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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  1. J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic crystals: Molding the flow of light (Princeton U. Press, Princeton, N.J., 1995).
  2. 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]
  3. 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]
  4. Special Issues on Photonic and Electromagnetic Crystals, R. M. De La Rue, ed., Opt. Quantum Electron. 2002, 34, No.1/3.
    [CrossRef]
  5. G. Qiu, F.Lin, and Y.P Li, �??Complete two-dimensional bandgap of photonic crystals of a rectangular Bravais lattice,�?? Opt. Commun. 219, 285-288 (2003).
    [CrossRef]
  6. 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]
  7. D. N. Chigrin, S. Enoch, C. M. Sotomayor Torres, and G. Tayeb, �??Self-guiding in two-dimensional photonic crystals,�?? Opt. Express 11, 1203-1211 (2003), <a href= "http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-10-1203">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-10-1203</a>.
    [CrossRef] [PubMed]
  8. J. Witzens and A. Scherer, �??Efficient excitation of self-collimated beams and single Bloch modes in planar PhCs,�?? J. Opt. Soc. Am. A 20, 935 (2003).
    [CrossRef]
  9. C. Chen, A. Sharkawy, D. M. Pustai, S. Shi, and D. W. Prather, �??Optimizing bending efficiency of self-collimated beams in non-channel planar photonic crystal waveguides,�?? Opt. Express 11, 3153-3159 (2003), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-23-3153">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-23-3153</a>.
    [CrossRef] [PubMed]
  10. 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]
  11. 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]
  12. 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]
  13. 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]
  14. 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]
  15. 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]
  16. 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]
  17. 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]
  18. Guided-Wave Optoelectronics, T.Tamir, ed. (Springer-Verlag, Berlin, 1990.
    [CrossRef]
  19. 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), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-8-3-173">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-8-3-173</a>.
    [CrossRef] [PubMed]
  20. A. Lavrinenko, P. I. Borel, L. H. Fradsen, M. Thorhauge, A. Harpoth, M. Kristensen, and T. Niemi, �??Comprehensive FDTD modeling of photonic crystal waveguide components,�?? Opt. Express 12, 234�??248 (2004), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-2-234">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-2-234</a>.
    [CrossRef] [PubMed]
  21. F. Ramos-Mendieta and P. Halevi, �??Surface modes in a 2D array of square dielectric cylinders,�?? Solid State Commun. 100, 311-314 (1996).
    [CrossRef]
  22. 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]
  23. 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]
  24. C. Vanneste and P. Sebbah, �??Selective excitation of localized modes in active random media,�?? Phys. Rev. Lett. 87, 183903 (2001).
    [CrossRef]

Appl. Phys. Lett. (2)

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. 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]

J. Appl. Phys. (1)

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]

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

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

Micr. Opt. Technol. Lett. (1)

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]

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).
[CrossRef] [PubMed]

Opt. Commun. (1)

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

Opt. Express (4)

Opt. Quantum Electr. (1)

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]

Opt. Quantum Electron. (1)

Special Issues on Photonic and Electromagnetic Crystals, R. M. De La Rue, ed., Opt. Quantum Electron. 2002, 34, No.1/3.
[CrossRef]

Photonic Crystals and Light Localization (1)

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]

Phys. Lett. A (1)

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]

Phys. Rev. B (4)

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]

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]

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]

Phys. Rev. Lett. (1)

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

Solid State Commun. (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]

Other (2)

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

Guided-Wave Optoelectronics, T.Tamir, ed. (Springer-Verlag, Berlin, 1990.
[CrossRef]

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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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