Abstract

The complex coupled-mode theory (CMT) is applied to optical fiber grating structures of circular cross section. The radiative fields are treated in terms of discrete complex modes similarly to the guided modes in the conventional CMT. The number of modes that contribute to the couplings may be effectively reduced by considering the phase-matching condition. Therefore, simple analytical expressions for mode amplitudes and powers are obtained. Examples of the Bragg gratings with various outer cladding refractive indexes, e.g., lower, equal to and higher than the inner cladding refractive index, are investigated and show excellent agreement with rigorous numerical solutions.

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  1. D. Marcuse, "Coupled mode theory of round optical fibers," Bell Syst. Tech. J. 52, 817-842 (1973).
  2. A. W. Synder, J. D. Love, Optical Waveguide Theory (Chapman & Hall, 1983).
  3. H. Haus, Waves and Fields in Optoelectronics xii+402 (Prentice-Hall, 1984).
  4. D. Marcuse, Theory of Dielectric Optical Waveguides, 2nd ed. (Academic, 1991).
  5. C. Vassallo, Optical Waveguide Concepts (Elsevier, 1991).
  6. S. L. Chuang, "A coupled mode formulation by reciprocity and a variational principle," J. Lightw. Technol. 5, 5-15 (1987).
  7. H. Wei-Ping, "Coupled-mode theory for optical waveguides: An overview," J. Opt. Soc. Amer. 11, 963-983 (1994).
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  9. R. Sammut, A. W. Snyder, "Leaky modes on a dielectric waveguide—Orthogonality and excitation," Appl. Opt. 15, 1040-1044 (1976).
  10. L. Changgui, C. Yiping, "Fiber Bragg grating spectra in multimode optical fibers," J. Lightw. Technol. 24, 598-604 (2006).
  11. 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 Photon. Technol. Lett. 8, 652-654 (1996).
  12. F. Ning-Ning, Z. Gui-Rong, X. Chenglin, H. Wei-Ping, "Computation of full-vector modes for bending waveguide using cylindrical perfectly matched layers," J. Lightw. Technol. 20, 1976-1980 (2002).
  13. J. P. Berenger, "A perfectly matched layer for the absorption of electromagnetic-waves," J. Comput. Phys. 114, 185-200 (1994).
  14. Y. C. Lu, L. Yang, W. P. Huang, S. S. Jian, "Improved full-vector finite-difference complex mode solver for optical waveguides of circular symmetry," J. Lightw. Technol. 26, 1868-1876 (2008).
  15. W. P. Huang, J. W. Mu, "Complex coupled mode theory for optical waveguides," Opt. Exp. 17, 19134-19152 (2009).
  16. W. C. Chew, J. M. Jin, E. Michielssen, "Complex coordinate stretching as a generalized absorbing boundary condition," Microw. Opt. Technol. Lett. 15, 363-369 (1997).
  17. M. Kuzuoglu, R. Mittra, "Investigation of nonplanar perfectly matched absorbers for finite-element mesh truncation," IEEE Trans. Antennas Propag. 45, 474-486 (1997).
  18. J. P. Berenger, "Application of the CFSPML to the absorption of evanescent waves in waveguides," IEEE Microw. Wireless Compon. Lett. 12, 218-220 (2002).
  19. C. L. Xu, W. P. Huang, M. S. Stern, S. K. Chaudhuri, "Full-vectorial mode calculation by finite difference method," Proc. Inst. Electr. Eng. Optoelectron. (1994) pp. 281-286.
  20. T. Erdogan, "Cladding-mode resonances in short- and long-period fiber grating filters," J. Opt. Soc. Amer. A, Opt. Image Sci. Vis. 14, 1760-1773 (1997).
  21. T. Erdogan, "Fiber grating spectra," J. Lightw. Technol. 15, 1277-1294 (1997).

2009 (1)

W. P. Huang, J. W. Mu, "Complex coupled mode theory for optical waveguides," Opt. Exp. 17, 19134-19152 (2009).

2008 (1)

Y. C. Lu, L. Yang, W. P. Huang, S. S. Jian, "Improved full-vector finite-difference complex mode solver for optical waveguides of circular symmetry," J. Lightw. Technol. 26, 1868-1876 (2008).

2006 (1)

L. Changgui, C. Yiping, "Fiber Bragg grating spectra in multimode optical fibers," J. Lightw. Technol. 24, 598-604 (2006).

2002 (2)

F. Ning-Ning, Z. Gui-Rong, X. Chenglin, H. Wei-Ping, "Computation of full-vector modes for bending waveguide using cylindrical perfectly matched layers," J. Lightw. Technol. 20, 1976-1980 (2002).

J. P. Berenger, "Application of the CFSPML to the absorption of evanescent waves in waveguides," IEEE Microw. Wireless Compon. Lett. 12, 218-220 (2002).

1999 (1)

D. B. Stegall, T. Erdogan, "Leaky cladding mode propagation in long-period fiber grating devices," IEEE Photon. Technol. Lett. 11, 343-345 (1999).

1997 (4)

T. Erdogan, "Cladding-mode resonances in short- and long-period fiber grating filters," J. Opt. Soc. Amer. A, Opt. Image Sci. Vis. 14, 1760-1773 (1997).

T. Erdogan, "Fiber grating spectra," J. Lightw. Technol. 15, 1277-1294 (1997).

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

M. Kuzuoglu, R. Mittra, "Investigation of nonplanar perfectly matched absorbers for finite-element mesh truncation," IEEE Trans. Antennas Propag. 45, 474-486 (1997).

1996 (1)

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 Photon. Technol. Lett. 8, 652-654 (1996).

1994 (2)

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

H. Wei-Ping, "Coupled-mode theory for optical waveguides: An overview," J. Opt. Soc. Amer. 11, 963-983 (1994).

1987 (1)

S. L. Chuang, "A coupled mode formulation by reciprocity and a variational principle," J. Lightw. Technol. 5, 5-15 (1987).

1976 (1)

1973 (1)

D. Marcuse, "Coupled mode theory of round optical fibers," Bell Syst. Tech. J. 52, 817-842 (1973).

Appl. Opt. (1)

Bell Syst. Tech. J. (1)

D. Marcuse, "Coupled mode theory of round optical fibers," Bell Syst. Tech. J. 52, 817-842 (1973).

IEEE Microw. Wireless Compon. Lett. (1)

J. P. Berenger, "Application of the CFSPML to the absorption of evanescent waves in waveguides," IEEE Microw. Wireless Compon. Lett. 12, 218-220 (2002).

IEEE Photon. Technol. Lett. (2)

D. B. Stegall, T. Erdogan, "Leaky cladding mode propagation in long-period fiber grating devices," IEEE Photon. Technol. Lett. 11, 343-345 (1999).

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 Photon. Technol. Lett. 8, 652-654 (1996).

IEEE Trans. Antennas Propag. (1)

M. Kuzuoglu, R. Mittra, "Investigation of nonplanar perfectly matched absorbers for finite-element mesh truncation," IEEE Trans. Antennas Propag. 45, 474-486 (1997).

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. (5)

Y. C. Lu, L. Yang, W. P. Huang, S. S. Jian, "Improved full-vector finite-difference complex mode solver for optical waveguides of circular symmetry," J. Lightw. Technol. 26, 1868-1876 (2008).

F. Ning-Ning, Z. Gui-Rong, X. Chenglin, H. Wei-Ping, "Computation of full-vector modes for bending waveguide using cylindrical perfectly matched layers," J. Lightw. Technol. 20, 1976-1980 (2002).

L. Changgui, C. Yiping, "Fiber Bragg grating spectra in multimode optical fibers," J. Lightw. Technol. 24, 598-604 (2006).

S. L. Chuang, "A coupled mode formulation by reciprocity and a variational principle," J. Lightw. Technol. 5, 5-15 (1987).

T. Erdogan, "Fiber grating spectra," J. Lightw. Technol. 15, 1277-1294 (1997).

J. Opt. Soc. Amer. (1)

H. Wei-Ping, "Coupled-mode theory for optical waveguides: An overview," J. Opt. Soc. Amer. 11, 963-983 (1994).

J. Opt. Soc. Amer. A, Opt. Image Sci. Vis. (1)

T. Erdogan, "Cladding-mode resonances in short- and long-period fiber grating filters," J. Opt. Soc. Amer. A, Opt. Image Sci. Vis. 14, 1760-1773 (1997).

Microw. Opt. Technol. Lett. (1)

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

Opt. Exp. (1)

W. P. Huang, J. W. Mu, "Complex coupled mode theory for optical waveguides," Opt. Exp. 17, 19134-19152 (2009).

Other (5)

C. L. Xu, W. P. Huang, M. S. Stern, S. K. Chaudhuri, "Full-vectorial mode calculation by finite difference method," Proc. Inst. Electr. Eng. Optoelectron. (1994) pp. 281-286.

A. W. Synder, J. D. Love, Optical Waveguide Theory (Chapman & Hall, 1983).

H. Haus, Waves and Fields in Optoelectronics xii+402 (Prentice-Hall, 1984).

D. Marcuse, Theory of Dielectric Optical Waveguides, 2nd ed. (Academic, 1991).

C. Vassallo, Optical Waveguide Concepts (Elsevier, 1991).

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