
  4. M. Eichenfield, R. Camacho, J. Chan, K. J. Vahala, and O. Painter, “A picogram- and nanometre-scale photonic crystal optomechanical cavity,” Nature 459, 550–555 (2009). [CrossRef]
  5. M. Li, W. H. P. Pernice, C. Xiong, T. Baehr-Jones, M. Hochberg, and H. X. Tang, “Harnessing optical forces in integrated photonic circuits,” Nature 456, 480–484 (2008). [CrossRef]
  6. 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, 103601 (2009). [CrossRef]
  7. G. S. Wiederhecker, L. Chen, A. Gondarenko, and M. Lipson, “Controlling photonic structures using optical forces,” Nature 462, 633–636 (2009). [CrossRef]
  8. J. Roels, I. De Vlaminck, L. Lagae, B. Maes, D. Van Thourhout, and R. Baets, “Tunable optical forces between nanophotonic waveguides,” Nat. Nanotechnol. 4, 510–513 (2009). [CrossRef]
  9. M. Eichenfield, J. Chan, R. M. Camacho, K. J. Vahala, and O. Painter, “Optomechanical crystals,” Nature 462, 78–82 (2009). [CrossRef]
  10. 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, 20078–20098 (2009). [CrossRef]
  11. O. J. Painter, A. Husain, A. Scherer, J. D. O’Brien, I. Kim, and P. D. Dapkus, “Room temperature photonic crystal defect lasers at near-infrared wavelengths in InGaAsP,” J. Lightwave Technol. 17, 2082 (1999). [CrossRef]
  12. O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-dimensional photonic band-gap defect mode laser,” Science 284, 1819–1821 (1999). [CrossRef]
  13. J. Vuckovic, M. Loncar, H. Mabuchi, and A. Scherer, “Design of photonic crystal microcavities for cavity qed,” Phys. Rev. E 65, 016608 (2001). [CrossRef]
  14. H. Takano, B.-S. Song, T. Asano, and S. Noda, “Highly efficient multi-channel drop filter in a two-dimensional hetero photonic crystal,” Opt. Express 14, 3491–3496 (2006). [CrossRef]
  15. B.-S. Song, T. Asano, Y. Akahane, Y. Tanaka, and S. Noda, “Multichannel add/drop filter based on in-plane hetero photonic crystals,” J. Lightwave Technol. 23, 1449–1455 (2005). [CrossRef]
  16. M. Notomi, A. Shinya, S. Mitsugi, G. Kira, E. Kuramochi, and T. Tanabe, “Optical bistable switching action of Si high-Q photonic-crystal nanocavities,” Opt. Express 13, 2678–2687 (2005). [CrossRef]
  17. R. H. OlssonIII, and I. El-Kady, “Microfabricated phononic crystal devices and applications,” Meas. Sci. Technol. 20, 012002 (2009). [CrossRef]
  18. J. V. Sanchez-Perez, D. Caballero, R. Martinez-Sala, C. Rubio, J. Sanchez-Dehesa, F. Meseguer, J. Llinares, and F. Galvez, “Sound attenuation by a two-dimensional array of rigid cylinders,” Phys. Rev. Lett. 80, 5325–5328 (1998). [CrossRef]
  19. J. O. Vasseur, A.-C. Hladky-Hennion, B. Djafari-Rouhani, F. Duval, B. Dubus, Y. Pennec, and P. A. Deymier, “Waveguiding in two-dimensional piezoelectric phononic crystal plates,” J. Appl. Phys. 101, 114904 (2007). [CrossRef]
  20. K.-B. Gu, C.-L. Chang, J.-C. Shieh, and W.-P. Shih, “Design and fabrication of 2d phononic crystals in surface acoustic wave micro devices,” in “Micro Electro Mechanical Systems, 2006. MEMS 2006 Istanbul. 19th IEEE International Conference on,” (2006), pp. 686–689.
  21. S. Mohammadi, A. A. Eftekhar, A. Khelif, W. D. Hunt, and A. Adibi, “Evidence of large high frequency complete phononic band gaps in silicon phononic crystal plates,” Appl. Phys. Lett. 92, 221905 (2008). [CrossRef]
  22. M. Maldovan, and E. Thomas, “Simultaneous complete elastic and electromagnetic band gaps in periodic structures,” Appl. Phys. B 83, 595–600 (2006). [CrossRef]
  23. T. Gorishnyy, C. Ullal, M. Maldovan, G. Fytas, and E. Thomas, “Hypersonic phononic crystals,” Phys. Rev. Lett. 94, 115501 (2005). [CrossRef]
  24. M. Maldovan, and E. L. Thomas, “Simultaneous localization of photons and phonons in two-dimensional periodic structures,” Appl. Phys. Lett. 88, 251907 (2006). [CrossRef]
  25. S. Mohammadi, A. A. Eftekhar, W. D. Hunt, and A. Adibi, “High-Q micromechanical resonators in a two-dimensional phononic crystal slab,” Appl. Phys. Lett. 94, 051906 (2009). [CrossRef]
  26. S. Mohammadi, A. Eftekhar, and A. Adibi, “Large simultaneous band gaps for photonic and phononic crystal slabs,” in “Lasers and Electro-Optics, 2008 and 2008 Conference on Quantum Electronics and Laser Science. CLEO/QELS 2008. Conference on,” (2008), pp. 1–2.
  27. S. Mohammadi, A. Eftekhar, A. Khelif, and A. Adibi, “Simultaneous two-dimensional phononic and photonic band gaps in opto-mechanical crystal slabs,” Opt. Express 18, 9164–9172 (2010). [CrossRef]
  28. M. Notomi, H. Taniyama, S. Mitsugi, and E. Kuramochi, “Optomechanical wavelength and energy conversion in high-Q double-layer cavities of photonic crystal slabs,” Phys. Rev. Lett. 97, 023903 (2006). [CrossRef]
  29. V. Laude, A. Khelif, S. Benchabane, M. Wilm, T. Sylvestre, B. Kibler, A. Mussot, J. Dudley, and H. Maillotte, “Phononic band-gap guidance of acoustic modes in photonic crystal fibers,” Phys. Rev. B 71, 045107 (2005). [CrossRef]
  30. P. Dainese, P. S. J. Russell, N. Joly, J. C. Knight, G. S. Wiederhecker, H. L. Fragnito, V. Laude, and A. Khelif, “Stimulated Brillouin scattering from multi-GHz-guided acoustic phonons in nanostructured photonic crystal fibres,” Nat. Phys. 2, 388–392 (2006). [CrossRef]
  31. A. Brenn, G. Wiederhecker, M. Kang, H. Hundertmark, N. Joly, and P. St. J. Russell, “Influence of air-filling fraction on forward Raman-like scattering by transversely trapped acoustic resonances in photonic crystal fibers,” J. Opt. Soc. Am. B 26, 1641–1648 (2009). [CrossRef]
  32. M. S. Kang, A. Nazarkin, A. Brenn, and P. S. J. Russell, “Tightly trapped acoustic phonons in photonic crystal fibres as highly nonlinear artificial raman oscillators,” Nat. Phys. 5, 276–280 (2009). [CrossRef]
  33. V. Leroy, A. Bretagne, M. Fink, H. Willaime, P. Tabeling, and A. Tourin, “Design and characterization of bubble phononic crystals,” Appl. Phys. Lett. 95, 171904 (2009). [CrossRef]
  34. C. Kittel, Introduction to Solid State Physics (John Wiley, 2005).
  35. COMSOL Multphysics3.5 (2009).
  36. S. Nemat-Nasser and M. Hori, Micromechanics: overall properties of heterogeneous materials (North-Holland, 1993).
  37. C. Mei, J. Auriault and C. Ng, “Some applications of the homogenization theory,” Adv. Appl. Mech. 32, 278–348 (1996).
  38. S. G. Johnson and J. D. Joannopoulos, “Block-iterative frequency-domain methods for Maxwell’s equations in a planewave basis,” Opt. Express 8, 173–190 (2001). [CrossRef]
  39. A. Chutinan and S. Noda, “Waveguides and waveguide bends in two-dimensional photonic crystal slabs,” Phys. Rev. B 82, 4488–4492 (2000). [CrossRef]
  40. S. G. Johnson, P. R. Villeneuve, S. Fan, and J. D. Joannopoulos, “Linear waveguides in photonic-crystal slabs,” Phys. Rev. B 62, 8212–8222 (2000). [CrossRef]
  41. B.-S. Song, S. Noda, T. Asano, and Y. Akahane, “Ultra-high-q photonic double-heterostructure nanocavity,” Nat. Mater. 4, 207–210 (2005). [CrossRef]
  42. 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, 041112 (2006). [CrossRef]
  43. P. E. Barclay, K. Srinivasan, and O. Painter, “Design of photonic crystal waveguides for evanescent coupling to optical fiber tapers and integration with high-Q cavities,” J. Opt. Soc. Am. B 20, 2274–2284 (2003). [CrossRef]
  44. P. Dainese, P. S. J. Russell, G. S. Wiederhecker, N. Joly, H. L. Fragnito, V. Laude, and A. Khelif, “Raman-like light scattering from acoustic phonons in photonic crystal fiber,” Opt. Express 14, 4141–4150 (2006). [CrossRef]
  45. R. W. Boyd, Nonlinear Optics, 3ed (Academic Press, 2008).
  46. 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 65, 066611 (2002). [CrossRef]
  47. G. Wannier, “Dynamics of band electrons in electric and magnetic fields,” Rev. Mod. Phys. 34, 645–655 (1962). [CrossRef]
  48. M. Charbonneau-Lefort, E. Istrate, M. Allard, J. Poon, and E. Sargent, “Photonic crystal heterostructures: waveguiding phenomena and methods of solution in an envelope function picture,” Phys. Rev. B 65, 125318 (2002). [CrossRef]
  49. E. Istrate, M. Charbonneau-Lefort, and E. Sargent, “Theory of photonic crystal heterostructures,” Phys. Rev. B 66, 075121 (2002). [CrossRef]
  50. O. Painter, K. Srinivasan, and P. Barclay, “Wannier-like equation for the resonant cavity modes of locally perturbed photonic crystals,” Phys. Rev. B 68, 035214 (2003). [CrossRef]
  51. D. Chang, A. H. Safavi-Naeini, M. Hafezi, and O. Painter, “Slowing and stopping light using an optomechanical crystal array,” arXiv:1006.3829 (2010).
  52. . P. Rabl, S. J. Kolkowitz, F. H. Koppens, J. G. E. Harris, P. Zoller, and M. D. Lukin, “A quantum spin transducer based on nano electro-mechanical resonator arrays,” arXiv:0908.0316v1 (2009).
  53. M. Wallquist, K. Hammerer, P. Rabl, M. Lukin, and P. Zoller, “Hybrid quantum devices and quantum engineering,” Phys. Scr. T 137, 014001 (2009).

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited