Abstract

We have theoretically investigated the characteristics of three-dimensional (3D) photonic crystal (PC) waveguides formed by the introduction of dielectric line defects. We show that the guided modes in 3D PC waveguides strongly depend on the volume, position and number of dielectric defects introduced. We have succeeded in designing a waveguide structure with a large single-mode bandwidth of 178 nm (range = 1,466 to 1,644 nm) for wavelengths used in optical communications. Our study indicates that there is great flexibility in the design of 3D PC waveguides and that a variety of desirable properties can be obtained by altering the configuration of the line defects appropriately.

© 2005 Optical Society of America

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  1. E. Yablonovitch , “ Inhibited spontaneous emission in solid-state physics and electronics ,” Phys. Rev. Lett.   58 , 2059 – 2062 ( 1987 ).
    [Crossref] [PubMed]
  2. S. John , “ Strong localization of photons in certain disordered dielectric superlattices ,” Phys. Rev. Lett.   58 , 2486 – 2489 ( 1987 ).
    [Crossref] [PubMed]
  3. S. Noda , K. Tomoda , N. Yamamoto , and A. Chutinan , “ Full three-dimensional photonic bandgap crystals at near-infrared wavelengths ,” Science   289 , 604 – 606 ( 2000 ).
    [Crossref] [PubMed]
  4. B-S. Song , S. Noda , and T. Asano , “ Photonic devices based on in-plane hetero photonic crystals ,” Science   300 , 1537 ( 2003 ).
    [Crossref] [PubMed]
  5. T. Matsumoto and T. Baba , “ Photonic crystal k-vector superprism ,” J. Lightwave Technol.   22 , 917 – 922 ( 2004 ).
    [Crossref]
  6. D. Mori and T. Baba , “ Dispersion-controlled optical group delay device by chirped photonic crystal waveguides ,” Appl. Phys. Lett.   85 , 1101 – 1103 ( 2004 ).
    [Crossref]
  7. H. Takano , B-S. Song , T. Asano , and S. Noda , “ Highly efficient in-plane channel drop filter in a two-dimensional heterophotonic crystal ,” Appl. Phys. Lett.   86 , 241101 ( 2005 ).
    [Crossref]
  8. S. Ogawa , M. Imada , S. Yoshimoto , M. Okano , and S. Noda , “ Control of light emission by 3D photonic crystals ,” Science   305 , 227 – 229 ( 2004 ).
    [Crossref] [PubMed]
  9. M. Deubel , G. V. Freymann , M. Wegener , S. Pereira , K. Busch , and C. M. Soukoulis , “ Direct laser writing of three-dimensional photonic-crystal templates for telecommunications ,” Nature Mater.   3 , 444 – 447 ( 2004 ).
    [Crossref]
  10. G. Subramania and S. Y. Lin , “ Fabrication of three-dimensional photonic crystal with alignment based on electron beam lithography ,” Appl. Phys. Lett.   85 , 5037 – 5039 ( 2004 ).
    [Crossref]
  11. M. Qi , E. Lidorikis , P. T. Rakich , S. G. Johnson , J. D. Joannopoulos , E. P. Ippen , and H. I. Smith , “ A three-dimensional optical photonic crystal with designed point defects ,” Nature   429 , 538 – 542 ( 2004 ).
    [Crossref] [PubMed]
  12. M. L. Povinelli , S. G. Johnson , S. Fan , and J. D. Joannopoulos , “ Emulation of two-dimensional photonic crystal defect modes in a photonic crystal with a three-dimensional photonic band gap ,” Phys. Rev. B   64 , 075313 ( 2001 ).
    [Crossref]
  13. M. Okano and S. Noda , “ Analysis of multimode point-defect cavities in three-dimensional photonic crystals using group theory in frequency and time domains ,” Phys. Rev. B   70 , 125105 ( 2004 ).
    [Crossref]
  14. E. Özbay , G. Tuttle , M. Sigalas , C. M. Soukoulis , and K. M. Ho , “ Defect structures in a layer-by-layer photonic band-gap crystal ,” Phy. Rev. B   51 , 13961 – 13965 ( 1995 ).
    [Crossref]
  15. A. Chutinan and S. Noda , “ Highly confined waveguides and waveguide bends in three-dimensional photonic crystal ,” Appl. Phys. Lett.   75 , 3739 – 3741 ( 1999 ).
    [Crossref]
  16. D. Roundy and J. Joannopoulos , “ Photonic crystal structure with square symmetry within each layer and a three-dimensional band gap ,” Appl. Phys. Lett.   82 , 3835 – 3837 ( 2003 ).
    [Crossref]
  17. M. Bayindir and E. Ozbay , “ Heavy photons at coupled-cavity waveguide band edges in a three-dimensional photonic crystal ,” Phys. Rev. B   62 , R2247 – R2250 ( 2000 ).
    [Crossref]
  18. C. Sell , C. Christensen , J. Muehlmeier , G. Tuttle , Z-Y. Li , and K-M. Ho , “ Waveguide networks in three-dimensional layer-by-layer photonic crystals ,” Appl. Phys. Lett.   84 , 4605 – 4607 ( 2004 ).
    [Crossref]
  19. A. Chutinan and S. Noda , “ Design for waveguides in three-dimensional photonic crystals ,” Jpn. J. Appl. Phys.   39 , 2353 – 2356 ( 2000 ).
    [Crossref]
  20. D. Roundy , E. Lidorikis , and J. D. Joannopoulos , “ Polarization-selective waveguide bends in a photonic crystal structure with layered square symmetry ,” J. Appl. Phys.   96 , 7750 – 7752 ( 2004 ).
    [Crossref]
  21. M. Bayindir and E. Ozbay , “ Dropping of electromagnetic waves through localized modes in three-dimensional photonic band gap structures ,” Appl. Phys. Lett.   81 , 4514 – 4516 ( 2002 ).
    [Crossref]
  22. M. Okano , S. Kako , and S. Noda , “ Coupling between a point-defect cavity and a line-defect waveguide in three-dimensional photonic crystal ,” Phys. Rev. B   68 , 235110 ( 2003 ).
    [Crossref]
  23. Y. Tanaka , T. Asano , Y. Akahane , B-S. Song , and S. Noda , “ Theoretical investigation of a two-dimensional photonic crystal slab with truncated cone air holes ,” Appl. Phys. Lett.   82 , 1661 – 1663 ( 2003 ).
    [Crossref]
  24. S. G. Johnson , S. Fan , P. R. Villeneuve , J. D. Joannopoulos , and L. A. Kolodziejski , “ Guided modes in photonic crystal slabs ,” Phys. Rev. B   60 , 5751 – 5758 ( 1999 ).
    [Crossref]
  25. K. M. Ho , C. T. Chan , C. M. Soukoulis , R. Biswas , and M. Sigalas , “ Photonic band gaps in three dimensions: new layer-by-layer periodic structures ,” Solid State Commun.   89 , 413 – 416 ( 1994 ).
    [Crossref]
  26. E. Özbay , E. Michel , G. Tuttle , R. Biswas , M. Sigalas , and K-M. Ho , “ Micromachined millimeter-wave photonic band-gap crystals ,” Appl. Phys. Lett.   64 , 2059 – 2061 ( 1994 ).
    [Crossref]
  27. H. S. Sözüer and J. P. Dowling , “ Photonic band calculations for woodpile structures ,” J. Mod. Opt.   41 , 231 – 239 ( 1994 ).
    [Crossref]
  28. K. M. Leung and Y. F. Liu , “ Full vector wave calculation of photonic band structures in face-centered-cubic dielectric media ,” Phys. Rev. Lett.   65 , 2646 – 2649 ( 1990 ).
    [Crossref] [PubMed]
  29. Z. Zhang and S. Satpathy , “ Electromagnetic wave propagation in periodic structures: Bloch wave solution of Maxwell’s equations ,” Phys. Rev. Lett.   65 , 2650 – 2653 ( 1990 ).
    [Crossref] [PubMed]
  30. K. M. Ho , C. T. Chan , and C. M. Soukoulis , “Photonic band gaps and localization,” in Proceedings of the NATO Advanced Science Institutes Series, C. M. Soukoulis , ed. ( Plenum, New York , 1993 ), pp. 235.

2005 (1)

H. Takano , B-S. Song , T. Asano , and S. Noda , “ Highly efficient in-plane channel drop filter in a two-dimensional heterophotonic crystal ,” Appl. Phys. Lett.   86 , 241101 ( 2005 ).
[Crossref]

2004 (9)

S. Ogawa , M. Imada , S. Yoshimoto , M. Okano , and S. Noda , “ Control of light emission by 3D photonic crystals ,” Science   305 , 227 – 229 ( 2004 ).
[Crossref] [PubMed]

M. Deubel , G. V. Freymann , M. Wegener , S. Pereira , K. Busch , and C. M. Soukoulis , “ Direct laser writing of three-dimensional photonic-crystal templates for telecommunications ,” Nature Mater.   3 , 444 – 447 ( 2004 ).
[Crossref]

G. Subramania and S. Y. Lin , “ Fabrication of three-dimensional photonic crystal with alignment based on electron beam lithography ,” Appl. Phys. Lett.   85 , 5037 – 5039 ( 2004 ).
[Crossref]

M. Qi , E. Lidorikis , P. T. Rakich , S. G. Johnson , J. D. Joannopoulos , E. P. Ippen , and H. I. Smith , “ A three-dimensional optical photonic crystal with designed point defects ,” Nature   429 , 538 – 542 ( 2004 ).
[Crossref] [PubMed]

M. Okano and S. Noda , “ Analysis of multimode point-defect cavities in three-dimensional photonic crystals using group theory in frequency and time domains ,” Phys. Rev. B   70 , 125105 ( 2004 ).
[Crossref]

D. Mori and T. Baba , “ Dispersion-controlled optical group delay device by chirped photonic crystal waveguides ,” Appl. Phys. Lett.   85 , 1101 – 1103 ( 2004 ).
[Crossref]

C. Sell , C. Christensen , J. Muehlmeier , G. Tuttle , Z-Y. Li , and K-M. Ho , “ Waveguide networks in three-dimensional layer-by-layer photonic crystals ,” Appl. Phys. Lett.   84 , 4605 – 4607 ( 2004 ).
[Crossref]

D. Roundy , E. Lidorikis , and J. D. Joannopoulos , “ Polarization-selective waveguide bends in a photonic crystal structure with layered square symmetry ,” J. Appl. Phys.   96 , 7750 – 7752 ( 2004 ).
[Crossref]

T. Matsumoto and T. Baba , “ Photonic crystal k-vector superprism ,” J. Lightwave Technol.   22 , 917 – 922 ( 2004 ).
[Crossref]

2003 (4)

B-S. Song , S. Noda , and T. Asano , “ Photonic devices based on in-plane hetero photonic crystals ,” Science   300 , 1537 ( 2003 ).
[Crossref] [PubMed]

D. Roundy and J. Joannopoulos , “ Photonic crystal structure with square symmetry within each layer and a three-dimensional band gap ,” Appl. Phys. Lett.   82 , 3835 – 3837 ( 2003 ).
[Crossref]

M. Okano , S. Kako , and S. Noda , “ Coupling between a point-defect cavity and a line-defect waveguide in three-dimensional photonic crystal ,” Phys. Rev. B   68 , 235110 ( 2003 ).
[Crossref]

Y. Tanaka , T. Asano , Y. Akahane , B-S. Song , and S. Noda , “ Theoretical investigation of a two-dimensional photonic crystal slab with truncated cone air holes ,” Appl. Phys. Lett.   82 , 1661 – 1663 ( 2003 ).
[Crossref]

2002 (1)

M. Bayindir and E. Ozbay , “ Dropping of electromagnetic waves through localized modes in three-dimensional photonic band gap structures ,” Appl. Phys. Lett.   81 , 4514 – 4516 ( 2002 ).
[Crossref]

2001 (1)

M. L. Povinelli , S. G. Johnson , S. Fan , and J. D. Joannopoulos , “ Emulation of two-dimensional photonic crystal defect modes in a photonic crystal with a three-dimensional photonic band gap ,” Phys. Rev. B   64 , 075313 ( 2001 ).
[Crossref]

2000 (3)

S. Noda , K. Tomoda , N. Yamamoto , and A. Chutinan , “ Full three-dimensional photonic bandgap crystals at near-infrared wavelengths ,” Science   289 , 604 – 606 ( 2000 ).
[Crossref] [PubMed]

M. Bayindir and E. Ozbay , “ Heavy photons at coupled-cavity waveguide band edges in a three-dimensional photonic crystal ,” Phys. Rev. B   62 , R2247 – R2250 ( 2000 ).
[Crossref]

A. Chutinan and S. Noda , “ Design for waveguides in three-dimensional photonic crystals ,” Jpn. J. Appl. Phys.   39 , 2353 – 2356 ( 2000 ).
[Crossref]

1999 (2)

A. Chutinan and S. Noda , “ Highly confined waveguides and waveguide bends in three-dimensional photonic crystal ,” Appl. Phys. Lett.   75 , 3739 – 3741 ( 1999 ).
[Crossref]

S. G. Johnson , S. Fan , P. R. Villeneuve , J. D. Joannopoulos , and L. A. Kolodziejski , “ Guided modes in photonic crystal slabs ,” Phys. Rev. B   60 , 5751 – 5758 ( 1999 ).
[Crossref]

1995 (1)

E. Özbay , G. Tuttle , M. Sigalas , C. M. Soukoulis , and K. M. Ho , “ Defect structures in a layer-by-layer photonic band-gap crystal ,” Phy. Rev. B   51 , 13961 – 13965 ( 1995 ).
[Crossref]

1994 (3)

K. M. Ho , C. T. Chan , C. M. Soukoulis , R. Biswas , and M. Sigalas , “ Photonic band gaps in three dimensions: new layer-by-layer periodic structures ,” Solid State Commun.   89 , 413 – 416 ( 1994 ).
[Crossref]

E. Özbay , E. Michel , G. Tuttle , R. Biswas , M. Sigalas , and K-M. Ho , “ Micromachined millimeter-wave photonic band-gap crystals ,” Appl. Phys. Lett.   64 , 2059 – 2061 ( 1994 ).
[Crossref]

H. S. Sözüer and J. P. Dowling , “ Photonic band calculations for woodpile structures ,” J. Mod. Opt.   41 , 231 – 239 ( 1994 ).
[Crossref]

1990 (2)

K. M. Leung and Y. F. Liu , “ Full vector wave calculation of photonic band structures in face-centered-cubic dielectric media ,” Phys. Rev. Lett.   65 , 2646 – 2649 ( 1990 ).
[Crossref] [PubMed]

Z. Zhang and S. Satpathy , “ Electromagnetic wave propagation in periodic structures: Bloch wave solution of Maxwell’s equations ,” Phys. Rev. Lett.   65 , 2650 – 2653 ( 1990 ).
[Crossref] [PubMed]

1987 (2)

E. Yablonovitch , “ Inhibited spontaneous emission in solid-state physics and electronics ,” Phys. Rev. Lett.   58 , 2059 – 2062 ( 1987 ).
[Crossref] [PubMed]

S. John , “ Strong localization of photons in certain disordered dielectric superlattices ,” Phys. Rev. Lett.   58 , 2486 – 2489 ( 1987 ).
[Crossref] [PubMed]

Akahane, Y.

Y. Tanaka , T. Asano , Y. Akahane , B-S. Song , and S. Noda , “ Theoretical investigation of a two-dimensional photonic crystal slab with truncated cone air holes ,” Appl. Phys. Lett.   82 , 1661 – 1663 ( 2003 ).
[Crossref]

Asano, T.

H. Takano , B-S. Song , T. Asano , and S. Noda , “ Highly efficient in-plane channel drop filter in a two-dimensional heterophotonic crystal ,” Appl. Phys. Lett.   86 , 241101 ( 2005 ).
[Crossref]

Y. Tanaka , T. Asano , Y. Akahane , B-S. Song , and S. Noda , “ Theoretical investigation of a two-dimensional photonic crystal slab with truncated cone air holes ,” Appl. Phys. Lett.   82 , 1661 – 1663 ( 2003 ).
[Crossref]

B-S. Song , S. Noda , and T. Asano , “ Photonic devices based on in-plane hetero photonic crystals ,” Science   300 , 1537 ( 2003 ).
[Crossref] [PubMed]

Baba, T.

T. Matsumoto and T. Baba , “ Photonic crystal k-vector superprism ,” J. Lightwave Technol.   22 , 917 – 922 ( 2004 ).
[Crossref]

D. Mori and T. Baba , “ Dispersion-controlled optical group delay device by chirped photonic crystal waveguides ,” Appl. Phys. Lett.   85 , 1101 – 1103 ( 2004 ).
[Crossref]

Bayindir, M.

M. Bayindir and E. Ozbay , “ Dropping of electromagnetic waves through localized modes in three-dimensional photonic band gap structures ,” Appl. Phys. Lett.   81 , 4514 – 4516 ( 2002 ).
[Crossref]

M. Bayindir and E. Ozbay , “ Heavy photons at coupled-cavity waveguide band edges in a three-dimensional photonic crystal ,” Phys. Rev. B   62 , R2247 – R2250 ( 2000 ).
[Crossref]

Biswas, R.

K. M. Ho , C. T. Chan , C. M. Soukoulis , R. Biswas , and M. Sigalas , “ Photonic band gaps in three dimensions: new layer-by-layer periodic structures ,” Solid State Commun.   89 , 413 – 416 ( 1994 ).
[Crossref]

E. Özbay , E. Michel , G. Tuttle , R. Biswas , M. Sigalas , and K-M. Ho , “ Micromachined millimeter-wave photonic band-gap crystals ,” Appl. Phys. Lett.   64 , 2059 – 2061 ( 1994 ).
[Crossref]

Busch, K.

M. Deubel , G. V. Freymann , M. Wegener , S. Pereira , K. Busch , and C. M. Soukoulis , “ Direct laser writing of three-dimensional photonic-crystal templates for telecommunications ,” Nature Mater.   3 , 444 – 447 ( 2004 ).
[Crossref]

Chan, C. T.

K. M. Ho , C. T. Chan , C. M. Soukoulis , R. Biswas , and M. Sigalas , “ Photonic band gaps in three dimensions: new layer-by-layer periodic structures ,” Solid State Commun.   89 , 413 – 416 ( 1994 ).
[Crossref]

K. M. Ho , C. T. Chan , and C. M. Soukoulis , “Photonic band gaps and localization,” in Proceedings of the NATO Advanced Science Institutes Series, C. M. Soukoulis , ed. ( Plenum, New York , 1993 ), pp. 235.

Christensen, C.

C. Sell , C. Christensen , J. Muehlmeier , G. Tuttle , Z-Y. Li , and K-M. Ho , “ Waveguide networks in three-dimensional layer-by-layer photonic crystals ,” Appl. Phys. Lett.   84 , 4605 – 4607 ( 2004 ).
[Crossref]

Chutinan, A.

A. Chutinan and S. Noda , “ Design for waveguides in three-dimensional photonic crystals ,” Jpn. J. Appl. Phys.   39 , 2353 – 2356 ( 2000 ).
[Crossref]

S. Noda , K. Tomoda , N. Yamamoto , and A. Chutinan , “ Full three-dimensional photonic bandgap crystals at near-infrared wavelengths ,” Science   289 , 604 – 606 ( 2000 ).
[Crossref] [PubMed]

A. Chutinan and S. Noda , “ Highly confined waveguides and waveguide bends in three-dimensional photonic crystal ,” Appl. Phys. Lett.   75 , 3739 – 3741 ( 1999 ).
[Crossref]

Deubel, M.

M. Deubel , G. V. Freymann , M. Wegener , S. Pereira , K. Busch , and C. M. Soukoulis , “ Direct laser writing of three-dimensional photonic-crystal templates for telecommunications ,” Nature Mater.   3 , 444 – 447 ( 2004 ).
[Crossref]

Dowling, J. P.

H. S. Sözüer and J. P. Dowling , “ Photonic band calculations for woodpile structures ,” J. Mod. Opt.   41 , 231 – 239 ( 1994 ).
[Crossref]

Fan, S.

M. L. Povinelli , S. G. Johnson , S. Fan , and J. D. Joannopoulos , “ Emulation of two-dimensional photonic crystal defect modes in a photonic crystal with a three-dimensional photonic band gap ,” Phys. Rev. B   64 , 075313 ( 2001 ).
[Crossref]

S. G. Johnson , S. Fan , P. R. Villeneuve , J. D. Joannopoulos , and L. A. Kolodziejski , “ Guided modes in photonic crystal slabs ,” Phys. Rev. B   60 , 5751 – 5758 ( 1999 ).
[Crossref]

Freymann, G. V.

M. Deubel , G. V. Freymann , M. Wegener , S. Pereira , K. Busch , and C. M. Soukoulis , “ Direct laser writing of three-dimensional photonic-crystal templates for telecommunications ,” Nature Mater.   3 , 444 – 447 ( 2004 ).
[Crossref]

Ho, K. M.

E. Özbay , G. Tuttle , M. Sigalas , C. M. Soukoulis , and K. M. Ho , “ Defect structures in a layer-by-layer photonic band-gap crystal ,” Phy. Rev. B   51 , 13961 – 13965 ( 1995 ).
[Crossref]

K. M. Ho , C. T. Chan , C. M. Soukoulis , R. Biswas , and M. Sigalas , “ Photonic band gaps in three dimensions: new layer-by-layer periodic structures ,” Solid State Commun.   89 , 413 – 416 ( 1994 ).
[Crossref]

K. M. Ho , C. T. Chan , and C. M. Soukoulis , “Photonic band gaps and localization,” in Proceedings of the NATO Advanced Science Institutes Series, C. M. Soukoulis , ed. ( Plenum, New York , 1993 ), pp. 235.

Ho, K-M.

C. Sell , C. Christensen , J. Muehlmeier , G. Tuttle , Z-Y. Li , and K-M. Ho , “ Waveguide networks in three-dimensional layer-by-layer photonic crystals ,” Appl. Phys. Lett.   84 , 4605 – 4607 ( 2004 ).
[Crossref]

E. Özbay , E. Michel , G. Tuttle , R. Biswas , M. Sigalas , and K-M. Ho , “ Micromachined millimeter-wave photonic band-gap crystals ,” Appl. Phys. Lett.   64 , 2059 – 2061 ( 1994 ).
[Crossref]

Imada, M.

S. Ogawa , M. Imada , S. Yoshimoto , M. Okano , and S. Noda , “ Control of light emission by 3D photonic crystals ,” Science   305 , 227 – 229 ( 2004 ).
[Crossref] [PubMed]

Ippen, E. P.

M. Qi , E. Lidorikis , P. T. Rakich , S. G. Johnson , J. D. Joannopoulos , E. P. Ippen , and H. I. Smith , “ A three-dimensional optical photonic crystal with designed point defects ,” Nature   429 , 538 – 542 ( 2004 ).
[Crossref] [PubMed]

Joannopoulos, J.

D. Roundy and J. Joannopoulos , “ Photonic crystal structure with square symmetry within each layer and a three-dimensional band gap ,” Appl. Phys. Lett.   82 , 3835 – 3837 ( 2003 ).
[Crossref]

Joannopoulos, J. D.

D. Roundy , E. Lidorikis , and J. D. Joannopoulos , “ Polarization-selective waveguide bends in a photonic crystal structure with layered square symmetry ,” J. Appl. Phys.   96 , 7750 – 7752 ( 2004 ).
[Crossref]

M. Qi , E. Lidorikis , P. T. Rakich , S. G. Johnson , J. D. Joannopoulos , E. P. Ippen , and H. I. Smith , “ A three-dimensional optical photonic crystal with designed point defects ,” Nature   429 , 538 – 542 ( 2004 ).
[Crossref] [PubMed]

M. L. Povinelli , S. G. Johnson , S. Fan , and J. D. Joannopoulos , “ Emulation of two-dimensional photonic crystal defect modes in a photonic crystal with a three-dimensional photonic band gap ,” Phys. Rev. B   64 , 075313 ( 2001 ).
[Crossref]

S. G. Johnson , S. Fan , P. R. Villeneuve , J. D. Joannopoulos , and L. A. Kolodziejski , “ Guided modes in photonic crystal slabs ,” Phys. Rev. B   60 , 5751 – 5758 ( 1999 ).
[Crossref]

John, S.

S. John , “ Strong localization of photons in certain disordered dielectric superlattices ,” Phys. Rev. Lett.   58 , 2486 – 2489 ( 1987 ).
[Crossref] [PubMed]

Johnson, S. G.

M. Qi , E. Lidorikis , P. T. Rakich , S. G. Johnson , J. D. Joannopoulos , E. P. Ippen , and H. I. Smith , “ A three-dimensional optical photonic crystal with designed point defects ,” Nature   429 , 538 – 542 ( 2004 ).
[Crossref] [PubMed]

M. L. Povinelli , S. G. Johnson , S. Fan , and J. D. Joannopoulos , “ Emulation of two-dimensional photonic crystal defect modes in a photonic crystal with a three-dimensional photonic band gap ,” Phys. Rev. B   64 , 075313 ( 2001 ).
[Crossref]

S. G. Johnson , S. Fan , P. R. Villeneuve , J. D. Joannopoulos , and L. A. Kolodziejski , “ Guided modes in photonic crystal slabs ,” Phys. Rev. B   60 , 5751 – 5758 ( 1999 ).
[Crossref]

Kako, S.

M. Okano , S. Kako , and S. Noda , “ Coupling between a point-defect cavity and a line-defect waveguide in three-dimensional photonic crystal ,” Phys. Rev. B   68 , 235110 ( 2003 ).
[Crossref]

Kolodziejski, L. A.

S. G. Johnson , S. Fan , P. R. Villeneuve , J. D. Joannopoulos , and L. A. Kolodziejski , “ Guided modes in photonic crystal slabs ,” Phys. Rev. B   60 , 5751 – 5758 ( 1999 ).
[Crossref]

Leung, K. M.

K. M. Leung and Y. F. Liu , “ Full vector wave calculation of photonic band structures in face-centered-cubic dielectric media ,” Phys. Rev. Lett.   65 , 2646 – 2649 ( 1990 ).
[Crossref] [PubMed]

Li, Z-Y.

C. Sell , C. Christensen , J. Muehlmeier , G. Tuttle , Z-Y. Li , and K-M. Ho , “ Waveguide networks in three-dimensional layer-by-layer photonic crystals ,” Appl. Phys. Lett.   84 , 4605 – 4607 ( 2004 ).
[Crossref]

Lidorikis, E.

D. Roundy , E. Lidorikis , and J. D. Joannopoulos , “ Polarization-selective waveguide bends in a photonic crystal structure with layered square symmetry ,” J. Appl. Phys.   96 , 7750 – 7752 ( 2004 ).
[Crossref]

M. Qi , E. Lidorikis , P. T. Rakich , S. G. Johnson , J. D. Joannopoulos , E. P. Ippen , and H. I. Smith , “ A three-dimensional optical photonic crystal with designed point defects ,” Nature   429 , 538 – 542 ( 2004 ).
[Crossref] [PubMed]

Lin, S. Y.

G. Subramania and S. Y. Lin , “ Fabrication of three-dimensional photonic crystal with alignment based on electron beam lithography ,” Appl. Phys. Lett.   85 , 5037 – 5039 ( 2004 ).
[Crossref]

Liu, Y. F.

K. M. Leung and Y. F. Liu , “ Full vector wave calculation of photonic band structures in face-centered-cubic dielectric media ,” Phys. Rev. Lett.   65 , 2646 – 2649 ( 1990 ).
[Crossref] [PubMed]

Matsumoto, T.

Michel, E.

E. Özbay , E. Michel , G. Tuttle , R. Biswas , M. Sigalas , and K-M. Ho , “ Micromachined millimeter-wave photonic band-gap crystals ,” Appl. Phys. Lett.   64 , 2059 – 2061 ( 1994 ).
[Crossref]

Mori, D.

D. Mori and T. Baba , “ Dispersion-controlled optical group delay device by chirped photonic crystal waveguides ,” Appl. Phys. Lett.   85 , 1101 – 1103 ( 2004 ).
[Crossref]

Muehlmeier, J.

C. Sell , C. Christensen , J. Muehlmeier , G. Tuttle , Z-Y. Li , and K-M. Ho , “ Waveguide networks in three-dimensional layer-by-layer photonic crystals ,” Appl. Phys. Lett.   84 , 4605 – 4607 ( 2004 ).
[Crossref]

Noda, S.

H. Takano , B-S. Song , T. Asano , and S. Noda , “ Highly efficient in-plane channel drop filter in a two-dimensional heterophotonic crystal ,” Appl. Phys. Lett.   86 , 241101 ( 2005 ).
[Crossref]

S. Ogawa , M. Imada , S. Yoshimoto , M. Okano , and S. Noda , “ Control of light emission by 3D photonic crystals ,” Science   305 , 227 – 229 ( 2004 ).
[Crossref] [PubMed]

M. Okano and S. Noda , “ Analysis of multimode point-defect cavities in three-dimensional photonic crystals using group theory in frequency and time domains ,” Phys. Rev. B   70 , 125105 ( 2004 ).
[Crossref]

M. Okano , S. Kako , and S. Noda , “ Coupling between a point-defect cavity and a line-defect waveguide in three-dimensional photonic crystal ,” Phys. Rev. B   68 , 235110 ( 2003 ).
[Crossref]

Y. Tanaka , T. Asano , Y. Akahane , B-S. Song , and S. Noda , “ Theoretical investigation of a two-dimensional photonic crystal slab with truncated cone air holes ,” Appl. Phys. Lett.   82 , 1661 – 1663 ( 2003 ).
[Crossref]

B-S. Song , S. Noda , and T. Asano , “ Photonic devices based on in-plane hetero photonic crystals ,” Science   300 , 1537 ( 2003 ).
[Crossref] [PubMed]

S. Noda , K. Tomoda , N. Yamamoto , and A. Chutinan , “ Full three-dimensional photonic bandgap crystals at near-infrared wavelengths ,” Science   289 , 604 – 606 ( 2000 ).
[Crossref] [PubMed]

A. Chutinan and S. Noda , “ Design for waveguides in three-dimensional photonic crystals ,” Jpn. J. Appl. Phys.   39 , 2353 – 2356 ( 2000 ).
[Crossref]

A. Chutinan and S. Noda , “ Highly confined waveguides and waveguide bends in three-dimensional photonic crystal ,” Appl. Phys. Lett.   75 , 3739 – 3741 ( 1999 ).
[Crossref]

Ogawa, S.

S. Ogawa , M. Imada , S. Yoshimoto , M. Okano , and S. Noda , “ Control of light emission by 3D photonic crystals ,” Science   305 , 227 – 229 ( 2004 ).
[Crossref] [PubMed]

Okano, M.

S. Ogawa , M. Imada , S. Yoshimoto , M. Okano , and S. Noda , “ Control of light emission by 3D photonic crystals ,” Science   305 , 227 – 229 ( 2004 ).
[Crossref] [PubMed]

M. Okano and S. Noda , “ Analysis of multimode point-defect cavities in three-dimensional photonic crystals using group theory in frequency and time domains ,” Phys. Rev. B   70 , 125105 ( 2004 ).
[Crossref]

M. Okano , S. Kako , and S. Noda , “ Coupling between a point-defect cavity and a line-defect waveguide in three-dimensional photonic crystal ,” Phys. Rev. B   68 , 235110 ( 2003 ).
[Crossref]

Ozbay, E.

M. Bayindir and E. Ozbay , “ Dropping of electromagnetic waves through localized modes in three-dimensional photonic band gap structures ,” Appl. Phys. Lett.   81 , 4514 – 4516 ( 2002 ).
[Crossref]

M. Bayindir and E. Ozbay , “ Heavy photons at coupled-cavity waveguide band edges in a three-dimensional photonic crystal ,” Phys. Rev. B   62 , R2247 – R2250 ( 2000 ).
[Crossref]

Özbay, E.

E. Özbay , G. Tuttle , M. Sigalas , C. M. Soukoulis , and K. M. Ho , “ Defect structures in a layer-by-layer photonic band-gap crystal ,” Phy. Rev. B   51 , 13961 – 13965 ( 1995 ).
[Crossref]

E. Özbay , E. Michel , G. Tuttle , R. Biswas , M. Sigalas , and K-M. Ho , “ Micromachined millimeter-wave photonic band-gap crystals ,” Appl. Phys. Lett.   64 , 2059 – 2061 ( 1994 ).
[Crossref]

Pereira, S.

M. Deubel , G. V. Freymann , M. Wegener , S. Pereira , K. Busch , and C. M. Soukoulis , “ Direct laser writing of three-dimensional photonic-crystal templates for telecommunications ,” Nature Mater.   3 , 444 – 447 ( 2004 ).
[Crossref]

Povinelli, M. L.

M. L. Povinelli , S. G. Johnson , S. Fan , and J. D. Joannopoulos , “ Emulation of two-dimensional photonic crystal defect modes in a photonic crystal with a three-dimensional photonic band gap ,” Phys. Rev. B   64 , 075313 ( 2001 ).
[Crossref]

Qi, M.

M. Qi , E. Lidorikis , P. T. Rakich , S. G. Johnson , J. D. Joannopoulos , E. P. Ippen , and H. I. Smith , “ A three-dimensional optical photonic crystal with designed point defects ,” Nature   429 , 538 – 542 ( 2004 ).
[Crossref] [PubMed]

Rakich, P. T.

M. Qi , E. Lidorikis , P. T. Rakich , S. G. Johnson , J. D. Joannopoulos , E. P. Ippen , and H. I. Smith , “ A three-dimensional optical photonic crystal with designed point defects ,” Nature   429 , 538 – 542 ( 2004 ).
[Crossref] [PubMed]

Roundy, D.

D. Roundy , E. Lidorikis , and J. D. Joannopoulos , “ Polarization-selective waveguide bends in a photonic crystal structure with layered square symmetry ,” J. Appl. Phys.   96 , 7750 – 7752 ( 2004 ).
[Crossref]

D. Roundy and J. Joannopoulos , “ Photonic crystal structure with square symmetry within each layer and a three-dimensional band gap ,” Appl. Phys. Lett.   82 , 3835 – 3837 ( 2003 ).
[Crossref]

Satpathy, S.

Z. Zhang and S. Satpathy , “ Electromagnetic wave propagation in periodic structures: Bloch wave solution of Maxwell’s equations ,” Phys. Rev. Lett.   65 , 2650 – 2653 ( 1990 ).
[Crossref] [PubMed]

Sell, C.

C. Sell , C. Christensen , J. Muehlmeier , G. Tuttle , Z-Y. Li , and K-M. Ho , “ Waveguide networks in three-dimensional layer-by-layer photonic crystals ,” Appl. Phys. Lett.   84 , 4605 – 4607 ( 2004 ).
[Crossref]

Sigalas, M.

E. Özbay , G. Tuttle , M. Sigalas , C. M. Soukoulis , and K. M. Ho , “ Defect structures in a layer-by-layer photonic band-gap crystal ,” Phy. Rev. B   51 , 13961 – 13965 ( 1995 ).
[Crossref]

K. M. Ho , C. T. Chan , C. M. Soukoulis , R. Biswas , and M. Sigalas , “ Photonic band gaps in three dimensions: new layer-by-layer periodic structures ,” Solid State Commun.   89 , 413 – 416 ( 1994 ).
[Crossref]

E. Özbay , E. Michel , G. Tuttle , R. Biswas , M. Sigalas , and K-M. Ho , “ Micromachined millimeter-wave photonic band-gap crystals ,” Appl. Phys. Lett.   64 , 2059 – 2061 ( 1994 ).
[Crossref]

Smith, H. I.

M. Qi , E. Lidorikis , P. T. Rakich , S. G. Johnson , J. D. Joannopoulos , E. P. Ippen , and H. I. Smith , “ A three-dimensional optical photonic crystal with designed point defects ,” Nature   429 , 538 – 542 ( 2004 ).
[Crossref] [PubMed]

Song, B-S.

H. Takano , B-S. Song , T. Asano , and S. Noda , “ Highly efficient in-plane channel drop filter in a two-dimensional heterophotonic crystal ,” Appl. Phys. Lett.   86 , 241101 ( 2005 ).
[Crossref]

Y. Tanaka , T. Asano , Y. Akahane , B-S. Song , and S. Noda , “ Theoretical investigation of a two-dimensional photonic crystal slab with truncated cone air holes ,” Appl. Phys. Lett.   82 , 1661 – 1663 ( 2003 ).
[Crossref]

B-S. Song , S. Noda , and T. Asano , “ Photonic devices based on in-plane hetero photonic crystals ,” Science   300 , 1537 ( 2003 ).
[Crossref] [PubMed]

Soukoulis, C. M.

M. Deubel , G. V. Freymann , M. Wegener , S. Pereira , K. Busch , and C. M. Soukoulis , “ Direct laser writing of three-dimensional photonic-crystal templates for telecommunications ,” Nature Mater.   3 , 444 – 447 ( 2004 ).
[Crossref]

E. Özbay , G. Tuttle , M. Sigalas , C. M. Soukoulis , and K. M. Ho , “ Defect structures in a layer-by-layer photonic band-gap crystal ,” Phy. Rev. B   51 , 13961 – 13965 ( 1995 ).
[Crossref]

K. M. Ho , C. T. Chan , C. M. Soukoulis , R. Biswas , and M. Sigalas , “ Photonic band gaps in three dimensions: new layer-by-layer periodic structures ,” Solid State Commun.   89 , 413 – 416 ( 1994 ).
[Crossref]

K. M. Ho , C. T. Chan , and C. M. Soukoulis , “Photonic band gaps and localization,” in Proceedings of the NATO Advanced Science Institutes Series, C. M. Soukoulis , ed. ( Plenum, New York , 1993 ), pp. 235.

Sözüer, H. S.

H. S. Sözüer and J. P. Dowling , “ Photonic band calculations for woodpile structures ,” J. Mod. Opt.   41 , 231 – 239 ( 1994 ).
[Crossref]

Subramania, G.

G. Subramania and S. Y. Lin , “ Fabrication of three-dimensional photonic crystal with alignment based on electron beam lithography ,” Appl. Phys. Lett.   85 , 5037 – 5039 ( 2004 ).
[Crossref]

Takano, H.

H. Takano , B-S. Song , T. Asano , and S. Noda , “ Highly efficient in-plane channel drop filter in a two-dimensional heterophotonic crystal ,” Appl. Phys. Lett.   86 , 241101 ( 2005 ).
[Crossref]

Tanaka, Y.

Y. Tanaka , T. Asano , Y. Akahane , B-S. Song , and S. Noda , “ Theoretical investigation of a two-dimensional photonic crystal slab with truncated cone air holes ,” Appl. Phys. Lett.   82 , 1661 – 1663 ( 2003 ).
[Crossref]

Tomoda, K.

S. Noda , K. Tomoda , N. Yamamoto , and A. Chutinan , “ Full three-dimensional photonic bandgap crystals at near-infrared wavelengths ,” Science   289 , 604 – 606 ( 2000 ).
[Crossref] [PubMed]

Tuttle, G.

C. Sell , C. Christensen , J. Muehlmeier , G. Tuttle , Z-Y. Li , and K-M. Ho , “ Waveguide networks in three-dimensional layer-by-layer photonic crystals ,” Appl. Phys. Lett.   84 , 4605 – 4607 ( 2004 ).
[Crossref]

E. Özbay , G. Tuttle , M. Sigalas , C. M. Soukoulis , and K. M. Ho , “ Defect structures in a layer-by-layer photonic band-gap crystal ,” Phy. Rev. B   51 , 13961 – 13965 ( 1995 ).
[Crossref]

E. Özbay , E. Michel , G. Tuttle , R. Biswas , M. Sigalas , and K-M. Ho , “ Micromachined millimeter-wave photonic band-gap crystals ,” Appl. Phys. Lett.   64 , 2059 – 2061 ( 1994 ).
[Crossref]

Villeneuve, P. R.

S. G. Johnson , S. Fan , P. R. Villeneuve , J. D. Joannopoulos , and L. A. Kolodziejski , “ Guided modes in photonic crystal slabs ,” Phys. Rev. B   60 , 5751 – 5758 ( 1999 ).
[Crossref]

Wegener, M.

M. Deubel , G. V. Freymann , M. Wegener , S. Pereira , K. Busch , and C. M. Soukoulis , “ Direct laser writing of three-dimensional photonic-crystal templates for telecommunications ,” Nature Mater.   3 , 444 – 447 ( 2004 ).
[Crossref]

Yablonovitch, E.

E. Yablonovitch , “ Inhibited spontaneous emission in solid-state physics and electronics ,” Phys. Rev. Lett.   58 , 2059 – 2062 ( 1987 ).
[Crossref] [PubMed]

Yamamoto, N.

S. Noda , K. Tomoda , N. Yamamoto , and A. Chutinan , “ Full three-dimensional photonic bandgap crystals at near-infrared wavelengths ,” Science   289 , 604 – 606 ( 2000 ).
[Crossref] [PubMed]

Yoshimoto, S.

S. Ogawa , M. Imada , S. Yoshimoto , M. Okano , and S. Noda , “ Control of light emission by 3D photonic crystals ,” Science   305 , 227 – 229 ( 2004 ).
[Crossref] [PubMed]

Zhang, Z.

Z. Zhang and S. Satpathy , “ Electromagnetic wave propagation in periodic structures: Bloch wave solution of Maxwell’s equations ,” Phys. Rev. Lett.   65 , 2650 – 2653 ( 1990 ).
[Crossref] [PubMed]

Appl. Phys. Lett. (9)

D. Mori and T. Baba , “ Dispersion-controlled optical group delay device by chirped photonic crystal waveguides ,” Appl. Phys. Lett.   85 , 1101 – 1103 ( 2004 ).
[Crossref]

H. Takano , B-S. Song , T. Asano , and S. Noda , “ Highly efficient in-plane channel drop filter in a two-dimensional heterophotonic crystal ,” Appl. Phys. Lett.   86 , 241101 ( 2005 ).
[Crossref]

G. Subramania and S. Y. Lin , “ Fabrication of three-dimensional photonic crystal with alignment based on electron beam lithography ,” Appl. Phys. Lett.   85 , 5037 – 5039 ( 2004 ).
[Crossref]

A. Chutinan and S. Noda , “ Highly confined waveguides and waveguide bends in three-dimensional photonic crystal ,” Appl. Phys. Lett.   75 , 3739 – 3741 ( 1999 ).
[Crossref]

D. Roundy and J. Joannopoulos , “ Photonic crystal structure with square symmetry within each layer and a three-dimensional band gap ,” Appl. Phys. Lett.   82 , 3835 – 3837 ( 2003 ).
[Crossref]

C. Sell , C. Christensen , J. Muehlmeier , G. Tuttle , Z-Y. Li , and K-M. Ho , “ Waveguide networks in three-dimensional layer-by-layer photonic crystals ,” Appl. Phys. Lett.   84 , 4605 – 4607 ( 2004 ).
[Crossref]

M. Bayindir and E. Ozbay , “ Dropping of electromagnetic waves through localized modes in three-dimensional photonic band gap structures ,” Appl. Phys. Lett.   81 , 4514 – 4516 ( 2002 ).
[Crossref]

E. Özbay , E. Michel , G. Tuttle , R. Biswas , M. Sigalas , and K-M. Ho , “ Micromachined millimeter-wave photonic band-gap crystals ,” Appl. Phys. Lett.   64 , 2059 – 2061 ( 1994 ).
[Crossref]

Y. Tanaka , T. Asano , Y. Akahane , B-S. Song , and S. Noda , “ Theoretical investigation of a two-dimensional photonic crystal slab with truncated cone air holes ,” Appl. Phys. Lett.   82 , 1661 – 1663 ( 2003 ).
[Crossref]

J. Appl. Phys. (1)

D. Roundy , E. Lidorikis , and J. D. Joannopoulos , “ Polarization-selective waveguide bends in a photonic crystal structure with layered square symmetry ,” J. Appl. Phys.   96 , 7750 – 7752 ( 2004 ).
[Crossref]

J. Lightwave Technol. (1)

J. Mod. Opt. (1)

H. S. Sözüer and J. P. Dowling , “ Photonic band calculations for woodpile structures ,” J. Mod. Opt.   41 , 231 – 239 ( 1994 ).
[Crossref]

Jpn. J. Appl. Phys. (1)

A. Chutinan and S. Noda , “ Design for waveguides in three-dimensional photonic crystals ,” Jpn. J. Appl. Phys.   39 , 2353 – 2356 ( 2000 ).
[Crossref]

Nature (1)

M. Qi , E. Lidorikis , P. T. Rakich , S. G. Johnson , J. D. Joannopoulos , E. P. Ippen , and H. I. Smith , “ A three-dimensional optical photonic crystal with designed point defects ,” Nature   429 , 538 – 542 ( 2004 ).
[Crossref] [PubMed]

Nature Mater. (1)

M. Deubel , G. V. Freymann , M. Wegener , S. Pereira , K. Busch , and C. M. Soukoulis , “ Direct laser writing of three-dimensional photonic-crystal templates for telecommunications ,” Nature Mater.   3 , 444 – 447 ( 2004 ).
[Crossref]

Phy. Rev. B (1)

E. Özbay , G. Tuttle , M. Sigalas , C. M. Soukoulis , and K. M. Ho , “ Defect structures in a layer-by-layer photonic band-gap crystal ,” Phy. Rev. B   51 , 13961 – 13965 ( 1995 ).
[Crossref]

Phys. Rev. B (5)

M. Okano , S. Kako , and S. Noda , “ Coupling between a point-defect cavity and a line-defect waveguide in three-dimensional photonic crystal ,” Phys. Rev. B   68 , 235110 ( 2003 ).
[Crossref]

S. G. Johnson , S. Fan , P. R. Villeneuve , J. D. Joannopoulos , and L. A. Kolodziejski , “ Guided modes in photonic crystal slabs ,” Phys. Rev. B   60 , 5751 – 5758 ( 1999 ).
[Crossref]

M. L. Povinelli , S. G. Johnson , S. Fan , and J. D. Joannopoulos , “ Emulation of two-dimensional photonic crystal defect modes in a photonic crystal with a three-dimensional photonic band gap ,” Phys. Rev. B   64 , 075313 ( 2001 ).
[Crossref]

M. Okano and S. Noda , “ Analysis of multimode point-defect cavities in three-dimensional photonic crystals using group theory in frequency and time domains ,” Phys. Rev. B   70 , 125105 ( 2004 ).
[Crossref]

M. Bayindir and E. Ozbay , “ Heavy photons at coupled-cavity waveguide band edges in a three-dimensional photonic crystal ,” Phys. Rev. B   62 , R2247 – R2250 ( 2000 ).
[Crossref]

Phys. Rev. Lett. (4)

E. Yablonovitch , “ Inhibited spontaneous emission in solid-state physics and electronics ,” Phys. Rev. Lett.   58 , 2059 – 2062 ( 1987 ).
[Crossref] [PubMed]

S. John , “ Strong localization of photons in certain disordered dielectric superlattices ,” Phys. Rev. Lett.   58 , 2486 – 2489 ( 1987 ).
[Crossref] [PubMed]

K. M. Leung and Y. F. Liu , “ Full vector wave calculation of photonic band structures in face-centered-cubic dielectric media ,” Phys. Rev. Lett.   65 , 2646 – 2649 ( 1990 ).
[Crossref] [PubMed]

Z. Zhang and S. Satpathy , “ Electromagnetic wave propagation in periodic structures: Bloch wave solution of Maxwell’s equations ,” Phys. Rev. Lett.   65 , 2650 – 2653 ( 1990 ).
[Crossref] [PubMed]

Science (3)

S. Noda , K. Tomoda , N. Yamamoto , and A. Chutinan , “ Full three-dimensional photonic bandgap crystals at near-infrared wavelengths ,” Science   289 , 604 – 606 ( 2000 ).
[Crossref] [PubMed]

B-S. Song , S. Noda , and T. Asano , “ Photonic devices based on in-plane hetero photonic crystals ,” Science   300 , 1537 ( 2003 ).
[Crossref] [PubMed]

S. Ogawa , M. Imada , S. Yoshimoto , M. Okano , and S. Noda , “ Control of light emission by 3D photonic crystals ,” Science   305 , 227 – 229 ( 2004 ).
[Crossref] [PubMed]

Solid State Commun. (1)

K. M. Ho , C. T. Chan , C. M. Soukoulis , R. Biswas , and M. Sigalas , “ Photonic band gaps in three dimensions: new layer-by-layer periodic structures ,” Solid State Commun.   89 , 413 – 416 ( 1994 ).
[Crossref]

Other (1)

K. M. Ho , C. T. Chan , and C. M. Soukoulis , “Photonic band gaps and localization,” in Proceedings of the NATO Advanced Science Institutes Series, C. M. Soukoulis , ed. ( Plenum, New York , 1993 ), pp. 235.

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Figures (9)

Fig. 1.
Fig. 1.

(a) Schematic representation of a 3D PC waveguide created by changing the width of the red rod. (b) Dispersion relations of guided modes for W A=0.7a (left) and W A=0.8a (right).

Fig. 2.
Fig. 2.

Vertical cross-section, orthogonal to the guided direction, of the magnetic-field component (Hz ) of mode A.

Fig. 3.
Fig. 3.

(a) Schematic representation of a 3D PC waveguide created by inserting an additional rod between two original rods. (b) The dispersion relation of the guided modes.

Fig. 4.
Fig. 4.

Vertical cross-section, orthogonal to the guided direction, of Hz of mode B.

Fig. 5.
Fig. 5.

(a) Schematic representation of a 3D PC waveguide created by introducing a dielectric rod that crosses the original rods. (b) Top view of the defect layer (left) and vertical cross-section of the waveguide structure (right).

Fig. 6.
Fig. 6.

(a) The dispersion relation of the guided modes. (b) Vertical cross-section, orthogonal to the guided direction, of Hx of mode C1.

Fig. 7.
Fig. 7.

(a) Schematic representation of the vertical cross-section of a 3D PC waveguide created by translation of the upper and lower neighboring rods of a single cross rod. (b) The dispersion relation of the guided modes. (c) Vertical cross-section, orthogonal to the guided direction, of Hx of mode C1.

Fig. 8.
Fig. 8.

(a) The layout of upper and lower layers with introduced cross-rod defects and the layout of the middle layer including the original rod. (b) Schematic representation of a 3D PC waveguide created by sandwiching the original rod between two cross rods. (c) Schematic vertical cross-section of the waveguide structure.

Fig. 9.
Fig. 9.

(a) The dispersion relation of the guided modes. (b) Vertical cross-section, orthogonal to the guided direction, of Hx of mode D.

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