Optical and Quantum Electronics

, Volume 37, Issue 1–3, pp 37–61

Analytic approach to dielectric optical bent slab waveguides

  • K. R. Hiremath
  • M. Hammer
  • R. Stoffer
  • L. Prkna
  • J. Čtyroký
Article

Abstract

A rigorous classical analytic frequency domain model of confined optical wave propagation along 2D bent slab waveguides and curved dielectric interfaces is investigated, based on a piecewise ansatz for bend mode profiles in terms of Bessel and Hankel functions. This approach provides a clear picture of the behaviour of bend modes, concerning their decay for large radial arguments or effects of varying bend radius. Fast and accurate routines are required to evaluate Bessel functions with large complex orders and large arguments. Our implementation enabled detailed studies of bent waveguide properties, including higher order bend modes and whispering gallery modes, their interference patterns, and issues related to bend mode normalization and orthogonality properties.

Keywords

bent waveguides Bessel functions eigenmode solver whispering gallery modes 

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References

  1. Abramowitz M., Stegun I.A. (1964). Handbook of Mathematical Functions (Applied Mathematics Series 55). National Bureau of Standards, Washington, D.C.Google Scholar
  2. Amos D.E. (1983). A Portable Package for Bessel Functions of a Complex Argument and Nonnegative Order. http://www.netlib.org/amos/.Google Scholar
  3. Balistreri, M.L.M., Klunder, D.J.W., Blom, F.C., Driessen, A., Korterik, J.P., Kuipers, L., Hulst, N.F. 2001J Opt Soc Am B18465Google Scholar
  4. Benech, P., Khalil, D.A.M., Andrèo, F.S. 1992Opt Commun8896CrossRefGoogle Scholar
  5. Berglund W., Gopinatho A. IEEE J. Lightwave Technol. 18, 1161–1166Google Scholar
  6. Bertolotti, M., A. Driessen,, F. Michelotti (eds), Microresonators as Building Blocks for VLSI Photonics, Vol. 709 of AIP Conference Proceedings. American Institute of Physics, Melville, New York, 2004.Google Scholar
  7. Bienstman, P., Six, E., Roelens, A., Vanwolleghem, M., Baets, R. 2002IEEE Photon Technol Lett14164CrossRefGoogle Scholar
  8. Hall, D.G., 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
  9. Hammer, M., K.R. Hiremath, R. Stoffer. In: Microresonators as building blocks for VLSI photonics eds. M. Bertolotti, A. Driessen and F. Michelotti , Vol. 709 of AIP conference proceedings. Melville, New York: American Institute of Physics, pp. 48–71. 2004. Proceedings of the International School of Quantum Electronics, 39th course, Erice, Sicily (October 2003).Google Scholar
  10. Heiblum, M., Harris, J.H. 1975IEEE J Quantum Electron11751975CrossRefGoogle Scholar
  11. Hiremath K.R. (2003). ‘Modeling of 2D Cylindrical Integrated Optical Microresonators’. Master’s thesis. University of Twente, Enschede, The Netherlands.Google Scholar
  12. Kim, S., Gopinath, A. 1996IEEE J Lightwave Technol142085CrossRefGoogle Scholar
  13. Klunder, D., Balisteri, M., Blom, F., Hoekstra, J., Driessen, A., Kuipers, L., Van Hulst, N. 2001IEEE Photon Technol Lett121531Google Scholar
  14. Klunder, D.J.W., Balistreri, M.L.M., Blom, F.C., Hoekstra, H.W.J.M., Driessen, A., Kuipers, L., Hulst, N.F. 2000IEEE J Lightwave Technol20519CrossRefGoogle Scholar
  15. Klunder, D.J.W., Krioukov, E., Tan, F.S., vander Veen, T., Bulthuis, H.F., Sengo, G., Otto, C., Hoekstra, H.W.J.M., Driessen, A. 2001Appl Phys B73603Google Scholar
  16. Lewin, L., Chang, D.C., Kuester, E.F. 2001Electromagnetic Waves and Curved StructuresPeter Peregrinus Ltd. (On behalf of IEE)Stevenage, EnglandGoogle Scholar
  17. Little, B.E., Chu, S.T., Haus, H.A., Foresi, J., Laine, J.-P. 1997J Lightwave Technol15998CrossRefGoogle Scholar
  18. Luke, Y.L. 1962Integrals of Bessel functionsMcGraw-HillNew YorkGoogle Scholar
  19. Marcatili E.A.J. (1969). Bell Sys Tech. J. September. 2103Google Scholar
  20. Marcuse D. (1971). Bell Sys Tech J October 2551.Google Scholar
  21. Marcuse, D. 1972Light Transmission OpticsVan Nostrand Reinhold CompanyNew York, USAGoogle Scholar
  22. Melloni, A., Carniel, F., Costa, R., Martinelli, M. 2001IEEE J Lightwave Technol19571CrossRefGoogle Scholar
  23. Morita, N., Yamada, R. 2001IEEE J Lightwave Technol816Google Scholar
  24. NAIS: project start: 2001, ‘Next-generation active integrated optic subsystems’. Information society technologies programme of the European Commission, project IST-2000-28018, http://www.mesaplus.utwente.nl/nais/, 2001.Google Scholar
  25. Pennings, E.C.M. Bends in Optical Ridge Waveguides, Modelling and Experiment. Ph.D. thesis, Delft University, The Netherlands, 1990.Google Scholar
  26. Pregla, R. 1996IEEE J Lightwave Technol14634Google Scholar
  27. Prkna, L.: ‘Rotationally symmetric resonant devices in integrated optics’. Ph.D. thesis, Faculty of Mathematics and Physics, Charles University, Prague, Czech Republic, 2004.Google Scholar
  28. Prkna, L., Hubálek, M., Čtyroký, J. 2004IEEE Photon Technol Lett162057Google Scholar
  29. Prkna, L., Čtyroký, J., Hubálek, M. 2004Opt Quant Electron36259Google Scholar
  30. Rivera, M. 1995IEEE J Lightwave Technol13233Google Scholar
  31. Rowland, D.R., Love, J.D. 1993IEE Proceedings Pt J140177Google Scholar
  32. Stoffer, R. ‘Uni- and Omnidirectional Simulation Tools for Integrated Optics’. Ph.D. thesis, University of Twente, Enschede, The Netherlands, 2001.Google Scholar
  33. Stoffer, R., K.R. Hiremath, M. Hammer. In: Microresonators as building blocks for VLSI photonics, M. Bertolotti, A. Driessen, and F. Michelotti (eds.): Vol. 709 of AIP conference proceedings. Melville, New York: American Institute of Physics, pp. 366, 2004. Proceedings of the International School of Quantum Electronics, 39th course, Erice, Sicily (October 2003).Google Scholar
  34. Stoffer, R., Hoekstra, H.J.W.M., Ridder, R.M., Groesen, E., Beckum, F.P.H. 2000Opt Quantum Electron3294Google Scholar
  35. Taflove, A. 1995Computational Electrodynamics: The Finite Difference Time Domain Method Artech House Inc.NorwoodMA, USAGoogle Scholar
  36. Temme, N.M. ‘Numerical Algorithms for Uniform Airy-type Asymptotic Expansions’. Technical Report MAS-R9706, Centrum voor Wiskunde en Informatica, Amsterdam, The Netherlands, 1997.Google Scholar
  37. vander Keur, J.M. Propagation Properties of a Circularly Curved, Transversely Inhomogeneous, Dielectric Slab Waveguide’. Technical Report Et/EM 1992–02, Electromagnetic Research Laboratory, Faculty of Electrical Engineering, University of Delft, The Netherlands, 1992.Google Scholar
  38. Vassallo, C. 1991Optical Waveguide ConceptsElsevierAmsterdamGoogle Scholar
  39. Čtyroký, J., L. Prkna,, M. Hubálek: In: Microresonators as building blocks for VLSI photonics, M. Bertolotti, A. Driessen,, F. Michelotti eds. Vol. 709 of AIP conference proceedings. Melville, New York: American Institute of Physics, pp. 72–90, 2004. Proceedings of the International School of Quantum Electronics, 39th course, Erice, Sicily (October 2003).Google Scholar
  40. Wassmann, F. 1999IEEE Journal of Lightwave Technology17957Google Scholar
  41. Yamamoto, T., Koshiba, M. 1994IEEE J Lightwave Technol1259Google Scholar
  42. Yee, K.S. 1966IEEE Trans on Antennas and Propagation14302Google Scholar

Copyright information

© Springer 2005

Authors and Affiliations

  • K. R. Hiremath
    • 1
  • M. Hammer
    • 1
  • R. Stoffer
    • 1
  • L. Prkna
    • 2
  • J. Čtyroký
    • 2
  1. 1.MESA+Research InstituteUniversity of TwenteEnschedeThe Netherlands
  2. 2.Institute of Radio Engineering and Electronics AS CRPragueCzech Republic

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