OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Vol. 20, Iss. 3 — Mar. 1, 2003
  • pp: 569–572

Temporal coupled-mode theory for the Fano resonance in optical resonators

Shanhui Fan, Wonjoo Suh, and J. D. Joannopoulos  »View Author Affiliations


JOSA A, Vol. 20, Issue 3, pp. 569-572 (2003)
http://dx.doi.org/10.1364/JOSAA.20.000569


View Full Text Article

Acrobat PDF (176 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 a theory of the Fano resonance for optical resonators, based on a temporal coupled-mode formalism. This theory is applicable to the general scheme of a single optical resonance coupled with multiple input and output ports. We show that the coupling constants in such a theory are strongly constrained by energy-conservation and time-reversal symmetry considerations. In particular, for a two-port symmetric structure, Fano-resonant line shape can be derived by using only these symmetry considerations. We validate the analysis by comparing the theoretical predictions with three-dimensional finite-difference time-domain simulations of guided resonance in photonic crystal slabs. Such a theory may prove to be useful for response-function synthesis in filter and sensor applications.

© 2003 Optical Society of America

OCIS Codes
(050.2770) Diffraction and gratings : Gratings
(230.3990) Optical devices : Micro-optical devices
(230.4040) Optical devices : Mirrors
(230.5750) Optical devices : Resonators

Citation
Shanhui Fan, Wonjoo Suh, and J. D. Joannopoulos, "Temporal coupled-mode theory for the Fano resonance in optical resonators," J. Opt. Soc. Am. A 20, 569-572 (2003)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-20-3-569


Sort:  Author  |  Year  |  Journal  |  Reset

References

  1. R. W. Wood, “On the remarkable case of uneven distribution of a light in a diffractived grating spectrum,” Philos. Mag. 4, 396–402 (1902).
  2. U. Fano, “The theory of anomalous diffraction gratings and of quasi-stationary waves on metallic surfaces (Sommerfeld’s waves),” J. Opt. Soc. Am. 31, 213–222 (1941).
  3. A. Hessel and A. A. Oliner, “A new theory of Wood’s anomalies on optical gratings,” Appl. Opt. 4, 1275–1297 (1965).
  4. D. Maystre, “General study of grating anomalies from electromagnetic surface modes,” in Electromagnetic Surface Modes, A. D. Boardman, ed. (Wiley, Chichester, UK, 1982).
  5. H. L. Bertoni, L.-H. S. Cheo, and T. Tamir, “Frequency-selective reflection and transmission by a periodic dielectric layer,” IEEE Trans. Antennas Propag. 37, 78–83 (1989).
  6. S. S. Wang, R. Magnuson, J. S. Bagby, and M. G. Moharam, “Guided-mode resonance in planar dielectric layer diffraction gratings,” J. Opt. Soc. Am. A 7, 1470–1474 (1990).
  7. R. Magnuson and S. Wang, “New principles for optical filters,” Appl. Phys. Lett. 61, 1022–1024 (1992).
  8. M. Nevière, E. Popov, and R. Reinisch, “Electromagnetic resonances in linear and nonlinear optics: phenomenological study of grating behavior through the poles and zeros of the scattering operator,” J. Opt. Soc. Am. A 12, 513–523 (1995).
  9. S. Peng and G. M. Morris, “Resonant scattering from two-dimensional gratings,” J. Opt. Soc. Am. A 13, 993–1005 (1996).
  10. A. Sharon, D. Rosenblatt, A. A. Friesem, H. G. Weber, H. Engel, and R. Steingrueber, “Light modulation with resonant grating-waveguide structures,” Opt. Lett. 21, 1564–1566 (1996).
  11. S. M. Norton, T. Erdogan, and G. M. Morris, “Coupled-mode theory of resonant-grating filters,” J. Opt. Soc. Am. A 14, 629–639 (1997).
  12. T. Tamir and S. Zhang, “Resonant scattering by multilayered dielectric gratings,” J. Opt. Soc. Am. A 14, 1607–1616 (1997).
  13. G. Levy-Yurista and A. A. Friesem, “Very narrow spectral filters with multilayered grating waveguide structures,” Appl. Phys. Lett. 77, 1596–1598 (2000).
  14. S. Fan, “Sharp asymmetric lineshapes in side-coupled waveguide-resonator systems,” Appl. Phys. Lett. 80, 910–912 (2002).
  15. M. Kanskar, P. Paddon, V. Pacradouni, R. Morin, A. Busch, J. F. Young, S. R. Johnson, J. MacKenzie, and T. Tiedje, “Observation of leaky slab modes in an air-bridged semiconductor waveguide with a two-dimensional photonic lattice,” Appl. Phys. Lett. 70, 1438–1440 (1997).
  16. V. N. Astratov, I. S. Culshaw, R. M. Stevenson, D. M. Whittaker, M. S. Skolnick, T. F. Kraus, and R. M. De La Rue, “Resonant coupling of near-infrared radiation to photonic band structure waveguides,” J. Lightwave Technol. 17, 2050–2057 (1999).
  17. H. A. Haus, Waves and Fields in Optoelectronics (Prentice-Hall, Englewood Cliffs, N.J., 1984).
  18. S. Fan and J. D. Joannopoulos, “Analysis of guided resonance in photonic crystal slabs,” Phys. Rev. B 65, art. no. 235112 (2002).
  19. P. Vincent, “Singularity expansions for cylinders of finite conductivity,” Appl. Phys. 17, 239–248 (1978).
  20. J. U. Nöckel and A. D. Stone, “Resonance line shapes in quasi-one-dimensional scattering,” Phys. Rev. B 50, 17415–17432 (1994).

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