Abstract

Enhancement of resonant tunnelling of a wide beam through vertical subwavelength slow-light photonic-crystal waveguides (SPCWs) is considered. An assistant horizontal SPCW with a thin side wall, whose guided modes have small propagation constants, is used as an input coupler for the vertical SPCW, and the two SPCWs form a compact composite structure to enhance drastically the resonant tunnelling. An incident wide beam can excite strongly the guided modes of the horizontal SPCW, and then resonantly tunnels through the vertical SPCW efficiently. To further improve the resonant tunnelling of a wide beam, a periodic array of vertical SPCWs (with a horizontal SPCW as an input coupler) is also investigated. With this periodic structure, a wide beam can be transmitted nearly completely. When a wide beam tunnels through the vertical SPCWs efficiently, the excited fields inside the SPCWs are very strong.

© 2008 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
  16. J. A. Porto, F. J. García-Vidal, and J. B. Pendry, "Transmission Resonances on Metallic Gratings with Very Narrow Slits," Phys. Rev. Lett. 83, 2845-2848 (1999).
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2008 (2)

2007 (4)

L. Yang, A. V. Lavrinenko, L. H. Frandsen, P. I. Borel, A. Tetu, and J. Fage-Pedersen, "Topology optimisation of slow light coupling to photonic crystal waveguides," Electron. Lett. 43, 923-924 (2007).
[CrossRef]

J. P. Hugonin, P. Lalanne, T. P. White, and T. F. Krauss, "Coupling into slow-mode photonic crystal waveguides," Opt. Lett. 32, 2638-2640 (2007).
[CrossRef] [PubMed]

P. Pottier, M. Gnan, and R. M. De La Rue, "Efficient coupling into slow-light photonic crystal channel guides using photonic crystal tapers," Opt. Express 15, 6569-6575 (2007).
[CrossRef] [PubMed]

T. F. Krauss, "Slow light in photonic crystal waveguides," J. Phys. D: Appl. Phys. 40, 2666-2670 (2007).
[CrossRef]

2006 (3)

Y. A. Vlasov and S. J. McNab, "Coupling into the slow light mode in slab-type photonic crystal waveguides," Opt. Lett. 31, 50-52 (2006).
[CrossRef] [PubMed]

K. Kiyota, T. Kise, N. Yokouchi, T. Ide, and T. Baba, "Various low group velocity effects in photonic crystal line defect waveguides and their demonstration by laser oscillation," Appl. Phys. Lett. 88, 201904 (2006).
[CrossRef]

R. S. Jacobsen,  et al., "Strained silicon as a new electro-optic material," Nature 441, 199-202 (2006).
[CrossRef] [PubMed]

2005 (1)

Y. A. Vlasov, M. O’Boyle, H. F. Hamann, and S. J. McNab, "Active control of slow light on a chip with photonic crystal waveguides," Nature 438, 65-69 (2005).
[CrossRef] [PubMed]

2004 (2)

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

A. Y. Petrov and M. Eich, "Zero dispersion at small group velocities in photonic crystal waveguides," Appl. Phys. Lett. 85, 4866-4868 (2004).
[CrossRef]

2002 (1)

2001 (1)

1999 (1)

J. A. Porto, F. J. García-Vidal, and J. B. Pendry, "Transmission Resonances on Metallic Gratings with Very Narrow Slits," Phys. Rev. Lett. 83, 2845-2848 (1999).
[CrossRef]

1998 (1)

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, "Extraordinary optical transmission through sub-wavelength hole arrays," Nature 391, 667-669 (1998).
[CrossRef]

Baba, T.

T. Baba, "Slow light in photonic crystals," Nature Photon. 2, 465-473 (2008).
[CrossRef]

K. Kiyota, T. Kise, N. Yokouchi, T. Ide, and T. Baba, "Various low group velocity effects in photonic crystal line defect waveguides and their demonstration by laser oscillation," Appl. Phys. Lett. 88, 201904 (2006).
[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]

Beggs, D. M.

Borel, P. I.

L. Yang, A. V. Lavrinenko, L. H. Frandsen, P. I. Borel, A. Tetu, and J. Fage-Pedersen, "Topology optimisation of slow light coupling to photonic crystal waveguides," Electron. Lett. 43, 923-924 (2007).
[CrossRef]

De La Rue, R. M.

Ebbesen, T. W.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, "Extraordinary optical transmission through sub-wavelength hole arrays," Nature 391, 667-669 (1998).
[CrossRef]

Eich, M.

A. Y. Petrov and M. Eich, "Zero dispersion at small group velocities in photonic crystal waveguides," Appl. Phys. Lett. 85, 4866-4868 (2004).
[CrossRef]

Fage-Pedersen, J.

L. Yang, A. V. Lavrinenko, L. H. Frandsen, P. I. Borel, A. Tetu, and J. Fage-Pedersen, "Topology optimisation of slow light coupling to photonic crystal waveguides," Electron. Lett. 43, 923-924 (2007).
[CrossRef]

Fan, S. H.

Frandsen, L. H.

L. Yang, A. V. Lavrinenko, L. H. Frandsen, P. I. Borel, A. Tetu, and J. Fage-Pedersen, "Topology optimisation of slow light coupling to photonic crystal waveguides," Electron. Lett. 43, 923-924 (2007).
[CrossRef]

García-Vidal, F. J.

J. A. Porto, F. J. García-Vidal, and J. B. Pendry, "Transmission Resonances on Metallic Gratings with Very Narrow Slits," Phys. Rev. Lett. 83, 2845-2848 (1999).
[CrossRef]

Ghaemi, H. F.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, "Extraordinary optical transmission through sub-wavelength hole arrays," Nature 391, 667-669 (1998).
[CrossRef]

Gnan, M.

Hamann, H. F.

Y. A. Vlasov, M. O’Boyle, H. F. Hamann, and S. J. McNab, "Active control of slow light on a chip with photonic crystal waveguides," Nature 438, 65-69 (2005).
[CrossRef] [PubMed]

Hugonin, J. P.

Ibanescu, M.

Ide, T.

K. Kiyota, T. Kise, N. Yokouchi, T. Ide, and T. Baba, "Various low group velocity effects in photonic crystal line defect waveguides and their demonstration by laser oscillation," Appl. Phys. Lett. 88, 201904 (2006).
[CrossRef]

Ippen, E.

Jacobsen, R. S.

R. S. Jacobsen,  et al., "Strained silicon as a new electro-optic material," Nature 441, 199-202 (2006).
[CrossRef] [PubMed]

Joannopoulos, J.

Joannopoulos, J. D.

Johnson, S.

Johnson, S. G.

Kise, T.

K. Kiyota, T. Kise, N. Yokouchi, T. Ide, and T. Baba, "Various low group velocity effects in photonic crystal line defect waveguides and their demonstration by laser oscillation," Appl. Phys. Lett. 88, 201904 (2006).
[CrossRef]

Kiyota, K.

K. Kiyota, T. Kise, N. Yokouchi, T. Ide, and T. Baba, "Various low group velocity effects in photonic crystal line defect waveguides and their demonstration by laser oscillation," Appl. Phys. Lett. 88, 201904 (2006).
[CrossRef]

Krauss, T. F.

Lalanne, P.

Lavrinenko, A. V.

L. Yang, A. V. Lavrinenko, L. H. Frandsen, P. I. Borel, A. Tetu, and J. Fage-Pedersen, "Topology optimisation of slow light coupling to photonic crystal waveguides," Electron. Lett. 43, 923-924 (2007).
[CrossRef]

Lezec, H. J.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, "Extraordinary optical transmission through sub-wavelength hole arrays," Nature 391, 667-669 (1998).
[CrossRef]

McNab, S. J.

Y. A. Vlasov and S. J. McNab, "Coupling into the slow light mode in slab-type photonic crystal waveguides," Opt. Lett. 31, 50-52 (2006).
[CrossRef] [PubMed]

Y. A. Vlasov, M. O’Boyle, H. F. Hamann, and S. J. McNab, "Active control of slow light on a chip with photonic crystal waveguides," Nature 438, 65-69 (2005).
[CrossRef] [PubMed]

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]

O’Boyle, M.

Y. A. Vlasov, M. O’Boyle, H. F. Hamann, and S. J. McNab, "Active control of slow light on a chip with photonic crystal waveguides," Nature 438, 65-69 (2005).
[CrossRef] [PubMed]

O’Faolain, L.

Pendry, J. B.

J. A. Porto, F. J. García-Vidal, and J. B. Pendry, "Transmission Resonances on Metallic Gratings with Very Narrow Slits," Phys. Rev. Lett. 83, 2845-2848 (1999).
[CrossRef]

Petrov, A. Y.

A. Y. Petrov and M. Eich, "Zero dispersion at small group velocities in photonic crystal waveguides," Appl. Phys. Lett. 85, 4866-4868 (2004).
[CrossRef]

Porto, J. A.

J. A. Porto, F. J. García-Vidal, and J. B. Pendry, "Transmission Resonances on Metallic Gratings with Very Narrow Slits," Phys. Rev. Lett. 83, 2845-2848 (1999).
[CrossRef]

Pottier, P.

Soljacic, M.

Tetu, A.

L. Yang, A. V. Lavrinenko, L. H. Frandsen, P. I. Borel, A. Tetu, and J. Fage-Pedersen, "Topology optimisation of slow light coupling to photonic crystal waveguides," Electron. Lett. 43, 923-924 (2007).
[CrossRef]

Thio, T.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, "Extraordinary optical transmission through sub-wavelength hole arrays," Nature 391, 667-669 (1998).
[CrossRef]

Vlasov, Y. A.

Y. A. Vlasov and S. J. McNab, "Coupling into the slow light mode in slab-type photonic crystal waveguides," Opt. Lett. 31, 50-52 (2006).
[CrossRef] [PubMed]

Y. A. Vlasov, M. O’Boyle, H. F. Hamann, and S. J. McNab, "Active control of slow light on a chip with photonic crystal waveguides," Nature 438, 65-69 (2005).
[CrossRef] [PubMed]

White, T. P.

Wolff, P. A.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, "Extraordinary optical transmission through sub-wavelength hole arrays," Nature 391, 667-669 (1998).
[CrossRef]

Yang, L.

L. Yang, A. V. Lavrinenko, L. H. Frandsen, P. I. Borel, A. Tetu, and J. Fage-Pedersen, "Topology optimisation of slow light coupling to photonic crystal waveguides," Electron. Lett. 43, 923-924 (2007).
[CrossRef]

Yokouchi, N.

K. Kiyota, T. Kise, N. Yokouchi, T. Ide, and T. Baba, "Various low group velocity effects in photonic crystal line defect waveguides and their demonstration by laser oscillation," Appl. Phys. Lett. 88, 201904 (2006).
[CrossRef]

Appl. Phys. Lett. (3)

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

A. Y. Petrov and M. Eich, "Zero dispersion at small group velocities in photonic crystal waveguides," Appl. Phys. Lett. 85, 4866-4868 (2004).
[CrossRef]

K. Kiyota, T. Kise, N. Yokouchi, T. Ide, and T. Baba, "Various low group velocity effects in photonic crystal line defect waveguides and their demonstration by laser oscillation," Appl. Phys. Lett. 88, 201904 (2006).
[CrossRef]

Electron. Lett. (1)

L. Yang, A. V. Lavrinenko, L. H. Frandsen, P. I. Borel, A. Tetu, and J. Fage-Pedersen, "Topology optimisation of slow light coupling to photonic crystal waveguides," Electron. Lett. 43, 923-924 (2007).
[CrossRef]

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

J. Phys. D: Appl. Phys. (1)

T. F. Krauss, "Slow light in photonic crystal waveguides," J. Phys. D: Appl. Phys. 40, 2666-2670 (2007).
[CrossRef]

Nature (3)

R. S. Jacobsen,  et al., "Strained silicon as a new electro-optic material," Nature 441, 199-202 (2006).
[CrossRef] [PubMed]

Y. A. Vlasov, M. O’Boyle, H. F. Hamann, and S. J. McNab, "Active control of slow light on a chip with photonic crystal waveguides," Nature 438, 65-69 (2005).
[CrossRef] [PubMed]

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, "Extraordinary optical transmission through sub-wavelength hole arrays," Nature 391, 667-669 (1998).
[CrossRef]

Nature Photon. (1)

T. Baba, "Slow light in photonic crystals," Nature Photon. 2, 465-473 (2008).
[CrossRef]

Opt. Express (2)

Opt. Lett. (3)

Phys. Rev. Lett. (1)

J. A. Porto, F. J. García-Vidal, and J. B. Pendry, "Transmission Resonances on Metallic Gratings with Very Narrow Slits," Phys. Rev. Lett. 83, 2845-2848 (1999).
[CrossRef]

Other (2)

A. Taflove and S. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, Norwood, 2000).

K. Sakoda, Optical Properties of Photonic Crystals (Springer, Berlin, 2001).

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Figures (4)

Fig. 1.
Fig. 1.

(a) Vertical waveguide formed by removing a line of cylinders in a square-lattice PC. The cylinders are of ε=12.96 and r=0.3a. (b) Dispersion curve of the waveguide. (c) RFs and Q values of the FP resonant modes for several different values of waveguide length L. Marks “+” represent the RFs and marks “.” represent the Q values. (d) Transmissivity t when a down-going Gaussian beam is normally incident on the top of the waveguide with L=20a. Curve 1 is for a beam with waist width w=13a and curve 2 for w=2a.

Fig. 2.
Fig. 2.

(a) Asymmetric (along the y axis) SPCW formed by keeping only two lines of dielectric cylinders for the top side wall of the waveguide. (b) Distribution of |E z | when a down-going plane wave is normally incident on the asymmetric SPCW at ω=0.26324(2πc/a). The solid circles represent the cylinders. |E z | is normalized by the amplitude of the plane wave. The arrow indicates the propagation direction of the incident wave.

Fig. 3.
Fig. 3.

(a) A horizontal asymmetric SPCW is put in front of a vertical SPCW as an input coupler. (b) Transmissivity t when a down-going beam is normally incident on the top of the composite structure. The length of the horizontal SPCW is 19a and that of the vertical SPCW is 20a. Curve 1 is for waist width w=13a and curve 2 for w=2a. (c) Distribution of |E z | when a down-going beam with w=13a is normally incident on the composite structure used in (b) at RF ω=0.26329(2πc/a). |E z | is normalized by the amplitude of the beam.

Fig. 4.
Fig. 4.

(a) Periodic array of vertical SPCWs with an infinitely long horizontal asymmetric SPCW as an input coupler. (b) Transmissivity t when a down-going plane wave is normally incident. Curve 1 is for the periodic composite structure in (a) with the length of the vertical SPCWs equal to 20a and the interval between two adjacent vertical SPCWs equal to 9a. Curve 2 is for removing the top two lines of cylinders from the structure. (c) Distribution of |E z | in a unit cell when a down-going plane wave is normally incident on the structure corresponding to curve 1 in (b) at RF ω=0.26311(2πc/a). |E z | is normalized by the amplitude of the plane wave.

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