Abstract

We present a novel type of a waveguide, which consists of several rows of periodically placed dielectric cylinders. In such a nanopillars photonic crystal waveguide, light confinement is due to the total internal reflection, while guided modes dispersion is strongly affected by waveguide periodicity. Nanopillars waveguide is multimode, where a number of modes is equal to the number of rows building the waveguide. We present a detailed study of guided modes properties, focusing on possibilities to tune their frequencies and spectral separation. An approach towards the specific mode excitation is proposed and prospects of nanopillars waveguides application as a laser resonator are discussed.

© 2004 Optical Society of America

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References

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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]

2004 (1)

2003 (5)

2002 (3)

M. Obert, B. Wild, G. Bacher, A. Forchel, R. Andre, and Le Si Dang, “Optical confinement in CdTe-based photonic dots,” Appl. Phys. Lett. 80, 1322–1324 (2002).
[Crossref]

V. Poborchii, T. Tada, and T. Kanayama, “Photonic-band-gap properties of two-dimensional lattices of Si nanopillars,” J. Appl. Phys. 91, 3299–3305 (2002).
[Crossref]

M. J. A. de Dood, E. Snoeks, A. Moroz, and A. Polman, “Design and optimization of 2D photonic crystal waveguides based on silicon,” Opt. Quantum Electr. 34, 145–159 (2002).
[Crossref]

2001 (5)

M. Qiu and S. He, “Surface modes in two-dimensional dielectric and metallic photonic band gap structures: a FDTD study,” Phys. Lett. A 282, 85–91 (2001).
[Crossref]

C. Vanneste and P. Sebbah, “Selective excitation of localized modes in active random media,” Phys. Rev. Lett. 87, 183903 (2001).
[Crossref]

S. G. Johnson and J. D. Joannopoulos, “Block-iterative frequency-domain methods for Maxwell’s equations in a planewave basis,” Opt. Express 8, 173–180 (2001), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-8-3-173
[Crossref] [PubMed]

G. Guttroff, M. Bayer, J. P. Reithmaier, A. Forchel, P. A. Knipp, and T. L. Reinecke, “Photonic defect states in chains of coupled microresonators,” Phys. Rev. B 64, 155313 (2001).
[Crossref]

L. Mendioroz, R. Gonzalo, and C. del Rio, “Design of electromagnetic crystal filters for rectangular waveguides,” Micr. Opt. Technol. Lett. 30, 81–84 (2001).
[Crossref]

2000 (2)

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

M. E. Zoorob, M. D. B. Charlton, G. J. Parker, J. J. Baumberg, and M. C. Netti, “Complete photonic bandgap in 12-fold symmetric quasicrystals,” Nature,  404, 740–743 (2000).
[Crossref] [PubMed]

1999 (2)

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

F. Ramos-Mendieta and P. Halevi, “Surface electromagnetic waves in two-dimensional photonic crystals: effect of the position of the surface plane,” Phys. Rev. B 59, 15112–15120 (1999).
[Crossref]

1996 (1)

F. Ramos-Mendieta and P. Halevi, “Surface modes in a 2D array of square dielectric cylinders,” Solid State Commun. 100, 311–314 (1996).
[Crossref]

1995 (1)

Andre, R.

M. Obert, B. Wild, G. Bacher, A. Forchel, R. Andre, and Le Si Dang, “Optical confinement in CdTe-based photonic dots,” Appl. Phys. Lett. 80, 1322–1324 (2002).
[Crossref]

Bacher, G.

M. Obert, B. Wild, G. Bacher, A. Forchel, R. Andre, and Le Si Dang, “Optical confinement in CdTe-based photonic dots,” Appl. Phys. Lett. 80, 1322–1324 (2002).
[Crossref]

Baumberg, J. J.

M. E. Zoorob, M. D. B. Charlton, G. J. Parker, J. J. Baumberg, and M. C. Netti, “Complete photonic bandgap in 12-fold symmetric quasicrystals,” Nature,  404, 740–743 (2000).
[Crossref] [PubMed]

Bayer, M.

G. Guttroff, M. Bayer, J. P. Reithmaier, A. Forchel, P. A. Knipp, and T. L. Reinecke, “Photonic defect states in chains of coupled microresonators,” Phys. Rev. B 64, 155313 (2001).
[Crossref]

Borel, P. I.

Charlton, M. D. B.

M. E. Zoorob, M. D. B. Charlton, G. J. Parker, J. J. Baumberg, and M. C. Netti, “Complete photonic bandgap in 12-fold symmetric quasicrystals,” Nature,  404, 740–743 (2000).
[Crossref] [PubMed]

Chen, C.

Chen, J. C.

Chigrin, D. N.

de Dood, M. J. A.

M. J. A. de Dood, E. Snoeks, A. Moroz, and A. Polman, “Design and optimization of 2D photonic crystal waveguides based on silicon,” Opt. Quantum Electr. 34, 145–159 (2002).
[Crossref]

M. J. A. de Dood, L. H. Slooff, T. M. Hensen, D. L. J. Vossen, A. Moroz, T. Zijlstra, E.W. J. M. Van der Drift, A. van Blaaderen, and A. Polman, “1, 2 and 3 dimensional photonic materials made using ion beams: fabrication and optical density-of-states.” In Photonic Crystals and Light Localization in the 21st Century.C. Soukoulis, ed., 555–566 (Kluwer Academic Publishers, Dordrecht, 2001).
[Crossref]

del Rio, C.

L. Mendioroz, R. Gonzalo, and C. del Rio, “Design of electromagnetic crystal filters for rectangular waveguides,” Micr. Opt. Technol. Lett. 30, 81–84 (2001).
[Crossref]

Devenyi, A.

Enoch, S.

Fan, S.

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

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

S. Fan, J. Winn, A. Devenyi, J. C. Chen, R. D. Meade, and J. D. Joannopoulos, “Guided and defect modes in periodic dielectric waveguides,” J. Opt. Soc. Am. B,  12, 1267–1272 (1995).
[Crossref]

Forchel, A.

M. Obert, B. Wild, G. Bacher, A. Forchel, R. Andre, and Le Si Dang, “Optical confinement in CdTe-based photonic dots,” Appl. Phys. Lett. 80, 1322–1324 (2002).
[Crossref]

G. Guttroff, M. Bayer, J. P. Reithmaier, A. Forchel, P. A. Knipp, and T. L. Reinecke, “Photonic defect states in chains of coupled microresonators,” Phys. Rev. B 64, 155313 (2001).
[Crossref]

Fradsen, L. H.

Gonzalo, R.

L. Mendioroz, R. Gonzalo, and C. del Rio, “Design of electromagnetic crystal filters for rectangular waveguides,” Micr. Opt. Technol. Lett. 30, 81–84 (2001).
[Crossref]

Guttroff, G.

G. Guttroff, M. Bayer, J. P. Reithmaier, A. Forchel, P. A. Knipp, and T. L. Reinecke, “Photonic defect states in chains of coupled microresonators,” Phys. Rev. B 64, 155313 (2001).
[Crossref]

Halevi, P.

F. Ramos-Mendieta and P. Halevi, “Surface electromagnetic waves in two-dimensional photonic crystals: effect of the position of the surface plane,” Phys. Rev. B 59, 15112–15120 (1999).
[Crossref]

F. Ramos-Mendieta and P. Halevi, “Surface modes in a 2D array of square dielectric cylinders,” Solid State Commun. 100, 311–314 (1996).
[Crossref]

Harpoth, A.

He, S.

M. Qiu and S. He, “Surface modes in two-dimensional dielectric and metallic photonic band gap structures: a FDTD study,” Phys. Lett. A 282, 85–91 (2001).
[Crossref]

Hensen, T. M.

M. J. A. de Dood, L. H. Slooff, T. M. Hensen, D. L. J. Vossen, A. Moroz, T. Zijlstra, E.W. J. M. Van der Drift, A. van Blaaderen, and A. Polman, “1, 2 and 3 dimensional photonic materials made using ion beams: fabrication and optical density-of-states.” In Photonic Crystals and Light Localization in the 21st Century.C. Soukoulis, ed., 555–566 (Kluwer Academic Publishers, Dordrecht, 2001).
[Crossref]

Joannopoulos, J. D.

S. G. Johnson and J. D. Joannopoulos, “Block-iterative frequency-domain methods for Maxwell’s equations in a planewave basis,” Opt. Express 8, 173–180 (2001), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-8-3-173
[Crossref] [PubMed]

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

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

S. Fan, J. Winn, A. Devenyi, J. C. Chen, R. D. Meade, and J. D. Joannopoulos, “Guided and defect modes in periodic dielectric waveguides,” J. Opt. Soc. Am. B,  12, 1267–1272 (1995).
[Crossref]

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic crystals: Molding the flow of light (Princeton U. Press, Princeton, N.J., 1995).

Johnson, S. G.

S. G. Johnson and J. D. Joannopoulos, “Block-iterative frequency-domain methods for Maxwell’s equations in a planewave basis,” Opt. Express 8, 173–180 (2001), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-8-3-173
[Crossref] [PubMed]

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

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

Kanayama, T.

V. Poborchii, T. Tada, T. Kanayama, and A. Moroz, “Silver-coated silicon pillar photonic crystals: Enhancement of a photonic band gap,” Appl. Phys. Lett. 82, 508–510 (2003).
[Crossref]

V. Poborchii, T. Tada, and T. Kanayama, “Photonic-band-gap properties of two-dimensional lattices of Si nanopillars,” J. Appl. Phys. 91, 3299–3305 (2002).
[Crossref]

Knipp, P. A.

G. Guttroff, M. Bayer, J. P. Reithmaier, A. Forchel, P. A. Knipp, and T. L. Reinecke, “Photonic defect states in chains of coupled microresonators,” Phys. Rev. B 64, 155313 (2001).
[Crossref]

Kristensen, M.

Lavrinenko, A.

Li, P Y.

G. Qiu, F. Lin, and P Y. Li, “Complete two-dimensional bandgap of photonic crystals of a rectangular Bravais lattice,” Opt. Commun.,  219, 285–288 (2003).
[Crossref]

Lin, F.

G. Qiu, F. Lin, and P Y. Li, “Complete two-dimensional bandgap of photonic crystals of a rectangular Bravais lattice,” Opt. Commun.,  219, 285–288 (2003).
[Crossref]

Meade, R. D.

S. Fan, J. Winn, A. Devenyi, J. C. Chen, R. D. Meade, and J. D. Joannopoulos, “Guided and defect modes in periodic dielectric waveguides,” J. Opt. Soc. Am. B,  12, 1267–1272 (1995).
[Crossref]

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic crystals: Molding the flow of light (Princeton U. Press, Princeton, N.J., 1995).

Mendioroz, L.

L. Mendioroz, R. Gonzalo, and C. del Rio, “Design of electromagnetic crystal filters for rectangular waveguides,” Micr. Opt. Technol. Lett. 30, 81–84 (2001).
[Crossref]

Moroz, A.

V. Poborchii, T. Tada, T. Kanayama, and A. Moroz, “Silver-coated silicon pillar photonic crystals: Enhancement of a photonic band gap,” Appl. Phys. Lett. 82, 508–510 (2003).
[Crossref]

M. J. A. de Dood, E. Snoeks, A. Moroz, and A. Polman, “Design and optimization of 2D photonic crystal waveguides based on silicon,” Opt. Quantum Electr. 34, 145–159 (2002).
[Crossref]

M. J. A. de Dood, L. H. Slooff, T. M. Hensen, D. L. J. Vossen, A. Moroz, T. Zijlstra, E.W. J. M. Van der Drift, A. van Blaaderen, and A. Polman, “1, 2 and 3 dimensional photonic materials made using ion beams: fabrication and optical density-of-states.” In Photonic Crystals and Light Localization in the 21st Century.C. Soukoulis, ed., 555–566 (Kluwer Academic Publishers, Dordrecht, 2001).
[Crossref]

Netti, M. C.

M. E. Zoorob, M. D. B. Charlton, G. J. Parker, J. J. Baumberg, and M. C. Netti, “Complete photonic bandgap in 12-fold symmetric quasicrystals,” Nature,  404, 740–743 (2000).
[Crossref] [PubMed]

Niemi, T.

Obert, M.

M. Obert, B. Wild, G. Bacher, A. Forchel, R. Andre, and Le Si Dang, “Optical confinement in CdTe-based photonic dots,” Appl. Phys. Lett. 80, 1322–1324 (2002).
[Crossref]

Parker, G. J.

M. E. Zoorob, M. D. B. Charlton, G. J. Parker, J. J. Baumberg, and M. C. Netti, “Complete photonic bandgap in 12-fold symmetric quasicrystals,” Nature,  404, 740–743 (2000).
[Crossref] [PubMed]

Poborchii, V.

V. Poborchii, T. Tada, T. Kanayama, and A. Moroz, “Silver-coated silicon pillar photonic crystals: Enhancement of a photonic band gap,” Appl. Phys. Lett. 82, 508–510 (2003).
[Crossref]

V. Poborchii, T. Tada, and T. Kanayama, “Photonic-band-gap properties of two-dimensional lattices of Si nanopillars,” J. Appl. Phys. 91, 3299–3305 (2002).
[Crossref]

Polman, A.

M. J. A. de Dood, E. Snoeks, A. Moroz, and A. Polman, “Design and optimization of 2D photonic crystal waveguides based on silicon,” Opt. Quantum Electr. 34, 145–159 (2002).
[Crossref]

M. J. A. de Dood, L. H. Slooff, T. M. Hensen, D. L. J. Vossen, A. Moroz, T. Zijlstra, E.W. J. M. Van der Drift, A. van Blaaderen, and A. Polman, “1, 2 and 3 dimensional photonic materials made using ion beams: fabrication and optical density-of-states.” In Photonic Crystals and Light Localization in the 21st Century.C. Soukoulis, ed., 555–566 (Kluwer Academic Publishers, Dordrecht, 2001).
[Crossref]

Prather, D. W.

Pustai, D. M.

Qiu, G.

G. Qiu, F. Lin, and P Y. Li, “Complete two-dimensional bandgap of photonic crystals of a rectangular Bravais lattice,” Opt. Commun.,  219, 285–288 (2003).
[Crossref]

Qiu, M.

M. Qiu and S. He, “Surface modes in two-dimensional dielectric and metallic photonic band gap structures: a FDTD study,” Phys. Lett. A 282, 85–91 (2001).
[Crossref]

Ramos-Mendieta, F.

F. Ramos-Mendieta and P. Halevi, “Surface electromagnetic waves in two-dimensional photonic crystals: effect of the position of the surface plane,” Phys. Rev. B 59, 15112–15120 (1999).
[Crossref]

F. Ramos-Mendieta and P. Halevi, “Surface modes in a 2D array of square dielectric cylinders,” Solid State Commun. 100, 311–314 (1996).
[Crossref]

Reinecke, T. L.

G. Guttroff, M. Bayer, J. P. Reithmaier, A. Forchel, P. A. Knipp, and T. L. Reinecke, “Photonic defect states in chains of coupled microresonators,” Phys. Rev. B 64, 155313 (2001).
[Crossref]

Reithmaier, J. P.

G. Guttroff, M. Bayer, J. P. Reithmaier, A. Forchel, P. A. Knipp, and T. L. Reinecke, “Photonic defect states in chains of coupled microresonators,” Phys. Rev. B 64, 155313 (2001).
[Crossref]

Scherer, A.

Sebbah, P.

C. Vanneste and P. Sebbah, “Selective excitation of localized modes in active random media,” Phys. Rev. Lett. 87, 183903 (2001).
[Crossref]

Sharkawy, A.

Shi, S.

Si Dang, Le

M. Obert, B. Wild, G. Bacher, A. Forchel, R. Andre, and Le Si Dang, “Optical confinement in CdTe-based photonic dots,” Appl. Phys. Lett. 80, 1322–1324 (2002).
[Crossref]

Slooff, L. H.

M. J. A. de Dood, L. H. Slooff, T. M. Hensen, D. L. J. Vossen, A. Moroz, T. Zijlstra, E.W. J. M. Van der Drift, A. van Blaaderen, and A. Polman, “1, 2 and 3 dimensional photonic materials made using ion beams: fabrication and optical density-of-states.” In Photonic Crystals and Light Localization in the 21st Century.C. Soukoulis, ed., 555–566 (Kluwer Academic Publishers, Dordrecht, 2001).
[Crossref]

Snoeks, E.

M. J. A. de Dood, E. Snoeks, A. Moroz, and A. Polman, “Design and optimization of 2D photonic crystal waveguides based on silicon,” Opt. Quantum Electr. 34, 145–159 (2002).
[Crossref]

Sotomayor Torres, C. M.

Tada, T.

V. Poborchii, T. Tada, T. Kanayama, and A. Moroz, “Silver-coated silicon pillar photonic crystals: Enhancement of a photonic band gap,” Appl. Phys. Lett. 82, 508–510 (2003).
[Crossref]

V. Poborchii, T. Tada, and T. Kanayama, “Photonic-band-gap properties of two-dimensional lattices of Si nanopillars,” J. Appl. Phys. 91, 3299–3305 (2002).
[Crossref]

Tayeb, G.

Thorhauge, M.

van Blaaderen, A.

M. J. A. de Dood, L. H. Slooff, T. M. Hensen, D. L. J. Vossen, A. Moroz, T. Zijlstra, E.W. J. M. Van der Drift, A. van Blaaderen, and A. Polman, “1, 2 and 3 dimensional photonic materials made using ion beams: fabrication and optical density-of-states.” In Photonic Crystals and Light Localization in the 21st Century.C. Soukoulis, ed., 555–566 (Kluwer Academic Publishers, Dordrecht, 2001).
[Crossref]

Van der Drift, E.W. J. M.

M. J. A. de Dood, L. H. Slooff, T. M. Hensen, D. L. J. Vossen, A. Moroz, T. Zijlstra, E.W. J. M. Van der Drift, A. van Blaaderen, and A. Polman, “1, 2 and 3 dimensional photonic materials made using ion beams: fabrication and optical density-of-states.” In Photonic Crystals and Light Localization in the 21st Century.C. Soukoulis, ed., 555–566 (Kluwer Academic Publishers, Dordrecht, 2001).
[Crossref]

Vanneste, C.

C. Vanneste and P. Sebbah, “Selective excitation of localized modes in active random media,” Phys. Rev. Lett. 87, 183903 (2001).
[Crossref]

Villeneuve, P. R.

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

Villeneuve, P.R.

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M. J. A. de Dood, L. H. Slooff, T. M. Hensen, D. L. J. Vossen, A. Moroz, T. Zijlstra, E.W. J. M. Van der Drift, A. van Blaaderen, and A. Polman, “1, 2 and 3 dimensional photonic materials made using ion beams: fabrication and optical density-of-states.” In Photonic Crystals and Light Localization in the 21st Century.C. Soukoulis, ed., 555–566 (Kluwer Academic Publishers, Dordrecht, 2001).
[Crossref]

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M. Obert, B. Wild, G. Bacher, A. Forchel, R. Andre, and Le Si Dang, “Optical confinement in CdTe-based photonic dots,” Appl. Phys. Lett. 80, 1322–1324 (2002).
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Winn, J.

Winn, J. N.

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic crystals: Molding the flow of light (Princeton U. Press, Princeton, N.J., 1995).

Witzens, J.

Zijlstra, T.

M. J. A. de Dood, L. H. Slooff, T. M. Hensen, D. L. J. Vossen, A. Moroz, T. Zijlstra, E.W. J. M. Van der Drift, A. van Blaaderen, and A. Polman, “1, 2 and 3 dimensional photonic materials made using ion beams: fabrication and optical density-of-states.” In Photonic Crystals and Light Localization in the 21st Century.C. Soukoulis, ed., 555–566 (Kluwer Academic Publishers, Dordrecht, 2001).
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M. E. Zoorob, M. D. B. Charlton, G. J. Parker, J. J. Baumberg, and M. C. Netti, “Complete photonic bandgap in 12-fold symmetric quasicrystals,” Nature,  404, 740–743 (2000).
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V. Poborchii, T. Tada, T. Kanayama, and A. Moroz, “Silver-coated silicon pillar photonic crystals: Enhancement of a photonic band gap,” Appl. Phys. Lett. 82, 508–510 (2003).
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M. Obert, B. Wild, G. Bacher, A. Forchel, R. Andre, and Le Si Dang, “Optical confinement in CdTe-based photonic dots,” Appl. Phys. Lett. 80, 1322–1324 (2002).
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V. Poborchii, T. Tada, and T. Kanayama, “Photonic-band-gap properties of two-dimensional lattices of Si nanopillars,” J. Appl. Phys. 91, 3299–3305 (2002).
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Nature (1)

M. E. Zoorob, M. D. B. Charlton, G. J. Parker, J. J. Baumberg, and M. C. Netti, “Complete photonic bandgap in 12-fold symmetric quasicrystals,” Nature,  404, 740–743 (2000).
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G. Qiu, F. Lin, and P Y. Li, “Complete two-dimensional bandgap of photonic crystals of a rectangular Bravais lattice,” Opt. Commun.,  219, 285–288 (2003).
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M. J. A. de Dood, E. Snoeks, A. Moroz, and A. Polman, “Design and optimization of 2D photonic crystal waveguides based on silicon,” Opt. Quantum Electr. 34, 145–159 (2002).
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S. G. Johnson, P.R. Villeneuve, S. Fan, and J. D. Joannopoulos, “Linear waveguides in photonic-crystal slabs,” Phys.Rev.B,  62, 8212–8222 (2000).
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M. J. A. de Dood, L. H. Slooff, T. M. Hensen, D. L. J. Vossen, A. Moroz, T. Zijlstra, E.W. J. M. Van der Drift, A. van Blaaderen, and A. Polman, “1, 2 and 3 dimensional photonic materials made using ion beams: fabrication and optical density-of-states.” In Photonic Crystals and Light Localization in the 21st Century.C. Soukoulis, ed., 555–566 (Kluwer Academic Publishers, Dordrecht, 2001).
[Crossref]

Guided-Wave OptoelectronicsT. Tamir, ed. (Springer-Verlag, Berlin, 1990).
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Special Issues on Photonic and Electromagnetic CrystalsR. M. De La Rue, ed., Opt. Quantum Electron.2002, 34, No.1/3.
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J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic crystals: Molding the flow of light (Princeton U. Press, Princeton, N.J., 1995).

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Figures (6)

Fig. 1.
Fig. 1.

Dispersion diagrams for nanopillars PCWs with 2, 3, 4 and 5 rows. Insets show a sketch of the waveguides. In the inset of the leftmost panel, coordinate system, together with the first quarter of the first BZ of the square lattice are shown. Grey area shows a continuum of radiated modes lying above the light line. Guided modes are shown in black solid lines. Projected band structure of 2D square lattice PhC is given in blue, where the bands in Γ-X (solid lines) and X-M directions (dashed lines) are shown.

Fig. 2.
Fig. 2.

Field patterns of the 4 lowest guided modes of W4 PCW. Modes 1 and 3 are even, 2 and 4 are odd. Ey component of the field is plotted. Zero fields are in green, positive and negative values are in red and blue.

Fig. 3.
Fig. 3.

Dispersion diagrams for different dielectric constant of rods. Grey area shows a continuum of radiated modes lying above the light line. Guided modes are shown in black solid lines. Projected band structure of 2D square lattice PhC is given in blue, where the bands in Γ-X (solid lines) and X-M directions (dashed lines) are shown.

Fig. 4.
Fig. 4.

Dispersion diagrams for different rectangular Bravais lattices; m=0.5 (left), 1.0 (center) and 2.0 (right). Insets show a sketch of waveguides, coordinate system and the first quarter of the first BZ of the corresponding lattice. Grey area shows a continuum of radiated modes lying above the light line. Guided modes are shown in black solid lines. Projected band structure of 2D PhC is given in blue, where the bands in Γ-P (Γ-X′) (solid lines) and X-M directions (dashed lines) are shown.

Fig. 5.
Fig. 5.

Dispersion curves (left) and transmission spectra for the 1st, 3rd (center), 2nd and 4th (right) modes of W4 waveguide.

Fig.6.
Fig.6.

Normalized energy spectra for different spatial patterns of the excitation for the 20 periods long W4 PCW. Spatial patterns of excitation reflecting the symmetry of the 1st (black), 2nd (red), 3rd (blue) and 4th (green) modes are shown in insets

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