Optical and Quantum Electronics

, Volume 36, Issue 1–3, pp 25–42 | Cite as

Modeling of grating assisted standing wave, microresonators for filter applications in integrated optics



A wide, multimode segment of a dielectric optical waveguide, enclosed by Bragg reflectors and evanescently coupled to adjacent port waveguides, can constitute the cavity in an integrated optical microresonator. It turns out that the device can be described adequately in terms of an approximate coupled mode theory model which involves only a few guided modes as basis fields. By reasoning along the coupled mode model, we motivate a simple design strategy for the resonator device. Rigorous two dimensional mode expansion simulations are applied to verify the predictions of the approximate model. The results exemplify the specific spectral response of the standing wave resonators. As refinements we discuss the single resonance of a device with nonsymmetrically detuned Bragg reflectors, and the cascading of two Fabry–Perot cavities, where the coupling across an intermediate shorter grating region establishes a power transfer characteristic that is suitable for an add-drop filter.

coupled mode theory integrated optics numerical modeling optical microresonators rectangular microcavities waveguide Bragg gratings 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Berends, J.H. Integrated Optical Bragg Reflectors as Narrow Band Wavelength Filters. University of Twente, Enschede, The Netherlands, Ph.D. Thesis, 1997.Google Scholar
  2. Blom, F.C., H. Kelderman, H.J.W.M. Hoekstra, A. Driessen, T.J.A. Popma, S.T. Chu and B.E. Little. Opt. Commun. 167 77, 1999.Google Scholar
  3. Boriskina, S.V., T.M. Benson, P. Sewell and A.I. Nosich. Opt. Quantum Electron. 35 545, 2003.Google Scholar
  4. Boriskina, S.V. and A.I. Nosich. IEEE Trans. Microwave Theory Tech. 47 224, 1999.Google Scholar
  5. Born, M. and E. Wolf. Principles of Optics, 7th Ed. Cambridge University Press, Cambridge, 1999.Google Scholar
  6. Chin, M.K. and S.T. Ho. J. Lightwave Technol. 16 1433, 1997.Google Scholar
  7. Chu, S.T., B.E. Little, W. Pan, T. Kaneko, S. Sato and Y. Kokubun. IEEE Photonics Technol. Lett. 11 691, 1999a.Google Scholar
  8. Chu, S.T., W. Pan, S. Sato, T. Kaneko, B.E. Little and Y. Kokubun. IEEE Photonics Technol. Lett. 11 688, 1999b.Google Scholar
  9. Čtyroký, J., S. Helfert, R. Pregla, P. Bienstmann, R. Baets, R. de Ridder, R. Stoffer, G. Klaase, J. Petráček, P. Lalanne, J.-P. Hugonin and R.M. De La Rue. Opt. Quantum Electron. 34 455, 2002.Google Scholar
  10. Chu, S.T., W. Pan, S. Suzuki, B.E. Little, S. Sato and Y. Kokubun. IEEE Photonics Technol. Lett. 11 1138, 1999c.Google Scholar
  11. Djordjev, K., S.-J. Choi, S.-J. Choi and P.D. Dapkus. J. Lightwave Technol. 20 105, 2002a.Google Scholar
  12. Djordjev, K., S.-J. Choi, S.-J. Choi and P.D. Dapkus. IEEE Photonics Technol. Lett. 14 1115, 2002b.Google Scholar
  13. Follonier, S., M. Fierz, I. Biaggio, U. Meier, C. Bosshard and P. Günter. J. Opt. Soc. Am. B 19 1990, 2002.Google Scholar
  14. Gornik, E. Science 280 1544, 1998.Google Scholar
  15. Hall, D.G. and B.J. Thompson (eds). Selected Papers on Coupled-Mode Theory in Guided-Wave Optics, Vol. MS 84 of SPIE Milestone Series. SPIE Optical Engineering Press, Bellingham, Washington USA, 1993.Google Scholar
  16. Hammer, M. Opt. Commun. 214 155, 2002.Google Scholar
  17. Hammer, M. and E. van Groesen. J. Lightwave Technol. 20 1549, 2002.Google Scholar
  18. Hammer, M. and D. Yudistira. In: Proceedings of the 11th European Conference on Integrated Optics ECIO'03, J. Čtyroký, M. Hubalek, and F. Ondracek (eds.) Vol. 1. Prague, p. 357, 2003.Google Scholar
  19. Klunder, D.J.W., M.L.M. Balistreri, F.C. Blom, H.J.W.M. Hoekstra, A. Driessen, L. Kuipers and N.F. van Hulst. J. Lightwave Technol. 20 519, 2002.Google Scholar
  20. Klunder, D.J.W., E. Krioukov, F.S. Tan, T. van der Veen, H.F. Bulthuis, G. Sengo, C. Otto, H.J.W.M. Hoekstra and A. Driessen. Appl. Phys. B 73 603, 2001.Google Scholar
  21. Kriswandhi, S. C2V application note A2002005, Concept to Volume b.v., http: //www.c2v.nl/software/support/appnotes/A2002005.pdf, 2002.Google Scholar
  22. Little, B.E., S.T. Chu, H.A. Haus, J. Foresi and J.-P. Laine. J. Lightwave Technol. 15 998, 1997.Google Scholar
  23. Little, B.E., S.T. Chu, W. Pan and Y. Kokubun. IEEE Photonics Technol. Lett. 12 323, 2000.Google Scholar
  24. Little, B.E., S.T. Chu, W. Pan, D. Ripin, T. Kaneko, Y. Kokubun and E. Ippen. IEEE Photonics Technol. Lett. 11 215, 1999a.Google Scholar
  25. Little, B.E., J.-P. Laine and H.A. Haus. J. Lightwave Technol. 17 704, 1999b.Google Scholar
  26. Lohmeyer, M. Opt. Quantum Electron. 34 541, 2002.Google Scholar
  27. Lohmeyer, M., N. Bahlmann, O. Zhuromskyy and P. Hertel. Opt. Quantum Electron. 31 877, 1999.Google Scholar
  28. Lohmeyer, M. and R. Stoffer. Opt. Quantum Electron. 33 413, 2001.Google Scholar
  29. Manolatou, C., M.J. Khan, S. Fan, P.R. Villeneuve, H.A. Haus and J.D. Joannopoulos. IEEE J. Quantum Electron. 35 1322, 1999.Google Scholar
  30. Marcatili, E.A.J. The Bell Syst. Tech. J. 2103, 1969.Google Scholar
  31. NAIS, 'Next-generation active integrated optic subsystems'. Information society technologies programme of the European Commission, project IST-2000-28018, http: //www.mesaplus.utwente.nl/nais/.Google Scholar
  32. Nöckel, J.U. and A.D. Stone. Nature 385 45, 1997.Google Scholar
  33. Olympios, 'OlympIOs Integrated Optics Software'. C2V, P.O. Box 318, 7500 AH Enschede, The Netherlands; http: //www.c2v.nl/software/.Google Scholar
  34. Rowland, D.R. and J.D. Love. IEE Proc. 140 177, 1993.Google Scholar
  35. Soref, R.A. and B.E. Little. IEEE Photonics Technol. Lett. 10 1121, 1998.Google Scholar
  36. Suzuki, S., Y. Hatakeyama, Y. Kokubun and S.T. Chu. J. Lightwave Technol. 20 745, 2002.Google Scholar
  37. Sztefka, G. and H.P. Nolting. IEEE Photonics Technol. Lett. 5 554, 1993.Google Scholar
  38. Vassallo, C. Optical Waveguide Concepts. Elsevier, Amsterdam, 1991.Google Scholar
  39. Yariv, A. and P. Yeh. Optical Waves in Crystals: Propagation and Control of Laser Radiation. Wiley, New York, 1984.Google Scholar

Copyright information

© Kluwer Academic Publishers 2004

Authors and Affiliations

  • Manfred Hammer
    • 1
  • Didit Yudistira
    • 1
  • Remco Stoffer
    • 1
  1. 1.Department of Applied Mathematics, MESA+ Research InstituteUniversity of TwenteEnschedeThe Netherlands

Personalised recommendations