Abstract

Couplings of core mode to guided cladding and unguided radiation modes in fiber Bragg and long-period gratings are investigated by a unified approach based on complex mode matching method (CMMM). With the combination of the perfectly matched layer (PML) and the perfectly reflecting boundary (PRB), the continuous radiation modes can be well represented by a set of discrete complex modes so that simulation of coupling to radiation modes is greatly simplified and may be treated in the same fashion as guided modes. Numerical results of fiber Bragg and long-period gratings with refractive index of the outer cladding lower, equal, and higher than that of the inner cladding indicate that the unified approach is highly effective in the simulation of couplings to cladding and radiation modes.

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  1. K. O. Hill, B. Malo, F. Bilodeau, D. C. Johnson, "Photosensitivity in optical fibers," Annu. Rev. Mater. Sci. 23, 125-157 (1993).
  2. K. Hill, G. Meltz, "Fiber bragg grating technology fundamentals and overview," J. Lightw. Technol. 15, 1263-1276 (1997).
  3. T. Erdogan, "Fiber grating spectra," J. Lightw. Technol. 15, 1277-1294 (1997).
  4. R. Kashyap, Fiber Bragg Gratings. (Academic, 1999).
  5. K. Hill, K. Hill, "Photosensitivity in optical fiber waveguides: From discovery to commercialization," IEEE J. Sel. Top. Quantum Electron. 6, 1186-1189 (2000).
  6. A. Vengsarkar, P. Lemaire, J. Judkins, V. Bhatia, T. Erdogan, J. Sipe, "Long-period fiber gratings as band-rejection filters," J. Lightw. Technol. 14, 58-65 (1996).
  7. V. Mizrahi, J. Sipe, "Optical properties of photosensitive fiber phase gratings," J. Lightw. Technol. 11, 1513-1517 (1993).
  8. H. Patrick, A. Kersey, F. Bucholtz, "Analysis of the response of long period fiber gratings to external index of refraction," J. Lightw. Technol. 16, 1606-1612 (1998).
  9. D. Stegall, T. Erdogan, "Leaky cladding mode propagation in long-period fiber grating devices," IEEE Photon. Technol. Lett. 11, 343-345 (1999).
  10. T. Erdogan, "Cladding-mode resonances in short- and long-period fiber grating filters," J. Opt. Soc. Amer. A 14, 1760-1773 (1997).
  11. B. H. Lee, Y. Liu, S. B. Lee, S. S. Choi, J. N. Jang, "Displacements of the resonant peaks of a long-period fiber grating induced by a change of ambient refractive index," Opt. Lett. 22, 1769-1771 (1997).
  12. Y. Koyamada, "Analysis of core-mode to radiation-mode coupling in fiber bragg gratings with finite cladding radius," J. Lightw. Technol. 18, 1220-1225 (2000).
  13. Y. Koyamada, "Numerical analysis of core-mode to radiation-mode coupling in long-period fiber gratings," IEEE Photon. Technol. Lett. 13, 308-310 (2001).
  14. R. Hou, Z. Ghassemlooy, A. Hassan, C. Lu, K. P. Dowker, "Modelling of long-period fibre grating response to refractive index higher than that of cladding," Meas. Sci. Technol. 1709 (2001).
  15. Y. Jeong, B. Lee, J. Nilsson, D. Richardson, "A quasi-mode interpretation of radiation modes in long-period fiber gratings," IEEE J. Quantum Electron. 39, 1135-1142 (2003).
  16. D. Marcuse, Theory of Dielectric Optical Waveguides (Academic Press, 1974).
  17. R. Sammut, A. W. Snyder, "Leaky modes on a dielectric waveguide: Orthogonality and excitation," Appl. Opt. 15, 1040-1044 (1976).
  18. K. Jiang, W.-P. Huang, "Finite-difference-based mode-matching method for 3-D waveguide structures under semivectorial approximation," J. Lightw. Technol. 23, 4239-4248 (2005).
  19. 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).
  20. H. Derudder, H. Derudder, D. de Zutter, F. Olyslager, "Analysis of waveguide discontinuities using perfectly matched layers," Electron. Lett 34, 2138-2140 (1998).
  21. P. Bienstman, P. Bienstman, H. Derudder, R. Baets, F. Olyslager, D. De Zutter, "Analysis of cylindrical waveguide discontinuities using vectorial eigenmodes and perfectly matched layers," IEEE Trans. Microw. Theory Tech. 49, 349-354 (2001).
  22. P. Bienstman, R. Baets, "Optical modelling of photonic crystals and VCSELs using eigenmode expansion and perfectly matched layers," Opt. Quantum Electron. 33, 327-341 (2001).
  23. J.-P. Berenger, "A perfectly matched layer for the absorption of electromagnetic waves," J. Comput. Phys. 114, 185-200 (1994).
  24. F. Teixeira, W. Chew, "Systematic derivation of anisotropic pml absorbing media in cylindrical and spherical coordinates," IEEE Microw. Guided Wave Lett. 7, 371-373 (1997).
  25. W. Chew, J. Jin, E. Michielssen, "Complex coordinate stretching as a generalized absorbing boundary condition," Microw. Opt. Tech. Lett. 15, 363-369 (1997).
  26. V. Bhatia, A. M. Vengsarkar, "Optical fiber long-period grating sensors," Opt. Lett. 21, 692 (1996).
  27. S. W. James, R. P. Tatam, "Optical fibre long-period grating sensors: Characteristics and application," Meas. Sci. Technol. 14, R49-R61 (2003).
  28. R. B. Lehoucq, D. C. Sorensen, "Deflation techniques for an implicitly restarted Arnoldi iteration," SIAM J. Matrix Anal. Appl. 17, 789-821 (1996).
  29. R. Lehoucq, D. Sorensen, C. Yang, ARPACK Users' Guide: Solution of Large-Scale Eigenvalue Problems With Implicitly Restarted Arnoldi Methods (SIAM, 1998).
  30. T. Erdogan, J. E. Sipe, "Radiation-mode coupling loss in tilted fiber phase gratings," Opt. Lett. 20, 1838-1840 (1995).
  31. T. Erdogan, J. E. Sipe, "Tilted fiber phase gratings," J. Opt. Soc. Amer. A 13, 296 (1996).
  32. G. Nemova, J. Chauve, R. Kashyap, "Design of sidetap fiber bragg grating filters," Opt. Commun. 259, 649-654 (2006).
  33. P. Bienstman, Rigorous and Efficient Modelling of Wavelength Scale Photonic Components Ph.D. dissertation Ghent Univ.GhentBelgium (2001) pp. 36.
  34. L. Li, "Multilayer modal method for diffraction gratings of arbitrary profile, depth, and permittivity," J. Opt. Soc. Amer. A 10, 2581-2591 (1993).
  35. L. Li, "Formulation and comparison of two recursive matrix algorithms for modeling layered diffraction gratings," J. Opt. Soc. Amer. A 13, 1024 (1996).

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)

G. Nemova, J. Chauve, R. Kashyap, "Design of sidetap fiber bragg grating filters," Opt. Commun. 259, 649-654 (2006).

2005 (1)

K. Jiang, W.-P. Huang, "Finite-difference-based mode-matching method for 3-D waveguide structures under semivectorial approximation," J. Lightw. Technol. 23, 4239-4248 (2005).

2003 (2)

Y. Jeong, B. Lee, J. Nilsson, D. Richardson, "A quasi-mode interpretation of radiation modes in long-period fiber gratings," IEEE J. Quantum Electron. 39, 1135-1142 (2003).

S. W. James, R. P. Tatam, "Optical fibre long-period grating sensors: Characteristics and application," Meas. Sci. Technol. 14, R49-R61 (2003).

2001 (4)

P. Bienstman, P. Bienstman, H. Derudder, R. Baets, F. Olyslager, D. De Zutter, "Analysis of cylindrical waveguide discontinuities using vectorial eigenmodes and perfectly matched layers," IEEE Trans. Microw. Theory Tech. 49, 349-354 (2001).

P. Bienstman, R. Baets, "Optical modelling of photonic crystals and VCSELs using eigenmode expansion and perfectly matched layers," Opt. Quantum Electron. 33, 327-341 (2001).

Y. Koyamada, "Numerical analysis of core-mode to radiation-mode coupling in long-period fiber gratings," IEEE Photon. Technol. Lett. 13, 308-310 (2001).

R. Hou, Z. Ghassemlooy, A. Hassan, C. Lu, K. P. Dowker, "Modelling of long-period fibre grating response to refractive index higher than that of cladding," Meas. Sci. Technol. 1709 (2001).

2000 (2)

Y. Koyamada, "Analysis of core-mode to radiation-mode coupling in fiber bragg gratings with finite cladding radius," J. Lightw. Technol. 18, 1220-1225 (2000).

K. Hill, K. Hill, "Photosensitivity in optical fiber waveguides: From discovery to commercialization," IEEE J. Sel. Top. Quantum Electron. 6, 1186-1189 (2000).

1999 (1)

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

1998 (2)

H. Patrick, A. Kersey, F. Bucholtz, "Analysis of the response of long period fiber gratings to external index of refraction," J. Lightw. Technol. 16, 1606-1612 (1998).

H. Derudder, H. Derudder, D. de Zutter, F. Olyslager, "Analysis of waveguide discontinuities using perfectly matched layers," Electron. Lett 34, 2138-2140 (1998).

1997 (6)

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

B. H. Lee, Y. Liu, S. B. Lee, S. S. Choi, J. N. Jang, "Displacements of the resonant peaks of a long-period fiber grating induced by a change of ambient refractive index," Opt. Lett. 22, 1769-1771 (1997).

K. Hill, G. Meltz, "Fiber bragg grating technology fundamentals and overview," J. Lightw. Technol. 15, 1263-1276 (1997).

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

F. Teixeira, W. Chew, "Systematic derivation of anisotropic pml absorbing media in cylindrical and spherical coordinates," IEEE Microw. Guided Wave Lett. 7, 371-373 (1997).

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

1996 (5)

V. Bhatia, A. M. Vengsarkar, "Optical fiber long-period grating sensors," Opt. Lett. 21, 692 (1996).

R. B. Lehoucq, D. C. Sorensen, "Deflation techniques for an implicitly restarted Arnoldi iteration," SIAM J. Matrix Anal. Appl. 17, 789-821 (1996).

T. Erdogan, J. E. Sipe, "Tilted fiber phase gratings," J. Opt. Soc. Amer. A 13, 296 (1996).

L. Li, "Formulation and comparison of two recursive matrix algorithms for modeling layered diffraction gratings," J. Opt. Soc. Amer. A 13, 1024 (1996).

A. Vengsarkar, P. Lemaire, J. Judkins, V. Bhatia, T. Erdogan, J. Sipe, "Long-period fiber gratings as band-rejection filters," J. Lightw. Technol. 14, 58-65 (1996).

1995 (1)

1994 (1)

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

1993 (3)

L. Li, "Multilayer modal method for diffraction gratings of arbitrary profile, depth, and permittivity," J. Opt. Soc. Amer. A 10, 2581-2591 (1993).

V. Mizrahi, J. Sipe, "Optical properties of photosensitive fiber phase gratings," J. Lightw. Technol. 11, 1513-1517 (1993).

K. O. Hill, B. Malo, F. Bilodeau, D. C. Johnson, "Photosensitivity in optical fibers," Annu. Rev. Mater. Sci. 23, 125-157 (1993).

1976 (1)

R. Sammut, A. W. Snyder, "Leaky modes on a dielectric waveguide: Orthogonality and excitation," Appl. Opt. 15, 1040-1044 (1976).

Annu. Rev. Mater. Sci. (1)

K. O. Hill, B. Malo, F. Bilodeau, D. C. Johnson, "Photosensitivity in optical fibers," Annu. Rev. Mater. Sci. 23, 125-157 (1993).

Appl. Opt. (1)

R. Sammut, A. W. Snyder, "Leaky modes on a dielectric waveguide: Orthogonality and excitation," Appl. Opt. 15, 1040-1044 (1976).

Electron. Lett (1)

H. Derudder, H. Derudder, D. de Zutter, F. Olyslager, "Analysis of waveguide discontinuities using perfectly matched layers," Electron. Lett 34, 2138-2140 (1998).

IEEE Photon. Technol. Lett. (1)

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

IEEE J. Quantum Electron. (1)

Y. Jeong, B. Lee, J. Nilsson, D. Richardson, "A quasi-mode interpretation of radiation modes in long-period fiber gratings," IEEE J. Quantum Electron. 39, 1135-1142 (2003).

IEEE J. Sel. Top. Quantum Electron. (1)

K. Hill, K. Hill, "Photosensitivity in optical fiber waveguides: From discovery to commercialization," IEEE J. Sel. Top. Quantum Electron. 6, 1186-1189 (2000).

IEEE Microw. Guided Wave Lett. (1)

F. Teixeira, W. Chew, "Systematic derivation of anisotropic pml absorbing media in cylindrical and spherical coordinates," IEEE Microw. Guided Wave Lett. 7, 371-373 (1997).

IEEE Photon. Technol. Lett. (1)

Y. Koyamada, "Numerical analysis of core-mode to radiation-mode coupling in long-period fiber gratings," IEEE Photon. Technol. Lett. 13, 308-310 (2001).

IEEE Trans. Microw. Theory Tech. (1)

P. Bienstman, P. Bienstman, H. Derudder, R. Baets, F. Olyslager, D. De Zutter, "Analysis of cylindrical waveguide discontinuities using vectorial eigenmodes and perfectly matched layers," IEEE Trans. Microw. Theory Tech. 49, 349-354 (2001).

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. Opt. Soc. Amer. A (1)

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

J. Lightw. Technol. (8)

K. Jiang, W.-P. Huang, "Finite-difference-based mode-matching method for 3-D waveguide structures under semivectorial approximation," J. Lightw. Technol. 23, 4239-4248 (2005).

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).

A. Vengsarkar, P. Lemaire, J. Judkins, V. Bhatia, T. Erdogan, J. Sipe, "Long-period fiber gratings as band-rejection filters," J. Lightw. Technol. 14, 58-65 (1996).

V. Mizrahi, J. Sipe, "Optical properties of photosensitive fiber phase gratings," J. Lightw. Technol. 11, 1513-1517 (1993).

H. Patrick, A. Kersey, F. Bucholtz, "Analysis of the response of long period fiber gratings to external index of refraction," J. Lightw. Technol. 16, 1606-1612 (1998).

K. Hill, G. Meltz, "Fiber bragg grating technology fundamentals and overview," J. Lightw. Technol. 15, 1263-1276 (1997).

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

Y. Koyamada, "Analysis of core-mode to radiation-mode coupling in fiber bragg gratings with finite cladding radius," J. Lightw. Technol. 18, 1220-1225 (2000).

J. Opt. Soc. Amer. A (3)

T. Erdogan, J. E. Sipe, "Tilted fiber phase gratings," J. Opt. Soc. Amer. A 13, 296 (1996).

L. Li, "Multilayer modal method for diffraction gratings of arbitrary profile, depth, and permittivity," J. Opt. Soc. Amer. A 10, 2581-2591 (1993).

L. Li, "Formulation and comparison of two recursive matrix algorithms for modeling layered diffraction gratings," J. Opt. Soc. Amer. A 13, 1024 (1996).

Meas. Sci. Technol. (2)

S. W. James, R. P. Tatam, "Optical fibre long-period grating sensors: Characteristics and application," Meas. Sci. Technol. 14, R49-R61 (2003).

R. Hou, Z. Ghassemlooy, A. Hassan, C. Lu, K. P. Dowker, "Modelling of long-period fibre grating response to refractive index higher than that of cladding," Meas. Sci. Technol. 1709 (2001).

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)

G. Nemova, J. Chauve, R. Kashyap, "Design of sidetap fiber bragg grating filters," Opt. Commun. 259, 649-654 (2006).

Opt. Lett. (3)

Opt. Quantum Electron. (1)

P. Bienstman, R. Baets, "Optical modelling of photonic crystals and VCSELs using eigenmode expansion and perfectly matched layers," Opt. Quantum Electron. 33, 327-341 (2001).

SIAM J. Matrix Anal. Appl. (1)

R. B. Lehoucq, D. C. Sorensen, "Deflation techniques for an implicitly restarted Arnoldi iteration," SIAM J. Matrix Anal. Appl. 17, 789-821 (1996).

Other (4)

R. Lehoucq, D. Sorensen, C. Yang, ARPACK Users' Guide: Solution of Large-Scale Eigenvalue Problems With Implicitly Restarted Arnoldi Methods (SIAM, 1998).

P. Bienstman, Rigorous and Efficient Modelling of Wavelength Scale Photonic Components Ph.D. dissertation Ghent Univ.GhentBelgium (2001) pp. 36.

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

R. Kashyap, Fiber Bragg Gratings. (Academic, 1999).

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