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Optics Express

Optics Express

  • Editor: Michael Duncan
  • Vol. 11, Iss. 4 — Feb. 24, 2003
  • pp: 381–391

Modeling and optimization of complex photonic resonant cavity circuits

M. Sumetsky and B. J. Eggleton  »View Author Affiliations


Optics Express, Vol. 11, Issue 4, pp. 381-391 (2003)
http://dx.doi.org/10.1364/OE.11.000381


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Abstract

The simple method for modeling of circuits of weakly coupled lossy resonant cavities, previously developed in quantum mechanics, is generalized to enable calculation of the transmission and reflection amplitudes and group delay of light. Our result is the generalized Breit-Wigner formula, which has a clear physical meaning and is convenient for fast modeling and optimization of complex resonant cavity circuits and, in particular, superstructure gratings in a way similar to modeling and optimization of electric circuits. As examples, we find the conditions when a finite linear chain of cavities and a linear chain with adjacent cavities act as bandpass and double bandpass filters, and the condition for a Y-shaped structure to act as a bandpass 50/50 light splitter. The group delay dependencies of the considered structures are also investigated.

© 2003 Optical Society of America

OCIS Codes
(130.2790) Integrated optics : Guided waves
(230.7370) Optical devices : Waveguides

ToC Category:
Research Papers

History
Original Manuscript: January 9, 2003
Revised Manuscript: February 19, 2003
Published: February 24, 2003

Citation
Michael Sumetsky and Benjamin Eggleton, "Modeling and optimization of complex photonic resonant cavity circuits," Opt. Express 11, 381-391 (2003)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-11-4-381


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References

  1. N. Stefanou and A. Modinos, �??Impurity bands in photonic insulators,�?? Phys. Rev. B 57, 12127 (1998). [CrossRef]
  2. A. Yariv, Y. Xu, R. K. Lee, and A. Scherer, �??Coupled-resonator optical waveguide: a proposal and analysis,�?? Opt. Lett. 24, 711 (1999). [CrossRef]
  3. M. Bayindir, B. Temelkuran, and E. Ozbay, �??Tight-binding description of the coupled defect modes in threedimensional photonic crystals,�?? Phys. Rev. Lett. 84, 2140 (2000). [CrossRef] [PubMed]
  4. E. Ozbay, M. Bayindir, I. Bulu, and E. Cubukcu, �??Investigation of localized coupled-cavity modes in twodimensional photonic bandgap structures,�?? IEEE J. Quant. Electron. 38, 837 (2002). [CrossRef]
  5. S. Lan, S. Nishikawa, and H. Ishikawa, �??Design of impurity band-based photonic crystal waveguides and delay lines for ultrashort optical pulses,�?? J. Appl. Phys. 90, 4321 (2001). [CrossRef]
  6. S. Mookherjea and A. Yariv, �??Coupled resonator optical waveguides,�?? IEEE J. Sel. Topics in Quant. Electron. 3, 448 (2002). [CrossRef]
  7. K. Hosomi and T. Katsuyama, �??A dispersion compenstor using coupled defects in a photonic crystal,�?? IEEE J. Quant. Electron. 38, 825 (2002). [CrossRef]
  8. M. Soljacic, S. G. Johnson, S. Fan, M. Ibanescu, E. Ippen, and J. D. Joannopoulos, �??Photonic- crystal slowlight enhancement of non-linear phase sensitivity,�?? J. Opt. Soc. Am. B 19, 2052 (2002). [CrossRef]
  9. S. Oliver, C. Smith, M. Rattier, H. Benisty, C. Weisbuch, T. Krauss, R. Houdré, and U.Oesterlé, �??Miniband transmission in a photonic crystal coupled-resonator optical waveguide,�?? Opt. Lett. 26, 1019 (2002). [CrossRef]
  10. S. Nishikawa, S. Lan, N. Ikeda, Y. Sugimoto, H. Ishikawa, and K. Asakawa, �??Optical characterization of photonic crystal delay lines based on one-dimensional coupled defects,�?? Opt. Lett. 27, 2079 (2002). [CrossRef]
  11. C. M. de Sterke, �??Superstructure gratings in the tight-binding approximation,�?? Phys. Rev. E 57, 3502 (1998). [CrossRef]
  12. R. Slavic and S. LaRochelle, �??Large-band periodic filters for DWDM using multiple-superimposed fiber Bragg gratings,�?? IEEE Photon. Technol. Lett. 14, 1704 (2002). [CrossRef]
  13. N. W. Ashcroft and N. D. Mermin, Solid state physics, (Saunders College, Philadelphia, 1976).
  14. . L. P. Kouwenhoven, C. M. Marcus, P. L. McEuen, S. Tarucha, R. M. Westervelt, and N. S. Wingreen, �??Electron Transport in Quantum Dots,�?? Proceedings of the NATO Advanced Study Institute on Mesoscopic Electron Transport, edited by L. L. Sohn, L. P. Kouwenhoven, and G. Schön, 1997, pp.105-214.
  15. Y. Xu, R. K. Lee, and A. Yariv, �??Adiabatic coupling between conventional dielectric waveguides and waveguides with discrete translational symmetry,�?? Opt. Lett. 25, 755 (2000). [CrossRef]
  16. A. Mekis and J. D. Joannopoulos, �??Tapered couplers for efficient interfacing between dielectric and photonic crystal waveguides,�?? J. Lightwave Technol. 19, 861 (2001). [CrossRef]
  17. D. W. Prather, J. Murakowski, S. Shi, S. Venkataraman, A. Sharkawy, C. Chen, and D. Pustai, �??Highlyefficiency coupling structure for a single-line-defect photonic-crystal waveguide,�?? Opt. Lett. 27, 1601 (2002). [CrossRef]
  18. P. Sanchis, J. Marti, J. Blasco, A. Martinez, and A. Garcia, �??Mode matching technique for highly efficient coupling between dielectric waveguides and planar photonic crystal circuits,�?? Opt. Express 10, 1391 (2002), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-24-1391">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-24-1391</a> [CrossRef] [PubMed]
  19. L. D. Landau and E. M. Lifshitz, Quantum mechanics, (Pergamon Press, 1958, pp. 440-449).
  20. M. Sumetskii, �??Modeling of complicated nanometer resonant tunneling devices with quantum dots,�?? J. Phys: Condens. Matter 3, 2651 (1991). [CrossRef]
  21. M. Sumetskii, �??Resistance resonances for resonant-tunneling structures of quantum dots," Phys. Rev. B 48, 4586 (1993). [CrossRef]
  22. M. Sumetskii, �??Narrow current dip for the double quantum dot resonant tunneling structure with three leads: Sensitive nanometer Y-branch switch,�?? Appl. Phys. Lett. 63, 3185 (1993). [CrossRef]
  23. G. Lenz, B. J. Eggleton, C. K. Madsen, and R. E. Slusher, �??Optical delay lines based on optical filters,�?? IEEE J. Quant. Electron. 27, 525 (2001). [CrossRef]
  24. R. Kashyap, Fiber Bragg Gratings, (Academic Press, 1999).
  25. G. Lenz and C. K. Madsen, �??General optical all-pass filter structures for dispersion control in WDM systems,�?? J. Lightwave Technol. 17, 1248 (1999). [CrossRef]
  26. Yu. N. Demkov and V. N. Ostrovskii, Zero-range potentials and their applications in atomic physics, (Plenum Press, 1988). [CrossRef]
  27. Y. Meir and N. S. Wingreen, �??Landauer Formula for the current through an interacting electron region,�?? Phys. Rev. Lett. 68, 2512 (1992). [CrossRef] [PubMed]
  28. S. Datta, Electronic transport in mesoscopic systems, (Cambridge University Press, 1995).
  29. M. Sumetskii, �??Forming of wave packets by one-dimensional tunneling structures having a time-dependent potential,�?? Phys. Rev. B 46, 4702 (1992). [CrossRef]

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