OSA's Digital Library

Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 17, Iss. 20 — Sep. 28, 2009
  • pp: 18116–18135

General Treatment of Optical Forces and Potentials in Mechanically Variable Photonic Systems

Peter T. Rakich, Miloš A. Popović, and Zheng Wang  »View Author Affiliations


Optics Express, Vol. 17, Issue 20, pp. 18116-18135 (2009)
http://dx.doi.org/10.1364/OE.17.018116


View Full Text Article

Enhanced HTML    Acrobat PDF (682 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

We present an analytical formalism for the treatment of the forces and potentials induced by light in mechanically variable photonic systems (or optomechanically variable systems) consisting of linear media. Through energy and photon-number conservation, we show that knowledge of the phase and the amplitude response of an optomechanically variable system, and its dependence on the mechanical coordinate of interest, is sufficient to compute the forces produced by light. This formalism not only offers a simple analytical alternative to computationally intensive Maxwell stress-tensor methods, but also greatly simplifies the analysis of mechanically variable photonic systems driven by multiple external laser sources. Furthermore, we show, through this formalism, that a scalar optical potential can be derived in terms of the phase and amplitude response of an arbitrary optomechanically variable one-port system and in generalized optomechanically variable multi-port systems, provided that their optical response is variable through a single mechanical degree of freedom. With these simplifications, well-established theories of optical filter synthesis could be extended to allow for the synthesis of complex optical force and potential profiles, independent of the construction of the underlying device or its field distribution.

© 2009 Optical Society of America

OCIS Codes
(030.4070) Coherence and statistical optics : Modes
(130.2790) Integrated optics : Guided waves
(130.3120) Integrated optics : Integrated optics devices
(230.5750) Optical devices : Resonators
(350.4238) Other areas of optics : Nanophotonics and photonic crystals
(350.4855) Other areas of optics : Optical tweezers or optical manipulation

ToC Category:
Optical Trapping and Manipulation

History
Original Manuscript: June 19, 2009
Revised Manuscript: September 8, 2009
Manuscript Accepted: September 10, 2009
Published: September 24, 2009

Citation
Peter T. Rakich, Miloš A. Popovic, and Zheng Wang, "General treatment of optical forces and potentials in mechanically variable photonic systems," Opt. Express 17, 18116-18135 (2009)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-20-18116


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. A. Ashkin, "Acceleration and trapping of particles by radiation pressure," Phys. Rev. Lett. 24, 156-159 (1970). [CrossRef]
  2. A. Ashkin, "Trapping of atoms by resonance radiation pressure," Phys. Rev. Lett. 40, 729-732 (1978). [CrossRef]
  3. A. Ashkin, and J. M. Dziedzic, "Observation of radiation pressure trapping of particles by alternating lightbeams," Phys. Rev. Lett. 54, 1245-1248 (1985). [CrossRef] [PubMed]
  4. A. Dorsel, J. D. McCullen, P. Meystre, E. Vignes, and H. Walther, "Optical bistability and mirror confinement induced by radiation pressure," Phys. Rev. Lett. 51, 1550-1553 (1983). [CrossRef]
  5. P. Meystre, E. M. Wright, J. D. McCullen, and E. Vignes, "Theory of radiation pressure driven interferometers," J. Opt. Soc. Am. B 2, 1830-1840 (1985). [CrossRef]
  6. M. Bhattacharya, and P. Meystre, "Trapping and cooling a mirror to its quantum mechanical ground state," Phys. Rev. Lett. 99, 073601 (2007). [CrossRef] [PubMed]
  7. M. Bhattacharya and P. Meystre, "Multiple membrane cavity optomechanics," Phys. Rev. A 78, 041801 (2008). [CrossRef]
  8. T. Carmon, H. Rokhsari, L. Yang, T. Kippenberg, and K. Vahala, "Temporal Behavior of Radiation-pressureinduced vibrations of an optical microcavity phonon mode," Phys. Rev. Lett. 94, 223902 (2005). [CrossRef] [PubMed]
  9. 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, 033901 (2005). [CrossRef] [PubMed]
  10. M. L. Povinelli, M. Loncar, M. Ibanescu, E. J. Smythe, S. G. Johnson, F. Capasso, and J. D. Joannopoulos, "Evanescent-wave bonding between optical waveguides," Opt. Lett. 30, 3042-3044 (2005). [CrossRef] [PubMed]
  11. M. Eichenfield, R. Camacho, J. Chan, K. J. Vahala, and O. Painter, "A picogram- and nanometre-scale photoniccrystal optomechanical cavity," Nature 459, 550-555 (2009). [CrossRef] [PubMed]
  12. M. Eichenfield, C. P. Michael, R. Perahia, and O. Painter, "Actuation of micro-optomechanical systems via cavity-enhanced optical dipole forces," Nat. Photonics 1, 416-422 (2007). [CrossRef]
  13. P. T. Rakich, M. A. Popovic, M. Soljacic and E. P. Ippen, "Trapping, corralling and spectral bonding of optical resonances through optically induced potentials," Nat. Photonics 1, 658-665 (2007). [CrossRef]
  14. M. L. Povinelli, S. G. Johnson, M. Loncar, M. Ibanescu, E. J. Smythe, F. Capasso, and J. D. Joannopoulos, "High-Q enhancement of attractive and repulsive optical forces between coupled whispering-gallery-mode resonators," Opt. Express 13, 8286-8295 (2005). [CrossRef] [PubMed]
  15. 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] [PubMed]
  16. A. Mizrahi and L. Schchter, "Two-slab all-optical spring," Opt. Lett. 32, 692-694 (2007). [CrossRef] [PubMed]
  17. 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] [PubMed]
  18. W. H. P. Pernice, M. Li, and H. X. Tang, "Theoretical investigation of the transverse optical force between a silicon nanowire waveguide and a substrate," Opt. Express 17, 1806-1816 (2009). [CrossRef] [PubMed]
  19. A. Mizrahi, and L. Schachter, "Mirror manipulation by attractive and repulsive forces of guided waves," Opt. Express 13, 9804-9811 (2005). [CrossRef] [PubMed]
  20. M. A. Popovic and P. T. Rakich, "Optonanomechanical self-adaptive photonic devices based on light forces: a path to robust high-index-contrast nanophotonic circuits," Proc. SPIE 7219, 72190A (Feb. 10, 2009) [CrossRef]
  21. J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1999).
  22. H. A. Haus, Waves and fields in optoelectronics (Prentice-Hall, Englewood Cliffs, NJ, 1984).
  23. B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J. P. Laine, "Microring resonator channel dropping filters," J. Lightwave Technol. 15, 998-1005 (1997). [CrossRef]
  24. M. A. Popovic, Theory and design of high-index-contrast microphotonic circuits, Ph.D. Thesis (MIT Archives, Cambridge, 2008)
  25. W. Suh, M. F. Yanik, O. Solgaard, and S. H. Fan, "Displacement-sensitive photonic crystal structures based on guided resonance in photonic crystal slabs," Appl. Phys. Lett. 82 (13), 1999-2001 (2003). [CrossRef]
  26. W. Suh, Z. Wang, and S. H. Fan, "Temporal coupled-mode theory and the presence of non-orthogonal modes in lossless multimode cavities," IEEE J. Quantum Electron. 40, 1511-1518 (2004). [CrossRef]
  27. C. K. Madsen, C. K. and J. H. Zhao, Optical filter design and analysis: a signal processing approach (Wiley, New York, 1999).
  28. W. Greiner, Classical mechanics: systems of particles and Hamiltonian dynamics (Springer, New York, 2003).
  29. H. Goldstein, C. P. Poole, and J. L. Safko, Classical Mechanics (Addison Wesley, San Francisco, 2002).
  30. D. J. Griffiths, Intoduction to Quantum Mechanics (Prentice-Hall, Englewood Cliffs, NJ, 1995).
  31. P. Penfield and H. A. Haus, Electrodynamics of moving media (MIT Press, Massachusetts, 1967)
  32. R. Loudon, The Quantum Theory of Light (Oxford Science Publications, 2000)
  33. C. K. Law, "Effective Hamiltonian for the radiation in a cavity with a moving mirror and a time-varying dielectric medium," Phys. Rev. A 49, 433-437 (1994). [CrossRef] [PubMed]
  34. G. T. Moore, "Quantum theory of the electromagnetic field in a variable-length one-dimensional cavity," J. Math. Phys. 11, 2679-2691 (1970). [CrossRef]
  35. F. Gires, and P. Tournois "Interferometre utilisable pour la compression d’impulsions lumineuses modulees en frequence," C. R. Acad. Sci. Paris 25861126115 (1964).
  36. P. T. Rakich, M. A. Popovic, M. R. Watts, T. Barwicz, H. I. Smith, and E. P. Ippen, "Ultrawide tuning of photonic microcavities via evanescent field perturbation," Opt. Lett. 31, 1241-1243 (2006). [CrossRef] [PubMed]

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