Skip to main content
SpringerLink
Log in

Modelling of diffraction in pillar vertical cavity surface-emitting lasers with embedded Bragg layers

  • Papers
  • Published:
Optical and Quantum Electronics Aims and scope Submit manuscript

Abstract

An analytical expression for the reflectivity between the active cavity of a circular symmetric pillar vertical cavity surface-emitting laser (VCSEL) and Bragg mirror, which takes account of diffraction at the interface, is derived. The method (mode-matching in Hankel space) is also used to determine the reflectivity with some of the Bragg layers embedded in the cavity region. The dependence of reflectivity upon various parameters, including number of Bragg pairs, cavity radius and mode number, is discussed. The validity of using the plane wave reflectivity value (which ignores diffraction effects) is seen to depend significantly upon these parameters. As an indicator of the importance of taking these effects into account for pillar diameters of ∼6 μm and less, the variation of threshold gain with cavity radius is given for a commonly used type of VCSEL structure.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. J. JEWELL, J. P. HARBISON, A. SCHERER Y. H. LEE and L. T. FLOREZ, IEEE J. Quantum Electron. QE-27 (1991) 1332.

    Google Scholar 

  2. T. E. SALE, Vertical Cavity Surface Emitting Lasers (Research Studies Press and Wiley, Taunton, 1995).

    Google Scholar 

  3. R. R. BURTON, M. S. STERN, P. C. KENDALL and P. N. ROBSON, IEE Proc. J. 142 (1995) 77.

    Google Scholar 

  4. D. I. BABIC, Y. CHUNG, N. DAGLI and J. E. BOWERS, IEEE J. Quantum Electron. QE-29 (1993) 1950.

    Google Scholar 

  5. D. S. JONES, Acoustic and Electromagnetic Fields (Oxford Science Publications, Clarendon Press, Oxford, 1986) pp. 391–5.

    Google Scholar 

  6. P. C. KENDALL, Rib Waveguide Theory by the Spectral Index Method, edited by P. N. Robson and P. C. Kendall (Research Studies Press and Wiley, Taunton, 1990) Ch. 2, pp. 9–33.

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

  9. S. V. BURKE, Opt. Quantum Electron. 26 (1994) 63.

    Google Scholar 

  10. M. A. HADLEY, G. C. WILSON, K. Y. LAU and J. S. SMITH, App. Phys. Lett. 63 (1993) 1607.

    Google Scholar 

  11. P. C. KENDALL, D. A. ROBERTS, P. N. ROBSON M. J. ADAMS and M. J. ROBERTSON, IEEE Proc. J. 140 (1993) 149.

    Google Scholar 

  12. J. K. BUTLER and J. ZOROOFCHI, IEEE J. Quantum Electron. QE-10 (1974) 809.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Applied Mathematics Section, School of Mathematics and Statistics, University of Sheffield, P.O. Box 597, S10 2UN, Sheffield, UK

    R. R. Burton & M. S. Stern

  2. Department of Electronic and Electrical Engineering, University of Sheffield, S1 3JD, Sheffield, UK

    P. C. Kendall & P. N. Robson

Authors
  1. R. R. Burton
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. S. Stern
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. P. C. Kendall
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. P. N. Robson
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Burton, R.R., Stern, M.S., Kendall, P.C. et al. Modelling of diffraction in pillar vertical cavity surface-emitting lasers with embedded Bragg layers. Opt Quant Electron 28, 1677–1684 (1996). https://doi.org/10.1007/BF00331057

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00331057

Keywords

Search

Navigation