OSA's Digital Library

Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 22 — Oct. 24, 2011
  • pp: 22337–22349

On optical forces in spherical whispering gallery mode resonators

J. T. Rubin and L. Deych  »View Author Affiliations

Optics Express, Vol. 19, Issue 22, pp. 22337-22349 (2011)

View Full Text Article

Enhanced HTML    Acrobat PDF (849 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



In this paper we discuss the force exerted by the field of an optical cavity on a polarizable dipole. We show that the modification of the cavity modes due to interaction with the dipole significantly alters the properties of the force. In particular, all components of the force are found to be non-conservative, and cannot, therefore, be derived from a potential energy. We also suggest a simple generalization of the standard formulas for the optical force on the dipole, which reproduces the results of calculations based on the Maxwell stress tensor.

© 2011 OSA

OCIS Codes
(140.7010) Lasers and laser optics : Laser trapping
(140.3945) Lasers and laser optics : Microcavities
(350.4855) Other areas of optics : Optical tweezers or optical manipulation

ToC Category:

Original Manuscript: July 1, 2011
Revised Manuscript: September 20, 2011
Manuscript Accepted: October 1, 2011
Published: October 24, 2011

Virtual Issues
Vol. 6, Iss. 11 Virtual Journal for Biomedical Optics
Collective Phenomena (2011) Optics Express

J. T. Rubin and L. Deych, "On optical forces in spherical whispering gallery mode resonators," Opt. Express 19, 22337-22349 (2011)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. A. Ashkin, “Acceleration and trapping of particles by radiation pressure,” Phys. Rev. Lett. 24, 156–159 (1970). [CrossRef]
  2. A. Ashkin, J. M. Dziedzic, J. E. Bjorkholm, and S. Chu, “Observation of a single-beam gradient force optical trap for dielectric particles,” Opt. Lett. 11, 288–290 (1986). [CrossRef] [PubMed]
  3. G. Anetsberger, O. Arcizet, Q. P. Unterreithmeier, R. Riviere, A. Schliesser, E. M. Weig, J. P. Kotthaus, and T. J. Kippenberg, “Near-field cavity optomechanics with nanomechanical oscillators,” Nat. Phys. 5, 909–914 (2009). [CrossRef]
  4. A. Schliesser, O. Arcizet, R. Riviere, G. Anetsberger, and T. J. Kippenberg, “Resolved-sideband cooling and position measurement of a micromechanical oscillator close to the heisenberg uncertainty limit,” Nat. Phys. 5, 509–514 (2009). [CrossRef]
  5. A. Schliesser, R. Riviere, G. Anetsberger, O. Arcizet, and T. J. Kippenberg, “Resolved-sideband cooling of a micromechanical oscillator,” Nat. Phys. 4, 415–419 (2008). [CrossRef]
  6. S. Groeblacher, K. Hammerer, M. R. Vanner, and M. Aspelmeyer, “Observation of strong coupling between a micromechanical resonator and an optical cavity field,” Nature 460, 724–727 (2009). [CrossRef]
  7. O. Arcizet, C. Molinelli, T. Briant, P.-F. Cohadon, A. Heidmann, J.-M. Mackowski, C. Michel, L. Pinard, O. Francais, and L. Rousseau, “Experimental optomechanics with silicon micromirrors,” N. J. Phys. 10, 125021 (2008). [CrossRef]
  8. A. M. Jayich, J. C. Sankey, B. M. Zwickl, C. Yang, J. D. Thompson, S. M. Girvin, A. A. Clerk, F. Marquardt, and J. G. E. Harris, “Dispersive optomechanics: a membrane inside a cavity,” N. J. Phys. 10, 095008 (2008). [CrossRef]
  9. D. J. Wilson, C. A. Regal, S. B. Papp, and H. J. Kimble, “Cavity optomechanics with stoichiometric sin films,” Phys. Rev. Lett. 103, 207204 (2009). [CrossRef]
  10. D. E. Chang, C. A. Regal, S. B. Papp, D. J. Wilson, J. Ye, O. Painter, H. J. Kimble, and P. Zoller, “Cavity opto-mechanics using an optically levitated nanosphere,” Proc. Natl. Acad. Sci. U.S.A. 107, 1005–1010 (2010). [CrossRef] [PubMed]
  11. O. Romero-Isart, M. L. Juan, R. Quidant, and J. I. Cirac, “Toward quantum superposition of living organisms,” N. J. Phys. 12, 033015 (2010). [CrossRef]
  12. P. F. Barker and M. N. Shneider, “Cavity cooling of an optically trapped nanoparticle,” Phys. Rev. A 81, 023826 (2010). [CrossRef]
  13. O. Romero-Isart, A. C. Pflanzer, M. L. Juan, R. Quidant, N. Kiesel, M. Aspelmeyer, and J. I. Cirac, “Optically levitating dielectrics in the quantum regime: theory and protocols,” Phys. Rev. A 83, 013803 (2011). [CrossRef]
  14. Z.-q. Yin, T. Li, and M. Feng, “Three-dimensional cooling and detection of a nanosphere with a single cavity,” Phys. Rev. A 83, 013816 (2011). [CrossRef]
  15. T. Li, S. Kheifets, and M. G. Raizen, “Millikelvin cooling of an optically trapped microsphere in vacuum,” Nat. Phys. 7, 527–530 (2011). [CrossRef]
  16. T. J. Kippenberg and K. J. Vahala, “Cavity optomechanics: Back-action at the mesoscale,” Science 321, 1172–1176 (2008). [CrossRef] [PubMed]
  17. A. Schliesser and T. J. Kippenberg, “Cavity optomechanics with whispering-gallery mode optical micro-resonators,” Adv. At. Mol. Opt. Phys. 58, 207–323 (2010). [CrossRef]
  18. V. Braginsky and A. Manukin, Measurment of Weak Forces in Physics Experiments (University of Chicago Press, 1977).
  19. R. J. Schulze, C. Genes, and H. Ritsch, “Optomechanical approach to cooling of small polarizable particles in a strongly pumped ring cavity,” Phys. Rev. A 81, 063820 (2010). [CrossRef]
  20. M. Nieto-Vesperinas, P. Chaumet, and A. Rahmani, “Near-field photonic forces,” Phil. Trans. R. Soc. Lond. A 362, 719–737 (2004). [CrossRef]
  21. J. Rubin and L. Deych, “Optical forces due to spherical microresonators and their manifestation in optically induced orbital motion of nanoparticles,” Phys. Rev. A 84, 023844 (2011). [CrossRef]
  22. S. Arnold, D. Keng, S. I. Shopova, S. Holler, W. Zurawsky, and F. Vollmer, “Whispering gallery mode carousel—a photonic mechanism for enhanced nanoparticle detection in biosensing,” Opt. Express 17, 6230–6238 (2009). [CrossRef] [PubMed]
  23. L. Landau, E. Lifshitz, and L. Pitaevskiĭ, Electrodynamics of continuous media, Course of theoretical physics (Butterworth-Heinemann, 1984).
  24. V. Wong and M. A. Ratner, “Explicit computation of gradient and nongradient contributions to optical forces in the discrete-dipole approximation,” J. Opt. Soc. Am. B 23, 1801–1814 (2006). [CrossRef]
  25. M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption and Emission of Light by Small Particles (Cambridge University Press, 2002).
  26. L. Deych and J. Rubin, “Rayleigh scattering of whispering gallery modes of microspheres due to a single dipole scatterer,” Phys. Rev. A 80, 061805 (2009). [CrossRef]
  27. J. T. Rubin and L. Deych, “Ab initio theory of defect scattering in spherical whispering-gallery-mode resonators,” Phys. Rev. A 81, 053827 (2010). [CrossRef]
  28. J. Hu, S. Lin, L. C. Kimerling, and K. Crozier, “Optical trapping of dielectric nanoparticles in resonant cavities,” Phys. Rev. A 82, 053819 (2010). [CrossRef]
  29. M. Abramowitz and I. Stegun, Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables (National Bureau of Standards, 1972).
  30. J. Chen, J. Ng, S. Liu, and Z. Lin, “Analytical calculation of axial optical force on a rayleigh particle illuminated by gaussian beams beyond the paraxial approximation,” Phys. Rev. E 80, 026607 (2010). [CrossRef]

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.


Fig. 1 Fig. 2

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited