Abstract

A nonuniform-shape photonic crystal taper integrated with a single-mode optical fiber and a photonic crystal waveguide for high-efficiency mode coupling is presented. The curvature of the tapering section is varied by the parameter α. For values of α set to 2 and 0.5, concave and convex tapers are obtained, respectively. Numerical calculations yield an average coupling efficiency greater than 97% at a short taper length of 20.52 μm for the convex-shape taper. Subsequently, the value of the parameter α is varied for investigating the effects of curvature on coupling efficiency and compactness of different types of taper.

© 2005 Optical Society of America

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References

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  1. J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton U. Press, 1995).
  2. S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and H. A. Haus, “Channel drop filters in photonic crystals,” Opt. Express 3, 4–11 (1998) http://www.opticsexpress.org/abstract.cfm?URI=OPEX-3-1-4.
    [Crossref] [PubMed]
  3. D. Falco, C. Conti, and C. G. Someda, “Coupling and decoupling of electromagnetic waves in parallel 2-D photonic crystal waveguides,” IEEE J. Quantum Electron. 38, 47–53 (2002).
    [Crossref]
  4. J. H. Wu, L. K. Ang, A. Q. Liu, H. G. Teo, and C. Lu, “Tunable high Q photonic bandgap Fabry-Perot resonator,” J. Opt. Soc. Am. B 22, 1770–1777 (2005).
    [Crossref]
  5. S. G. Johnson, P. R. Villeneuve, S. H. Fan, and J. D. Joannopoulos, “Linear waveguide in photonic crystal slab,” Phys. Rev. B 62, 8212–8222 (2000).
    [Crossref]
  6. D. Tailaert, W. Bogaerts, P. Bienstman, T. Krauss, P. V. Daele, I. Moerman, S. Verstuyft, K. D. Mesel, and R. Baets, “An out-of plane grating coupler for efficient butt coupling between compact planar waveguides and single mode fibres,” IEEE J. Quantum Electron. 38, 949–954 (2002).
    [Crossref]
  7. P. E. Barclay, K. Srinivasan, M. Borselli, and O. Painter, “Efficient input and output fiber coupling to a photonic crystal waveguide,” Opt. Lett. 29, 697–699 (2004).
    [Crossref] [PubMed]
  8. D. W. Prather, J. Murakowski, S. Shi, S. Venkataraman, C. Chen, and D. Pustai, “High-efficiency coupling structure for a single-line-defect photonic crystal waveguide,” Opt. Lett. 27, 1601–1603 (2002).
    [Crossref]
  9. A. Mekis and J. D. Joannopoulos, “Tapered couplers for efficient interfacing between dielectric and photonic crystal waveguides,” J. Lightwave Technol. 19, 861–865 (2001).
    [Crossref]
  10. Ph. Lalanne and A. Talneau, “Modal conversion with artificial materials for photonic-crystal waveguides,” Opt. Express 10, 354–359 (2002) http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-8-354.
    [PubMed]
  11. M. Palamaru and Ph. Lalanne, “Photonic crystal waveguides: out-of-plane losses and adiabatic mode conversion,” Appl. Phys. Lett. 78, 1466–1468 (2001).
    [Crossref]
  12. T. D. Happ, M. Kamp, and A. Forchel, “Photonic crystal tapers for ultracompact mode conversion,” Opt. Lett. 26, 1102–1104 (2001).
    [Crossref]
  13. P. Bienstman, S. Assefa, S. G. Johnson, J. D. Joannopoulos, G. S. Petrich, and L. A. Kolodziejski, “Taper structures for coupling into photonic crystal slab waveguide,” J. Opt. Soc. Am. B 20, 1817–1821 (2003).
    [Crossref]
  14. P. Pottier, I. Ntakis, and R. M. De La Rue, “Photonic crystal continuous taper for low-loss direct coupling into photonic crystal channel waveguides and further device functionality,” Opt. Commun. 223, 339–347 (2003).
    [Crossref]
  15. C. Wei, F. Groen, M. K. Smit, I. Moerman, P. V. Daele, and R. Baets, “Integrated optical elliptic couplers: modeling, design, and applications,” J. Lightwave Technol. 15, 906–911 (1997).
    [Crossref]
  16. C. C. Constantinou and R. C. Jones, “Path-integral analysis of arbitrarily tapered multimode, graded-index waveguide: the inverse-square-law and parabolic tapers,” IEE Proceedings 139, 365–375 (1992).
  17. D. Marcuse, “Radiation losses of tapered dielectric slab waveguides,” Bell Syst. Tech. J. 49, 273–290 (1969).
  18. W. K. Burns and A. F. Milton, “Mode conversion in planar-dielectric separating waveguide,” IEEE J. Quantum Electron. 11, 32–39 (1975).
    [Crossref]
  19. S. G. Johnson, P. Bienstman, M. A. Skorobogatiy, M. Ibanescu, E. Lidorikis, and J. D. Joannopoulos, “Adiabatic theorem and continuous couple-mode theory for efficient taper transition” Phys. Rev. E 66, 066608 (2002).
    [Crossref]
  20. F. Sporleder and H. G. Unger, Waveguide tapers transition and couplers (IEE, 1979).
  21. G. Tayeb and D. Maystre, “Rigorous theoretical study of finite-size two-dimensional photonic crystals doped by microcavities,” J. Opt. Soc. Am. A 14, 3323–3332 (1997).
    [Crossref]
  22. J. Yonekura, M. Ikeda, and T. Baba, “Analysis of finite 2-D photonic crystals of columns and lightwave devices using the scattering matrix method,” J. Lightwave Technol. 17, 1500–1508 (1999).
    [Crossref]
  23. G. O. Olaofe, “Scattering by two cylinders,” Radio Sci. 5, 1351–1360 (1970).
    [Crossref]
  24. H. Benisty, “Modal analysis of optical guides with two-dimensional photonic band-gap boundaries,” J. Appl. Phys. 79, 7483–7492 (1996).
    [Crossref]

2005 (1)

2004 (1)

2003 (2)

P. Bienstman, S. Assefa, S. G. Johnson, J. D. Joannopoulos, G. S. Petrich, and L. A. Kolodziejski, “Taper structures for coupling into photonic crystal slab waveguide,” J. Opt. Soc. Am. B 20, 1817–1821 (2003).
[Crossref]

P. Pottier, I. Ntakis, and R. M. De La Rue, “Photonic crystal continuous taper for low-loss direct coupling into photonic crystal channel waveguides and further device functionality,” Opt. Commun. 223, 339–347 (2003).
[Crossref]

2002 (5)

D. Falco, C. Conti, and C. G. Someda, “Coupling and decoupling of electromagnetic waves in parallel 2-D photonic crystal waveguides,” IEEE J. Quantum Electron. 38, 47–53 (2002).
[Crossref]

D. Tailaert, W. Bogaerts, P. Bienstman, T. Krauss, P. V. Daele, I. Moerman, S. Verstuyft, K. D. Mesel, and R. Baets, “An out-of plane grating coupler for efficient butt coupling between compact planar waveguides and single mode fibres,” IEEE J. Quantum Electron. 38, 949–954 (2002).
[Crossref]

S. G. Johnson, P. Bienstman, M. A. Skorobogatiy, M. Ibanescu, E. Lidorikis, and J. D. Joannopoulos, “Adiabatic theorem and continuous couple-mode theory for efficient taper transition” Phys. Rev. E 66, 066608 (2002).
[Crossref]

Ph. Lalanne and A. Talneau, “Modal conversion with artificial materials for photonic-crystal waveguides,” Opt. Express 10, 354–359 (2002) http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-8-354.
[PubMed]

D. W. Prather, J. Murakowski, S. Shi, S. Venkataraman, C. Chen, and D. Pustai, “High-efficiency coupling structure for a single-line-defect photonic crystal waveguide,” Opt. Lett. 27, 1601–1603 (2002).
[Crossref]

2001 (3)

2000 (1)

S. G. Johnson, P. R. Villeneuve, S. H. Fan, and J. D. Joannopoulos, “Linear waveguide in photonic crystal slab,” Phys. Rev. B 62, 8212–8222 (2000).
[Crossref]

1999 (1)

1998 (1)

1997 (2)

G. Tayeb and D. Maystre, “Rigorous theoretical study of finite-size two-dimensional photonic crystals doped by microcavities,” J. Opt. Soc. Am. A 14, 3323–3332 (1997).
[Crossref]

C. Wei, F. Groen, M. K. Smit, I. Moerman, P. V. Daele, and R. Baets, “Integrated optical elliptic couplers: modeling, design, and applications,” J. Lightwave Technol. 15, 906–911 (1997).
[Crossref]

1996 (1)

H. Benisty, “Modal analysis of optical guides with two-dimensional photonic band-gap boundaries,” J. Appl. Phys. 79, 7483–7492 (1996).
[Crossref]

1992 (1)

C. C. Constantinou and R. C. Jones, “Path-integral analysis of arbitrarily tapered multimode, graded-index waveguide: the inverse-square-law and parabolic tapers,” IEE Proceedings 139, 365–375 (1992).

1975 (1)

W. K. Burns and A. F. Milton, “Mode conversion in planar-dielectric separating waveguide,” IEEE J. Quantum Electron. 11, 32–39 (1975).
[Crossref]

1970 (1)

G. O. Olaofe, “Scattering by two cylinders,” Radio Sci. 5, 1351–1360 (1970).
[Crossref]

1969 (1)

D. Marcuse, “Radiation losses of tapered dielectric slab waveguides,” Bell Syst. Tech. J. 49, 273–290 (1969).

Ang, L. K.

Assefa, S.

Baba, T.

Baets, R.

D. Tailaert, W. Bogaerts, P. Bienstman, T. Krauss, P. V. Daele, I. Moerman, S. Verstuyft, K. D. Mesel, and R. Baets, “An out-of plane grating coupler for efficient butt coupling between compact planar waveguides and single mode fibres,” IEEE J. Quantum Electron. 38, 949–954 (2002).
[Crossref]

C. Wei, F. Groen, M. K. Smit, I. Moerman, P. V. Daele, and R. Baets, “Integrated optical elliptic couplers: modeling, design, and applications,” J. Lightwave Technol. 15, 906–911 (1997).
[Crossref]

Barclay, P. E.

Benisty, H.

H. Benisty, “Modal analysis of optical guides with two-dimensional photonic band-gap boundaries,” J. Appl. Phys. 79, 7483–7492 (1996).
[Crossref]

Bienstman, P.

P. Bienstman, S. Assefa, S. G. Johnson, J. D. Joannopoulos, G. S. Petrich, and L. A. Kolodziejski, “Taper structures for coupling into photonic crystal slab waveguide,” J. Opt. Soc. Am. B 20, 1817–1821 (2003).
[Crossref]

S. G. Johnson, P. Bienstman, M. A. Skorobogatiy, M. Ibanescu, E. Lidorikis, and J. D. Joannopoulos, “Adiabatic theorem and continuous couple-mode theory for efficient taper transition” Phys. Rev. E 66, 066608 (2002).
[Crossref]

D. Tailaert, W. Bogaerts, P. Bienstman, T. Krauss, P. V. Daele, I. Moerman, S. Verstuyft, K. D. Mesel, and R. Baets, “An out-of plane grating coupler for efficient butt coupling between compact planar waveguides and single mode fibres,” IEEE J. Quantum Electron. 38, 949–954 (2002).
[Crossref]

Bogaerts, W.

D. Tailaert, W. Bogaerts, P. Bienstman, T. Krauss, P. V. Daele, I. Moerman, S. Verstuyft, K. D. Mesel, and R. Baets, “An out-of plane grating coupler for efficient butt coupling between compact planar waveguides and single mode fibres,” IEEE J. Quantum Electron. 38, 949–954 (2002).
[Crossref]

Borselli, M.

Burns, W. K.

W. K. Burns and A. F. Milton, “Mode conversion in planar-dielectric separating waveguide,” IEEE J. Quantum Electron. 11, 32–39 (1975).
[Crossref]

Chen, C.

Constantinou, C. C.

C. C. Constantinou and R. C. Jones, “Path-integral analysis of arbitrarily tapered multimode, graded-index waveguide: the inverse-square-law and parabolic tapers,” IEE Proceedings 139, 365–375 (1992).

Conti, C.

D. Falco, C. Conti, and C. G. Someda, “Coupling and decoupling of electromagnetic waves in parallel 2-D photonic crystal waveguides,” IEEE J. Quantum Electron. 38, 47–53 (2002).
[Crossref]

Daele, P. V.

D. Tailaert, W. Bogaerts, P. Bienstman, T. Krauss, P. V. Daele, I. Moerman, S. Verstuyft, K. D. Mesel, and R. Baets, “An out-of plane grating coupler for efficient butt coupling between compact planar waveguides and single mode fibres,” IEEE J. Quantum Electron. 38, 949–954 (2002).
[Crossref]

C. Wei, F. Groen, M. K. Smit, I. Moerman, P. V. Daele, and R. Baets, “Integrated optical elliptic couplers: modeling, design, and applications,” J. Lightwave Technol. 15, 906–911 (1997).
[Crossref]

Falco, D.

D. Falco, C. Conti, and C. G. Someda, “Coupling and decoupling of electromagnetic waves in parallel 2-D photonic crystal waveguides,” IEEE J. Quantum Electron. 38, 47–53 (2002).
[Crossref]

Fan, S.

Fan, S. H.

S. G. Johnson, P. R. Villeneuve, S. H. Fan, and J. D. Joannopoulos, “Linear waveguide in photonic crystal slab,” Phys. Rev. B 62, 8212–8222 (2000).
[Crossref]

Forchel, A.

Groen, F.

C. Wei, F. Groen, M. K. Smit, I. Moerman, P. V. Daele, and R. Baets, “Integrated optical elliptic couplers: modeling, design, and applications,” J. Lightwave Technol. 15, 906–911 (1997).
[Crossref]

Happ, T. D.

Haus, H. A.

Ibanescu, M.

S. G. Johnson, P. Bienstman, M. A. Skorobogatiy, M. Ibanescu, E. Lidorikis, and J. D. Joannopoulos, “Adiabatic theorem and continuous couple-mode theory for efficient taper transition” Phys. Rev. E 66, 066608 (2002).
[Crossref]

Ikeda, M.

Joannopoulos, J. D.

P. Bienstman, S. Assefa, S. G. Johnson, J. D. Joannopoulos, G. S. Petrich, and L. A. Kolodziejski, “Taper structures for coupling into photonic crystal slab waveguide,” J. Opt. Soc. Am. B 20, 1817–1821 (2003).
[Crossref]

S. G. Johnson, P. Bienstman, M. A. Skorobogatiy, M. Ibanescu, E. Lidorikis, and J. D. Joannopoulos, “Adiabatic theorem and continuous couple-mode theory for efficient taper transition” Phys. Rev. E 66, 066608 (2002).
[Crossref]

A. Mekis and J. D. Joannopoulos, “Tapered couplers for efficient interfacing between dielectric and photonic crystal waveguides,” J. Lightwave Technol. 19, 861–865 (2001).
[Crossref]

S. G. Johnson, P. R. Villeneuve, S. H. Fan, and J. D. Joannopoulos, “Linear waveguide in photonic crystal slab,” Phys. Rev. B 62, 8212–8222 (2000).
[Crossref]

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and H. A. Haus, “Channel drop filters in photonic crystals,” Opt. Express 3, 4–11 (1998) http://www.opticsexpress.org/abstract.cfm?URI=OPEX-3-1-4.
[Crossref] [PubMed]

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

Johnson, S. G.

P. Bienstman, S. Assefa, S. G. Johnson, J. D. Joannopoulos, G. S. Petrich, and L. A. Kolodziejski, “Taper structures for coupling into photonic crystal slab waveguide,” J. Opt. Soc. Am. B 20, 1817–1821 (2003).
[Crossref]

S. G. Johnson, P. Bienstman, M. A. Skorobogatiy, M. Ibanescu, E. Lidorikis, and J. D. Joannopoulos, “Adiabatic theorem and continuous couple-mode theory for efficient taper transition” Phys. Rev. E 66, 066608 (2002).
[Crossref]

S. G. Johnson, P. R. Villeneuve, S. H. Fan, and J. D. Joannopoulos, “Linear waveguide in photonic crystal slab,” Phys. Rev. B 62, 8212–8222 (2000).
[Crossref]

Jones, R. C.

C. C. Constantinou and R. C. Jones, “Path-integral analysis of arbitrarily tapered multimode, graded-index waveguide: the inverse-square-law and parabolic tapers,” IEE Proceedings 139, 365–375 (1992).

Kamp, M.

Kolodziejski, L. A.

Krauss, T.

D. Tailaert, W. Bogaerts, P. Bienstman, T. Krauss, P. V. Daele, I. Moerman, S. Verstuyft, K. D. Mesel, and R. Baets, “An out-of plane grating coupler for efficient butt coupling between compact planar waveguides and single mode fibres,” IEEE J. Quantum Electron. 38, 949–954 (2002).
[Crossref]

Lalanne, Ph.

Ph. Lalanne and A. Talneau, “Modal conversion with artificial materials for photonic-crystal waveguides,” Opt. Express 10, 354–359 (2002) http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-8-354.
[PubMed]

M. Palamaru and Ph. Lalanne, “Photonic crystal waveguides: out-of-plane losses and adiabatic mode conversion,” Appl. Phys. Lett. 78, 1466–1468 (2001).
[Crossref]

Lidorikis, E.

S. G. Johnson, P. Bienstman, M. A. Skorobogatiy, M. Ibanescu, E. Lidorikis, and J. D. Joannopoulos, “Adiabatic theorem and continuous couple-mode theory for efficient taper transition” Phys. Rev. E 66, 066608 (2002).
[Crossref]

Liu, A. Q.

Lu, C.

Marcuse, D.

D. Marcuse, “Radiation losses of tapered dielectric slab waveguides,” Bell Syst. Tech. J. 49, 273–290 (1969).

Maystre, D.

Meade, R. D.

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

Mekis, A.

Mesel, K. D.

D. Tailaert, W. Bogaerts, P. Bienstman, T. Krauss, P. V. Daele, I. Moerman, S. Verstuyft, K. D. Mesel, and R. Baets, “An out-of plane grating coupler for efficient butt coupling between compact planar waveguides and single mode fibres,” IEEE J. Quantum Electron. 38, 949–954 (2002).
[Crossref]

Milton, A. F.

W. K. Burns and A. F. Milton, “Mode conversion in planar-dielectric separating waveguide,” IEEE J. Quantum Electron. 11, 32–39 (1975).
[Crossref]

Moerman, I.

D. Tailaert, W. Bogaerts, P. Bienstman, T. Krauss, P. V. Daele, I. Moerman, S. Verstuyft, K. D. Mesel, and R. Baets, “An out-of plane grating coupler for efficient butt coupling between compact planar waveguides and single mode fibres,” IEEE J. Quantum Electron. 38, 949–954 (2002).
[Crossref]

C. Wei, F. Groen, M. K. Smit, I. Moerman, P. V. Daele, and R. Baets, “Integrated optical elliptic couplers: modeling, design, and applications,” J. Lightwave Technol. 15, 906–911 (1997).
[Crossref]

Murakowski, J.

Ntakis, I.

P. Pottier, I. Ntakis, and R. M. De La Rue, “Photonic crystal continuous taper for low-loss direct coupling into photonic crystal channel waveguides and further device functionality,” Opt. Commun. 223, 339–347 (2003).
[Crossref]

Olaofe, G. O.

G. O. Olaofe, “Scattering by two cylinders,” Radio Sci. 5, 1351–1360 (1970).
[Crossref]

Painter, O.

Palamaru, M.

M. Palamaru and Ph. Lalanne, “Photonic crystal waveguides: out-of-plane losses and adiabatic mode conversion,” Appl. Phys. Lett. 78, 1466–1468 (2001).
[Crossref]

Petrich, G. S.

Pottier, P.

P. Pottier, I. Ntakis, and R. M. De La Rue, “Photonic crystal continuous taper for low-loss direct coupling into photonic crystal channel waveguides and further device functionality,” Opt. Commun. 223, 339–347 (2003).
[Crossref]

Prather, D. W.

Pustai, D.

Rue, R. M. De La

P. Pottier, I. Ntakis, and R. M. De La Rue, “Photonic crystal continuous taper for low-loss direct coupling into photonic crystal channel waveguides and further device functionality,” Opt. Commun. 223, 339–347 (2003).
[Crossref]

Shi, S.

Skorobogatiy, M. A.

S. G. Johnson, P. Bienstman, M. A. Skorobogatiy, M. Ibanescu, E. Lidorikis, and J. D. Joannopoulos, “Adiabatic theorem and continuous couple-mode theory for efficient taper transition” Phys. Rev. E 66, 066608 (2002).
[Crossref]

Smit, M. K.

C. Wei, F. Groen, M. K. Smit, I. Moerman, P. V. Daele, and R. Baets, “Integrated optical elliptic couplers: modeling, design, and applications,” J. Lightwave Technol. 15, 906–911 (1997).
[Crossref]

Someda, C. G.

D. Falco, C. Conti, and C. G. Someda, “Coupling and decoupling of electromagnetic waves in parallel 2-D photonic crystal waveguides,” IEEE J. Quantum Electron. 38, 47–53 (2002).
[Crossref]

Sporleder, F.

F. Sporleder and H. G. Unger, Waveguide tapers transition and couplers (IEE, 1979).

Srinivasan, K.

Tailaert, D.

D. Tailaert, W. Bogaerts, P. Bienstman, T. Krauss, P. V. Daele, I. Moerman, S. Verstuyft, K. D. Mesel, and R. Baets, “An out-of plane grating coupler for efficient butt coupling between compact planar waveguides and single mode fibres,” IEEE J. Quantum Electron. 38, 949–954 (2002).
[Crossref]

Talneau, A.

Tayeb, G.

Teo, H. G.

Unger, H. G.

F. Sporleder and H. G. Unger, Waveguide tapers transition and couplers (IEE, 1979).

Venkataraman, S.

Verstuyft, S.

D. Tailaert, W. Bogaerts, P. Bienstman, T. Krauss, P. V. Daele, I. Moerman, S. Verstuyft, K. D. Mesel, and R. Baets, “An out-of plane grating coupler for efficient butt coupling between compact planar waveguides and single mode fibres,” IEEE J. Quantum Electron. 38, 949–954 (2002).
[Crossref]

Villeneuve, P. R.

S. G. Johnson, P. R. Villeneuve, S. H. Fan, and J. D. Joannopoulos, “Linear waveguide in photonic crystal slab,” Phys. Rev. B 62, 8212–8222 (2000).
[Crossref]

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and H. A. Haus, “Channel drop filters in photonic crystals,” Opt. Express 3, 4–11 (1998) http://www.opticsexpress.org/abstract.cfm?URI=OPEX-3-1-4.
[Crossref] [PubMed]

Wei, C.

C. Wei, F. Groen, M. K. Smit, I. Moerman, P. V. Daele, and R. Baets, “Integrated optical elliptic couplers: modeling, design, and applications,” J. Lightwave Technol. 15, 906–911 (1997).
[Crossref]

Winn, J. N.

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

Wu, J. H.

Yonekura, J.

Appl. Phys. Lett. (1)

M. Palamaru and Ph. Lalanne, “Photonic crystal waveguides: out-of-plane losses and adiabatic mode conversion,” Appl. Phys. Lett. 78, 1466–1468 (2001).
[Crossref]

Bell Syst. Tech. J. (1)

D. Marcuse, “Radiation losses of tapered dielectric slab waveguides,” Bell Syst. Tech. J. 49, 273–290 (1969).

IEE Proceedings (1)

C. C. Constantinou and R. C. Jones, “Path-integral analysis of arbitrarily tapered multimode, graded-index waveguide: the inverse-square-law and parabolic tapers,” IEE Proceedings 139, 365–375 (1992).

IEEE J. Quantum Electron. (3)

W. K. Burns and A. F. Milton, “Mode conversion in planar-dielectric separating waveguide,” IEEE J. Quantum Electron. 11, 32–39 (1975).
[Crossref]

D. Falco, C. Conti, and C. G. Someda, “Coupling and decoupling of electromagnetic waves in parallel 2-D photonic crystal waveguides,” IEEE J. Quantum Electron. 38, 47–53 (2002).
[Crossref]

D. Tailaert, W. Bogaerts, P. Bienstman, T. Krauss, P. V. Daele, I. Moerman, S. Verstuyft, K. D. Mesel, and R. Baets, “An out-of plane grating coupler for efficient butt coupling between compact planar waveguides and single mode fibres,” IEEE J. Quantum Electron. 38, 949–954 (2002).
[Crossref]

J. Appl. Phys. (1)

H. Benisty, “Modal analysis of optical guides with two-dimensional photonic band-gap boundaries,” J. Appl. Phys. 79, 7483–7492 (1996).
[Crossref]

J. Lightwave Technol. (3)

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

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

Opt. Commun. (1)

P. Pottier, I. Ntakis, and R. M. De La Rue, “Photonic crystal continuous taper for low-loss direct coupling into photonic crystal channel waveguides and further device functionality,” Opt. Commun. 223, 339–347 (2003).
[Crossref]

Opt. Express (2)

Opt. Lett. (3)

Phys. Rev. B (1)

S. G. Johnson, P. R. Villeneuve, S. H. Fan, and J. D. Joannopoulos, “Linear waveguide in photonic crystal slab,” Phys. Rev. B 62, 8212–8222 (2000).
[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 couple-mode theory for efficient taper transition” Phys. Rev. E 66, 066608 (2002).
[Crossref]

Radio Sci. (1)

G. O. Olaofe, “Scattering by two cylinders,” Radio Sci. 5, 1351–1360 (1970).
[Crossref]

Other (2)

F. Sporleder and H. G. Unger, Waveguide tapers transition and couplers (IEE, 1979).

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

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Figures (9)

Fig. 1.
Fig. 1.

Top: General layout of taper waveguide. Bottom: Diagram showing step analysis for mode conversion in a taper waveguide.

Fig. 2.
Fig. 2.

Tapered-waveguide shapes for different values of α. For α = 1, the taper shape corresponds to the linear taper. For α = 2 and α = 0.5, the taper shape corresponds to concave and convex taper, respectively.

Fig. 3.
Fig. 3.

Schematic layout of the PC taper: (a) linear; (b) convex; (c) concave.

Fig. 4.
Fig. 4.

Field distribution of the simulation layout: (a) linear taper; (b) convex taper; (c) concave taper.

Fig. 5.
Fig. 5.

Normalized field intensity of the propagating wave as a function of taper position for different taper shapes.

Fig. 6.
Fig. 6.

Transmission spectra for the various taper shapes: (a) and (b) linear PC taper for l = 9.69 μm and 18.24 μm; (c) and (d) nonuniform PC taper l = 9.69 μm and 18.24 μm.

Fig. 7.
Fig. 7.

Normalized loss power versus relative position for a linear taper with (a) l = 9.69 μm and (b) l = 18.24 μm. The area under the curve gives the total loss for the taper.

Fig. 8.
Fig. 8.

Transmittance vs taper length plots for different values of α. (a) Convex shaped taper for values of α = 0.333, 0.5, 0.667. (b) Concave shaped taper for values of α = 1, 1.5, 2, 3

Fig. 9.
Fig. 9.

Spectrum distortion for concave taper of length 5.7 μm.

Tables (1)

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Table 1. Saturated Length and Maximum Transmittance for Different Values of α

Equations (8)

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z ( x ) = m λ 2 n core 2 n g 2
r = ( β 1 β 2 β 1 + β 2 ) exp ( i 2 β 1 )
c = 2 β 1 β 2 ( β 1 + β 2 ) I 1,2 I 1,1 I 2,2 exp [ i ( β 1 + β 2 ) ]
I α , γ = E α E γ dz α , γ = 1,2
n g = c ( ω k ) 1
z = d i + ( d i d o ) [ ( 1 x l ) α 1 ]
ψ ( P ) = ψ inc ( P ) + v = 1 N m = m = + b n , m H m ( 1 ) ( k 0 R n ( P ) ) exp ( jm θ n ( P ) )
S v = [ n J m ( k 0 r ) J m ( k 0 nr ) γ J m ( k 0 r ) J m ( k 0 nr ) n H m ( k 0 r ) J m ( k 0 nr ) γ H m ( k 0 r ) J m ( k 0 nr ) ]

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