OSA's Digital Library

Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 12 — Jun. 17, 2013
  • pp: 14169–14180

Finite element simulation of a perturbed axial-symmetric whispering-gallery mode and its use for intensity enhancement with a nanoparticle coupled to a microtoroid

Alex Kaplan, Matthew Tomes, Tal Carmon, Maxim Kozlov, Oren Cohen, Guy Bartal, and Harald G. L. Schwefel  »View Author Affiliations

Optics Express, Vol. 21, Issue 12, pp. 14169-14180 (2013)

View Full Text Article

Enhanced HTML    Acrobat PDF (2963 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



We present an optical mode solver for a whispering gallery resonator coupled to an adjacent arbitrary shaped nano-particle that breaks the axial symmetry of the resonator. Such a hybrid resonator-nanoparticle is similar to what was recently used for bio-detection and for field enhancement. We demonstrate our solver by parametrically studying a toroid-nanoplasmonic device and get the optimal nano-plasmonic size for maximal enhancement. We investigate cases near a plasmonic resonance as well as far from a plasmonic resonance. Unlike common plasmons that typically benefit from working near their resonance, here working far from plasmonic resonance provides comparable performance. This is because the plasmonic resonance enhancement is accompanied by cavity quality degradation through plasmonic absorption.

© 2013 OSA

OCIS Codes
(230.5750) Optical devices : Resonators
(050.1755) Diffraction and gratings : Computational electromagnetic methods
(250.5403) Optoelectronics : Plasmonics

ToC Category:
Optical Devices

Original Manuscript: March 25, 2013
Revised Manuscript: May 3, 2013
Manuscript Accepted: May 24, 2013
Published: June 6, 2013

Alex Kaplan, Matthew Tomes, Tal Carmon, Maxim Kozlov, Oren Cohen, Guy Bartal, and Harald G. L. Schwefel, "Finite element simulation of a perturbed axial-symmetric whispering-gallery mode and its use for intensity enhancement with a nanoparticle coupled to a microtoroid," Opt. Express 21, 14169-14180 (2013)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Ultra-high-Q toroid microcavity on a chip,” Nature421(6926), 925–928 (2003). [CrossRef] [PubMed]
  2. V. B. Braginsky, M. L. Gorodetsky, and V. S. Ilchenko, “Quality-factor and nonlinear properties of optical whispering-gallery modes,” Phys. Lett. A137(7-8), 393–397 (1989). [CrossRef]
  3. I. S. Grudinin, A. B. Matsko, A. A. Savchenkov, D. Strekalov, V. S. Ilchenko, and L. Maleki, “Ultra high Q crystalline microcavities,” Opt. Commun.265(1), 33–38 (2006). [CrossRef]
  4. B. Sprenger, H. G. L. Schwefel, Z. H. Lu, S. Svitlov, and L. J. Wang, “CaF2 whispering-gallery-mode-resonator stabilized-narrow-linewidth laser,” Opt. Lett.35(17), 2870–2872 (2010). [CrossRef] [PubMed]
  5. B. Sprenger, H. G. L. Schwefel, and L. J. Wang, “Whispering-gallery-mode-resonator-stabilized narrow-linewidth fiber loop laser,” Opt. Lett.34(21), 3370–3372 (2009). [CrossRef] [PubMed]
  6. J. U. Fürst, D. V. Strekalov, D. Elser, A. Aiello, U. L. Andersen, Ch. Marquardt, and G. Leuchs, “Low-Threshold Optical Parametric Oscillations in a Whispering Gallery Mode Resonator,” Phys. Rev. Lett.105(26), 263904 (2010). [CrossRef] [PubMed]
  7. T. Beckmann, H. Linnenbank, H. Steigerwald, B. Sturman, D. Haertle, K. Buse, and I. Breunig, “Highly tunable low-threshold optical parametric oscillation in radially poled whispering gallery resonators,” Phys. Rev. Lett.106(14), 143903 (2011). [CrossRef] [PubMed]
  8. J. U. Fürst, D. V. Strekalov, D. Elser, M. Lassen, U. L. Andersen, C. Marquardt, and G. Leuchs, “Naturally phase-matched second-harmonic generation in a whispering-gallery-mode resonator,” Phys. Rev. Lett.104(15), 153901 (2010). [CrossRef] [PubMed]
  9. K. J. Vahala, “Optical microcavities,” Nature424(6950), 839–846 (2003). [CrossRef] [PubMed]
  10. T. Carmon and K. J. Vahala, “Visible continuous emission from a silica microphotonic device by third-harmonic generation,” Nat. Phys.3(6), 430–435 (2007). [CrossRef]
  11. J. Moore, M. Tomes, T. Carmon, and M. Jarrahi, “Continuous-wave ultraviolet emission through fourth-harmonic generation in a whispering-gallery resonator,” Opt. Express19(24), 24139–24146 (2011). [CrossRef] [PubMed]
  12. 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]
  13. D. V. Strekalov, H. G. L. Schwefel, A. A. Savchenkov, A. B. Matsko, L. J. Wang, and N. Yu, “Microwave whispering-gallery resonator for efficient optical up-conversion,” Phys. Rev. A80(3), 033810 (2009). [CrossRef]
  14. M. Tomes and T. Carmon, “Photonic micro-electromechanical systems vibrating at X-band (11-GHz) Rates,” Phys. Rev. Lett.102(11), 113601 (2009). [CrossRef] [PubMed]
  15. I. S. Grudinin, A. B. Matsko, and L. Maleki, “Brillouin lasing with a CaF2 whispering gallery mode resonator,” Phys. Rev. Lett.102(4), 043902 (2009). [CrossRef] [PubMed]
  16. G. Bahl, J. Zehnpfennig, M. Tomes, and T. Carmon, “Stimulated optomechanical excitation of surface acoustic waves in a microdevice,” Nat Commun2, 403 (2011). [CrossRef] [PubMed]
  17. G. Bahl, M. Tomes, F. Marquardt, and T. Carmon, “Observation of spontaneous Brillouin cooling,” Nat. Phys.8(3), 203–207 (2012). [CrossRef]
  18. J. U. Fürst, D. V. Strekalov, D. Elser, A. Aiello, U. L. Andersen, Ch. Marquardt, and G. Leuchs, “Quantum light from a whispering-gallery-mode disk resonator,” Phys. Rev. Lett.106(11), 113901 (2011). [CrossRef] [PubMed]
  19. H. Lee, T. Chen, J. Li, K. Y. Yang, S. Jeon, O. Painter, and K. J. Vahala, “Chemically etched ultrahigh-Q wedge-resonator on a silicon chip,” Nat. Photonics6(6), 369–373 (2012). [CrossRef]
  20. J. Hofer, A. Schliesser, and T. J. Kippenberg, “Cavity optomechanics with ultrahigh-Q crystalline microresonators,” Phys. Rev. A82(3), 031804 (2010). [CrossRef]
  21. J. Alnis, A. Schliesser, C. Y. Wang, J. Hofer, T. J. Kippenberg, and T. W. Hänsch, “Thermal-noise-limited crystalline whispering-gallery-mode resonator for laser stabilization,” Phys. Rev. A84(1), 011804 (2011). [CrossRef]
  22. M. Oxborrow, “Traceable 2-D finite-element simulation of the whispering-gallery modes of axisymmetric electromagnetic resonators,” Microwave Theory and Techniques, IEEE Transactions on55(6), 1209–1218 (2007). [CrossRef]
  23. W. Kim, V. P. Safonov, V. M. Shalaev, and R. L. Armstrong, “Fractals in microcavities: Giant coupled, multiplicative enhancement of optical responses,” Phys. Rev. Lett.82(24), 4811–4814 (1999). [CrossRef]
  24. K. A. Fuller and D. D. Smith, “Cascaded photoenhancement from coupled nanoparticle and microcavity resonance effects,” Opt. Express15(6), 3575–3580 (2007). [CrossRef] [PubMed]
  25. I. M. White, H. Oveys, and X. Fan, “Increasing the Enhancement of SERS with dielectric microsphere resonators,” Spectroscopy21, 36–42 (2006).
  26. S. I. Shopova, C. W. Blackledge, and A. T. Rosenberger, “Enhanced evanescent coupling to whispering-gallery modes due to gold nanorods grown on the microresonator surface,” Appl. Phys. B93(1), 183–187 (2008). [CrossRef]
  27. J. Zhu, S. K. Ozdemir, Y.-F. Xiao, L. Li, L. He, D.-R. Chen, and L. Yang, “On-chip single nanoparticle detection and sizing by mode splitting in an ultrahigh-Q microresonator,” Nat. Photonics4(1), 46–49 (2010). [CrossRef]
  28. J. D. Swaim, J. Knittel, and W. P. Bowen, “Detection limits in whispering gallery biosensors with plasmonic enhancement,” Appl. Phys. Lett.99(24), 243109 (2011). [CrossRef]
  29. S. I. Shopova, R. Rajmangal, S. Holler, and S. Arnold, “Plasmonic enhancement of a whispering-gallery-mode biosensor for single nanoparticle detection,” Appl. Phys. Lett.98(24), 243104 (2011). [CrossRef]
  30. M. A. Santiago-Cordoba, S. V. Boriskina, F. Vollmer, and M. C. Demirel, “Nanoparticle-based protein detection by optical shift of a resonant microcavity,” Appl. Phys. Lett.99(7), 073701 (2011). [CrossRef]
  31. V. R. Dantham, S. Holler, V. Kolchenko, Z. Wan, and S. Arnold, “Taking whispering gallery-mode single virus detection and sizing to the limit,” Appl. Phys. Lett.101(4), 043704 (2012). [CrossRef]
  32. Y.-F. Xiao, Y.-C. Liu, B.-B. Li, Y.-L. Chen, Y. Li, and Q. Gong, “Strongly enhanced light-matter interaction in a hybrid photonic-plasmonic resonator,” Phys. Rev. A85(3), 031805 (2012). [CrossRef]
  33. “COMSOL Multiphysics,” (2010).
  34. W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature424(6950), 824–830 (2003). [CrossRef] [PubMed]
  35. M. I. Stockman, “Nanofocusing of optical energy in tapered plasmonic waveguides,” Phys. Rev. Lett.93(13), 137404 (2004). [CrossRef] [PubMed]
  36. A. Kinkhabwala, Z. Yu, S. Fan, Y. Avlasevich, K. Müllen, and W. E. Moerner, “Large single-molecule fluorescence enhancements produced by a bowtie nanoantenna,” Nat. Photonics3(11), 654–657 (2009). [CrossRef]
  37. L. Novotny and N. van Hulst, “Antennas for light,” Nat. Photonics5(2), 83–90 (2011). [CrossRef]
  38. K. Jiang, M. Bosnick, Maillard, and L. Brus, “Single molecule raman spectroscopy at the junctions of large ag Nanocrystals,” J. Phys. Chem. B107(37), 9964–9972 (2003). [CrossRef]
  39. S. Kim, J. Jin, Y.-J. Kim, I.-Y. Park, Y. Kim, and S.-W. Kim, “High-harmonic generation by resonant plasmon field enhancement,” Nature453(7196), 757–760 (2008). [CrossRef] [PubMed]
  40. M. T. Hill, M. Marell, E. S. P. Leong, B. Smalbrugge, Y. Zhu, M. Sun, P. J. van Veldhoven, E. J. Geluk, F. Karouta, Y.-S. Oei, R. Nötzel, C.-Z. Ning, and M. K. Smit, “Lasing in metal-insulator-metal sub-wavelength plasmonic waveguides,” Opt. Express17(13), 11107–11112 (2009). [CrossRef] [PubMed]
  41. M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, and U. Wiesner, “Demonstration of a spaser-based nanolaser,” Nature460(7259), 1110–1112 (2009). [CrossRef] [PubMed]
  42. R. F. Oulton, V. J. Sorger, T. Zentgraf, R.-M. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature461(7264), 629–632 (2009). [CrossRef] [PubMed]
  43. B. Min, E. Ostby, V. Sorger, E. Ulin-Avila, L. Yang, X. Zhang, and K. Vahala, “High-Q surface-plasmon-polariton whispering-gallery microcavity,” Nature457(7228), 455–458 (2009). [CrossRef] [PubMed]
  44. V. J. Sorger, R. F. Oulton, J. Yao, G. Bartal, and X. Zhang, “Plasmonic Fabry-Pérot nanocavity,” Nano Lett.9(10), 3489–3493 (2009). [CrossRef] [PubMed]
  45. S. A. Maier, Plasmonics: Fundamentals and Applications (Springer, 2007).
  46. S. A. Maier and H. A. Atwater, “Plasmonics: Localization and guiding of electromagnetic energy in metal/dielectric structures,” J. Appl. Phys.98(1), 011101 (2005). [CrossRef]
  47. M. Kozlov, O. Kfir, A. Fleischer, A. Kaplan, T. Carmon, H. G. L. Schwefel, G. Bartal, and O. Cohen, “Narrow-bandwidth high-order harmonics driven by long-duration hot spots,” New J. Phys.14(6), 063036 (2012). [CrossRef]
  48. M. A. Santiago-Cordoba, M. Cetinkaya, S. V. Boriskina, F. Vollmer, and M. C. Demirel, “Ultrasensitive detection of a protein by optical trapping in a photonic-plasmonic microcavity,” J Biophotonics5(8-9), 629–638 (2012). [CrossRef] [PubMed]
  49. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley-Interscience, 1998).
  50. M. Quinten, A. Pack, and R. Wannemacher, “Scattering and extinction of evanescent waves by small particles,” Appl. Phys. B68(1), 87–92 (1999). [CrossRef]
  51. U. Kreibig and M. Vollmer, Optical Properties of Metal Clusters (Springer Series in Materials Science, 1995).
  52. K. L. Kelly, E. Coronado, L. L. Zhao, and G. C. Schatz, “The optical properties of metal nanoparticles: the influence of size, shape, and dielectric environment,” J. Phys. Chem. B107(3), 668–677 (2003). [CrossRef]
  53. P. K. Jain, K. S. Lee, I. H. El-Sayed, and M. A. El-Sayed, “Calculated absorption and scattering properties of gold nanoparticles of different size, shape, and composition: Applications in biological imaging and biomedicine,” J. Phys. Chem. B110(14), 7238–7248 (2006). [CrossRef] [PubMed]
  54. J. Wiersig, “Boundary element method for resonances in dielectric microcavities,” JOSA A5, 53–60 (2003).
  55. H. G. L. Schwefel and C. G. Poulton, “An improved method for calculating resonances of multiple dielectric disks arbitrarily positioned in the plane,” Opt. Express17(15), 13178–13186 (2009). [CrossRef] [PubMed]
  56. C.-L. Zou, H. G. L. Schwefel, F.-W. Sun, Z.-F. Han, and G.-C. Guo, “Quick root searching method for resonances of dielectric optical microcavities with the boundary element method,” Opt. Express19(17), 15669–15678 (2011). [CrossRef] [PubMed]
  57. A. N. Oraevsky, “Whispering-gallery waves,” Quantum Electron.32(5), 377–400 (2002). [CrossRef]
  58. R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, “A hybrid plasmonic waveguide for subwavelength confinement and long-range propagation,” Nat. Photonics2(8), 496–500 (2008). [CrossRef]
  59. P. Nordlander and F. Le, “Plasmonic structure and electromagnetic field enhancements in the metallic nanoparticle-film system,” Appl. Phys. B84(1-2), 35–41 (2006). [CrossRef]
  60. D. F. P. Pile and D. K. Gramotnev, “Channel plasmon-polariton in a triangular groove on a metal surface,” Opt. Lett.29(10), 1069–1071 (2004). [CrossRef] [PubMed]
  61. S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, and T. W. Ebbesen, “Channel plasmon-polariton guiding by subwavelength metal grooves,” Phys. Rev. Lett.95(4), 046802 (2005). [CrossRef] [PubMed]
  62. E. D. Palik, Handbook of Optical Constants of Solids (Elsevier Science & Tech, 1998).
  63. http://www.quantumchaos.de/Media/comsol2013/Supplement_Script_for_Fig.3_Comsol_4.3a.mph

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