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.
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References
Abramowitz M., Stegun I.A. (1964). Handbook of Mathematical Functions (Applied Mathematics Series 55). National Bureau of Standards, Washington, D.C.
Amos D.E. (1983). A Portable Package for Bessel Functions of a Complex Argument and Nonnegative Order. http://www.netlib.org/amos/.
M.L.M. Balistreri D.J.W. Klunder F.C. Blom A. Driessen J.P. Korterik L. Kuipers N.F. Hulst Particlevan (2001) J Opt Soc Am B 18 465 Occurrence Handle1:CAS:528:DC%2BD3MXisVyrtrw%3D
P. Benech D.A.M. Khalil F.S. Andrèo (1992) Opt Commun 88 96 Occurrence Handle10.1016/0030-4018(92)90492-A
Berglund W., Gopinatho A. IEEE J. Lightwave Technol. 18, 1161–1166
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.
P. Bienstman E. Six A. Roelens M. Vanwolleghem R. Baets (2002) IEEE Photon Technol Lett 14 164 Occurrence Handle10.1109/68.980493
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.
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).
M. Heiblum J.H. Harris (1975) IEEE J Quantum Electron 11 75–1975 Occurrence Handle10.1109/JQE.1975.1068563
Hiremath K.R. (2003). ‘Modeling of 2D Cylindrical Integrated Optical Microresonators’. Master’s thesis. University of Twente, Enschede, The Netherlands.
S. Kim A. Gopinath (1996) IEEE J Lightwave Technol 14 2085 Occurrence Handle10.1109/50.536977
D. Klunder M. Balisteri F. Blom J. Hoekstra A. Driessen L. Kuipers N. Van Hulst (2001) IEEE Photon Technol Lett 12 1531
D.J.W. Klunder M.L.M. Balistreri F.C. Blom H.W.J.M. Hoekstra A. Driessen L. Kuipers N.F. Hulst Particlevan (2000) IEEE J Lightwave Technol 20 519 Occurrence Handle10.1109/50.989003
D.J.W. Klunder E. Krioukov F.S. Tan T. vander Veen H.F. Bulthuis G. Sengo C. Otto H.W.J.M. Hoekstra A. Driessen (2001) Appl Phys B 73 603 Occurrence Handle1:CAS:528:DC%2BD3MXptVamsro%3D
L. Lewin D.C. Chang E.F. Kuester (2001) Electromagnetic Waves and Curved Structures Peter Peregrinus Ltd. (On behalf of IEE) Stevenage, England
B.E. Little S.T. Chu H.A. Haus J. Foresi J.-P. Laine (1997) J Lightwave Technol 15 998 Occurrence Handle10.1109/50.588673
Y.L. Luke (1962) Integrals of Bessel functions McGraw-Hill New York
Marcatili E.A.J. (1969). Bell Sys Tech. J. September. 2103
Marcuse D. (1971). Bell Sys Tech J October 2551.
D. Marcuse (1972) Light Transmission Optics Van Nostrand Reinhold Company New York, USA
A. Melloni F. Carniel R. Costa M. Martinelli (2001) IEEE J Lightwave Technol 19 571 Occurrence Handle10.1109/50.920856
N. Morita R. Yamada (2001) IEEE J Lightwave Technol 8 16
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.
Pennings, E.C.M. Bends in Optical Ridge Waveguides, Modelling and Experiment. Ph.D. thesis, Delft University, The Netherlands, 1990.
R. Pregla (1996) IEEE J Lightwave Technol 14 634
Prkna, L.: ‘Rotationally symmetric resonant devices in integrated optics’. Ph.D. thesis, Faculty of Mathematics and Physics, Charles University, Prague, Czech Republic, 2004.
L. Prkna M. Hubálek J. Čtyroký (2004) IEEE Photon Technol Lett 16 2057
L. Prkna J. Čtyroký M. Hubálek (2004) Opt Quant Electron 36 259
M. Rivera (1995) IEEE J Lightwave Technol 13 233
D.R. Rowland J.D. Love (1993) IEE Proceedings Pt J 140 177
Stoffer, R. ‘Uni- and Omnidirectional Simulation Tools for Integrated Optics’. Ph.D. thesis, University of Twente, Enschede, The Netherlands, 2001.
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).
R. Stoffer H.J.W.M. Hoekstra R.M. Ridder Particlede E. Groesen Particlevan F.P.H. Beckum Particlevan (2000) Opt Quantum Electron 32 94
A. Taflove (1995) Computational Electrodynamics: The Finite Difference Time Domain Method Artech House Inc. Norwood MA, USA
Temme, N.M. ‘Numerical Algorithms for Uniform Airy-type Asymptotic Expansions’. Technical Report MAS-R9706, Centrum voor Wiskunde en Informatica, Amsterdam, The Netherlands, 1997.
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.
C. Vassallo (1991) Optical Waveguide Concepts Elsevier Amsterdam
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).
F. Wassmann (1999) IEEE Journal of Lightwave Technology 17 IssueID5 957
T. Yamamoto M. Koshiba (1994) IEEE J Lightwave Technol 12 59
K.S. Yee (1966) IEEE Trans on Antennas and Propagation 14 302
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1Partly these notions originate from the use of a ray picture for the description of bent waveguides, or from approximate models in terms of “equivalent” leaky straight waveguide profiles. We will avoid these viewpoints in the present paper.
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Hiremath, K.R., Hammer, M., Stoffer, R. et al. Analytic approach to dielectric optical bent slab waveguides. Opt Quant Electron 37, 37–61 (2005). https://doi.org/10.1007/s11082-005-1118-3
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DOI: https://doi.org/10.1007/s11082-005-1118-3