Skip to main content
SpringerLink
Log in

Surface integral method to determine guided modes in uniaxially anisotropic embedded waveguides

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

Abstract

A surface integral method is presented to calculate the eigenmodes of an uniaxially anisotropic embedded channel waveguide. The electromagnetic field components are expressed with electric and magnetic vector potentials which are parallel with the optic axis and for which the scalar Helmholtz-equations hold using surface integral representation and the Green's functions of the vector potentials. The single component vector potentials are expanded in Fourier-series on the internal side of the dielectric interface. The Fourier-coefficients and the corresponding eigenvalues are obtained by minimizing the quadratic difference of the longitudinal field components in the cladding and core along the dielectric interface. The convergence of the series expansion is examined numerically and the eigenvalues obtained with the surface integral method agree with those obtained by Finite Element Method up to 5 significant digits.

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

  • Abramowitz, M. and I.A. Stegun. Handbook of Mathematical Functions, Dover, NY, 1970.

  • Barabás, M. et al. Opt. Commun. 123 259–267, (1996).

    Google Scholar 

  • Bardi, I. and O. Biro. IEEE Trans on Microwave Theory and Techn. 39 1133–1139, 1991.

    Google Scholar 

  • Bastiaansen, H.J.M. et al. IEEE Trans. on Microwave Theory and Techn. 40 1918–1926, 1992.

    Google Scholar 

  • Berezin, I.S. and N.P. Zhidkov. Computing methods, Pergamon Press, Oxford, 1965.

    Google Scholar 

  • Fachè, N. et al. IEEE Trans. On Microwave Theory and Techn. 39 673–680, 1991.

    Google Scholar 

  • Gaá, Sz. et al. Journal of Optics and Quantum Electronics 30 413–425, 1998.

    Google Scholar 

  • Gaál, Sz. et al. Opt. Commun. 125 368–375, 1998.

    Google Scholar 

  • Hadley, G.R. Opt. Lett. 16 624, (1991).

    Google Scholar 

  • Huang, W.P. et al. IEEE Photonics Technology Letters 8 649, (1996).

    Google Scholar 

  • Kraut, E.A. Fundamentals of Mathematical Physics, McGraw-Hill, NY, 1967.

    Google Scholar 

  • Olyslager, F. et al. IEEE Trans. on Microwave Theory and Techn. 41 79–87, 1993.

    Google Scholar 

  • Singh, S. et al. IEEE Trans. on Microwave Theory and Techn. 40 168–171, 1992a.

    Google Scholar 

  • Singh, S. et al. IEEE Trans. on Microwave Theory and Techn. 40 171–174, 1992b.

    Google Scholar 

  • Su, C. IEEE Trans. on Microwave Theory and Techn. 33 1114–1119, 1985.

    Google Scholar 

  • Urbach, H.P. et al. IEEE Trans. on Microwave Theory and Techn. 42 118–126, 1994.

    Google Scholar 

  • Vassallo, C. Opt. Quantum Electron. 29 157, (1997).

    Google Scholar 

  • Wang, L. et al. J. Opt. Soc. Am. 15 92–100, 1998.

    Google Scholar 

  • Zheng, J. et al. IEEE Trans. on Microwave Theory and Techn. 46 1339–1343, 1998.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Atomic Physics, Technical University of Budapest, H-1111 Budapest, Budafoki ut, 8, Hungary

    Szabolcs GaÁl

Authors
  1. Szabolcs GaÁl
    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

GaÁl, S. Surface integral method to determine guided modes in uniaxially anisotropic embedded waveguides. Optical and Quantum Electronics 31, 763–780 (1999). https://doi.org/10.1023/A:1006941620417

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1006941620417

Search

Navigation