Skip to main content
SpringerLink
Log in

Mode solvers and related methods

  • Chapter
Photonic Devices for Telecommunications

  • 512 Accesses

Abstract

To determine propagation constants and spatial optical field distributions of eigenmodes of integrated optical waveguide structures is a fundamental problem of their modelling. The knowledge of (generally complex) propagation constants, or the phase and attenuation constants, and spatial field distributions of guided modes of the waveguide structure helps make important decisions, e. g., whether the waveguide can be used for a particular application. In particular, the field distribution shows whether a waveguide is prone to radiation loss due to irregularities introduced in the fabrication process. Bends of homogeneous waveguides can be analysed by eigenmode solvers; the spatial field distribution of modes furnishes a physical insight into the radiation loss.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. W.P. Huang, ed., "Methods for Modeling and Simulation of Guided-Wave Optoelectronic Devices Part II : Waves and Interactions“. PIER 11 in Progress in Electromagnetic Research, BMW Publishing, Cambridge, Massachusetts, USA, 1995.”

    Google Scholar 

  2. W.P. Huang, ed.,“Methods for Modeling and Simulation of Guided-Wave Optoelectronic Devices: Part I : Modes and Couplings”, PIER 10 in Progress in Electromagnetic Research, EMW Publishing, Cambridge, Massachusetts, USA, 1995.

    Google Scholar 

  3. T. Itoh, ed., Numerical Techniques for Microwave and Millimeter Wave Passive Structures.J. Wiley Publishing, New York, 1989.

    Google Scholar 

  4. C. Vassallo, “1993-1995 Optical mode solvers”, Opt. Quantum Electron., vol. 29, No. 2, pp. 95–114, 1997.

    Article  Google Scholar 

  5. R.E. Collin, Field Theory of Guided Waves, IEEE Press, 2nd ed., pp. 419, 1990.

    Google Scholar 

  6. G. Kowalski and R. Pregla, “Dispersion Characteristics of Shielded Microstrips with Finite Thickness”, AEU, vol. 25, pp. 193–196, 1971.

    Article  Google Scholar 

  7. E. Kiihn,“A Mode Matching Method for Solving Field Problems in Waveguide and Resonator Circuits”, AEU, vol. 27, pp. 511–518, 1973.

    Google Scholar 

  8. R. Pregla, “The Method of Lines for the Unified Analysis of Microstrip and Dielectric Waveguides”, Electromagnetics, vol. 15, pp. 441–456, 1995.

    Article  Google Scholar 

  9. R. Pregla and W. Pascher, “The Method of Lines”, inT. Itoh, ed., Numerical Techniques for Microwave and Millimeter-Wave Passive Structures, J. Wiley Publ., New York, pp. 381–446, 1989.

    Google Scholar 

  10. R. Pregla, “The Method of Lines as Generalized Transmission Line Technique for the An alysis of Multilayered Structures”, AEU, vol. 50, No. 5, pp. 293–300, 1996.

    Google Scholar 

  11. R. Sorrentino, “Transverse resonance technique,” Ch. 11 in Itoh’s book [3].

    Google Scholar 

  12. W. Schlosser and H.G. Unger, “Partially filled waveguides and surface waveguides of rectangular cross-section”, in Advances in Microwaves, pp. 319–387, Academic Press, New York, 1966.

    Google Scholar 

  13. D. Marcuse, Theory of Dielectric Optical Waveguides, second edition, Academic Press, San Diego, 1991.

    Google Scholar 

  14. S.T. Peng and A.A. Oliner, “Guidance and leakage properties of a class of open dielectric waveguides: Part I - Mathematical formulations,” IEEE Trans. Microwave Theory Tech., vol. MTT-29, pp. 843–855, 1981.

    Article  MathSciNet  Google Scholar 

  15. A.S. Sudbø, “Film mode matching: A versatile method for mode field calculations in dielectric waveguides,” Pure Appl. Opt. (J. Europ. Opt. Soc. A), vol. 2, pp. 211–233, 1993.

    Article  Google Scholar 

  16. A.S. Sudbø, “Improved formulation of the film mode matching method for mode field calculations in dielectric waveguides,” Pure Appl. Opt. (J. Europ. Opt. Soc. A), vol. 3, pp. 381–388, 1994.

    Article  Google Scholar 

  17. Available from Photon Design, 86 Courtland Road, Oxford OX4 4JB, UK, fax +44 1865 395480, email dfgg@photond.com.

    Google Scholar 

  18. R. Pregla and W. Pascher, The method of lines, Ch. 6 in Itoh’s book [3].

    Google Scholar 

  19. U. Rogge and R. Pregla, “Method of Lines for the analysis of dielectric waveguides,” J. Lightwave Technol., vol. 11, pp. 2015–2020, 1993.

    Article  Google Scholar 

  20. A.S. Sudbø, “Problems in vector mode calculations for dielectric waveguides,” Linear and Nonlinear Integrated Optics, SPIE Europto Series Proceedings, vol. 2212, pp. 26–35, 1994.

    Google Scholar 

  21. M.S. Stern, P.C. Kendall, and P.W.A. Mcllroy, “ Analysis of the spectral index method for vector modes of rib waveguides,” IEE Proc. J, vol. 137, pp. 21–26, 1990.

    Google Scholar 

  22. G. Sztefka and H.P. Nolting, “ Bidirectional eigenmode propagation for large refractive index steps,” IEEE Photonics Technol. Lett., vol. 5, pp. 554–557, 1993.

    Article  Google Scholar 

  23. J.J. Gerdes, “Bidirectional eigenmode propagation analysis of optical waveguides based on the method of lines,” Electron. Lett., vol. 30, pp. 550–551, 1994.

    Article  Google Scholar 

  24. R. Pregla, “MoL-BPM Method of Lines Based Beam Propagation Method, Methods for Modeling and Simulation of Guided-Wave Optoelectronic Devices,”W.P. Huang(ed), PIER 11, Progress in Electromagnetic Research, EMW Publishing, Cambridge, Massachusetts, USA, pp. 51–102, 1995.

    Google Scholar 

  25. The name ’angular repetency’ for k() is an ISO standard that has been adopted to get around the conflicting traditions that ’propagation constant’ is k() in optics, whereas it isy’&o for microwaves, and ’wave number’ is k() in optics, whereas it is k()l(2n) in spectroscopy.

    Google Scholar 

  26. A.S. Sudbø and P.I. Jensen, “Stable bidirectional eigenmode propagation of optical fields in waveguide devices,” Integrated Photonics Research, OSA Topical Meeting, Dana Point, CA, Feb. 23-25, 1995, paper IThB4.

    Google Scholar 

  27. A.S. Sudbø, “Numerically Stable Formulation of the Transverse Resonance Method for Vector Mode-Field Calculations in Dielectric Waveguides,” IEEE Photonics Technol. Lett., vol. 5, pp. 342–344, 1993.

    Article  Google Scholar 

  28. J. van Bladel, Singular electromagnetic fields and sources, Ch. 4, Clarendon Press, Oxford, 1991.

    Google Scholar 

  29. A.S. Sudbø, “Why are accurate computations of mode fields in rectangular dielectric waveguides difficult?” J. Lightwave Technol., vol. 10, pp. 418–419, 1992.

    Article  Google Scholar 

  30. G. Golub and C.F. Van Loan, Matrix Computations, Johns Hopkins University Press, Baltimore 1983.

    MATH  Google Scholar 

  31. E. Anderson, Z. Bai, C. Bischof, J. Demmel, J. Dongarra, J. Du Croz, A. Greenbaum, S. Hammarling, A. McKenney, S. Ostrouchov, and D. Sorensen, LAPACK Users’ Guide, Society for Industrial and Applied Mathemathics (SIAM), Philadelphia 1992.

    Google Scholar 

  32. Matlab® is available from The Math Works Inc., 24 Prime Park Way, Natick, MA 01760-1500, USA, fax +1 508-647-7001, email info@mathworks.com.

    Google Scholar 

  33. A. Dreher and R. Pregla, “ Analysis of planar waveguides with the method of lines and absorbing boundary conditions,” IEEE Microwave Guided Wave Lett., vol. 1, pp. 138–140, 1991.

    Article  Google Scholar 

  34. C. Vassallo and J.M. van der Keur, “ Comparison of a few transparent boundary conditions for finite-difference optical mode solvers,” J. Lightwave Technol., vol. 15, pp. 397–402, 1997

    Article  Google Scholar 

  35. C. Vassallo and F. Collino, “Highly efficient absorbing boundary conditions for the beam propagation method,” J. Lightwave TechnoL, vol. 14, pp. 1570–1577, 1996.

    Article  Google Scholar 

  36. J.S. Gu, P.A. Besse, and H. Melchior, “Method of Lines for the analysis of the propagation characteristics of curved optical rib waveguides,” IEEEJ. Quantum Electron., vol. 27, pp. 531–537, 1991, with corrections in vol. 28, pp. 1835-1836, 1992

    Article  Google Scholar 

  37. R.S. Burton and T.E. Schlesinger, “Comparative analysis of the Method-of-Lines for three-dimensional curved dielectric waveguides,” J. Lightwave TechnoL, vol. 14, pp. 209–215, 1996.

    Article  Google Scholar 

  38. R. Pregla, E. Ahlers, and S. Helfert, “Efficient and accurate analysis of photonic devices with the Method of Lines,” Progress in Electromagnetic Research Symposium (PIERS), Hong Kong, Jan. 6-9, 1997.

    Google Scholar 

  39. K. Ramm, P. Liisse, and H.G. Unger, “ Multigrid eigenvalue solver for mode calculation of planar optical waveguides,” IEEE Photonics TechnoL Lett., vol. 9, pp. 967–969, 1997.

    Article  Google Scholar 

  40. M. Reed, T.M. Benson, P. Sewell, P.C. Kendall, G.M. Berry, and S.V. Dewar: “ Free space radiation mode analysis of rectangular dielectric waveguides”, Opt. Quantum Electron., vol. 28, pp. 1175–1179, 1996.

    Article  Google Scholar 

  41. M. Reed, PhD Thesis, University of Nottingham, 1998.

    Google Scholar 

  42. P. Sewell, M. Reed, T.M. Benson, P.C. Kendall, and M. Noureddine, “Computationally efficient analysis of buried rectangular and rib waveguides with applications to semiconductor lasers”, IEE Proc. Optoelectron., vol. 144, No. 1, pp. 14–18, 1997.

    Article  Google Scholar 

  43. Finite difference results provided by S. Sujecki.

    Google Scholar 

  44. P.C. Kendall, D.A. Roberts, P.N. Robson, M.J. Adams, and M.J. Robertson, “ Semiconductor laser facet reflectivities using free space radiation modes” IEE Proc. J, vol. 140, No. 1, pp. 49–55, 1993.

    Article  Google Scholar 

  45. M. Reed, T.M. Benson, P.C. Kendall, and P. Sewell, “Antireflection-coated angled facet design” IEE Proc. Optoelectron., vol. 143, No. 4, pp. 214–220, 1996.

    Article  Google Scholar 

  46. P. Sewell, M. Reed, T.M. Benson, and P.C. Kendall, “ Full vector analysis of two dimensional angled and coated optical waveguide facets”, IEEEJ . Quantum Electron., vol. 33, No. 11, 1997.

    Google Scholar 

  47. P. Kaczmarski, R. Baets, G. Franssens, and P.E. Lagasse, “ Extension of bidirectional BPM method to TM polarisation and application to laser facet reflectivity”, Electron. Lett., No. 25, pp. 716–717, 1989.

    Article  Google Scholar 

  48. M. Reed, P. Sewell, T.M. Benson, and P.C. Kendall, “Limitations of one dimensional models of waveguide facets” Microwave Opt. TechnoL Lett., vol. 15, No. 4, pp. 196–198, 1997.

    Article  Google Scholar 

  49. C.J. Smartt, T.M. Benson, and P.C. Kendall, “ Free space radiation mode method for the analysis of propagation in optical waveguide devices”, IEE Proc. J, vol. 140, pp. 56–61, 1993.

    Google Scholar 

  50. M. Reed, P. Sewell, T.M. Benson, and P.C. Kendall, “An efficient propagation algorithm for 3D optical waveguides”, IEE Special Issue on Semiconductor Optoelectronics, February 1998.

    Google Scholar 

Download references

Authors
  1. R. Pregla
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. Sudbø
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ph. Sewell
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Mikro- und Optoelektronik ETH-Hönggerbergn, HPT, ETH Zürich, Institut für Quantenelektronik, CH-8093, Zürich, Switzerland

    George Guekos

Rights and permissions

Reprints and permissions

Copyright information

© 1999 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Pregla, R., Sudbø, A., Sewell, P. (1999). Mode solvers and related methods. In: Guekos, G. (eds) Photonic Devices for Telecommunications. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-59889-0_1

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-59889-0_1

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-64168-8

  • Online ISBN: 978-3-642-59889-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation