Abstract

We demonstrate that the fundamental mode of the two coupled photonic crystal waveguides (PCWs) can be odd parity in a triangular photonic crystal and their dispersion curves do intersect. Thus, the PCWs are decoupled at the crossing point. By employing the decoupling at the crossing-point frequency and ultra short coupling length for another frequency, we designed a dual-wavelength demultiplexer with a coupling length of only two wavelengths and output power ratio as high as 15 dB. A loop-shape PCW is adapted to eliminate the backward energy flow.

© 2004 Optical Society of America

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Appl. Optics (1)

A. Sharkawy, S. Shi, and D. W. Prather, �??Multichannel wavelength division multiplexing with photonic crystals,�?? Appl. Optics 40, 2247-2252 (2001).
[CrossRef]

Appl. Phys. Lett. (1)

V. N. Astratov, R. M. Stevenson, I. S. Culshaw, D. M. Whittaker, M. S. Skolnick, T. F. Krauss and R. M. De La Rue, �??Heavy photon dispersions in photonic crystal waveguides,�?? Appl. Phys. Lett. 77, 178-180 (2000).
[CrossRef]

IEEE J. Quantum Electron. (3)

K. Hosomi, and T. Katsuyama, �??A dispersion compensator using coupled defects in a photonic crystal,�?? IEEE J. Quantum Electron. 38, 825-829 (2002).
[CrossRef]

S. Boscolo, M. Midrio, C. G. Someda, �??Coupling and decoupling of electromagnetic waves in parallel 2-D photonic crystal waveguides,�?? IEEE J. Quantum Electron. 38, 47-53 (2002).
[CrossRef]

I. Vorobeichik, M. Orenstein, and N. Moiseyev, �??Intermediate-mode-assisted optical directional couplers via embedded periodic structure,�?? IEEE J. Quantum Electron. 34, 1772-1781 (1998).
[CrossRef]

IEEE J. Quantum. Electron. (1)

S. Kuchinsky, V. Y. Golyatin, A. Y. Kutikov, T. P. Pearsall, D. Nedeljkovic, �??Coupling between photonic crystal waveguides,�?? IEEE J. Quantum. Electron. 38, 1349-1352 (2002).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

A. Martinez, F. Cuesta, and J. Marti, �??Ultrashort 2-D photonic crystal directional couplers,�?? IEEE Photon. Technol. Lett. 15, 694-696 (2003).
[CrossRef]

J. Appl. Phys. (1)

R. D. Meade, A. Devenyi, J. D. Joannopoulos, O. L. Alerhand, D. A. Smith, and K. Kash, �??Novel applications of photonic band gap materials: low-loss bends and high Q cavities,�?? J. Appl. Phys. 75, 4753-4755 (1994).
[CrossRef]

J. Lightwave Technol. (1)

J. Opt. Soc. Am. B (2)

Opt. Express (2)

Opt. Lett. (3)

Phys. Rev. B (1)

S. G. Johnson, P. R. Villeneuve, S. Fan, and J. D. Joannopoulos, �??Linear waveguides on photonic-crystal slabs,�?? Phys. Rev. B 62, 8212-8222 (2000).
[CrossRef]

Phys. Rev. Lett. (5)

E. Yablonovitch, �??Inhibited spontaneous emission on solid-state physics and electronics,�?? Phys. Rev. Lett. 58, 2059-2062 (1987).
[CrossRef] [PubMed]

S. John, �??Strong localization of photons on certain disordered dielectric superlattices,�?? Phys. Rev. Lett. 58, 2486-2488 (1987).
[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, 253902-1 (2001).
[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. Bayindir, B. Temelkuran, and E. Ozbay, �??Tight-binding description of the coupled defect modes in the three-dimensional photonic crystals,�?? Phys. Rev. Lett. 84, 2140-2143 (2000).
[CrossRef] [PubMed]

Prog. Quantum Electron. (1)

T. F. Krauss, and R. M. De La Rue, �??Photonic crystals in the optical regime past, present and future,�?? Prog. Quantum Electron. 23, 51-96 (1999).
[CrossRef]

Other (2)

A. Taflove, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Norwood, MA, Artech, 1995).

J. D. Joannopoulos, R. D. Meade and J. N. Winn, Photonic Crystals Molding the Flow of Light (Princeton University Press, Princeton, 1995).

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Figures (4)

Fig. 1.
Fig. 1.

(a) The energy band structures of the extended modes and defect modes of two coupled linear PCWs (I and II). The defect modes of the coupled PCWs are split into two eigenmodes, which cross at the point A. (b) The electric field patterns appear as even parity at the points of e1 and e2, and odd parity at o1 and o2. The poor confinement of the electric field at point o2 is a result of being close to the band edge.

Fig. 2.
Fig. 2.

(a) The plot of the coupling length L as the function of frequency. The L varies rapidly near f A=0.432 (L over 75 Λ is not shown). FDTD simulated electric field maps of the coupled PCWs at f A (b) and f B (=0.361) (c) fed into PCW I. The coupling length of f A is well beyond the simulated extent and that of f B is 4.6 Λ. The field intensity in (c) decreases because part of the power flows backward, as discussed in Section 3.

Fig. 3.
Fig. 3.

FDTD simulated electric field maps of coupled PCWs; a bar state for f A (a) and cross state for f B (b), while both forward and backward couplings happen to f B. As the feeding port of PCW II is removed (c), the wave of f B transfers back to PCW I.

Fig. 4.
Fig. 4.

(a) The loop layout applied to the PCW II for eliminating the backward coupling. The coupled forward and backward waves are in phase at the merging point (marked with the red circle). (b) The coupling efficiency decreases, as the waves are not in phase at the merging point. The frequency is f B.

Tables (1)

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Table 1. Output Power Ratios of Demultiplexers*

Equations (1)

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f = Ω [ 1 + κ cos ( k x Λ ) ] ,

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