Skip to main content
SpringerLink
Log in

Optical waveguide analysis using alternative direction implicit (ADI) method in combination with successive over-relaxation (SOR) algorithm

  • Research Article
  • Published:
Journal of Optics Aims and scope Submit manuscript

Abstract

The aim of this research is to implement an implicit two step but unconditionally stable numerical scheme which is capable of efficiently solving two-dimensional Helmholtz wave equation in different rib waveguide structures in GaAs material system. In particular, we use alternative direction implicit (ADI) method in combination with successive over-relaxation (SOR) algorithm for optical modal analysis in terms of effective index (or modal index) and normalised index. It is observed that the computed normalised index and modal index exhibit great agreement with other published findings.

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

Similar content being viewed by others

References

  1. A.K. Thander, S. Bhattacharyya, Optical Confinement study of different semi conductor rib wave guides using higher order compact finite difference method. Optik 127, 2116–2120 (2016)

    Article  CAS  ADS  Google Scholar 

  2. A.K. Thander, S. Bhattacharyya, Study of optical modal index for semi conductor rib wave guides using higher order compact finite difference method. Optik 131, 775–784 (2017)

    Article  CAS  ADS  Google Scholar 

  3. D. Wang, K. Dong, J. Li, C. Grigoropoulos, J. Yao, J. Hong, Wu. Junqiao, Low-loss, geometry-invariant optical waveguides with near-zero-index materials. Nanophotonics 11(21), 4747–4753 (2022)

    Article  CAS  Google Scholar 

  4. M.S. Stern, Semivectorial polarised H field solutions for dielectric waveguides with arbitrary index profiles. IEE Proc. J. 135, 333–338 (1988)

    Google Scholar 

  5. W. Huang, H.A. Hauss, A simple variational approach to optical Rib waveguides. J. Lightwave Technol. 9(1), 56–61 (1991)

    Article  ADS  Google Scholar 

  6. M.S. Stern, Finite difference analysis of planar optical waveguides. Progr. Electromagn. Res. PIER 10, 123–186 (1995)

    Article  Google Scholar 

  7. S.P. Chan, V.M.N. Passaro, G.T. Reed, Singlemode and polarisation free conditions for small silicon –on-insulator waveguides. Electron. Lett. 41(9), 528 (2005)

    Article  CAS  ADS  Google Scholar 

  8. C.-C. Huang, C.-C. Huang, J.-Y. Yang, A full-vectorial pseudospectral modal analysis of dielectric optical waveguides with stepped refractive index profile. IEEE J. Sel. Top. Quantum Electron. 11(2), 457–465 (2005)

    Article  CAS  ADS  Google Scholar 

  9. W.P. Huang, C.L. Xu, W. Lui, K. Yokoyama, The perfectly matched layer boundary condition for modal analysis of optical waveguides: leaky mode calculations. IEEE Photonics Technol. Lett. 8(5), 652–654 (1996)

    Article  ADS  Google Scholar 

  10. S. Bhattacharyya, A.K. Thander, Study of H-field using higher-order compact (HOC) finite difference method (FDM) in semiconductor rib waveguide structure. J. Opt. 48, 345–356 (2019)

    Article  Google Scholar 

  11. W.P. Huang, C.L. Xu, Simulation of three dimensional optical waveguides by a full vector beam propagation method. IEEE J. Quantum Electron 29(10), 2639–2649 (1993)

    Article  ADS  Google Scholar 

  12. A.K. Thander, S. Bhattacharyya, Study of optical wave guide using HOC scheme. Appl Math Sci 8(79), 3931–3938 (2014)

    Google Scholar 

  13. P.-J. Chiang, C.-L. Wu, C.-H. Teng, C.-S. Yang, H.-C. Chang, Full –vectorial optical waveguide mode solvers using multidomain pseudospectral frequency –domain (PSFD) formulations. IEEE J. Quantum Electron. 44(1), 56–66 (2007)

    Article  ADS  Google Scholar 

  14. S.K. Pandit, J.C. Kalita, D.C. Dalal, A transient higher order compact scheme for incompressible viscous flows on geometries beyond rectangular. J. Comput. Phys. 225, 1100–1124 (2007)

    Article  MathSciNet  ADS  Google Scholar 

  15. Y.P. Chiou, Y.C. Chiang, C.H. Lai, C.H. Du, H.C. Chang, Finite-difference modeling of dielectric waveguides with corners and slanted facets. J. Lightwave Technol. 27(12), 2077–2086 (2009)

    Article  ADS  Google Scholar 

  16. S. Selleri, J. Petracek, Modal analysis of rib waveguide through finite element and mode matching methods. Opt Quantum Electron 33, 373–386 (2001)

    Article  Google Scholar 

  17. A.K. Thander and S. Bhattacharyya, “Optimization of structure parameters of a rib wave guide using optical modal Index analysis through higher order compact FDM”.in 2016 IEEE Uttar Pradesh Section International Conference on Electrical, Computer and Electronics Engineering (UPCON), pp. 151–155 (2016) .

  18. T.M. Benson, P.C. Kendall, Variational techniques including effective and weighted index methods. Prog. Electromag. Res. PIER 10, 1–40 (1995)

    Article  Google Scholar 

  19. I. Molina de la Peña, M.L. Calvo, R.F. Alvarez-Estrada, Neutron optics: new algorithm based on green’s functions for simulating waveguides with dirichlet boundary conditions. Appl. Math. Model. 101, 694–715 (2022)

    Article  MathSciNet  Google Scholar 

  20. J.D. Hoffman, Numerical Methods for Engineers and Scientists (Marcel Dekker, Inc., New York, 1992)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Applied Science and Humanities, Guru Nanak Institute of Technology, Kolkata, 700114, India

    Anup Kumar Thander & Goutam Mandal

Authors
  1. Anup Kumar Thander
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Goutam Mandal
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Anup Kumar Thander.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Thander, A.K., Mandal, G. Optical waveguide analysis using alternative direction implicit (ADI) method in combination with successive over-relaxation (SOR) algorithm. J Opt 53, 475–481 (2024). https://doi.org/10.1007/s12596-023-01206-w

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12596-023-01206-w

Keywords

Search

Navigation