A new higher order finite-difference approximation scheme for the method of lines

Journal of Lightwave Technology

Volumn 19, Issue 3, 2001, Pages 398-404

  Jamid, Hussain A ^a,b   Akram, Muhammad Nadeem ^a,c,d,e,f  

^a KING FAHD UNIVERSITY OF PETROLEUM AND MINERALS   (Saudi Arabia)

^b ARIZONA STATE UNIVERSITY   (United States)

^c UNIVERSITY OF ENGINEERING AND TECHNOLOGY   (Pakistan)

^d Zelin Medical Systems (Pvt)   (Pakistan)

^e Carrier Telephone Industries   (Pakistan)

^f AERO (Pvt)   (Pakistan)

Author keywords

Finite difference methods; Higher order approximations; Method of lines (MoL); Optical waveguides; Surface plasmon mode

Indexed keywords

METHOD OF LINES (MOL);

APPROXIMATION THEORY; DIELECTRIC MATERIALS; FINITE DIFFERENCE METHOD; MATHEMATICAL OPERATORS; OPTIMIZATION;

PARTIAL DIFFERENTIAL EQUATIONS;

EID: 0035269970     PISSN: 07338724     EISSN: None     Source Type: Journal    
DOI: 10.1109/50.918894     Document Type: Article

References (22)

1. V. Vemuri and W. J. Karplus, Digital Computer Treatment of Partial Differential Equations, Series in Computational Mathematics. Englewood Cliffs, NJ: Prentice Hall, 1981.
2. T. Itoh, Numerical Techniques for Microwave and Millimeter-Wave Passive Structures. New York: Wiley, 1989.
3. J. Gerdes and R. Pregla, "Beam-propagation algorithm based on the method of lines," Opt. Soc. Amer. B. Opt. Phys., vol. 8, pp. 389-394, Feb. 1991.
4. U. Rogge and R. Pregla, "Method of lines for the analysis of strip-loaded optical waveguides," Opt. Soc. Amer. B, Opt. Phys., vol. 8, pp. 459-463, Feb. 1991.
5. U. Rogge, "Method of Lines for the Analysis of Dielectric Waveguides," Ph.D. dissertation, Fern Univ., Hagen, Germany, 1991.
6. W. Yang, "Method of Lines for Analysis of Passive and Active Integrated Optical Devices," Ph.D. dissertation, Fern Univ., Hagen, Germany, 1996.
7. A. A. Shittu, "Study of periodic waveguides by the finite-difference time-domain method and the Method of Lines," Ph.D. dissertation, King Fahad University of Petroleum and Minerals, Dhahran, Saudi Arabia, Sept. 1994.
8. C. Vassallo, "Improvement of finite-difference methods for step-index optical waveguides," Proc. IEEE, vol. 139, pp. 137-142, Apr. 1992.
9. S. F. Helfert and R. Pregla, "Finite difference expressions for arbitrarily positioned dielectric steps in waveguide structures," J. Lightwave Technol., vol. 14, pp. 2414-2421, Oct. 1996.
10. A. Kornatz, "Increase of the order of approximation and improvement of the interface conditions for the method of lines," J. Lightwave Technol., vol. 11, pp. 249-251, Feb. 1993.
11. J. Yamauchi, M. Sekiguchi, O. Uchiyama, J. Shibayama, and H. Nakano, "Modified finite-difference formula for the analysis of semivectorial modes in step-index optical waveguides," IEEE Photon. Technol., vol. 9, pp. 961-963, July 1997.
12. S. Xiao, R. Vahldieck, H. Jin, and Z. Cai, "A modified MoL algorithm with faster convergence and improved computational efficiency," Microwave Symp. Dig., IEEE MTT-S Int., vol. 1, pp. 357-360, 1991.
13. R. Pregla, "High order approximation for the difference operators in the method of lines," IEEE Microwave Guided Wave Lett., vol. 5, pp. 53-55, Feb. 1995.
14. R. Stoffer, "Efficient interface conditions based on a 5-point finite difference operator," Opt. Quantum Electron., vol. 30, pp. 375-383, 1998.
15. S. F. Helfert and R. Pregla, "Modeling of thin dielectric layers in finite-difference schemes," Integr. Photonics Research, Tech. Dig., pp. 253-255, July.
16. J. Yamauchi, J. Shibayama, and H. Nakano, "Modified finite-difference beam propagation method based on the generalized Douglas scheme for variable coefficients," IEEE Photon. Technol. Lett., vol. 7, pp. 661-663, June 1995.
17. J. Yamauchi, J. Shibayama, M. Sekiguchi, and H. Nakano, "Finite-difference beam propagation method based on the generalized Douglas scheme for a nonuniform grid," IEEE Photon. Technol. Lett., vol. 9, pp. 67-69, Jan. 1997.
18. J. , J. Shibayama, K. Matsubara, M. Sekiguchi, J. Yamauchi. and H. Nakano, "Efficient nonuniform schemes for paraxial and wide-angle finite-difference beam propagation methods," J. Lightwave Technol.., vol. 17, pp. 677-683, Apr. 1999.
19. G. R. Hadley, "Low-truncation-error finite difference equations for photonics simulation I: Beam propagation," J. Lightwave Technol.., vol. 16, pp. 134-141, Jan. 1998.
20. O. Conradi, S. Helfert, and R. Pregla, "Modification of the finite-difference scheme for efficient analysis of thin film lossy metal layers in optical devices," Opt. Quantum Electron., pp. 369-373, 1998.
21. F. J. Schmuckle and R. Pregla, "The method of lines for the analysis of lossy planar waveguides," IEEE Trans. Microwave Theory Tech., vol. 38, pp. 1473-1479, Oct. 1990.
22. M. N. Akram, "Analysis of anti-resonant reflecting optical waveguide (ARROW) grating using the method of lines," M.S. thesis, King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia, Apr. 2000.