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Planar waveguide analysis by the spectral index method: II. Multiple layers, optical gain and loss

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Abstract

The most general form of the spectral index method is presented for the analysis of multiple-layered rib and related semiconductor waveguide structures where the ribs have vertical sidewalls and are surrounded by air. The model allows for the presence of loss or gain in any layer and the generalization of the method to such complex problems is described. A detailed account is provided on how to set up the transcendental equation to solve problems for single ribs, and both symmetric and asymmetric couplers. Finally, a polarization filter in the form of an asymmetric coupler with one of its ribs capped with metal is analysed numerically to illustrate the technique for a realistic design problem.

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References

  1. P. C.KENDALL, M. S.STERN and S. V.BURKE,Opt. Quantum Electron. 25 (1993) 771.

    Google Scholar 

  2. P. C.KENDALL, P. W. A.McILROY and M. S.STERN,Electron. Lett. 25 (1989) 107.

    Google Scholar 

  3. P. C. KENDALL, P. W. A. McILROY and M. S. STERN,IEE Colloquium on Integrated Optics, IEE Digest No. 1989/93, 13/1–13/4.

  4. P. W. A.McILROY, M. S.STERN and P. C.KENDALL,Electron. Lett. 25 (1989) 1586.

    Google Scholar 

  5. R. C.HEWSON-BROWNE and P. C.KENDALL,Electron. Lett. 25 (1989) 1153.

    Google Scholar 

  6. P. W. A.McILROY, M. S.STERN and P. C.KENDALL,IEEE J. Lightwave Technol. LT-8 (1990) 113.

    Google Scholar 

  7. M. S.STERN, P. C.KENDALL and P. W. A.McILROY,IEE Proc. 137, Pt. J (1990) 21.

    Google Scholar 

  8. P. N.ROBSON and P. C.KENDALL (eds.),Rib Waveguide Theory by the Spectral Index Method (Research Studies Press and Wiley, New York, 1990).

    Google Scholar 

  9. C.VASSALLO and Y.-H.WANG,IEEE J. Lightwave Technol. LT-8 (1990) 56.

    Google Scholar 

  10. C.VASSALLO,Optical Waveguide Concepts (Elsevier, New York, 1991).

    Google Scholar 

  11. S. V.BURKE,Electron. Lett. 25 (1989) 605.

    Google Scholar 

  12. S. V.BURKE,IEE Proc. 137, Pt. J (1990) 7.

    Google Scholar 

  13. S. V. BURKE, in ref. [8], ch. 7, p. 123.

  14. S. V. BURKE, PhD Thesis, Dept. of Electronic and Electrical Engineering, University of Sheffield, UK, 1991.

  15. S. V.BURKE,IEE Proc. 137, Pt. J (1990) 289.

    Google Scholar 

  16. S. V.BURKE,Technical Digest on Integrated Photonics Research 5 (1990) 86.

    Google Scholar 

  17. S. V.BURKE and P. C.KENDALL,Technical Digest on Integrated Photonics Research 8 (1991) 117.

    Google Scholar 

  18. S. V.BURKE, P. C.KENDALL, S.RITCHIE, M. J.ROBERTSON and P. N.ROBSON,IEE Proc. 139 Pt. J (1992) 59.

    Google Scholar 

  19. S. V.BURKE, M. J.ADAMS, P. C.KENDALL, P. N.ROBSON and G. J.REES,Electron. Lett. 28 (1992) 841.

    Google Scholar 

  20. S. V.BURKE, M. J.ADAMS, P. C.KENDALL, P. N.ROBSON and G. J.REES,Technical Digest on Integrated Photonics Research 10 (1992) 170.

    Google Scholar 

  21. J. HONG, W. P. HUANG and T. MAKINO, Modelling of ridge waveguide MQW DFB lasers based on spectral index transfer matrix approach, to be published.

  22. S. V.BURKE,Electron. Lett. 28 (1992) 2280.

    Google Scholar 

  23. S. V.BURKE, T. M.BENSON, R. J.BOZEAT and M. A.MATIN,Technical Digest on Integrated Photonics Research 10 (1993) 35.

    Google Scholar 

  24. J.BUUS,IEEE J. Quantum. Electron. QE-18 (1982) 1083.

    Google Scholar 

  25. M. I.OKSANEN and I. V.LINDELL,IEE Proc.,136 Pt. H (1989) 281.

    Google Scholar 

  26. C. H.CHEN and Y.-W.KIANG, The variational formulation of physical problems and the associated numerical techniques,Research Topics in Electromagnetic Wave Theory, edited by J. A.Kong (Wiley, New York, 1981).

    Google Scholar 

  27. M. N. JONES, in ref. [8], ch. 3, p. 35.

  28. P. C.KENDALL, M. S.STERN and P. N.ROBSON,Opt. Quantum Electron. 22 (1990) 555.

    Google Scholar 

  29. M. S.STERN,Rib Waveguide Theory by the Spectral Index Method (Research Studies Press and Wiley, New York, 1990). p. 106.

    Google Scholar 

  30. R.UULRICH and R. J.MARTIN,Appl. Opt. 10 (1971) 2077.

    Google Scholar 

  31. M. J.ADAMS,An Introduction to Optical Waveguides (Wiley, New York, 1981).

    Google Scholar 

  32. P. W. A. McILROY, in ref. [8], ch. 5, p. 70.

  33. S.RAMO, J. R.WHINNERY and T.VANDUZER,Fields and Waves in Communication Electronics, 2nd edn (Wiley, New York, 1984).

    Google Scholar 

  34. R. E.COLLIN,Field Theory of Guided Waves, 2nd edn (IEEE Press, Washington DC, 1991) p. 188.

    Google Scholar 

  35. J. R.WAIT,Electromagnetic Waves in Stratified Media, 2nd edn (Pergamon Press, London, 1970).

    Google Scholar 

  36. V. W.HANSEN,Numerical Solution of Antennas in Layered Media (Research Studies Press and Wiley, New York, 1989).

    Google Scholar 

  37. E. K.SHARMA, M. P.SINGH and P. C.KENDALL,Electron. Lett. 27 (1991) 408.

    Google Scholar 

  38. P.ALBRECHT, M.HAMACHER, H.HEIDRICH, D.HOFFMANN, H.-P.NOLTING and C. M.WEINERT,IEEE Photon. Technol. Lett. 2 (1990) 114.

    Google Scholar 

  39. D. E.GRAY (ed.),American Institute of Physics Handbook, 3rd edn (McGraw-Hill, New York, 1992).

    Google Scholar 

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Burke, S.V. Planar waveguide analysis by the spectral index method: II. Multiple layers, optical gain and loss. Opt Quant Electron 26, 63–77 (1994). https://doi.org/10.1007/BF00558142

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