Abstract

An improved full-vector finite-difference (FD) complex mode solver for circularly symmetric optical waveguides is developed and validated. The formulations are derived from Taylor expansion of transverse electric and magnetic fields and match of boundary conditions at radial index discontinuities. Calculation of the guided and leaky modes of step index fibers, Bragg fibers, and surface plasmon polaritons structures shows significant improvement in terms of accuracy and rate of convergence without increase of computational efforts, in comparison with the conventional FD scheme based on the average-index approximation. It is demonstrated that the performance of the new scheme is robust for high-order modes and waveguides with high index contrast. Contrary to the conventional FD solvers that claim the magnetic field formulation is more rigorous than the electric field formulation, the improved solver yields practically identical results for both formulations.

© 2008 IEEE

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  1. D. Marcuse, Theory of Dielectric Optical Waveguides (Academic, 1974).
  2. L. Tong, J. Lou, E. Mazur, "Single-mode guiding properties of subwavelength-diameter silica and silicon wire waveguides," Opt. Expr. 12, 1025-1035 (2004).
  3. P. Yeh}, A. Yariv, E. Marom, "Theory of Bragg fiber," J. Opt. Soc. Amer. 68, 1196-1201 (1978).
  4. I. Bassett, A. Argyros, "Elimination of polarization degeneracy in round waveguides," Opt. Expr. 10, 1342-1346 (2002).
  5. Y. Xu, G. Ouyang, R. Lee, A. Yariv, "Asymptotic matrix theory of Bragg fibers," J. Lightw. Technol 20, 428-440 (2002).
  6. S. Guo, S. Albin, R. Rogowski, "Comparative analysis of Bragg fibers," Opt. Expr. 12, 198-207 (2004).
  7. H. Khosravi, D. R. Tilley, R. Loudon, "Surface polaritons in cylindrical optical fibers," J. Opt. Soc. Amer. A 8, 112-122 (1991).
  8. S. J. Al-Bader, M. Imtaar, "Optical fiber hybrid-surface plasmon polaritons," J. Opt. Soc. Amer. B: Opt. Phys. 10, 83-88 (1993).
  9. Y.-J. He, Y.-L. Lo, J.-F. Huang, "Optical-fiber surface-plasmon-resonance sensor employing long-period fiber gratings in multiplexing," J. Opt. Soc. Amer. B: Opt. Phys. 23, 801-811 (2006).
  10. C. Themistos, B. M. A. Rahman, M. Rajarajan, K. Kalli, K. T. V. Grattan, "Characterization of surface-plasmon modes in metal-clad optical waveguides," Appl. Opt. 45, 8523-8530 (2006).
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  13. C.-C. Su, C. H. Chen, "Calculation of propagation constants and cutoff frequencies of radially inhomogeneous optical fibers," IEEE Trans. Microwave Theory Tech. MTT-34, 328-332 (1986).
  14. F. Wu, S. Guo, K. Ikram, S. Albin, H. Tai, R. S. Rogowski, "Numerical analysis of Bragg fibers using a compact 1D finite-difference frequency-domain method," Opt. Commun. 255, 167-174 (2005).
  15. L. Yang, K. Jiang, C.-L. Xu, W.-P. Huang, P. Mathieu, "A highly efficient and accurate full vector solver for guided and leaky modes of optical fibers," Proc. SPIE 6343, 63431C (2006).
  16. Y.-P. Chiou, Y.-C. Chiang, H.-C. Chang, "Improved three-point formulas considering the interface conditions in the finite-difference analysis of step-index optical devices," J. Lightw. Technol. 18, 243-251 (2000).
  17. T. P. Horikis, W. L. Kath, "Modal analysis of circular Bragg fibers with arbitrary index profiles," Opt. Lett. 31, 3417-3419 (2006).
  18. Y.-C. Chiang, Y.-P. Chiou, H.-C. Chang, "Improved full-vectorial finite-difference mode solver for optical waveguides with step-index profiles," J. Lightwave Technol. 20, 1609 (2002).
  19. W. Chew, J. Jin, E. Michielssen, "Complex coordinate stretching as a generalized absorbing boundary condition," Microw. Opt. Tech. Lett. 15, 363-369 (1997).
  20. N.-N. Feng, G.-R. Zhou, C. Xu, W.-P. Huang, "Computation of full-vector modes for bending waveguide using cylindrical perfectly matched layers," J. Lightw. Technol. 20, 1976-1980 (2002).
  21. J.-P. Berenger, "A perfectly matched layer for the absorption of electromagnetic waves," J. Comput. Phys. 114, 185-200 (1994).

2006 (5)

Y.-J. He, Y.-L. Lo, J.-F. Huang, "Optical-fiber surface-plasmon-resonance sensor employing long-period fiber gratings in multiplexing," J. Opt. Soc. Amer. B: Opt. Phys. 23, 801-811 (2006).

C. Themistos, B. M. A. Rahman, M. Rajarajan, K. Kalli, K. T. V. Grattan, "Characterization of surface-plasmon modes in metal-clad optical waveguides," Appl. Opt. 45, 8523-8530 (2006).

W. Mohammed, X. Gu, P. W. E. Smith, "Full vectorial modal analysis of specialty fibers and their Bragg grating characterization," Appl. Opt. 45, 3307-3316 (2006).

L. Yang, K. Jiang, C.-L. Xu, W.-P. Huang, P. Mathieu, "A highly efficient and accurate full vector solver for guided and leaky modes of optical fibers," Proc. SPIE 6343, 63431C (2006).

T. P. Horikis, W. L. Kath, "Modal analysis of circular Bragg fibers with arbitrary index profiles," Opt. Lett. 31, 3417-3419 (2006).

2005 (1)

F. Wu, S. Guo, K. Ikram, S. Albin, H. Tai, R. S. Rogowski, "Numerical analysis of Bragg fibers using a compact 1D finite-difference frequency-domain method," Opt. Commun. 255, 167-174 (2005).

2004 (2)

S. Guo, S. Albin, R. Rogowski, "Comparative analysis of Bragg fibers," Opt. Expr. 12, 198-207 (2004).

L. Tong, J. Lou, E. Mazur, "Single-mode guiding properties of subwavelength-diameter silica and silicon wire waveguides," Opt. Expr. 12, 1025-1035 (2004).

2002 (4)

I. Bassett, A. Argyros, "Elimination of polarization degeneracy in round waveguides," Opt. Expr. 10, 1342-1346 (2002).

Y. Xu, G. Ouyang, R. Lee, A. Yariv, "Asymptotic matrix theory of Bragg fibers," J. Lightw. Technol 20, 428-440 (2002).

Y.-C. Chiang, Y.-P. Chiou, H.-C. Chang, "Improved full-vectorial finite-difference mode solver for optical waveguides with step-index profiles," J. Lightwave Technol. 20, 1609 (2002).

N.-N. Feng, G.-R. Zhou, C. Xu, W.-P. Huang, "Computation of full-vector modes for bending waveguide using cylindrical perfectly matched layers," J. Lightw. Technol. 20, 1976-1980 (2002).

2000 (1)

Y.-P. Chiou, Y.-C. Chiang, H.-C. Chang, "Improved three-point formulas considering the interface conditions in the finite-difference analysis of step-index optical devices," J. Lightw. Technol. 18, 243-251 (2000).

1997 (1)

W. Chew, J. Jin, E. Michielssen, "Complex coordinate stretching as a generalized absorbing boundary condition," Microw. Opt. Tech. Lett. 15, 363-369 (1997).

1994 (1)

J.-P. Berenger, "A perfectly matched layer for the absorption of electromagnetic waves," J. Comput. Phys. 114, 185-200 (1994).

1993 (1)

S. J. Al-Bader, M. Imtaar, "Optical fiber hybrid-surface plasmon polaritons," J. Opt. Soc. Amer. B: Opt. Phys. 10, 83-88 (1993).

1991 (1)

H. Khosravi, D. R. Tilley, R. Loudon, "Surface polaritons in cylindrical optical fibers," J. Opt. Soc. Amer. A 8, 112-122 (1991).

1986 (1)

C.-C. Su, C. H. Chen, "Calculation of propagation constants and cutoff frequencies of radially inhomogeneous optical fibers," IEEE Trans. Microwave Theory Tech. MTT-34, 328-332 (1986).

1978 (1)

P. Yeh}, A. Yariv, E. Marom, "Theory of Bragg fiber," J. Opt. Soc. Amer. 68, 1196-1201 (1978).

Appl. Opt. (2)

IEEE Trans. Microwave Theory Tech. (1)

C.-C. Su, C. H. Chen, "Calculation of propagation constants and cutoff frequencies of radially inhomogeneous optical fibers," IEEE Trans. Microwave Theory Tech. MTT-34, 328-332 (1986).

J. Lightwave Technol. (1)

Y.-C. Chiang, Y.-P. Chiou, H.-C. Chang, "Improved full-vectorial finite-difference mode solver for optical waveguides with step-index profiles," J. Lightwave Technol. 20, 1609 (2002).

J. Comput. Phys. (1)

J.-P. Berenger, "A perfectly matched layer for the absorption of electromagnetic waves," J. Comput. Phys. 114, 185-200 (1994).

J. Lightw. Technol (1)

Y. Xu, G. Ouyang, R. Lee, A. Yariv, "Asymptotic matrix theory of Bragg fibers," J. Lightw. Technol 20, 428-440 (2002).

J. Lightw. Technol. (2)

Y.-P. Chiou, Y.-C. Chiang, H.-C. Chang, "Improved three-point formulas considering the interface conditions in the finite-difference analysis of step-index optical devices," J. Lightw. Technol. 18, 243-251 (2000).

N.-N. Feng, G.-R. Zhou, C. Xu, W.-P. Huang, "Computation of full-vector modes for bending waveguide using cylindrical perfectly matched layers," J. Lightw. Technol. 20, 1976-1980 (2002).

J. Opt. Soc. Amer. (1)

P. Yeh}, A. Yariv, E. Marom, "Theory of Bragg fiber," J. Opt. Soc. Amer. 68, 1196-1201 (1978).

J. Opt. Soc. Amer. A (1)

H. Khosravi, D. R. Tilley, R. Loudon, "Surface polaritons in cylindrical optical fibers," J. Opt. Soc. Amer. A 8, 112-122 (1991).

J. Opt. Soc. Amer. B: Opt. Phys. (2)

S. J. Al-Bader, M. Imtaar, "Optical fiber hybrid-surface plasmon polaritons," J. Opt. Soc. Amer. B: Opt. Phys. 10, 83-88 (1993).

Y.-J. He, Y.-L. Lo, J.-F. Huang, "Optical-fiber surface-plasmon-resonance sensor employing long-period fiber gratings in multiplexing," J. Opt. Soc. Amer. B: Opt. Phys. 23, 801-811 (2006).

Microw. Opt. Tech. Lett. (1)

W. Chew, J. Jin, E. Michielssen, "Complex coordinate stretching as a generalized absorbing boundary condition," Microw. Opt. Tech. Lett. 15, 363-369 (1997).

Opt. Commun. (1)

F. Wu, S. Guo, K. Ikram, S. Albin, H. Tai, R. S. Rogowski, "Numerical analysis of Bragg fibers using a compact 1D finite-difference frequency-domain method," Opt. Commun. 255, 167-174 (2005).

Opt. Expr. (3)

S. Guo, S. Albin, R. Rogowski, "Comparative analysis of Bragg fibers," Opt. Expr. 12, 198-207 (2004).

I. Bassett, A. Argyros, "Elimination of polarization degeneracy in round waveguides," Opt. Expr. 10, 1342-1346 (2002).

L. Tong, J. Lou, E. Mazur, "Single-mode guiding properties of subwavelength-diameter silica and silicon wire waveguides," Opt. Expr. 12, 1025-1035 (2004).

Opt. Lett. (1)

Proc. SPIE (1)

L. Yang, K. Jiang, C.-L. Xu, W.-P. Huang, P. Mathieu, "A highly efficient and accurate full vector solver for guided and leaky modes of optical fibers," Proc. SPIE 6343, 63431C (2006).

Other (2)

W. C. Chew, Waves and Fields in Inhomogeneous Media (Van Nostrand Reinhold, 1990).

D. Marcuse, Theory of Dielectric Optical Waveguides (Academic, 1974).

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