Abstract

We consider the modes of coupled photonic crystal waveguides. We find that the fundamental modes of these structures can be either even or odd, in contrast with the behavior in coupled conventional waveguides, in which the fundamental mode is always even. We explain this finding using an asymptotic model that is valid for long wavelengths.

© 2004 Optical Society of America

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References

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  1. K. Iizuka, Elements of Photonics, Vol. 2 (Wiley, New York, 2002), Chap. 9.
  2. M. Koshiba, J. Lightwave Technol. 19, 1970 (2001).
    [Crossref]
  3. S. Boscolo, M. Midrio, and C. G. Someda, IEEE J. Quantum Electron. 38, 47 (2002).
    [Crossref]
  4. A. Sharkawy, S. Shi, D. W. Prather, and R. A. Soref, Opt. Express 10, 1048 (2002), http://www.opticsexpress.org .
    [Crossref] [PubMed]
  5. L. C. Botten, N. A. Nicorovici, R. C. McPhedran, C. Martijn de Sterke, and A. A. Asatryan, Phys. Rev. E 64, 046603 (2001).
    [Crossref]
  6. M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1980).
  7. L. D. Landau and E. M. Lifshitz, Quantum Mechanics (Non-Relativistic Theory), 3rd ed. (Pergamon, Oxford, 1977), Sec. 21.

2002 (2)

2001 (2)

L. C. Botten, N. A. Nicorovici, R. C. McPhedran, C. Martijn de Sterke, and A. A. Asatryan, Phys. Rev. E 64, 046603 (2001).
[Crossref]

M. Koshiba, J. Lightwave Technol. 19, 1970 (2001).
[Crossref]

Asatryan, A. A.

L. C. Botten, N. A. Nicorovici, R. C. McPhedran, C. Martijn de Sterke, and A. A. Asatryan, Phys. Rev. E 64, 046603 (2001).
[Crossref]

Born, M.

M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1980).

Boscolo, S.

S. Boscolo, M. Midrio, and C. G. Someda, IEEE J. Quantum Electron. 38, 47 (2002).
[Crossref]

Botten, L. C.

L. C. Botten, N. A. Nicorovici, R. C. McPhedran, C. Martijn de Sterke, and A. A. Asatryan, Phys. Rev. E 64, 046603 (2001).
[Crossref]

Iizuka, K.

K. Iizuka, Elements of Photonics, Vol. 2 (Wiley, New York, 2002), Chap. 9.

Koshiba, M.

Landau, L. D.

L. D. Landau and E. M. Lifshitz, Quantum Mechanics (Non-Relativistic Theory), 3rd ed. (Pergamon, Oxford, 1977), Sec. 21.

Lifshitz, E. M.

L. D. Landau and E. M. Lifshitz, Quantum Mechanics (Non-Relativistic Theory), 3rd ed. (Pergamon, Oxford, 1977), Sec. 21.

Martijn de Sterke, C.

L. C. Botten, N. A. Nicorovici, R. C. McPhedran, C. Martijn de Sterke, and A. A. Asatryan, Phys. Rev. E 64, 046603 (2001).
[Crossref]

McPhedran, R. C.

L. C. Botten, N. A. Nicorovici, R. C. McPhedran, C. Martijn de Sterke, and A. A. Asatryan, Phys. Rev. E 64, 046603 (2001).
[Crossref]

Midrio, M.

S. Boscolo, M. Midrio, and C. G. Someda, IEEE J. Quantum Electron. 38, 47 (2002).
[Crossref]

Nicorovici, N. A.

L. C. Botten, N. A. Nicorovici, R. C. McPhedran, C. Martijn de Sterke, and A. A. Asatryan, Phys. Rev. E 64, 046603 (2001).
[Crossref]

Prather, D. W.

Sharkawy, A.

Shi, S.

Someda, C. G.

S. Boscolo, M. Midrio, and C. G. Someda, IEEE J. Quantum Electron. 38, 47 (2002).
[Crossref]

Soref, R. A.

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1980).

IEEE J. Quantum Electron. (1)

S. Boscolo, M. Midrio, and C. G. Someda, IEEE J. Quantum Electron. 38, 47 (2002).
[Crossref]

J. Lightwave Technol. (1)

Opt. Express (1)

Phys. Rev. E (1)

L. C. Botten, N. A. Nicorovici, R. C. McPhedran, C. Martijn de Sterke, and A. A. Asatryan, Phys. Rev. E 64, 046603 (2001).
[Crossref]

Other (3)

M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1980).

L. D. Landau and E. M. Lifshitz, Quantum Mechanics (Non-Relativistic Theory), 3rd ed. (Pergamon, Oxford, 1977), Sec. 21.

K. Iizuka, Elements of Photonics, Vol. 2 (Wiley, New York, 2002), Chap. 9.

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Figures (3)

Fig. 1
Fig. 1

Schematics of the geometries considered: (a) planar waveguide, (b) layered structures, (c) two-dimensional photonic crystal with square lattice. For each geometry, the electric field is orthogonal to the plane, and the mode propagates in the plane.

Fig. 2
Fig. 2

Projected band structure for a two-dimensional bulk photonic crystal with parameters given in the text. The dark-shaded regions indicate bands, the white regions indicate gaps with μ<0, and the light-shaded regions indicate gaps with μ>0. CWM dispersion relations are also given for (solid curves) even and (dashed curves) odd modes.

Fig. 3
Fig. 3

Electric field in a two-dimensional photonic crystal with two coupled waveguides. (a), (b) odd CWM; (c), (d) even CWM. (a), (c) electric field contours; (b) and (d) field profiles through vertical lines in (a) and (c), respectively. The dark regions indicate the cylinders.

Equations (8)

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Ex,y=p=-+χp-1/2f1p- exp-iχpy-y0+iβpx.
f1-=RPf1+,    f1+=RNPf1-+TNPf2+,f2-=TNPf1-+RNPf2+,    f2+=RPF2-.
U=I-RPRNP-1RPTNP,
I-σU=I-RPRNP-1I-RPRN+σTNP.
RN=R-QNRQNI-RQNRQN-1,TN=I-R2QNI-RQNRQN-1,
detI-RPR+σQNI+σRQN-1P=0.
R2P21+σμN/R1+σμNR=1,
χ0h+argR+σμN=mπ.

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