Abstract

In this paper, the mathematical model of the modified step-theory is derived based on the platform of two-dimensional photonic crystal structure that is infinitely long in third dimension. The mode coupling mechanism of photonic crystal tapers is theoretically studied using the modified step-theory. The model is verified by comparing the transmission spectrum obtained for the input/output defect coupler where it shows a good match of less than 5% discrepancy. The modified step-theory is applied to different taper structures to investigate the power loss during the transmission. The power loss at the relative position of the taper provides an explanation as to which taper designs give the highest coupling efficiency.

© 2006 Optical Society of America

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  5. Y. Akahane, M. Mochizuki, T. Asano, Y. Tanaka, and S. Noda, "Design of a channel drop filter by using a donor-type cavity with high-quality factor in a two-dimensional photonic crystal slab," Appl. Phys. Lett. 82, 1341-1343 (2003).
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  27. M. Qiu, K. Azizi, A. Karlsson, M. Swillo, and B. Jaskorzynska, "Numerical studies of mode gaps and coupling efficiency for line-defect waveguides in two-dimensional photonic crystals," Phys. Rev. B 64, 155113 (2001).
    [CrossRef]
  28. S. Assefa, P. T. Rakich, P. Bienstman, S. G. Johnson, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, E. P. Ippen, and H. I. Smith, "Guiding 1.5 μm light in photonic crystals based on dielectric rods," Appl. Phys. Lett. 85, 6110-6112 (2004).
    [CrossRef]
  29. P. Bienstman, and R. Baets, "Optical modelling of photonic crystals and VCSELs using eigenmode expansion and perfectly matched layers," Opt. and Quantum Electron.  33, 327-341 (2001).
    [CrossRef]
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    [CrossRef]

2005 (1)

2004 (3)

M. Skorobogatiy, "Modeling the impact of imperfections in high-index-contrast photonic crystal waveguides," Phys. Rev. E 70, 046609 (2004).
[CrossRef]

T. Fujisawa, and M. Koshiba, "Time-domain beam propagation method for nonlinear optical propagation analysis and its application to photonic Crystal circuits," J. Lightwave Technol. 22, 684-691 (2004).
[CrossRef]

S. Assefa, P. T. Rakich, P. Bienstman, S. G. Johnson, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, E. P. Ippen, and H. I. Smith, "Guiding 1.5 μm light in photonic crystals based on dielectric rods," Appl. Phys. Lett. 85, 6110-6112 (2004).
[CrossRef]

2003 (5)

A. Lavrinenko, P. Borel, L. Frandsen, M. Thorhauge, A. Harpøth, M. Kristensen, T. Niemi, and H. Chong, "Comprehensive FDTD modelling of photonic crystal waveguide components," Opt. Express 12, 234-248 (2003).
[CrossRef]

M. Skorobogatiy, S. G. Johnson, S. A. Jacobs, and Y. Fink, "Dielectric profile variations in high-index-contrast waveguides, coupled mode theory, and perturbation expansions," Phys. Rev. E 67, 046613 (2003).
[CrossRef]

Y. Akahane, M. Mochizuki, T. Asano, Y. Tanaka, and S. Noda, "Design of a channel drop filter by using a donor-type cavity with high-quality factor in a two-dimensional photonic crystal slab," Appl. Phys. Lett. 82, 1341-1343 (2003).
[CrossRef]

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," 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 (2)

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 transition," Phys. Rev. E 66, 066608 (2002).
[CrossRef]

Ph. Lalanne, and A. Talneau, "Modal conversion with artificial materials for photonic-crystal waveguide," Opt. Express 10, 354-359 (2002).
[PubMed]

2001 (4)

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

T. D. Happ, M. Kamp, and A. Forchel, "Photonic crystal tapers for ultracompact mode conversion," Opt. Lett. 26, 1102-1104 (2001).
[CrossRef]

M. Qiu, K. Azizi, A. Karlsson, M. Swillo, and B. Jaskorzynska, "Numerical studies of mode gaps and coupling efficiency for line-defect waveguides in two-dimensional photonic crystals," Phys. Rev. B 64, 155113 (2001).
[CrossRef]

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

2000 (4)

M. Bayindir, B. Temelkuran, and E. Ozbar, "Photonic-crystal-based beam splitter," Appl. Phys. Lett. 77, 3902-3904 (2000).
[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]

A. A Asatryan, P. A. Robinson, L. C. Botten, R. C. McPhedran, N. A. Nicorovici, and C. Martin de Sterke, "Effects of geometric and refractive index disorder on wave propagation in two-dimensional photonic crystals," Phys. Rev. E 62, 5711 (2000).
[CrossRef]

M. Koshiba, Y. Tsuji, and M. Hikari, "Time-domain beam propagation method and its application to photonic crystal circuits," J. Lightwave Technology 18, 102-110 (2000).
[CrossRef]

1999 (1)

A. A Asatryan, P. A. Robinson, L. C. Botten, R. C. McPhedran, N. A. Nicorovici, and C. Martin de Sterke, "Effects of disorder on wave propagation in two-dimensional photonic crystals," Phys. Rev. E 60, 6118 (1999).
[CrossRef]

1998 (2)

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and H. A. Haus, "Channel add-drop filters in photonic crystal," Opt. Express 3, 4-11 (1998).
[CrossRef] [PubMed]

A. Mekis, S. Fan, and J. D. Joannopoulos, "Bound states in photonic crystal waveguides and waveguide bends," Phys. Rev. B 58, 4809-4817 (1998).
[CrossRef]

1997 (1)

J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, "Photonic crystals: putting a new twist on light," Nature,  386, 143 (1997)
[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 Waveguide," Phys. Rev. Lett. 77, 3787-3790 (1996).
[CrossRef] [PubMed]

1994 (1)

O. Mitomi, K. Kasaya, and H. Miyazawa, "Design of a single-mode tapered waveguide for low-loss chip-to-fiber coupling," IEEE J. Quantum Electron. 30, 1787-1793 (1994).
[CrossRef]

1975 (2)

A. F. Milton, and W. K. Burns, "Mode Conversion in planar dielectric separating waveguides," IEEE J. Quantum Electron. 11, 32-39 (1975).
[CrossRef]

A. R. Nelson, "Coupling optical waveguides by tapers," Appl. Opt. 14, 3012-3015 (1975).
[PubMed]

Akahane, Y.

Y. Akahane, M. Mochizuki, T. Asano, Y. Tanaka, and S. Noda, "Design of a channel drop filter by using a donor-type cavity with high-quality factor in a two-dimensional photonic crystal slab," Appl. Phys. Lett. 82, 1341-1343 (2003).
[CrossRef]

Asano, T.

Y. Akahane, M. Mochizuki, T. Asano, Y. Tanaka, and S. Noda, "Design of a channel drop filter by using a donor-type cavity with high-quality factor in a two-dimensional photonic crystal slab," Appl. Phys. Lett. 82, 1341-1343 (2003).
[CrossRef]

Asatryan, A. A

A. A Asatryan, P. A. Robinson, L. C. Botten, R. C. McPhedran, N. A. Nicorovici, and C. Martin de Sterke, "Effects of geometric and refractive index disorder on wave propagation in two-dimensional photonic crystals," Phys. Rev. E 62, 5711 (2000).
[CrossRef]

A. A Asatryan, P. A. Robinson, L. C. Botten, R. C. McPhedran, N. A. Nicorovici, and C. Martin de Sterke, "Effects of disorder on wave propagation in two-dimensional photonic crystals," Phys. Rev. E 60, 6118 (1999).
[CrossRef]

Assefa, S.

S. Assefa, P. T. Rakich, P. Bienstman, S. G. Johnson, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, E. P. Ippen, and H. I. Smith, "Guiding 1.5 μm light in photonic crystals based on dielectric rods," Appl. Phys. Lett. 85, 6110-6112 (2004).
[CrossRef]

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," Opt. Soc. Am. B 20, 1817-1821 (2003).
[CrossRef]

Azizi, K.

M. Qiu, K. Azizi, A. Karlsson, M. Swillo, and B. Jaskorzynska, "Numerical studies of mode gaps and coupling efficiency for line-defect waveguides in two-dimensional photonic crystals," Phys. Rev. B 64, 155113 (2001).
[CrossRef]

Baets, R.

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

Bayindir, M.

M. Bayindir, B. Temelkuran, and E. Ozbar, "Photonic-crystal-based beam splitter," Appl. Phys. Lett. 77, 3902-3904 (2000).
[CrossRef]

Bienstman, P.

S. Assefa, P. T. Rakich, P. Bienstman, S. G. Johnson, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, E. P. Ippen, and H. I. Smith, "Guiding 1.5 μm light in photonic crystals based on dielectric rods," Appl. Phys. Lett. 85, 6110-6112 (2004).
[CrossRef]

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," 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 coupled mode theory for efficient taper transition," Phys. Rev. E 66, 066608 (2002).
[CrossRef]

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

Borel, P.

Botten, L. C.

A. A Asatryan, P. A. Robinson, L. C. Botten, R. C. McPhedran, N. A. Nicorovici, and C. Martin de Sterke, "Effects of geometric and refractive index disorder on wave propagation in two-dimensional photonic crystals," Phys. Rev. E 62, 5711 (2000).
[CrossRef]

A. A Asatryan, P. A. Robinson, L. C. Botten, R. C. McPhedran, N. A. Nicorovici, and C. Martin de Sterke, "Effects of disorder on wave propagation in two-dimensional photonic crystals," Phys. Rev. E 60, 6118 (1999).
[CrossRef]

Burns, W. K.

A. F. Milton, and W. K. Burns, "Mode Conversion in planar dielectric separating waveguides," IEEE J. Quantum Electron. 11, 32-39 (1975).
[CrossRef]

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 Waveguide," Phys. Rev. Lett. 77, 3787-3790 (1996).
[CrossRef] [PubMed]

Chong, H.

De La Rue, R. M.

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]

de Sterke, Martin

A. A Asatryan, P. A. Robinson, L. C. Botten, R. C. McPhedran, N. A. Nicorovici, and C. Martin de Sterke, "Effects of geometric and refractive index disorder on wave propagation in two-dimensional photonic crystals," Phys. Rev. E 62, 5711 (2000).
[CrossRef]

Fan, S.

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and H. A. Haus, "Channel add-drop filters in photonic crystal," Opt. Express 3, 4-11 (1998).
[CrossRef] [PubMed]

A. Mekis, S. Fan, and J. D. Joannopoulos, "Bound states in photonic crystal waveguides and waveguide bends," Phys. Rev. B 58, 4809-4817 (1998).
[CrossRef]

J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, "Photonic crystals: putting a new twist on light," Nature,  386, 143 (1997)
[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 Waveguide," Phys. Rev. Lett. 77, 3787-3790 (1996).
[CrossRef] [PubMed]

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]

Fink, Y.

M. Skorobogatiy, S. G. Johnson, S. A. Jacobs, and Y. Fink, "Dielectric profile variations in high-index-contrast waveguides, coupled mode theory, and perturbation expansions," Phys. Rev. E 67, 046613 (2003).
[CrossRef]

Forchel, A.

Frandsen, L.

Fujisawa, T.

Happ, T. D.

Harpøth, A.

Haus, H. A.

Hikari, M.

M. Koshiba, Y. Tsuji, and M. Hikari, "Time-domain beam propagation method and its application to photonic crystal circuits," J. Lightwave Technology 18, 102-110 (2000).
[CrossRef]

Ibanescu, M.

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 transition," Phys. Rev. E 66, 066608 (2002).
[CrossRef]

Ippen, E. P.

S. Assefa, P. T. Rakich, P. Bienstman, S. G. Johnson, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, E. P. Ippen, and H. I. Smith, "Guiding 1.5 μm light in photonic crystals based on dielectric rods," Appl. Phys. Lett. 85, 6110-6112 (2004).
[CrossRef]

Jacobs, S. A.

M. Skorobogatiy, S. G. Johnson, S. A. Jacobs, and Y. Fink, "Dielectric profile variations in high-index-contrast waveguides, coupled mode theory, and perturbation expansions," Phys. Rev. E 67, 046613 (2003).
[CrossRef]

Jaskorzynska, B.

M. Qiu, K. Azizi, A. Karlsson, M. Swillo, and B. Jaskorzynska, "Numerical studies of mode gaps and coupling efficiency for line-defect waveguides in two-dimensional photonic crystals," Phys. Rev. B 64, 155113 (2001).
[CrossRef]

Joannopoulos, J. D.

S. Assefa, P. T. Rakich, P. Bienstman, S. G. Johnson, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, E. P. Ippen, and H. I. Smith, "Guiding 1.5 μm light in photonic crystals based on dielectric rods," Appl. Phys. Lett. 85, 6110-6112 (2004).
[CrossRef]

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," 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 coupled 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]

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and H. A. Haus, "Channel add-drop filters in photonic crystal," Opt. Express 3, 4-11 (1998).
[CrossRef] [PubMed]

A. Mekis, S. Fan, and J. D. Joannopoulos, "Bound states in photonic crystal waveguides and waveguide bends," Phys. Rev. B 58, 4809-4817 (1998).
[CrossRef]

J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, "Photonic crystals: putting a new twist on light," Nature,  386, 143 (1997)
[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 Waveguide," Phys. Rev. Lett. 77, 3787-3790 (1996).
[CrossRef] [PubMed]

Johnson, S. G.

S. Assefa, P. T. Rakich, P. Bienstman, S. G. Johnson, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, E. P. Ippen, and H. I. Smith, "Guiding 1.5 μm light in photonic crystals based on dielectric rods," Appl. Phys. Lett. 85, 6110-6112 (2004).
[CrossRef]

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," Opt. Soc. Am. B 20, 1817-1821 (2003).
[CrossRef]

M. Skorobogatiy, S. G. Johnson, S. A. Jacobs, and Y. Fink, "Dielectric profile variations in high-index-contrast waveguides, coupled mode theory, and perturbation expansions," Phys. Rev. E 67, 046613 (2003).
[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 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]

Kamp, M.

Karlsson, A.

M. Qiu, K. Azizi, A. Karlsson, M. Swillo, and B. Jaskorzynska, "Numerical studies of mode gaps and coupling efficiency for line-defect waveguides in two-dimensional photonic crystals," Phys. Rev. B 64, 155113 (2001).
[CrossRef]

Kasaya, K.

O. Mitomi, K. Kasaya, and H. Miyazawa, "Design of a single-mode tapered waveguide for low-loss chip-to-fiber coupling," IEEE J. Quantum Electron. 30, 1787-1793 (1994).
[CrossRef]

Khoo, E. H.

Kolodziejski, L. A.

S. Assefa, P. T. Rakich, P. Bienstman, S. G. Johnson, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, E. P. Ippen, and H. I. Smith, "Guiding 1.5 μm light in photonic crystals based on dielectric rods," Appl. Phys. Lett. 85, 6110-6112 (2004).
[CrossRef]

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," Opt. Soc. Am. B 20, 1817-1821 (2003).
[CrossRef]

Koshiba, M.

T. Fujisawa, and M. Koshiba, "Time-domain beam propagation method for nonlinear optical propagation analysis and its application to photonic Crystal circuits," J. Lightwave Technol. 22, 684-691 (2004).
[CrossRef]

M. Koshiba, Y. Tsuji, and M. Hikari, "Time-domain beam propagation method and its application to photonic crystal circuits," J. Lightwave Technology 18, 102-110 (2000).
[CrossRef]

Kristensen, M.

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 Waveguide," Phys. Rev. Lett. 77, 3787-3790 (1996).
[CrossRef] [PubMed]

Lalanne, Ph.

Ph. Lalanne, and A. Talneau, "Modal conversion with artificial materials for photonic-crystal waveguide," Opt. Express 10, 354-359 (2002).
[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]

Lavrinenko, A.

Lidorikis, E.

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 transition," Phys. Rev. E 66, 066608 (2002).
[CrossRef]

Liu, A. Q.

Martin de Sterke, C.

A. A Asatryan, P. A. Robinson, L. C. Botten, R. C. McPhedran, N. A. Nicorovici, and C. Martin de Sterke, "Effects of disorder on wave propagation in two-dimensional photonic crystals," Phys. Rev. E 60, 6118 (1999).
[CrossRef]

McPhedran, R. C.

A. A Asatryan, P. A. Robinson, L. C. Botten, R. C. McPhedran, N. A. Nicorovici, and C. Martin de Sterke, "Effects of geometric and refractive index disorder on wave propagation in two-dimensional photonic crystals," Phys. Rev. E 62, 5711 (2000).
[CrossRef]

A. A Asatryan, P. A. Robinson, L. C. Botten, R. C. McPhedran, N. A. Nicorovici, and C. Martin de Sterke, "Effects of disorder on wave propagation in two-dimensional photonic crystals," Phys. Rev. E 60, 6118 (1999).
[CrossRef]

Mekis, A.

A. Mekis, S. Fan, and J. D. Joannopoulos, "Bound states in photonic crystal waveguides and waveguide bends," Phys. Rev. B 58, 4809-4817 (1998).
[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 Waveguide," Phys. Rev. Lett. 77, 3787-3790 (1996).
[CrossRef] [PubMed]

Milton, A. F.

A. F. Milton, and W. K. Burns, "Mode Conversion in planar dielectric separating waveguides," IEEE J. Quantum Electron. 11, 32-39 (1975).
[CrossRef]

Mitomi, O.

O. Mitomi, K. Kasaya, and H. Miyazawa, "Design of a single-mode tapered waveguide for low-loss chip-to-fiber coupling," IEEE J. Quantum Electron. 30, 1787-1793 (1994).
[CrossRef]

Miyazawa, H.

O. Mitomi, K. Kasaya, and H. Miyazawa, "Design of a single-mode tapered waveguide for low-loss chip-to-fiber coupling," IEEE J. Quantum Electron. 30, 1787-1793 (1994).
[CrossRef]

Mochizuki, M.

Y. Akahane, M. Mochizuki, T. Asano, Y. Tanaka, and S. Noda, "Design of a channel drop filter by using a donor-type cavity with high-quality factor in a two-dimensional photonic crystal slab," Appl. Phys. Lett. 82, 1341-1343 (2003).
[CrossRef]

Nelson, A. R.

Nicorovici, N. A.

A. A Asatryan, P. A. Robinson, L. C. Botten, R. C. McPhedran, N. A. Nicorovici, and C. Martin de Sterke, "Effects of geometric and refractive index disorder on wave propagation in two-dimensional photonic crystals," Phys. Rev. E 62, 5711 (2000).
[CrossRef]

A. A Asatryan, P. A. Robinson, L. C. Botten, R. C. McPhedran, N. A. Nicorovici, and C. Martin de Sterke, "Effects of disorder on wave propagation in two-dimensional photonic crystals," Phys. Rev. E 60, 6118 (1999).
[CrossRef]

Niemi, T.

Noda, S.

Y. Akahane, M. Mochizuki, T. Asano, Y. Tanaka, and S. Noda, "Design of a channel drop filter by using a donor-type cavity with high-quality factor in a two-dimensional photonic crystal slab," Appl. Phys. Lett. 82, 1341-1343 (2003).
[CrossRef]

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]

Ozbar, E.

M. Bayindir, B. Temelkuran, and E. Ozbar, "Photonic-crystal-based beam splitter," Appl. Phys. Lett. 77, 3902-3904 (2000).
[CrossRef]

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.

S. Assefa, P. T. Rakich, P. Bienstman, S. G. Johnson, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, E. P. Ippen, and H. I. Smith, "Guiding 1.5 μm light in photonic crystals based on dielectric rods," Appl. Phys. Lett. 85, 6110-6112 (2004).
[CrossRef]

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," Opt. Soc. Am. B 20, 1817-1821 (2003).
[CrossRef]

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]

Qiu, M.

M. Qiu, K. Azizi, A. Karlsson, M. Swillo, and B. Jaskorzynska, "Numerical studies of mode gaps and coupling efficiency for line-defect waveguides in two-dimensional photonic crystals," Phys. Rev. B 64, 155113 (2001).
[CrossRef]

Rakich, P. T.

S. Assefa, P. T. Rakich, P. Bienstman, S. G. Johnson, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, E. P. Ippen, and H. I. Smith, "Guiding 1.5 μm light in photonic crystals based on dielectric rods," Appl. Phys. Lett. 85, 6110-6112 (2004).
[CrossRef]

Robinson, P. A.

A. A Asatryan, P. A. Robinson, L. C. Botten, R. C. McPhedran, N. A. Nicorovici, and C. Martin de Sterke, "Effects of geometric and refractive index disorder on wave propagation in two-dimensional photonic crystals," Phys. Rev. E 62, 5711 (2000).
[CrossRef]

A. A Asatryan, P. A. Robinson, L. C. Botten, R. C. McPhedran, N. A. Nicorovici, and C. Martin de Sterke, "Effects of disorder on wave propagation in two-dimensional photonic crystals," Phys. Rev. E 60, 6118 (1999).
[CrossRef]

Skorobogatiy, M.

M. Skorobogatiy, "Modeling the impact of imperfections in high-index-contrast photonic crystal waveguides," Phys. Rev. E 70, 046609 (2004).
[CrossRef]

M. Skorobogatiy, S. G. Johnson, S. A. Jacobs, and Y. Fink, "Dielectric profile variations in high-index-contrast waveguides, coupled mode theory, and perturbation expansions," Phys. Rev. E 67, 046613 (2003).
[CrossRef]

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 transition," Phys. Rev. E 66, 066608 (2002).
[CrossRef]

Smith, H. I.

S. Assefa, P. T. Rakich, P. Bienstman, S. G. Johnson, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, E. P. Ippen, and H. I. Smith, "Guiding 1.5 μm light in photonic crystals based on dielectric rods," Appl. Phys. Lett. 85, 6110-6112 (2004).
[CrossRef]

Swillo, M.

M. Qiu, K. Azizi, A. Karlsson, M. Swillo, and B. Jaskorzynska, "Numerical studies of mode gaps and coupling efficiency for line-defect waveguides in two-dimensional photonic crystals," Phys. Rev. B 64, 155113 (2001).
[CrossRef]

Talneau, A.

Tanaka, Y.

Y. Akahane, M. Mochizuki, T. Asano, Y. Tanaka, and S. Noda, "Design of a channel drop filter by using a donor-type cavity with high-quality factor in a two-dimensional photonic crystal slab," Appl. Phys. Lett. 82, 1341-1343 (2003).
[CrossRef]

Temelkuran, B.

M. Bayindir, B. Temelkuran, and E. Ozbar, "Photonic-crystal-based beam splitter," Appl. Phys. Lett. 77, 3902-3904 (2000).
[CrossRef]

Thorhauge, M.

Tsuji, Y.

M. Koshiba, Y. Tsuji, and M. Hikari, "Time-domain beam propagation method and its application to photonic crystal circuits," J. Lightwave Technology 18, 102-110 (2000).
[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 add-drop filters in photonic crystal," Opt. Express 3, 4-11 (1998).
[CrossRef] [PubMed]

J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, "Photonic crystals: putting a new twist on light," Nature,  386, 143 (1997)
[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 Waveguide," Phys. Rev. Lett. 77, 3787-3790 (1996).
[CrossRef] [PubMed]

Wu, J. H.

Appl. Opt. (1)

Appl. Phys. Lett. (4)

S. Assefa, P. T. Rakich, P. Bienstman, S. G. Johnson, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, E. P. Ippen, and H. I. Smith, "Guiding 1.5 μm light in photonic crystals based on dielectric rods," Appl. Phys. Lett. 85, 6110-6112 (2004).
[CrossRef]

M. Bayindir, B. Temelkuran, and E. Ozbar, "Photonic-crystal-based beam splitter," Appl. Phys. Lett. 77, 3902-3904 (2000).
[CrossRef]

Y. Akahane, M. Mochizuki, T. Asano, Y. Tanaka, and S. Noda, "Design of a channel drop filter by using a donor-type cavity with high-quality factor in a two-dimensional photonic crystal slab," Appl. Phys. Lett. 82, 1341-1343 (2003).
[CrossRef]

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

IEEE J. Quantum Electron. (2)

A. F. Milton, and W. K. Burns, "Mode Conversion in planar dielectric separating waveguides," IEEE J. Quantum Electron. 11, 32-39 (1975).
[CrossRef]

O. Mitomi, K. Kasaya, and H. Miyazawa, "Design of a single-mode tapered waveguide for low-loss chip-to-fiber coupling," IEEE J. Quantum Electron. 30, 1787-1793 (1994).
[CrossRef]

J. Lightwave Technol. (1)

J. Lightwave Technology (1)

M. Koshiba, Y. Tsuji, and M. Hikari, "Time-domain beam propagation method and its application to photonic crystal circuits," J. Lightwave Technology 18, 102-110 (2000).
[CrossRef]

Nature (1)

J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, "Photonic crystals: putting a new twist on light," Nature,  386, 143 (1997)
[CrossRef]

Opt. and Quantum Electron. (1)

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

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 (4)

Opt. Lett. (1)

Opt. Soc. Am. B (1)

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," Opt. Soc. Am. B 20, 1817-1821 (2003).
[CrossRef]

Phys. Rev. B (3)

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]

A. Mekis, S. Fan, and J. D. Joannopoulos, "Bound states in photonic crystal waveguides and waveguide bends," Phys. Rev. B 58, 4809-4817 (1998).
[CrossRef]

M. Qiu, K. Azizi, A. Karlsson, M. Swillo, and B. Jaskorzynska, "Numerical studies of mode gaps and coupling efficiency for line-defect waveguides in two-dimensional photonic crystals," Phys. Rev. B 64, 155113 (2001).
[CrossRef]

Phys. Rev. E (5)

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 transition," Phys. Rev. E 66, 066608 (2002).
[CrossRef]

M. Skorobogatiy, S. G. Johnson, S. A. Jacobs, and Y. Fink, "Dielectric profile variations in high-index-contrast waveguides, coupled mode theory, and perturbation expansions," Phys. Rev. E 67, 046613 (2003).
[CrossRef]

M. Skorobogatiy, "Modeling the impact of imperfections in high-index-contrast photonic crystal waveguides," Phys. Rev. E 70, 046609 (2004).
[CrossRef]

A. A Asatryan, P. A. Robinson, L. C. Botten, R. C. McPhedran, N. A. Nicorovici, and C. Martin de Sterke, "Effects of disorder on wave propagation in two-dimensional photonic crystals," Phys. Rev. E 60, 6118 (1999).
[CrossRef]

A. A Asatryan, P. A. Robinson, L. C. Botten, R. C. McPhedran, N. A. Nicorovici, and C. Martin de Sterke, "Effects of geometric and refractive index disorder on wave propagation in two-dimensional photonic crystals," Phys. Rev. E 62, 5711 (2000).
[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 Waveguide," Phys. Rev. Lett. 77, 3787-3790 (1996).
[CrossRef] [PubMed]

Other (3)

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

J. David Jackson, Classical Electrodynamics (John Wiley & Sons, United States of America, 1998).

D. Marcuse, Theory of Dielectric Optical Waveguide (Academic Press, San Diego, 1991).

Cited By

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Figures (13)

Fig. 1.
Fig. 1.

(a) Structure of the linear defect photonic crystal waveguide with input taper and output taper (b) Comparison of transmission spectra by scattering method and modified step-theory

Fig. 2.
Fig. 2.

Structure of two PCWG cascaded together to form a abrupt step waveguide with different widths

Fig. 3.
Fig. 3.

(a) Projected band diagram of the waveguide with single line defects (b) Projected band diagram of the waveguide with three line defects. The red line is odd mode while the black lines are even modes.

Fig. 4.
Fig. 4.

(a) Field transmission of the even fundamental mode to the narrower waveguide (b) Transmission of the odd second order mode to the narrow waveguide. Because odd mode cannot couple to even mode, there is no transmission.

Fig. 5.
Fig. 5.

Lattice layout of the “step” taper waveguide

Fig. 6.
Fig. 6.

Comparison of the transmitted power by modified step-theory and the scattering method

Fig. 7.
Fig. 7.

Field distribution for non-adiabatic behaviour of step taper at step length of 6a

Fig. 8.
Fig. 8.

Transmitted power vs relative position for the step taper with step length of 3a and 5a

Fig. 9.
Fig. 9.

Transmission vs taper length plots for α values of 1, 2 and 0.5

Fig. 10.
Fig. 10.

(a) Power loss vs relative position for (a) linear taper (b) convex taper and (c) concave taper at 9.69 and 18.24 µm

Fig. 11.
Fig. 11.

Power transmission of the fundamental mode for (a) linear taper (b) convex taper (c) concave taper at length 9.69 and 18.24 µm

Fig. 12.
Fig. 12.

Power transmission of the fundamental modes for linear, convex and concave taper at length 20.52 µm.

Fig. 13.
Fig. 13.

Field distribution for the different taper at 20.52 µm. (a) Linear taper (b) Convex taper (c) Concave taper

Equations (38)

Equations on this page are rendered with MathJax. Learn more.

E = E 0 ξ ( z ) × e i β x
E k x , k z ( r ) exp ( i k x x ) × exp ( i k z z ) × u k x , k z ( x , z )
E = E 0 sin ( m π ( z b + 1 2 ) ) exp [ i ψ ( x ) ]
ψ ( x ) = ( β + 2 π η d ) x η = 0 , ± 1 , ± 2 , ,
A j n + 1 exp ( i ψ j n + 1 ) = c ij A in exp ( i ψ in ) + c jj A jn exp ( i ψ jn )
c ij = ψ jn ψ in G I in , jn + 1 I in , in I jn + 1 , jn + 1
where G = 2 β in β jn + 2 β in β in + 1 + γ 2 + 2 γ β in + γ β jn + γ β in + 1 ( β jn + β jn + 1 + γ ) ( β in + β in + 1 + γ )
and γ = 4 π η d
I in , jn + 1 = sin [ m in π ( z b + 1 2 ) ] sin [ m jn + 1 π ( z b + 1 2 ) ] dz
A jn + 1 exp ( i ψ jn + 1 ) = i c ij A in exp ( i ψ in )
A jn + 1 = [ ( i c ij A in cos ψ in ) 2 + ( i c ij A in sin ψ in ) 2 ] 1 2
ψ jn + 1 = tan 1 ( l c ij A in sin ψ in l c ij A in cos ψ in )
z ( x ) = d i + ( d i d o ) [ ( 1 x l ) α 1 ]
× E = μ H t
× H = ε E t
× ( × E ) = ( ω ν ) 2 E
ν = 1 ε μ = c n
2 E = ( ω ν ) 2 E
E = E 0 ξ ( z ) × e i β x
E = E 0 sin ( m π ( z b + 1 2 ) ) exp [ i ψ ( x ) ]
ψ ( x ) = ( β + 2 π η d ) x η = 0 , ± 1 , ± 2 , ,
E in ζ in exp ( i ψ in ) + E jn ζ jn exp ( i ψ jn ) + E in R ζ in exp ( i ψ in R ) + E jn R ζ jn exp ( i ψ jn R ) + E ref
= E in + 1 ζ in + 1 exp ( i ψ in + 1 ) + E jn + 1 ζ jn + 1 exp ( i ψ jn + 1 ) + E trans
ψ in E in ζ in exp ( i ψ in ) + ψ jn E jn ζ jn exp ( + i ψ jn ) + ψ in R E in R ζ in exp ( i ψ in R )
β jn R E jn R ζ jn exp ( i ψ jn R ) + H ref
= ψ in + 1 E in + 1 ζ in + 1 exp ( i ψ in + 1 ) + ψ jn + 1 E jn + 1 ζ jn + 1 exp ( i ψ jn + 1 ) + H trans
E in R exp ( i ψ in R ) = ( ψ in ψ in + 1 ψ in + ψ in + 1 ) E in exp ( i ψ in )
E jn + 1 I jn + 1 , jn + 1 exp ( i ψ jn + 1 ) = ( 2 ψ in ψ jn + ψ jn + 1 ) ( ψ jn + ψ in + 1 ψ in + ψ in + 1 ) E in I in , jn + 1 exp ( i ψ in )
+ 2 ( ψ jn ψ jn + ψ jn + 1 ) E jn I jn , jn + 1 exp ( i ψ jn )
where I in , jn + 1 = ζ in ζ jn + 1 dx
P mj = ( E mj ) 2 ψ jn + 1 2 k 0 I jn + 1 , jn + 1 = 1
A jn + 1 exp ( i ψ jn + 1 ) = c ij A in exp ( i ψ in ) + c jj A jn exp ( i ψ jn )
c ij = ψ jn ψ in G I in , jn + 1 I in , in I jn + 1 , jn + 1
where G = 2 β in β jn + 2 β in β in + 1 + γ 2 + 2 γ β in + γ β in + γ β in + 1 ( β jn + β jn + 1 + γ ) ( β in + β in + 1 + γ )
and γ = 4 π η d
A jn + 1 exp ( i α jn + 1 ) = i c ij A in exp ( i α in )
A jn + 1 = [ ( i c ij A in cos α in ) 2 + ( i c ij A in sin α in ) 2 ] 1 2
α jn + 1 = tan 1 ( l c ij A in sin α in l c ij A in cos α in )

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