Advertisement

Journal of Computational Electronics

, Volume 3, Issue 2, pp 67–80 | Cite as

A Rigorous, Coupled-Wave Transfer Matrix Method for Two-Dimensional Threshold Analysis of Distributed Feedback Semiconductor Lasers

  • Ahmed A. Abouelsaood
  • Sahar A. El-Naggar
Article

Abstract

A rigorous, truly two-dimensional method for threshold analysis of distributed feedback (DFB) lasers based on a coupled wave transfer matrix formalism is presented. The method makes it possible to systematically study the effect of the various structural and material properties parameters of the laser on the threshold gain and lasing frequency. Since the optical fields inside and outside the laser are very accurately represented in our analysis, the small differences in gain of pairs of longitudinal laser modes symmetrically located on both sides of the gap can be more accurately calculated than in any previous work. The analysis is applicable to gratings of any shape for both the TE and TM modes, but numerical results are given only for first-order gratings with rectangular and triangular tooth-shape. Reflectivities of the laser end facets have been calculated from first principles in some typical cases rather than treated as given parameters.

Keywords

distributed feedback (DFB) laser dielectric relief grating rigorous coupled-wave analysis (RGWA) 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    H. Kogelnik and C.V. Shank, “Coupled-wave theory of distributed feedback lasers,” J. Appl. Phys, 43, 2327 (1972).CrossRefGoogle Scholar
  2. 2.
    S.R. Chinn, “Effects of mirror reflectivity in a distributed feedback laser,” IEEE J. Quantum Electron, 9, 574 (1973).CrossRefGoogle Scholar
  3. 3.
    S. Wang, “Principles of distributed feedback and distributed bragg-reflector lasers,” IEEE J. Quantum Electron, 10, 413 (1974).CrossRefGoogle Scholar
  4. 4.
    W. Streifer, D.R. Scifres, and R.D. Burnham, “Effect of external reflectors on longitudinal modes of distributed feedback lasers,” IEEE J. Quantum Electron, 11, 154 (1975).CrossRefGoogle Scholar
  5. 5.
    W. Streifer, D.R. Scifres, and R.D. Burnham, “TM-mode coupling coefficients in guided-wave distributed feedback lasers,” IEEE J. Quantum Electron, 12, 74 (1976).CrossRefGoogle Scholar
  6. 6.
    S.L. McCall and P.M. Platzman, “An optimized π/2 distributed feedback laser,” IEEE J. Quantum Electron, 21, 1899 (1985).CrossRefGoogle Scholar
  7. 7.
    J.E.A. Whiteaway et al., “The design and assessment of λ/4 phase-shifted DFB Laser structures,” IEEE J. Quantum Electron, 25, 1261 (1989).CrossRefGoogle Scholar
  8. 8.
    G.P. Agrawal and A.H. Bobeck, “Modeling of distributed feedback semiconductor lasers with axially-varying parameters,” IEEE J. Quantum Electron, 24, 2407 (1988).CrossRefGoogle Scholar
  9. 9.
    W. Streifer, D.R. Scifres, and R.D. Burnham, “Analysis of grating-coupled radiation in GaAs:GaAlAs lasers and waveguides,” IEEE J. Quantum Electron, 12, 422 (1976).CrossRefGoogle Scholar
  10. 10.
    W. Streifer, R.D. Burnham, and D.R. Scifres, “Analysis of grating-coupled radiation in GaAs:GaAlAs lasers and waveguides- II:Blazing effects”, IEEE J. Quantum Electron, 12, 494 (1976).CrossRefGoogle Scholar
  11. 11.
    W. Streifer, R.D. Burnham, and D.R. Scifres, “Radiation losses in distributed lasers and longitudinal mode selection,” IEEE J. Quantum Electron, 12, 737 (1976).CrossRefGoogle Scholar
  12. 12.
    W. Streifer, D.R. Scifres, and R.D. Burnham, “Coupled wave analysis of DFB and DBR lasers,” IEEE J. Quantum Electron, 13, 134 (1977).CrossRefGoogle Scholar
  13. 13.
    W. Streifer and A. Hardy, “Analysis of two-dimensional waveguides with misaligned or curved gratings,” IEEE J. Quantum Electron, 14, 935 (1978).CrossRefGoogle Scholar
  14. 14.
    A. Hardy, D.F. Welch, and W. Streifer, “Analysis of second order gratings,” IEEE J. Quantum Electron, 25, 2096 (1989).CrossRefGoogle Scholar
  15. 15.
    H. Sato and Y. Hori, “Two-dimensional theory of distributed feedback semiconductor lasers,” IEEE J. Quantum Electron, 26, 567 (1990).CrossRefGoogle Scholar
  16. 16.
    Y. Hori and H. Sato, “Analysis of distributed feedback semiconductor lasers by two-dimensional theory,” IEEE J. Quantum Electron, 26, 655 (1990).CrossRefGoogle Scholar
  17. 17.
    T. Makino, “Effective-index matrix analysis of distributed feedback semiconductor lasers,” IEEE J. Quantum Electron, 28, 434 (1992).CrossRefGoogle Scholar
  18. 18.
    B.M. Yu and J. Liu, “Gain margin analysis of distributed feedback lasers for both transverse electric and magnetic modes,” IEEE J. Quantum Electron, 28, 822 (1992).CrossRefGoogle Scholar
  19. 19.
    J. Kinoshita, “Analysis of radiation mode effects on oscillating properties of DFB lasers,” IEEE J. Quantum Electron, 35, 1569 (1999).CrossRefGoogle Scholar
  20. 20.
    K. Yokoyama, T. Yamanaka, and S. Seki, “Two-dimensional numerical simulator for multielectrode distributed feedback laser diodes,” IEEE J. Quantum Electron, 29, 856 (1993).CrossRefGoogle Scholar
  21. 21.
    X. Li, A.D. Sadovnikov, W.P. Huang, and T. Makino, “A physics-based three-dimensional model for distributed feedback laser diodes,” IEEE J. Quantum Electron, 34, 1545 (1998).CrossRefGoogle Scholar
  22. 22.
    M.G. Moharam and T.K. Gaylord, “Diffraction analysis of dielectric surface-relief gratings,” J. Opt. Soc. Am, 72, 1385 (1982).Google Scholar
  23. 23.
    M.G. Moharam and T.K. Gaylord, “Analysis and applications of optical diffraction gratings,” Proc. IEEE 73, 894 (1985).Google Scholar
  24. 24.
    E.N. Glytsis and T.K. Gaylord, “Rigorous three-dimensional coupled-wave diffraction analysis of single and cascaded anisotropic gratings,” J. Opt. Soc. Am. A 4, 2061 (1987).Google Scholar
  25. 25.
    E.N. Glytsis and T.K. Gaylord, “Formulation for stable and efficient implementation of the rigorous coupled-wave analysis of binary gratings,” J. Opt. Soc. Am. A 12, 1068 (1995).Google Scholar
  26. 26.
    M.G. Moharam, D.A. Pommet, E.B. Grann, and T.K. Gaylord, “Stable implementation of the rigorous coupled-wave Analysis for surface-relief gratings: Enhanced transmittance matrix approach,” J. Opt. Soc. Am. A 12, 1077 (1995).Google Scholar
  27. 27.
    L. Li, “Formulation and comparison of two recursive matrix algorithms for modeling layered diffraction gratings,” J. Opt. Soc. Am. A 13, 1024 (1996).Google Scholar
  28. 28.
    Ph. Lalanne and E. Silberstein, “Fourier-modal methods applied to waveguide computation problems,” Opt. Lett, 25, 1092 (2000).Google Scholar
  29. 29.
    E. Silberstein, Ph. Lalanne, J.P. Hugonin, and Q. Cao, “Use of grating theories in integrated optics,” J. Opt. Soc. Am. A 18, 2865 (2001).Google Scholar
  30. 30.
    Q. Cao, Ph. Lalanne, and J.P. Hugonin, “Stable and efficient Bloch-mode computational method for one-dimensional grating waveguides,” J. Opt. Soc. Am, A19, 335 (2002).Google Scholar
  31. 31.
    M. Balamaru and Ph. Lalanne, “Photonic crystal waveguides: Out-of-plane losses and adiabatic modal conversion,” Appl. Phys. Lett, 78, 1466 (2001).CrossRefGoogle Scholar
  32. 32.
    B. Gralak, S. Enoch, and G. Tayeb, “From scattering or impedance matrices to Bloch modes of photonic crystals,” J. Opt. Soc. Am. A 19, 1547 (2002).Google Scholar

Copyright information

© Kluwer Academic Publishers 2004

Authors and Affiliations

  1. 1.Physics DepartmentThe American University in CairoCairoEgypt
  2. 2.Department of Engineering Math. and Physics, Faculty of EngineeringCairo UniversityGuizaEgypt

Personalised recommendations