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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Editor: Stephen A. Burns
  • Vol. 26, Iss. 12 — Dec. 1, 2009
  • pp: 2623–2633

Magnetic field integral equation analysis of interaction between a surface plasmon polariton and a circular dielectric cavity embedded in the metal

Ioannis Chremmos  »View Author Affiliations

JOSA A, Vol. 26, Issue 12, pp. 2623-2633 (2009)

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A rigorous integral equation (IE) analysis of the interaction between a surface plasmon polariton (SPP) and a circular dielectric cavity embedded in a metal half-space is presented. The device is addressed as the plasmonic counterpart of the established integrated optics filter comprising a whispering gallery (WG) resonator coupled to a waveguide. The mathematical formulation is that of a transverse magnetic scattering problem. Using a magnetic-type Green’s function of the two-layer medium with boundary conditions that cancel the line integral contributions along the interface, an IE for the magnetic field inside the cavity is obtained. The IE is treated through an entire-domain method of moments (MoM) with cylindrical-harmonic basis functions. The entries of the MoM matrix are determined analytically by utilizing the inverse Fourier transform of Green’s function and the Jacobi–Anger formula for interchanging between plane and cylindrical waves. Complex analysis techniques are applied to determine the transmitted, reflected, and radiated field quantities in series forms. The numerical results show that the scattered SPPs’ spectra exhibit pronounced wavelength selectivity that is related to the excitation of WG-like cavity modes. It seems feasible to exploit the device as a bandstop or reflective filter or even as an efficient radiating element. In addition, the dependence of transmission on the cavity refractive index endows this structure with a sensing functionality.

© 2009 Optical Society of America

OCIS Codes
(240.5420) Optics at surfaces : Polaritons
(240.6680) Optics at surfaces : Surface plasmons
(240.6690) Optics at surfaces : Surface waves
(290.5825) Scattering : Scattering theory

ToC Category:
Optics at Surfaces

Original Manuscript: August 25, 2009
Revised Manuscript: October 18, 2009
Manuscript Accepted: October 19, 2009
Published: November 19, 2009

Ioannis Chremmos, "Magnetic field integral equation analysis of interaction between a surface plasmon polariton and a circular dielectric cavity embedded in the metal," J. Opt. Soc. Am. A 26, 2623-2633 (2009)

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  1. J. Takahara, S. Yamagishi, H. Taki, A. Morimoto, and T. Kobayashi, “Guiding of a one-dimensional optical beam with nanometer diameter,” Opt. Lett. 22, 475-477 (1997). [CrossRef] [PubMed]
  2. E. Ozbay, “Plasmonics: merging photonics and electronics at nanoscale dimensions,” Science 311, 189-193 (2006). [CrossRef] [PubMed]
  3. K. Tanaka and M. Tanaka, “Simulations of nanometric optical circuits based on surface plasmon polariton gap waveguide,” Appl. Phys. Lett. 82, 1158-1160 (2003). [CrossRef]
  4. D. K. Gramotnev and D. F. P. Pile, “Single-mode subwavelength waveguide with channel plasmon-polaritons in triangular grooves on a metal surface,” Appl. Phys. Lett. 85, 6323-6325 (2004). [CrossRef]
  5. Z. Han, L. Liu, and E. Forsberg, “Ultra-compact directional couplers and Mach-Zehnder interferometers employing surface plasmon polaritons,” Opt. Commun. 259, 690-695 (2006). [CrossRef]
  6. S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J.-Y. Laluet, and T. W. Ebbesen, “Channel plasmon subwavelength waveguide components including interferometers and ring resonators,” Nature 440, 508-511 (2006). [CrossRef] [PubMed]
  7. S. Xiao, L. Liu, and M. Qiu, “Resonator channel drop filters in a plasmon-polaritons metal,” Opt. Express 14, 2932-2937 (2006). [CrossRef] [PubMed]
  8. A. Hosseini and Y. Massoud, “Nanoscale surface plasmon based resonator using rectangular geometry,” Appl. Phys. Lett. 90, 181102 (2007). [CrossRef]
  9. D. G. Rabus, Integrated Ring Resonators: The Compendium (Springer, 2007).
  10. J.B.Khurgin and R.S.Tucker, eds. Slow Light: Science and Applications (CRC Press2009).
  11. V. S. Volkov and S. I. Bozhevolnyi, “Waveguide-ring resonator-based photonic components utilizing channel plasmon polaritons,” Proc. SPIE 6896, 68960M (2008). [CrossRef]
  12. H.-M. Gong, L. Zhou, X.-R. Su, S. Xiao, S.-D. Liu, and Q.-Q. Wang, “Illuminating dark plasmons of silver nanoantenna rings to enhance exciton-plasmon interactions,” Adv. Function. Mat. 19, 298-303 (2009). [CrossRef]
  13. F. Hao, P. Nordlander, M. T. Burnett, and S. A. Maier, “Enhanced tunability and linewidth sharpening of plasmon resonances in hybridized metallic ring/disk nanocavities,” Phys. Rev. B 76, 245417 (2007). [CrossRef]
  14. F. Hao, P. Nordlander, Y. Sonnefraud, P. Van Dorpe, and S. A. Maier, “Tunability of subradiant dipolar and fano-type plasmon resonances in metallic ring/disk cavities: implications for nanoscale optical sensing,” ACS Nano. 3, 643-652 (2009). [CrossRef] [PubMed]
  15. A. K. Sheridan, A. W. Clark, A. Glidle, J. M. Cooper, and D. R. S. Cumming, “Fabrication and tuning of nanoscale metallic ring and split-ring arrays,” J. Vac. Sci. Technol. B 25, 2628-2631 (2007). [CrossRef]
  16. R.-L. Chern, “Magnetic and surface plasmon resonances for periodic lattices of plasmonic split-ring resonators,” Phys. Rev. B 78, 085116 (2008). [CrossRef]
  17. Y.-T. Chang, D.-C. Tzuang, Y.-T. Wu, C.-F. Chan, Y.-H. Ye, T.-H. Hung, Y.-F. Chen, and S.-C. Lee, “Surface plasmon on aluminum concentric rings arranged in a long-range periodic structure,” Appl. Phys. Lett. 92, 253111 (2008). [CrossRef]
  18. J. Sone, J. Fujita, Y. Ochiai, S. Manako, S. Matsui, E. Nomura, T. Baba, H. Kawaura, T. Sakamoto, C. D. Chen, Y. Nakamura, and J. S. Tsai, “Nanofabrication toward sub-10 nm and its application to novel nanodevices,” Nanotechnology 10, 135-141 (1999). [CrossRef]
  19. C. A. Volkert and A. M. Minor, “Focused ion beam microscopy and micromachining,” MRS Bull. 32, 389-399 (2007). [CrossRef]
  20. S. V. Boriskina and A. I. Nosich, “Radiation and absorption losses of the whispering-gallery-mode dielectric resonators excited by a dielectric waveguide,” IEEE Trans. Microwave Theory Tech. 47, 224-231 (1999). [CrossRef]
  21. J. A. Sánchez-Gil and A. A. Maradudin, “Near-field and far-field scattering of surface plasmon polaritons by one-dimensional surface defects,” Phys. Rev. B 60, 8359-8367 (1999). [CrossRef]
  22. A. Yu. Nikitin, F. López-Tejeira, and L. Martín-Moreno, “Scattering of surface plasmon polaritons by one-dimensional inhomogeneities,” Phys. Rev. B 75, 035129 (2007). [CrossRef]
  23. F. Pincemin, A. A. Maradudin, A. D. Boardman, and J.-J. Greffet, “Scattering of a surface plasmon polariton by a surface defect,” Phys. Rev. B 50, 15261-15275 (1994). [CrossRef]
  24. A. B. Evlyukhin, G. Brucoli, L. Martín-Moreno, S. I Bozhevolnyi, and F. J. García-Vidal, “Surface plasmon polariton scattering by finite-size nanoparticles,” Phys. Rev. B 76, 075426 (2007). [CrossRef]
  25. X.-S. Lin and X.-G. Huang, “Tooth-shaped plasmonic waveguide filters with nanometric sizes,” Opt. Lett. 33, 2874-2876 (2008). [CrossRef] [PubMed]
  26. A. L. Cullen, “Reflection from cylinder in surface-wave field,” Electron. Lett. 11, 479-480 (1975). [CrossRef]
  27. A. Nosich, “Radiation conditions, limiting absorption principle, and general relations in open waveguide scattering,” J. Electromagn. Waves Appl. 8, 329-353 (1994). [CrossRef]
  28. W. C. Chew, Waves and Fields in Inhomogenous Media, 2nd ed. (Wiley-IEEE Press, 1999). [CrossRef]
  29. R. F. Harrington, Field Computation by Moment Methods (IEEE Press, 1993). [CrossRef]
  30. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Dover, 1972).
  31. P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370-4379 (1972). [CrossRef]
  32. S. C. Hagness, D. Rafizadeh, S. T. Ho, and A. Taflove, “FDTD microcavity simulations: design and experimental realization of waveguide-coupled single-mode ring and whispering-gallery-mode disk resonators,” J. Lightwave Technol. 15, 2154-2165 (1997). [CrossRef]
  33. I. D. Chremmos and N. K. Uzunoglu, “Transmission and radiation in a slab waveguide coupled to a whispering gallery resonator: volume integral equation analysis,” J. Opt. Soc. Am. A 21, 839-846 (2004). [CrossRef]
  34. F. Xu, P. Horak, and G. Brambilla, “Optical microfiber coil resonator refractometric sensor,” Opt. Express 15, 7888-7893 (2007). [CrossRef] [PubMed]
  35. S. V. Boriskina, T. M. Benson, P. Sewell, and A. I. Nosich, “Effect of a layered environment on the complex natural frequencies of two-dimensional WGM dielectric-ring resonators,” J. Lightwave Technol. 20, 1563-1572 (2002). [CrossRef]
  36. A. I. Nosich, “Method of analytical regularization in wave-scattering and eigenvalue problems: foundations and review of solutions,” IEEE Antennas Propag. Mag. 41, 34-39 (1999). [CrossRef]

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