Abstract

The application of the mode-matching (MM) method in the case of photonic crystal waveguide discontinuities is presented. The structure under consideration is divided into a number of cells, and the modes of each cell are calculated by an alternative formulation of the plane-wave expansion (PWE) method. This formulation allows the calculation of both guided and evanescent modes at a given frequency. A matrix equation is then formed relating the modal amplitudes at the beginning and the end of the structure. The accuracy of the MM method is compared to the finite-difference frequency-domain (FDFD) method and the finite-difference time-domain (FDTD) method, and good agreement is observed. The MM method requires far fewer resources than the FDFD and the FDTD methods while providing a useful physical insight to the calculation of the frequency response of waveguide discontinuities. The method is also applied to the calculation of power loss due to structural fabrication-induced variations.

© 2007 Optical Society of America

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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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  20. S. D. Wu and E. N. Glytsis, "Finite-number-of-periods holographic gratings with finite-width incident beams: analysis using the finite-difference frequency-domain methods," J. Opt. Soc. Am. A 19, 2018-2029 (2002).
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    [CrossRef]
  23. R. E. Collin, Field Theory of Guided Waves (McGraw-Hill, 1992).
  24. M. Skorobogatiy, M. Ibanescu, S. G. Johnson, O. Weisberg, T. D. Engeness, M. Soljacic, S. A. Jacobs, and Y. Fink, "Analysis of general geometric scaling perturbations in a transmitting waveguide: fundamental connection between polarizarion-mode dispersion and group-velocity dispersion," J. Opt. Soc. Am. B 19, 2867-2875 (2002).
    [CrossRef]
  25. S. G. Johnson, P. Bienstman, M. A. Skorobogatiy, M. Ibanescu, E. Lidorikis, and J. D. Joannopoulos, "Adiabatic theorem and continuous coupled-mode theory for efficient taper transitions in photonic crystals," Phys. Rev. E 66, 066608 (2002).
    [CrossRef]
  26. M. L. Povinelli, S. G. Johnson, E. Lidorikis, and J. D. Joannopoulos, "Effect of a photonic band gap on scattering from waveguide disorder," Appl. Phys. Lett. 84, 3639-3641 (2004).
    [CrossRef]
  27. D. Marcuse, Theory of Dielectric Optical Waveguides, 2nd ed. (Academic Press, 1991).
  28. G. A. Gesell and I. R. Ciric, "Recurrence model analysis for multiple waveguide discontinuities and its application to circular structures," IEEE Trans. Microwave Theory Tech. 41, 484-490 (1993).
    [CrossRef]
  29. T. Kamalakis and T. Sphicopoulos, "Numerical study of the implications of size nonuniformities in the performance of photonic crystal couplers using couple mode theory," IEEE J. Quantum Electron. 41, 863-871 (2005).
    [CrossRef]

2005 (3)

2004 (3)

2003 (2)

R. Costa, A. Melloni, and M. Martinelli, "Bandpass resonant filters in photonic-crystal waveguides," IEEE Photon. Technol. Lett. 15, 401-403 (2003).
[CrossRef]

M. F. Yanik, S. Fan, M. Soljacic, and J. D. Joannopoulos "All-optical transistor action with bistable switching in a photonic crystal cross-waveguide geometry," Opt. Lett. 28, 2506-2508 (2003).
[CrossRef] [PubMed]

2002 (7)

Y. Hibino, "Recent advances in high-density and large-scale AWG multi/demultiplexers with higher index contrast-based PLCs," IEEE J. Sel. Top. Quantum Electron. 8, 1090-1101 (2002).
[CrossRef]

I. Vurgaftman and J. R. Meyer, "Photonic-crystal distributed-feedback quantum cascade lasers," IEEE J. Quantum Electron. 38, 592-602 (2002).
[CrossRef]

M. Imada, S. Noda, A. Chutinan, M. Mochizuki, and T. Tanaka, "Channel drop filter using a single defect in a 2-D photonic crystal slab waveguide," J. Lightwave Technol. 20, 873-878 (2002).
[CrossRef]

E. Heebner, R. W. Boyd, and Q-H. Park, "SCISSOR solitons and other novel propagation effects in microresonator-modified waveguides," J. Opt. Soc. Am. B 19, 722-731 (2002).
[CrossRef]

S. D. Wu and E. N. Glytsis, "Finite-number-of-periods holographic gratings with finite-width incident beams: analysis using the finite-difference frequency-domain methods," J. Opt. Soc. Am. A 19, 2018-2029 (2002).
[CrossRef]

M. Skorobogatiy, M. Ibanescu, S. G. Johnson, O. Weisberg, T. D. Engeness, M. Soljacic, S. A. Jacobs, and Y. Fink, "Analysis of general geometric scaling perturbations in a transmitting waveguide: fundamental connection between polarizarion-mode dispersion and group-velocity dispersion," J. Opt. Soc. Am. B 19, 2867-2875 (2002).
[CrossRef]

S. G. Johnson, P. Bienstman, M. A. Skorobogatiy, M. Ibanescu, E. Lidorikis, and J. D. Joannopoulos, "Adiabatic theorem and continuous coupled-mode theory for efficient taper transitions in photonic crystals," Phys. Rev. E 66, 066608 (2002).
[CrossRef]

2001 (2)

M. Koshiba, Y. Tsuji, and S. Sasaki "High-performance absorbing boundary conditions for photonic crystal waveguide simulations," IEEE Microw. Wirel. Compon. Lett. 11, 152-154 (2001).
[CrossRef]

M. Koshiba, "Wavelength division multiplexing and demultiplexing with photonic crystal waveguide couplers," J. Lightwave Technol. 19, 1970-1975 (2001).
[CrossRef]

2000 (1)

1999 (2)

B. E. Little, S. T. Chu, W. Pan, D. Ripin, T. Kaneko, Y. Kokubun, and E. Ippen, "Vertically coupled glass microring resonator channel dropping filters," IEEE Photon. Technol. Lett. 11, 215-217 (1999).
[CrossRef]

A. Yariv, Y. Xu, R. K. Lee, and A. Scherer, "Coupled-resonator optical waveguide: a proposal and analysis," Opt. Lett. 24, 711-713 (1999).
[CrossRef]

1998 (1)

N. Stefanou and A. Modinos, "Impurity bands in photonic insulators," Phys. Rev. B 57, 12127-12133, (1998).
[CrossRef]

1996 (1)

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, "High transmission through sharp bends in photonic crystal waveguides," Phys. Rev. Lett. 77, 3787-3790 (1996).
[CrossRef] [PubMed]

1993 (1)

G. A. Gesell and I. R. Ciric, "Recurrence model analysis for multiple waveguide discontinuities and its application to circular structures," IEEE Trans. Microwave Theory Tech. 41, 484-490 (1993).
[CrossRef]

1989 (1)

H. Shigesawa and M. Tsuji, "A new equivalent network method for the analyzing discontinuity properties of open dielectric waveguides," IEEE Trans. Microwave Theory Tech. 37, 3-14 (1989).
[CrossRef]

Baba, T.

Bienstman, P.

S. G. Johnson, P. Bienstman, M. A. Skorobogatiy, M. Ibanescu, E. Lidorikis, and J. D. Joannopoulos, "Adiabatic theorem and continuous coupled-mode theory for efficient taper transitions in photonic crystals," Phys. Rev. E 66, 066608 (2002).
[CrossRef]

Boyd, R. W.

Chen, J. C.

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, "High transmission through sharp bends in photonic crystal waveguides," Phys. Rev. Lett. 77, 3787-3790 (1996).
[CrossRef] [PubMed]

Chu, S. T.

B. E. Little, S. T. Chu, W. Pan, D. Ripin, T. Kaneko, Y. Kokubun, and E. Ippen, "Vertically coupled glass microring resonator channel dropping filters," IEEE Photon. Technol. Lett. 11, 215-217 (1999).
[CrossRef]

Chutinan, A.

M. Imada, S. Noda, A. Chutinan, M. Mochizuki, and T. Tanaka, "Channel drop filter using a single defect in a 2-D photonic crystal slab waveguide," J. Lightwave Technol. 20, 873-878 (2002).
[CrossRef]

Ciric, I. R.

G. A. Gesell and I. R. Ciric, "Recurrence model analysis for multiple waveguide discontinuities and its application to circular structures," IEEE Trans. Microwave Theory Tech. 41, 484-490 (1993).
[CrossRef]

Collin, R. E.

R. E. Collin, Field Theory of Guided Waves (McGraw-Hill, 1992).

Costa, R.

R. Costa, A. Melloni, and M. Martinelli, "Bandpass resonant filters in photonic-crystal waveguides," IEEE Photon. Technol. Lett. 15, 401-403 (2003).
[CrossRef]

Dutton, R. W.

Engeness, T. D.

Fan, S.

Fink, Y.

Gesell, G. A.

G. A. Gesell and I. R. Ciric, "Recurrence model analysis for multiple waveguide discontinuities and its application to circular structures," IEEE Trans. Microwave Theory Tech. 41, 484-490 (1993).
[CrossRef]

Glytsis, E. N.

Hagness, S.

A. Tafflove and S. Hagness, Computational Electrodynamics: the Finite Difference Time-Domain Method (Artech House, 2000).

Heebner, E.

Hibino, Y.

Y. Hibino, "Recent advances in high-density and large-scale AWG multi/demultiplexers with higher index contrast-based PLCs," IEEE J. Sel. Top. Quantum Electron. 8, 1090-1101 (2002).
[CrossRef]

Ibanescu, M.

M. Skorobogatiy, M. Ibanescu, S. G. Johnson, O. Weisberg, T. D. Engeness, M. Soljacic, S. A. Jacobs, and Y. Fink, "Analysis of general geometric scaling perturbations in a transmitting waveguide: fundamental connection between polarizarion-mode dispersion and group-velocity dispersion," J. Opt. Soc. Am. B 19, 2867-2875 (2002).
[CrossRef]

S. G. Johnson, P. Bienstman, M. A. Skorobogatiy, M. Ibanescu, E. Lidorikis, and J. D. Joannopoulos, "Adiabatic theorem and continuous coupled-mode theory for efficient taper transitions in photonic crystals," Phys. Rev. E 66, 066608 (2002).
[CrossRef]

Imada, M.

M. Imada, S. Noda, A. Chutinan, M. Mochizuki, and T. Tanaka, "Channel drop filter using a single defect in a 2-D photonic crystal slab waveguide," J. Lightwave Technol. 20, 873-878 (2002).
[CrossRef]

Ippen, E.

B. E. Little, S. T. Chu, W. Pan, D. Ripin, T. Kaneko, Y. Kokubun, and E. Ippen, "Vertically coupled glass microring resonator channel dropping filters," IEEE Photon. Technol. Lett. 11, 215-217 (1999).
[CrossRef]

Jacobs, S. A.

Joannopoulos, J. D.

M. L. Povinelli, S. G. Johnson, E. Lidorikis, and J. D. Joannopoulos, "Effect of a photonic band gap on scattering from waveguide disorder," Appl. Phys. Lett. 84, 3639-3641 (2004).
[CrossRef]

M. F. Yanik, S. Fan, M. Soljacic, and J. D. Joannopoulos "All-optical transistor action with bistable switching in a photonic crystal cross-waveguide geometry," Opt. Lett. 28, 2506-2508 (2003).
[CrossRef] [PubMed]

S. G. Johnson, P. Bienstman, M. A. Skorobogatiy, M. Ibanescu, E. Lidorikis, and J. D. Joannopoulos, "Adiabatic theorem and continuous coupled-mode theory for efficient taper transitions in photonic crystals," Phys. Rev. E 66, 066608 (2002).
[CrossRef]

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, "High transmission through sharp bends in photonic crystal waveguides," Phys. Rev. Lett. 77, 3787-3790 (1996).
[CrossRef] [PubMed]

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crytals, Molding the Flow of Light (Princeton U. Press, 1995).

Johnson, S. G.

M. L. Povinelli, S. G. Johnson, E. Lidorikis, and J. D. Joannopoulos, "Effect of a photonic band gap on scattering from waveguide disorder," Appl. Phys. Lett. 84, 3639-3641 (2004).
[CrossRef]

M. Skorobogatiy, M. Ibanescu, S. G. Johnson, O. Weisberg, T. D. Engeness, M. Soljacic, S. A. Jacobs, and Y. Fink, "Analysis of general geometric scaling perturbations in a transmitting waveguide: fundamental connection between polarizarion-mode dispersion and group-velocity dispersion," J. Opt. Soc. Am. B 19, 2867-2875 (2002).
[CrossRef]

S. G. Johnson, P. Bienstman, M. A. Skorobogatiy, M. Ibanescu, E. Lidorikis, and J. D. Joannopoulos, "Adiabatic theorem and continuous coupled-mode theory for efficient taper transitions in photonic crystals," Phys. Rev. E 66, 066608 (2002).
[CrossRef]

Kamalakis, T.

T. Kamalakis and T. Sphicopoulos, "Numerical study of the implications of size nonuniformities in the performance of photonic crystal couplers using couple mode theory," IEEE J. Quantum Electron. 41, 863-871 (2005).
[CrossRef]

Kaneko, T.

B. E. Little, S. T. Chu, W. Pan, D. Ripin, T. Kaneko, Y. Kokubun, and E. Ippen, "Vertically coupled glass microring resonator channel dropping filters," IEEE Photon. Technol. Lett. 11, 215-217 (1999).
[CrossRef]

Khurgin, J. B.

Kim, S.

Kokubun, Y.

B. E. Little, S. T. Chu, W. Pan, D. Ripin, T. Kaneko, Y. Kokubun, and E. Ippen, "Vertically coupled glass microring resonator channel dropping filters," IEEE Photon. Technol. Lett. 11, 215-217 (1999).
[CrossRef]

Koshiba, M.

M. Koshiba, Y. Tsuji, and S. Sasaki "High-performance absorbing boundary conditions for photonic crystal waveguide simulations," IEEE Microw. Wirel. Compon. Lett. 11, 152-154 (2001).
[CrossRef]

M. Koshiba, "Wavelength division multiplexing and demultiplexing with photonic crystal waveguide couplers," J. Lightwave Technol. 19, 1970-1975 (2001).
[CrossRef]

Kurland, I.

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, "High transmission through sharp bends in photonic crystal waveguides," Phys. Rev. Lett. 77, 3787-3790 (1996).
[CrossRef] [PubMed]

Lee, R. K.

Lidorikis, E.

M. L. Povinelli, S. G. Johnson, E. Lidorikis, and J. D. Joannopoulos, "Effect of a photonic band gap on scattering from waveguide disorder," Appl. Phys. Lett. 84, 3639-3641 (2004).
[CrossRef]

S. G. Johnson, P. Bienstman, M. A. Skorobogatiy, M. Ibanescu, E. Lidorikis, and J. D. Joannopoulos, "Adiabatic theorem and continuous coupled-mode theory for efficient taper transitions in photonic crystals," Phys. Rev. E 66, 066608 (2002).
[CrossRef]

Lim, H.

Little, B. E.

B. E. Little, S. T. Chu, W. Pan, D. Ripin, T. Kaneko, Y. Kokubun, and E. Ippen, "Vertically coupled glass microring resonator channel dropping filters," IEEE Photon. Technol. Lett. 11, 215-217 (1999).
[CrossRef]

Madsen, C. K.

Marcuse, D.

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

Martinelli, M.

R. Costa, A. Melloni, and M. Martinelli, "Bandpass resonant filters in photonic-crystal waveguides," IEEE Photon. Technol. Lett. 15, 401-403 (2003).
[CrossRef]

Matsumoto, T.

Meade, R. D.

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crytals, Molding the Flow of Light (Princeton U. Press, 1995).

Mekis, A.

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, "High transmission through sharp bends in photonic crystal waveguides," Phys. Rev. Lett. 77, 3787-3790 (1996).
[CrossRef] [PubMed]

Melloni, A.

R. Costa, A. Melloni, and M. Martinelli, "Bandpass resonant filters in photonic-crystal waveguides," IEEE Photon. Technol. Lett. 15, 401-403 (2003).
[CrossRef]

Meyer, J. R.

I. Vurgaftman and J. R. Meyer, "Photonic-crystal distributed-feedback quantum cascade lasers," IEEE J. Quantum Electron. 38, 592-602 (2002).
[CrossRef]

Mochizuki, M.

M. Imada, S. Noda, A. Chutinan, M. Mochizuki, and T. Tanaka, "Channel drop filter using a single defect in a 2-D photonic crystal slab waveguide," J. Lightwave Technol. 20, 873-878 (2002).
[CrossRef]

Modinos, A.

N. Stefanou and A. Modinos, "Impurity bands in photonic insulators," Phys. Rev. B 57, 12127-12133, (1998).
[CrossRef]

Noda, S.

M. Imada, S. Noda, A. Chutinan, M. Mochizuki, and T. Tanaka, "Channel drop filter using a single defect in a 2-D photonic crystal slab waveguide," J. Lightwave Technol. 20, 873-878 (2002).
[CrossRef]

Pan, W.

B. E. Little, S. T. Chu, W. Pan, D. Ripin, T. Kaneko, Y. Kokubun, and E. Ippen, "Vertically coupled glass microring resonator channel dropping filters," IEEE Photon. Technol. Lett. 11, 215-217 (1999).
[CrossRef]

Park, D.

Park, I.

Park, Q-H.

Povinelli, M. L.

M. L. Povinelli, S. G. Johnson, E. Lidorikis, and J. D. Joannopoulos, "Effect of a photonic band gap on scattering from waveguide disorder," Appl. Phys. Lett. 84, 3639-3641 (2004).
[CrossRef]

Ripin, D.

B. E. Little, S. T. Chu, W. Pan, D. Ripin, T. Kaneko, Y. Kokubun, and E. Ippen, "Vertically coupled glass microring resonator channel dropping filters," IEEE Photon. Technol. Lett. 11, 215-217 (1999).
[CrossRef]

Sakoda, K.

K. Sakoda, Optical Properties of Photonic Crystals (Springer-Verlag, 2001).

Sasaki, S.

M. Koshiba, Y. Tsuji, and S. Sasaki "High-performance absorbing boundary conditions for photonic crystal waveguide simulations," IEEE Microw. Wirel. Compon. Lett. 11, 152-154 (2001).
[CrossRef]

Scherer, A.

Shigesawa, H.

H. Shigesawa and M. Tsuji, "A new equivalent network method for the analyzing discontinuity properties of open dielectric waveguides," IEEE Trans. Microwave Theory Tech. 37, 3-14 (1989).
[CrossRef]

Skorobogatiy, M.

Skorobogatiy, M. A.

S. G. Johnson, P. Bienstman, M. A. Skorobogatiy, M. Ibanescu, E. Lidorikis, and J. D. Joannopoulos, "Adiabatic theorem and continuous coupled-mode theory for efficient taper transitions in photonic crystals," Phys. Rev. E 66, 066608 (2002).
[CrossRef]

Soljacic, M.

Sphicopoulos, T.

T. Kamalakis and T. Sphicopoulos, "Numerical study of the implications of size nonuniformities in the performance of photonic crystal couplers using couple mode theory," IEEE J. Quantum Electron. 41, 863-871 (2005).
[CrossRef]

Stefanou, N.

N. Stefanou and A. Modinos, "Impurity bands in photonic insulators," Phys. Rev. B 57, 12127-12133, (1998).
[CrossRef]

Tafflove, A.

A. Tafflove and S. Hagness, Computational Electrodynamics: the Finite Difference Time-Domain Method (Artech House, 2000).

Tanaka, T.

M. Imada, S. Noda, A. Chutinan, M. Mochizuki, and T. Tanaka, "Channel drop filter using a single defect in a 2-D photonic crystal slab waveguide," J. Lightwave Technol. 20, 873-878 (2002).
[CrossRef]

Tsuji, M.

H. Shigesawa and M. Tsuji, "A new equivalent network method for the analyzing discontinuity properties of open dielectric waveguides," IEEE Trans. Microwave Theory Tech. 37, 3-14 (1989).
[CrossRef]

Tsuji, Y.

M. Koshiba, Y. Tsuji, and S. Sasaki "High-performance absorbing boundary conditions for photonic crystal waveguide simulations," IEEE Microw. Wirel. Compon. Lett. 11, 152-154 (2001).
[CrossRef]

Veronis, G.

Villeneuve, P. R.

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, "High transmission through sharp bends in photonic crystal waveguides," Phys. Rev. Lett. 77, 3787-3790 (1996).
[CrossRef] [PubMed]

Vurgaftman, I.

I. Vurgaftman and J. R. Meyer, "Photonic-crystal distributed-feedback quantum cascade lasers," IEEE J. Quantum Electron. 38, 592-602 (2002).
[CrossRef]

Weisberg, O.

Winn, J. N.

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crytals, Molding the Flow of Light (Princeton U. Press, 1995).

Wu, S. D.

Xu, Y.

Yanik, M. F.

Yariv, A.

Appl. Phys. Lett. (1)

M. L. Povinelli, S. G. Johnson, E. Lidorikis, and J. D. Joannopoulos, "Effect of a photonic band gap on scattering from waveguide disorder," Appl. Phys. Lett. 84, 3639-3641 (2004).
[CrossRef]

IEEE J. Quantum Electron. (2)

T. Kamalakis and T. Sphicopoulos, "Numerical study of the implications of size nonuniformities in the performance of photonic crystal couplers using couple mode theory," IEEE J. Quantum Electron. 41, 863-871 (2005).
[CrossRef]

I. Vurgaftman and J. R. Meyer, "Photonic-crystal distributed-feedback quantum cascade lasers," IEEE J. Quantum Electron. 38, 592-602 (2002).
[CrossRef]

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

Y. Hibino, "Recent advances in high-density and large-scale AWG multi/demultiplexers with higher index contrast-based PLCs," IEEE J. Sel. Top. Quantum Electron. 8, 1090-1101 (2002).
[CrossRef]

IEEE Microw. Wirel. Compon. Lett. (1)

M. Koshiba, Y. Tsuji, and S. Sasaki "High-performance absorbing boundary conditions for photonic crystal waveguide simulations," IEEE Microw. Wirel. Compon. Lett. 11, 152-154 (2001).
[CrossRef]

IEEE Photon. Technol. Lett. (2)

R. Costa, A. Melloni, and M. Martinelli, "Bandpass resonant filters in photonic-crystal waveguides," IEEE Photon. Technol. Lett. 15, 401-403 (2003).
[CrossRef]

B. E. Little, S. T. Chu, W. Pan, D. Ripin, T. Kaneko, Y. Kokubun, and E. Ippen, "Vertically coupled glass microring resonator channel dropping filters," IEEE Photon. Technol. Lett. 11, 215-217 (1999).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (2)

G. A. Gesell and I. R. Ciric, "Recurrence model analysis for multiple waveguide discontinuities and its application to circular structures," IEEE Trans. Microwave Theory Tech. 41, 484-490 (1993).
[CrossRef]

H. Shigesawa and M. Tsuji, "A new equivalent network method for the analyzing discontinuity properties of open dielectric waveguides," IEEE Trans. Microwave Theory Tech. 37, 3-14 (1989).
[CrossRef]

J. Lightwave Technol. (5)

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

J. Opt. Soc. Am. B (2)

Opt. Lett. (4)

Phys. Rev. B (1)

N. Stefanou and A. Modinos, "Impurity bands in photonic insulators," Phys. Rev. B 57, 12127-12133, (1998).
[CrossRef]

Phys. Rev. E (1)

S. G. Johnson, P. Bienstman, M. A. Skorobogatiy, M. Ibanescu, E. Lidorikis, and J. D. Joannopoulos, "Adiabatic theorem and continuous coupled-mode theory for efficient taper transitions in photonic crystals," Phys. Rev. E 66, 066608 (2002).
[CrossRef]

Phys. Rev. Lett. (1)

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, "High transmission through sharp bends in photonic crystal waveguides," Phys. Rev. Lett. 77, 3787-3790 (1996).
[CrossRef] [PubMed]

Other (5)

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crytals, Molding the Flow of Light (Princeton U. Press, 1995).

K. Sakoda, Optical Properties of Photonic Crystals (Springer-Verlag, 2001).

A. Tafflove and S. Hagness, Computational Electrodynamics: the Finite Difference Time-Domain Method (Artech House, 2000).

R. E. Collin, Field Theory of Guided Waves (McGraw-Hill, 1992).

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

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Figures (9)

Fig. 1
Fig. 1

Cell of a periodic waveguide comprised of dielectric rods having arbitrary centers and radii.

Fig. 2
Fig. 2

Examples of guided and evanescent modes of a 2D photonic crystal waveguide: (a) the guided mode, (b) the evanescent mode with the smallest dumping constant, and (c) the evanescent mode with the smallest purely imaginary β.

Fig. 3
Fig. 3

Structure comprised of discontinuities with arbitrarily positioned dielectric rods between two PCW cells.

Fig. 4
Fig. 4

Widely spaced waveguide discontinuities.

Fig. 5
Fig. 5

Comparison of power reflection coefficient of the MM and the FDFD methods for (a) single, (b) double, and (c) triple defect rods inside a PCW.

Fig. 6
Fig. 6

Convergence of the MM method with (a) increasing N x and (b) increasing N z for various cell sizes.

Fig. 7
Fig. 7

(a) SCISSOR comprising of four PC defect cavities side-coupled to a PCW, (b) comparison of the power transmission obtained by the FDTD and the MM method.

Fig. 8
Fig. 8

Power loss (expressed in dB/mm) due to scattering obtained considering 100 perturbed PCWs assuming (a) Δ = 1 nm , (b) 3 nm , and (c) 5 nm .

Fig. 9
Fig. 9

(a) Structure used in order to compare the conventional MM method and its 2 × 2 TM simplification, (b) power transmissions obtained by the two methods.

Tables (2)

Tables Icon

Table 1 Comparison between the FDFD and MM Method for Various Defect Rod Positions

Tables Icon

Table 2 Mean Value and Standard Deviation of the Power Loss Due to Scattering

Equations (33)

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E ( r ) = u ( r ) e j β z ,
H ( r ) = v ( r ) e j β z ,
Ψ β = ( u t , v t ) T = ( u x , u y , v x , v y ) T ,
( A ̂ + j z B ) Ψ β = β B ̂ Ψ β ,
A ̂ = ( ω ε 1 ω t × 1 μ t × 0 0 ω μ 1 ω t × 1 ω t × )
B ̂ = ( 0 z × z × 0 ) .
Ψ β = m , n , l B ( G m n l ) sin ( G m x x 2 ) sin ( G n y y 2 ) e j G l z z ,
M V = β V ,
V = ( V 1 , , V N , U 1 , , U N ) T
M = [ M G M ε M ω M G ] ,
[ M ε ] p q = ω 1 2 k = 1 4 ( 1 ) k ε ̃ ( G p q ( k ) ) G q x 2 ω μ δ p q .
ε ̃ ( G ) = 1 S S d r ε ( r ) e j G r ,
G p q ( 1 ) = ( G p x + G q x , G p z G q z ) T ,
G p q ( 2 ) = ( G p x G q x , G p z G q z ) T ,
G p q ( 3 ) = ( G p x G q x , G p z G q z ) T ,
G p q ( 4 ) = ( G p x + G q x , G p z G q z ) T .
ε ̃ ( G ) = { 2 ( ε a ε b ) n f n J 1 ( G r n ) G r n e j G p n , G 0 ( ε a ε b ) n f n + ε b , G = 0 .
E t i = m a m ( i ) e t m ( i ) e j β m ( i ) ( z z i 1 ) + m b m ( i ) e t m ( i ) e j β m ( i ) ( z z i ) ,
H t i = m a m ( i ) h t m ( i ) e j β m ( i ) ( z z i 1 ) + m b m ( i ) h t m ( i ) e j β m ( i ) ( z z i ) ,
E t i ( z i ) = E t i + 1 ( z i ) ,
H t i ( z i ) = H t i + 1 ( z i ) .
f , g = V f g d V
( A i + 1 B i + 1 ) = Z i ( A i B i ) ,
Z i = Y i 1 X i ,
[ X i ] n m = { e t m ( i ) , h t n ( i + 1 ) e j β m ( i ) a 1 m , n M e t m ( i ) , h t n ( i + 1 ) 1 m M , n M h t n ( i ) , e t n ( i ) e j β t n ( i ) a 1 m , n M M h t m ( i ) , e t n ( i ) M + 1 m , n 2 M
[ Y i ] n m = { e t m ( i + 1 ) , h t n ( i + 1 ) 1 m , n M e t m ( i + 1 ) , h t n ( i + 1 ) e j β m ( i + 1 ) a 1 m M , n M h t m ( i + 1 ) , e t n ( i ) 1 m , n M M h t m ( i + 1 ) , e t n ( i ) e j β m ( i + 1 ) a M + 1 m , n 2 M .
( A N B N ) = Z ( A 1 B 1 ) ,
Z = Z N 1 Z 1 .
B 1 = Z 22 1 Z 21 A 1 ,
A N = Z 11 A 1 + Z 12 B 1 ,
Z = [ Z 11 Z 12 Z 21 Z 22 ] .
Z = Z A D Z B ,
D = [ e j β g L 0 0 e j β g L ]

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