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Considering azimuthal dependence in the numerical modeling of VCSELs

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Abstract

A method is proposed for the analysis of vertical cavity laser diodes where the cylinder symmetry has been perturbed. The full vectorial wave equation is used. The analysis is performed with the method of lines in cylindrical coordinates where the permittivity ε(r, ϕ) and the fields are expanded in Fourier series in azimuthal direction. The discretization is done only in radial direction. As an example the original cylindrical geometry of a vertical cavity laser has been deformed and the influence on the wavelength of the lowest order cavity resonances and on the optical field is shown.

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References

  • Ahlers, E., S.F. Helfert and R. Pregla. Modelling of VCSELs by the Method of Lines. In Integr. Photo. Resear. Technic. Digest, Vol. 6, 340–343. Boston, USA, 1996.

    Google Scholar 

  • Collin, R.E. Field Theory of Guided Waves, Series of Electromagnetic Waves, 2nd edn. IEEE press, New York, 1991.

    Google Scholar 

  • Conradi, O. Opt. Quantum Electron. 31 1047, 1999.

    Google Scholar 

  • Demeulenaere, B., P. Bienstman, B. Dhoedt and R.G. Baets. IEEE J. Quantum Electron. 35(3), 358, 1999.

    Google Scholar 

  • Faltin, K. Untersuchungen zur Nahfeldverteilung von Transversalmoden in Laserdioden mit Vertikalreson-ator. Ph.D. thesis, Shaker Verlag, Aachen, 1999.

    Google Scholar 

  • Hadley, G.R. Optics Letters 20(13) 1483, 1995.

    Google Scholar 

  • Hadley, G.R., K.L. Lear, M.E. Warren, K.D. Choquette, J.W. Scott and S.W. Corzine. IEEE JQE 32(4) 607, 1996.

    Google Scholar 

  • Kremer, D. Electron. Lett. 30(13) 1088, 1994.

    Google Scholar 

  • Pregla, R. and E. Ahlers. New Vector-BPM in Cylindrical Coordinates Based on the Method of Lines. In Integr. Photo. Resear. Technic. Digest, Vol. 7, 24–26. Dana Point, USA, 1995.

    Google Scholar 

  • Pregla, R. and W. Pascher. The Method of Lines. In Numerical Techniques for Microwave and Millimeter Wave Passive Structures, ed. T. Itoh, 381–446. J. Wiley Publ., New York, USA, 1989.

    Google Scholar 

  • Rogge, U. and R. Pregla. J. Lightwave Technol. 11(12) 2015, 1993.

    Google Scholar 

  • Tsao, C. Optical Fibre Waveguide Analysis. Oxford University Press, Oxford, New York, Tokyo, 1992.

    Google Scholar 

  • Vakhshoori, D., J.D. Wynn, G.J. Zydzik, R.E. Leibenguth, M.T. Asom, K. Kojima and R.A. Morgan. Appl. Phys. Lett. 62 1448, 1992.

    Google Scholar 

  • Weigl, B., M. Grabherr, G. Reiner and K. Ebeling. Electron. Lett. 32(6) 557, 1996.

    Google Scholar 

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Conradi, O., Pregla, R. Considering azimuthal dependence in the numerical modeling of VCSELs. Optical and Quantum Electronics 32, 759–767 (2000). https://doi.org/10.1023/A:1007058210442

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  • DOI: https://doi.org/10.1023/A:1007058210442

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