Abstract

We investigate photonic crystal waveguides that are formed by holes of reduced diameter within a hexagonal lattice of cylindrical airholes in thin freestanding silicon slabs. The waveguides operate in both an even-symmetry bandgap and a partial gap of odd-symmetry modes that form a complete two-dimensional bandgap under the light line. The operating frequency is tuned by the small-hole diameter to fit within the range of both bandgaps and to match a free-space wavelength of 1550nm. Their narrow bandwidth and low group velocity of light propagation renders the waveguides useful as filters or sensing elements. Because of the strong dependence of the waveguide mode characteristics on structural changes, the highest-precision lithographic fabrication techniques must be applied.

© 2009 Optical Society of America

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  1. J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light (Princeton U. Press, 2008).
  2. K. Busch, S. Lölkes, R. B. Wehrspohn, and H. Föll, Photonic Crystals (Wiley, 2004).
    [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. M. Loncar, T. Doll, J. Kovi, and A. Scherer, “Design and fabrication of silicon photonic crystal optical waveguides,” J. Lightwave Technol. 18, 1402-1411 (2000).
    [Crossref]
  5. M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, “Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs,” Phys. Rev. Lett. 87, 253902 (2001).
    [Crossref] [PubMed]
  6. C. Jamois, R. B. Wehrspohn, L. C. Andreani, C. Hermann, O. Hess, and U. Gösele, “Silicon-based two-dimensional photonic crystal waveguides,” Photon. Nanostruct. Fundam. Appl. 1, 1-13 (2003).
    [Crossref]
  7. A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett. 77, 3787-3790 (1996).
    [Crossref] [PubMed]
  8. A. Chutinan and S. Noda, “Waveguides and waveguide bends in two-dimensional photonic crystal slabs,” Phys. Rev. B 62, 4488-4492 (2000).
    [Crossref]
  9. S. Assefa, S. J. McNab, and Y. A. Vlasov, “Transmission of slow light through photonic crystal waveguide bends,” Opt. Lett. 31, 745-747 (2006).
    [Crossref] [PubMed]
  10. 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]
  11. A. Taflove and S. C. Hagness, Computational Electrodynamics (Artech House, 2005).
  12. FDTD Solutions, Lumerical Solutions, Inc., Vancouver, British Columbia, Canada.
  13. J.-P. Berenger, “Three-dimensional perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 127, 363-379 (1996).
    [Crossref]
  14. S. Hughes, L. Ramunno, J. F. Young, and J. E. Sipe, “Extrinsic optical scattering loss in photonic crystal waveguides: role of fabrication disorder and photon group velocity,” Phys. Rev. Lett. 94, 033903 (2005).
    [Crossref] [PubMed]
  15. D. Gerace and L. C. Andreani, “Disorder-induced losses in photonic crystal waveguides with line defects,” Opt. Lett. 29, 1897-1899 (2004).
    [Crossref] [PubMed]
  16. K. R. Maskaly, C. Carter, R. D. Averitt, and J. D. Maxwell, “The effect of interfacial roughness on the normal incidence bandgap of one-dimensional photonic crystals,” Opt. Express 13, 8380-8389 (2005).
    [Crossref] [PubMed]
  17. J. Topolancik, F. Vollmer, R. Ilic, and M. Crescimanno, “Out-of-plane scattering from vertically asymmetric photonic crystal slab waveguides with in-plane disorder,” Opt. Express 17, 12470-12480 (2009).
    [Crossref] [PubMed]
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    [Crossref]

2009 (1)

2006 (1)

2005 (2)

S. Hughes, L. Ramunno, J. F. Young, and J. E. Sipe, “Extrinsic optical scattering loss in photonic crystal waveguides: role of fabrication disorder and photon group velocity,” Phys. Rev. Lett. 94, 033903 (2005).
[Crossref] [PubMed]

K. R. Maskaly, C. Carter, R. D. Averitt, and J. D. Maxwell, “The effect of interfacial roughness on the normal incidence bandgap of one-dimensional photonic crystals,” Opt. Express 13, 8380-8389 (2005).
[Crossref] [PubMed]

2004 (1)

2003 (1)

C. Jamois, R. B. Wehrspohn, L. C. Andreani, C. Hermann, O. Hess, and U. Gösele, “Silicon-based two-dimensional photonic crystal waveguides,” Photon. Nanostruct. Fundam. Appl. 1, 1-13 (2003).
[Crossref]

2001 (1)

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, “Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs,” Phys. Rev. Lett. 87, 253902 (2001).
[Crossref] [PubMed]

2000 (3)

A. Chutinan and S. Noda, “Waveguides and waveguide bends in two-dimensional photonic crystal slabs,” Phys. Rev. B 62, 4488-4492 (2000).
[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]

M. Loncar, T. Doll, J. Kovi, and A. Scherer, “Design and fabrication of silicon photonic crystal optical waveguides,” J. Lightwave Technol. 18, 1402-1411 (2000).
[Crossref]

1999 (1)

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]

1996 (2)

J.-P. Berenger, “Three-dimensional perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 127, 363-379 (1996).
[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 waveguides,” Phys. Rev. Lett. 77, 3787-3790 (1996).
[Crossref] [PubMed]

1987 (1)

D.-B. Kao, J. P. McVittie, W. D. Nix, and K. C. Saraswat, “Two-dimensional thermal oxidation of silicon. I. Experiments,” IEEE Trans. Electron. Devices 34, 1008-1017(1987).
[Crossref]

Andreani, L. C.

D. Gerace and L. C. Andreani, “Disorder-induced losses in photonic crystal waveguides with line defects,” Opt. Lett. 29, 1897-1899 (2004).
[Crossref] [PubMed]

C. Jamois, R. B. Wehrspohn, L. C. Andreani, C. Hermann, O. Hess, and U. Gösele, “Silicon-based two-dimensional photonic crystal waveguides,” Photon. Nanostruct. Fundam. Appl. 1, 1-13 (2003).
[Crossref]

Assefa, S.

Averitt, R. D.

Berenger, J.-P.

J.-P. Berenger, “Three-dimensional perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 127, 363-379 (1996).
[Crossref]

Busch, K.

K. Busch, S. Lölkes, R. B. Wehrspohn, and H. Föll, Photonic Crystals (Wiley, 2004).
[Crossref]

Carter, C.

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 waveguides,” Phys. Rev. Lett. 77, 3787-3790 (1996).
[Crossref] [PubMed]

Chutinan, A.

A. Chutinan and S. Noda, “Waveguides and waveguide bends in two-dimensional photonic crystal slabs,” Phys. Rev. B 62, 4488-4492 (2000).
[Crossref]

Crescimanno, M.

Doll, T.

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, 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]

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett. 77, 3787-3790 (1996).
[Crossref] [PubMed]

Föll, H.

K. Busch, S. Lölkes, R. B. Wehrspohn, and H. Föll, Photonic Crystals (Wiley, 2004).
[Crossref]

Gerace, D.

Gösele, U.

C. Jamois, R. B. Wehrspohn, L. C. Andreani, C. Hermann, O. Hess, and U. Gösele, “Silicon-based two-dimensional photonic crystal waveguides,” Photon. Nanostruct. Fundam. Appl. 1, 1-13 (2003).
[Crossref]

Hagness, S. C.

A. Taflove and S. C. Hagness, Computational Electrodynamics (Artech House, 2005).

Hermann, C.

C. Jamois, R. B. Wehrspohn, L. C. Andreani, C. Hermann, O. Hess, and U. Gösele, “Silicon-based two-dimensional photonic crystal waveguides,” Photon. Nanostruct. Fundam. Appl. 1, 1-13 (2003).
[Crossref]

Hess, O.

C. Jamois, R. B. Wehrspohn, L. C. Andreani, C. Hermann, O. Hess, and U. Gösele, “Silicon-based two-dimensional photonic crystal waveguides,” Photon. Nanostruct. Fundam. Appl. 1, 1-13 (2003).
[Crossref]

Hughes, S.

S. Hughes, L. Ramunno, J. F. Young, and J. E. Sipe, “Extrinsic optical scattering loss in photonic crystal waveguides: role of fabrication disorder and photon group velocity,” Phys. Rev. Lett. 94, 033903 (2005).
[Crossref] [PubMed]

Ilic, R.

Jamois, C.

C. Jamois, R. B. Wehrspohn, L. C. Andreani, C. Hermann, O. Hess, and U. Gösele, “Silicon-based two-dimensional photonic crystal waveguides,” Photon. Nanostruct. Fundam. Appl. 1, 1-13 (2003).
[Crossref]

Joannopoulos, J. D.

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, 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]

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett. 77, 3787-3790 (1996).
[Crossref] [PubMed]

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light (Princeton U. Press, 2008).

Johnson, S. G.

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, 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]

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light (Princeton U. Press, 2008).

Kao, D.-B.

D.-B. Kao, J. P. McVittie, W. D. Nix, and K. C. Saraswat, “Two-dimensional thermal oxidation of silicon. I. Experiments,” IEEE Trans. Electron. Devices 34, 1008-1017(1987).
[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]

Kovi, J.

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 waveguides,” Phys. Rev. Lett. 77, 3787-3790 (1996).
[Crossref] [PubMed]

Lölkes, S.

K. Busch, S. Lölkes, R. B. Wehrspohn, and H. Föll, Photonic Crystals (Wiley, 2004).
[Crossref]

Loncar, M.

Maskaly, K. R.

Maxwell, J. D.

McNab, S. J.

McVittie, J. P.

D.-B. Kao, J. P. McVittie, W. D. Nix, and K. C. Saraswat, “Two-dimensional thermal oxidation of silicon. I. Experiments,” IEEE Trans. Electron. Devices 34, 1008-1017(1987).
[Crossref]

Meade, R. D.

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light (Princeton U. Press, 2008).

Mekis, A.

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett. 77, 3787-3790 (1996).
[Crossref] [PubMed]

Nix, W. D.

D.-B. Kao, J. P. McVittie, W. D. Nix, and K. C. Saraswat, “Two-dimensional thermal oxidation of silicon. I. Experiments,” IEEE Trans. Electron. Devices 34, 1008-1017(1987).
[Crossref]

Noda, S.

A. Chutinan and S. Noda, “Waveguides and waveguide bends in two-dimensional photonic crystal slabs,” Phys. Rev. B 62, 4488-4492 (2000).
[Crossref]

Notomi, M.

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, “Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs,” Phys. Rev. Lett. 87, 253902 (2001).
[Crossref] [PubMed]

Ramunno, L.

S. Hughes, L. Ramunno, J. F. Young, and J. E. Sipe, “Extrinsic optical scattering loss in photonic crystal waveguides: role of fabrication disorder and photon group velocity,” Phys. Rev. Lett. 94, 033903 (2005).
[Crossref] [PubMed]

Saraswat, K. C.

D.-B. Kao, J. P. McVittie, W. D. Nix, and K. C. Saraswat, “Two-dimensional thermal oxidation of silicon. I. Experiments,” IEEE Trans. Electron. Devices 34, 1008-1017(1987).
[Crossref]

Scherer, A.

Shinya, A.

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, “Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs,” Phys. Rev. Lett. 87, 253902 (2001).
[Crossref] [PubMed]

Sipe, J. E.

S. Hughes, L. Ramunno, J. F. Young, and J. E. Sipe, “Extrinsic optical scattering loss in photonic crystal waveguides: role of fabrication disorder and photon group velocity,” Phys. Rev. Lett. 94, 033903 (2005).
[Crossref] [PubMed]

Taflove, A.

A. Taflove and S. C. Hagness, Computational Electrodynamics (Artech House, 2005).

Takahashi, C.

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, “Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs,” Phys. Rev. Lett. 87, 253902 (2001).
[Crossref] [PubMed]

Takahashi, J.

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, “Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs,” Phys. Rev. Lett. 87, 253902 (2001).
[Crossref] [PubMed]

Topolancik, J.

Villeneuve, P. R.

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, 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]

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett. 77, 3787-3790 (1996).
[Crossref] [PubMed]

Vlasov, Y. A.

Vollmer, F.

Wehrspohn, R. B.

C. Jamois, R. B. Wehrspohn, L. C. Andreani, C. Hermann, O. Hess, and U. Gösele, “Silicon-based two-dimensional photonic crystal waveguides,” Photon. Nanostruct. Fundam. Appl. 1, 1-13 (2003).
[Crossref]

K. Busch, S. Lölkes, R. B. Wehrspohn, and H. Föll, Photonic Crystals (Wiley, 2004).
[Crossref]

Winn, J. N.

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light (Princeton U. Press, 2008).

Yamada, K.

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, “Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs,” Phys. Rev. Lett. 87, 253902 (2001).
[Crossref] [PubMed]

Yokohama, I.

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, “Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs,” Phys. Rev. Lett. 87, 253902 (2001).
[Crossref] [PubMed]

Young, J. F.

S. Hughes, L. Ramunno, J. F. Young, and J. E. Sipe, “Extrinsic optical scattering loss in photonic crystal waveguides: role of fabrication disorder and photon group velocity,” Phys. Rev. Lett. 94, 033903 (2005).
[Crossref] [PubMed]

IEEE Trans. Electron. Devices (1)

D.-B. Kao, J. P. McVittie, W. D. Nix, and K. C. Saraswat, “Two-dimensional thermal oxidation of silicon. I. Experiments,” IEEE Trans. Electron. Devices 34, 1008-1017(1987).
[Crossref]

J. Comput. Phys. (1)

J.-P. Berenger, “Three-dimensional perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 127, 363-379 (1996).
[Crossref]

J. Lightwave Technol. (1)

Opt. Express (2)

Opt. Lett. (2)

Photon. Nanostruct. Fundam. Appl. (1)

C. Jamois, R. B. Wehrspohn, L. C. Andreani, C. Hermann, O. Hess, and U. Gösele, “Silicon-based two-dimensional photonic crystal waveguides,” Photon. Nanostruct. Fundam. Appl. 1, 1-13 (2003).
[Crossref]

Phys. Rev. B (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]

A. Chutinan and S. Noda, “Waveguides and waveguide bends in two-dimensional photonic crystal slabs,” Phys. Rev. B 62, 4488-4492 (2000).
[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]

Phys. Rev. Lett. (3)

S. Hughes, L. Ramunno, J. F. Young, and J. E. Sipe, “Extrinsic optical scattering loss in photonic crystal waveguides: role of fabrication disorder and photon group velocity,” Phys. Rev. Lett. 94, 033903 (2005).
[Crossref] [PubMed]

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett. 77, 3787-3790 (1996).
[Crossref] [PubMed]

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, “Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs,” Phys. Rev. Lett. 87, 253902 (2001).
[Crossref] [PubMed]

Other (4)

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light (Princeton U. Press, 2008).

K. Busch, S. Lölkes, R. B. Wehrspohn, and H. Föll, Photonic Crystals (Wiley, 2004).
[Crossref]

A. Taflove and S. C. Hagness, Computational Electrodynamics (Artech House, 2005).

FDTD Solutions, Lumerical Solutions, Inc., Vancouver, British Columbia, Canada.

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Figures (6)

Fig. 1
Fig. 1

Simulation setup for the FDTD calculations of (a) lattice and (d) waveguide bands. A rectangular cell comprising the freestanding silicon slab as well as a block of silicon substrate. Small circles indicate dipole positions for excitation (c). At the sides of the cells BBCs are set according to the outer path of the irreducible Brillouin zone (b); at the top and the bottom PML boundary conditions are applied. The waveguide unit cell consists of a small hole centered within an appropriate number of lattice holes. The arrow indicates the direction of light propagation (e).

Fig. 2
Fig. 2

Dispersion diagram of lattice modes along the Γ M K Γ path of the irreducible Brillouin zone. The even-symmetry bandgap is indicated by horizontal dotted lines. Within this gap a partial odd-symmetry gap exists below the light line as marked by dashed lines. At the lattice parameters chosen ( h / a = 0.5 , r / a = 0.41 , a = 700 nm ) the desired wavelength λ = 1550 nm of waveguide operation corresponding to a normalized frequency of 0.4516 c / a is included in both gaps.

Fig. 3
Fig. 3

Dispersion diagram of even-symmetry waveguide modes calculated at the lattice parameters of Fig. 2 using a small-hole radius r s / a = 0.36 . The lower-frequency waveguide mode has a laterally even symmetry, whereas the higher-frequency mode is laterally odd. The graph also shows slab modes of even and odd symmetry as projected in the Γ K direction.

Fig. 4
Fig. 4

Amplitude profile of the magnetic field H z of the first (bottom) and second even-symmetry waveguide mode (top) as calculated at the K symmetry point. Dark and bright areas indicate amplitude maxima as well as the phase difference of π of the magnetic field. The serrated hole edges emerge from spatial discretization within the FDTD algorithm.

Fig. 5
Fig. 5

Mode frequency, group velocity, and loss per unit cell of the first even-symmetry waveguide mode as it propagates at wave vectors between Γ and K . The group velocity and loss figures are determined by a polynomial fit of the frequency data.

Fig. 6
Fig. 6

Hexagonal hole lattice in silicon manufactured by 365 nm photolithography and reactive ion etching. The hole diameter was expanded to approximately 760 nm by thermal oxidation and subsequent HF dip etching, thereby reducing the width of the silicon bars between the holes to less than 50 nm .

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