Abstract

We describe a two-step-size tapered structure with one defect pair that can markedly enhance the coupling efficiency at the entrance and exit terminals of a planar photonic crystal (PPC) waveguide. PPC waveguides are composed of circular dielectric rods set in two-dimensional square lattices. On the basis of our simulations, we found that the optimized scheme maximizes the power transmission above 90% at a wavelength of 1.55 μm. Besides, one can control the central frequency for optical communications by determining this defect configuration in an optimization procedure. Moreover, by properly adjusting the defect radii in PPC tapers, one can use the PPC circuit as a good reflector.

© 2004 Optical Society of America

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  1. T. F. Krauss, R. M. De La Rue, S. Brand, “Two-dimensional photonic-bandgap structures operating at near-infrared wavelength,” Nature 383, 699–702 (1996).
    [CrossRef]
  2. L.-L. Lin, Z.-Y. Li, “Sensitivity to termination morphology of light coupling in photonic-crystal waveguides,” Phys. Rev. B 69, 193103 (2004).
    [CrossRef]
  3. M. E. Potter, R. W. Ziolkowski, “Two compact structures for perpendicular coupling of optical signals between dielectric and photonic crystal waveguides,” Opt. Express 10, 691 (2002), http://www.opticsexpress.org .
    [CrossRef] [PubMed]
  4. Y. Xu, R. Lee, A. Yariv, “Adiabatic coupling between conventional dielectric waveguides and waveguides with discrete translational symmetry,” Opt. Lett. 25, 755–757 (2000).
    [CrossRef]
  5. A. Mekis, J. D. Joannopoulos, “Tapered couplers for efficient interfacing between dielectric and photonic crystal waveguides,” IEEE J. Lightwave Technol. 19, 861–865 (2001).
    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  12. See http://ab-initio.mit.ed/mpb .
  13. S. G. Johnson, J. D. Joannopoulos, “Block-iterative frequency-domain methods for Maxwell’s equations in a plane-wave basis,” Opt. Express 8, 173–190 (2001), http://www.opticsexpress.org .
    [CrossRef] [PubMed]
  14. M. Bayindir, B. Temelkuran, E. Ozbay, “Tight-binding description of the coupled defect modes in three-dimensional photonic crystals,” Phys. Rev. Lett. 84, 2140–2143 (2000).
    [CrossRef] [PubMed]
  15. T. J. Karle, D. H. Brown, R. Wilson, M. Steer, T. E. Karuss, “Photonic crystal light deflection devices using the superprism effect,” IEEE J. Sel. Top. Quantum Electron. 8, 909–918 (2002).
    [CrossRef]
  16. Y. Xu, R. Lee, A. Yariv, “Adiabatic coupling between conventional dielectric waveguides and waveguides with discrete translational symmetry,” Opt. Lett. 25, 755–757 (2000).
    [CrossRef]
  17. A. Taflove, Computational Electrodynamics (Artech House, Norwood, Mass., 1995).
  18. J. P. Berenger, “A perfectly matched layer for the absorbing boundary condition,” J. Comput. Phys. 114, 185–200 (1994).
    [CrossRef]

2004 (1)

L.-L. Lin, Z.-Y. Li, “Sensitivity to termination morphology of light coupling in photonic-crystal waveguides,” Phys. Rev. B 69, 193103 (2004).
[CrossRef]

2003 (1)

2002 (4)

P. Sanchis, J. Marti, A. Garcia, A. Martinez, J. Blasco, “High efficiency coupling technique for planar photonic crystal waveguides,” Electron. Lett. 38, 961–962 (2002).
[CrossRef]

P. Sanchis, J. Marti, J. Blasco, A. Martinez, A. Garcia, “Mode matching technique for highly efficient coupling between dielectric waveguides and planar photonic crystal circuits,” Opt. Express 10, 1391–1397 (2002), http://www.opticsexpress.org .
[CrossRef] [PubMed]

M. E. Potter, R. W. Ziolkowski, “Two compact structures for perpendicular coupling of optical signals between dielectric and photonic crystal waveguides,” Opt. Express 10, 691 (2002), http://www.opticsexpress.org .
[CrossRef] [PubMed]

T. J. Karle, D. H. Brown, R. Wilson, M. Steer, T. E. Karuss, “Photonic crystal light deflection devices using the superprism effect,” IEEE J. Sel. Top. Quantum Electron. 8, 909–918 (2002).
[CrossRef]

2001 (3)

2000 (3)

1998 (1)

S.-Y. Lin, E. Chow, V. Hietala, P. R. Villeneuve, J. D. Joannopoulos, “Experimental demonstration of guiding and bending of electromagnetic waves in a photonic crystal,” Science 282, 274–276 (1998).
[CrossRef] [PubMed]

1996 (2)

T. F. Krauss, R. M. De La Rue, S. Brand, “Two-dimensional photonic-bandgap structures operating at near-infrared wavelength,” Nature 383, 699–702 (1996).
[CrossRef]

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

1994 (1)

J. P. Berenger, “A perfectly matched layer for the absorbing boundary condition,” J. Comput. Phys. 114, 185–200 (1994).
[CrossRef]

Bayindir, M.

M. Bayindir, B. Temelkuran, E. Ozbay, “Tight-binding description of the coupled defect modes in three-dimensional photonic crystals,” Phys. Rev. Lett. 84, 2140–2143 (2000).
[CrossRef] [PubMed]

Berenger, J. P.

J. P. Berenger, “A perfectly matched layer for the absorbing boundary condition,” J. Comput. Phys. 114, 185–200 (1994).
[CrossRef]

Blasco, J.

Brand, S.

T. F. Krauss, R. M. De La Rue, S. Brand, “Two-dimensional photonic-bandgap structures operating at near-infrared wavelength,” Nature 383, 699–702 (1996).
[CrossRef]

Brown, D. H.

T. J. Karle, D. H. Brown, R. Wilson, M. Steer, T. E. Karuss, “Photonic crystal light deflection devices using the superprism effect,” IEEE J. Sel. Top. Quantum Electron. 8, 909–918 (2002).
[CrossRef]

Cai, J.

Chen, J. C.

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

Chow, E.

S.-Y. Lin, E. Chow, V. Hietala, P. R. Villeneuve, J. D. Joannopoulos, “Experimental demonstration of guiding and bending of electromagnetic waves in a photonic crystal,” Science 282, 274–276 (1998).
[CrossRef] [PubMed]

De La Rue, R. M.

T. F. Krauss, R. M. De La Rue, S. Brand, “Two-dimensional photonic-bandgap structures operating at near-infrared wavelength,” Nature 383, 699–702 (1996).
[CrossRef]

Fan, S.

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

Forchel, A.

Garcia, A.

Happ, T. D.

Hietala, V.

S.-Y. Lin, E. Chow, V. Hietala, P. R. Villeneuve, J. D. Joannopoulos, “Experimental demonstration of guiding and bending of electromagnetic waves in a photonic crystal,” Science 282, 274–276 (1998).
[CrossRef] [PubMed]

Jiang, J.

Joannopoulos, J. D.

S. G. Johnson, J. D. Joannopoulos, “Block-iterative frequency-domain methods for Maxwell’s equations in a plane-wave basis,” Opt. Express 8, 173–190 (2001), http://www.opticsexpress.org .
[CrossRef] [PubMed]

A. Mekis, J. D. Joannopoulos, “Tapered couplers for efficient interfacing between dielectric and photonic crystal waveguides,” IEEE J. Lightwave Technol. 19, 861–865 (2001).
[CrossRef]

S.-Y. Lin, E. Chow, V. Hietala, P. R. Villeneuve, J. D. Joannopoulos, “Experimental demonstration of guiding and bending of electromagnetic waves in a photonic crystal,” Science 282, 274–276 (1998).
[CrossRef] [PubMed]

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

Johnson, S. G.

Kamp, M.

Karle, T. J.

T. J. Karle, D. H. Brown, R. Wilson, M. Steer, T. E. Karuss, “Photonic crystal light deflection devices using the superprism effect,” IEEE J. Sel. Top. Quantum Electron. 8, 909–918 (2002).
[CrossRef]

Karuss, T. E.

T. J. Karle, D. H. Brown, R. Wilson, M. Steer, T. E. Karuss, “Photonic crystal light deflection devices using the superprism effect,” IEEE J. Sel. Top. Quantum Electron. 8, 909–918 (2002).
[CrossRef]

Krauss, T. F.

T. F. Krauss, R. M. De La Rue, S. Brand, “Two-dimensional photonic-bandgap structures operating at near-infrared wavelength,” Nature 383, 699–702 (1996).
[CrossRef]

Kurland, I.

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

Lee, R.

Li, L.

Li, Z.-Y.

L.-L. Lin, Z.-Y. Li, “Sensitivity to termination morphology of light coupling in photonic-crystal waveguides,” Phys. Rev. B 69, 193103 (2004).
[CrossRef]

Lin, L.-L.

L.-L. Lin, Z.-Y. Li, “Sensitivity to termination morphology of light coupling in photonic-crystal waveguides,” Phys. Rev. B 69, 193103 (2004).
[CrossRef]

Lin, S.-Y.

S.-Y. Lin, E. Chow, V. Hietala, P. R. Villeneuve, J. D. Joannopoulos, “Experimental demonstration of guiding and bending of electromagnetic waves in a photonic crystal,” Science 282, 274–276 (1998).
[CrossRef] [PubMed]

Marti, J.

Martinez, A.

Mekis, A.

A. Mekis, J. D. Joannopoulos, “Tapered couplers for efficient interfacing between dielectric and photonic crystal waveguides,” IEEE J. Lightwave Technol. 19, 861–865 (2001).
[CrossRef]

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

Nordin, G. P.

Ozbay, E.

M. Bayindir, B. Temelkuran, E. Ozbay, “Tight-binding description of the coupled defect modes in three-dimensional photonic crystals,” Phys. Rev. Lett. 84, 2140–2143 (2000).
[CrossRef] [PubMed]

Potter, M. E.

Sanchis, P.

Steer, M.

T. J. Karle, D. H. Brown, R. Wilson, M. Steer, T. E. Karuss, “Photonic crystal light deflection devices using the superprism effect,” IEEE J. Sel. Top. Quantum Electron. 8, 909–918 (2002).
[CrossRef]

Taflove, A.

A. Taflove, Computational Electrodynamics (Artech House, Norwood, Mass., 1995).

Temelkuran, B.

M. Bayindir, B. Temelkuran, E. Ozbay, “Tight-binding description of the coupled defect modes in three-dimensional photonic crystals,” Phys. Rev. Lett. 84, 2140–2143 (2000).
[CrossRef] [PubMed]

Villeneuve, P. R.

S.-Y. Lin, E. Chow, V. Hietala, P. R. Villeneuve, J. D. Joannopoulos, “Experimental demonstration of guiding and bending of electromagnetic waves in a photonic crystal,” Science 282, 274–276 (1998).
[CrossRef] [PubMed]

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

Wilson, R.

T. J. Karle, D. H. Brown, R. Wilson, M. Steer, T. E. Karuss, “Photonic crystal light deflection devices using the superprism effect,” IEEE J. Sel. Top. Quantum Electron. 8, 909–918 (2002).
[CrossRef]

Xu, Y.

Yariv, A.

Ziolkowski, R. W.

Electron. Lett. (1)

P. Sanchis, J. Marti, A. Garcia, A. Martinez, J. Blasco, “High efficiency coupling technique for planar photonic crystal waveguides,” Electron. Lett. 38, 961–962 (2002).
[CrossRef]

IEEE J. Lightwave Technol. (1)

A. Mekis, J. D. Joannopoulos, “Tapered couplers for efficient interfacing between dielectric and photonic crystal waveguides,” IEEE J. Lightwave Technol. 19, 861–865 (2001).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

T. J. Karle, D. H. Brown, R. Wilson, M. Steer, T. E. Karuss, “Photonic crystal light deflection devices using the superprism effect,” IEEE J. Sel. Top. Quantum Electron. 8, 909–918 (2002).
[CrossRef]

J. Comput. Phys. (1)

J. P. Berenger, “A perfectly matched layer for the absorbing boundary condition,” J. Comput. Phys. 114, 185–200 (1994).
[CrossRef]

Nature (1)

T. F. Krauss, R. M. De La Rue, S. Brand, “Two-dimensional photonic-bandgap structures operating at near-infrared wavelength,” Nature 383, 699–702 (1996).
[CrossRef]

Opt. Express (3)

Opt. Lett. (4)

Phys. Rev. B (1)

L.-L. Lin, Z.-Y. Li, “Sensitivity to termination morphology of light coupling in photonic-crystal waveguides,” Phys. Rev. B 69, 193103 (2004).
[CrossRef]

Phys. Rev. Lett. (2)

M. Bayindir, B. Temelkuran, E. Ozbay, “Tight-binding description of the coupled defect modes in three-dimensional photonic crystals,” Phys. Rev. Lett. 84, 2140–2143 (2000).
[CrossRef] [PubMed]

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

Science (1)

S.-Y. Lin, E. Chow, V. Hietala, P. R. Villeneuve, J. D. Joannopoulos, “Experimental demonstration of guiding and bending of electromagnetic waves in a photonic crystal,” Science 282, 274–276 (1998).
[CrossRef] [PubMed]

Other (2)

See http://ab-initio.mit.ed/mpb .

A. Taflove, Computational Electrodynamics (Artech House, Norwood, Mass., 1995).

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Figures (7)

Fig. 1
Fig. 1

Schematic view of the structures considered. A 2.4-μm-wide-4a-long two-step-size lattice constant PPC taper (where a is the lattice constant) with a radius of defect configuration is introduced into a PPC taper employed to couple light both into and out of a finite-length (15 rows) PPC waveguide from a SWG. The optical power transmitted through the PPC waveguide is measured with two power monitors, one placed inside the waveguide at point A and the other at the output end at point B.

Fig. 2
Fig. 2

Dispersion relations for the TM band structures for three (W1, W3 and W5) PPC waveguides in a 2-D square array of dielectric rods of lattice constant a surrounded by a homogeneous dielectric medium, where W1 (W3, W5) is created by removal of one (three, five) rod(s) of the original PPC waveguide. The three modes A, B, and C (arrows) indicate guide modes W1, W3, and W5, respectively.

Fig. 3
Fig. 3

Normalized transmission spectra as a function of w/a for a wavelength of incident light that corresponds to λ = a/0.3 = 1.55 μm, where a = 0.465 μm, for four cases: (1) a butt-coupled structure; (2) a conventional PPC taper; (3) a two-step-size lattice constant PPC taper without defects; and (4) the same as case (3), except with a defect rod, where the defect radius is r = 0.3 μm and defect pairs are located at (0, -9.7a) and (0, +9.7a). The transmitted field is measured at the output end of the SWG (point B) by a power monitor covering the exit of the PPC waveguide as shown in Fig. 1.

Fig. 4
Fig. 4

Normalized transmission spectra as a function of r/a for a wavelength of incident light that corresponds to λ = a/0.3 = 1.55 μm, for SWG width w = 2.4 μm. The defect pairs are located at (0, -9.7a) and (0, +9.7a). The optical power transmitted through the PPC waveguide is measured with two power monitors, one at the exit terminal of the PPC waveguide (point A) and other at the output end of the SWG (point B), as shown in Fig. 1, where a denotes the lattice constant and λ is the wavelength of light in vacuum.

Fig. 5
Fig. 5

Normalized transmitted power obtained as a function of z/a at points A and B for a wavelength of incident light corresponding to λ = a/0.3 = 1.55 μm, for SWG width u = 2.4 μm, defect radius r = 0.289 μm, and defect position z.

Fig. 6
Fig. 6

Steady state of the electric field (E y ) for input-output coupling (a) with the conventional PPC tapers without defects and (b) with two-step-size PPC tapers with optimum defects (w = 2.4 μm, r = 0.289 μm, and z opt = 10.4a). The wavelength of the incident light corresponds to λ = a/0.3 = 1.55 μm. The size of each image plane displayed is 30 μm × 10 μm.

Fig. 7
Fig. 7

Normalized transmission spectra of a 15-row PPC waveguide coupled to the entrance and exit terminals relative to a/λ for (1) a 0.5-μm width, two-step-size lattice constant PPC taper with a defect (a/λ = 0.3), (2) a 2.4 μm-width, two-step-size lattice constant PPC taper without a defect (a/λ = 0.3), (3) the same as case (2) except with a defect, (4) the same as case (3) except that a/λ = 0.289, and (5) the same as case (3) except that a/λ = 0.306.

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