Abstract

We present general criteria for crossing perpendicular waveguides with nearly 100% throughput and 0% cross talk. Our design applies even when the waveguide width is of the order of the wavelength. The theoretical basis for this phenomenon is explained in terms of symmetry considerations and resonant tunneling and is then illustrated with numerical simulations for both a two-dimensional photonic crystal and a conventional high-index-contrast waveguide crossing. Cross-talk reduction by up to 8 orders of magnitude is achieved relative to unmodified crossings.

© 1998 Optical Society of America

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References

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  1. K. Aretz and H. Bülow, Electron. Lett. 25, 730 (1989).
    [CrossRef]
  2. M. G. Daly, P. E. Jessop, and D. Yevick, J. Lightwave Technol. 14, 1695 (1996).
    [CrossRef]
  3. H. A. Haus, Waves and Fields in Optoelectronics (Prentice-Hall, Englewood Cliffs, N.J., 1984), Chap. 7.
  4. See, e.g., M. Tinkham, Group Theory and Quantum Mechanics (McGraw-Hill, New York, 1964).
  5. J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, Nature (London) 386, 143 (1997).
    [CrossRef]
  6. P. R. Villeneuve, S. Fan, and J. D. Joannopoulos, Phys. Rev. B 54, 7837 (1996).
    [CrossRef]
  7. See, e.g., K. S. Kunz and R. J. Luebbers, The Finite-Difference Time-Domain Methods (CRC, Boca Raton, Fla., 1993).
  8. S. Fan, J. N. Winn, A. Devenyi, J. C. Chen, R. D. Meade, and J. D. Joannopoulos, J. Opt. Soc. Am. B 12, 1267 (1995).
    [CrossRef]
  9. See, e.g., H. A. Haus and Y. Lai, IEEE J. Quantum Electron. 28, 205 (1992).
    [CrossRef]

1997 (1)

J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, Nature (London) 386, 143 (1997).
[CrossRef]

1996 (2)

P. R. Villeneuve, S. Fan, and J. D. Joannopoulos, Phys. Rev. B 54, 7837 (1996).
[CrossRef]

M. G. Daly, P. E. Jessop, and D. Yevick, J. Lightwave Technol. 14, 1695 (1996).
[CrossRef]

1995 (1)

1992 (1)

See, e.g., H. A. Haus and Y. Lai, IEEE J. Quantum Electron. 28, 205 (1992).
[CrossRef]

1989 (1)

K. Aretz and H. Bülow, Electron. Lett. 25, 730 (1989).
[CrossRef]

Aretz, K.

K. Aretz and H. Bülow, Electron. Lett. 25, 730 (1989).
[CrossRef]

Bülow, H.

K. Aretz and H. Bülow, Electron. Lett. 25, 730 (1989).
[CrossRef]

Chen, J. C.

Daly, M. G.

M. G. Daly, P. E. Jessop, and D. Yevick, J. Lightwave Technol. 14, 1695 (1996).
[CrossRef]

Devenyi, A.

Fan, S.

J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, Nature (London) 386, 143 (1997).
[CrossRef]

P. R. Villeneuve, S. Fan, and J. D. Joannopoulos, Phys. Rev. B 54, 7837 (1996).
[CrossRef]

S. Fan, J. N. Winn, A. Devenyi, J. C. Chen, R. D. Meade, and J. D. Joannopoulos, J. Opt. Soc. Am. B 12, 1267 (1995).
[CrossRef]

Haus, H. A.

See, e.g., H. A. Haus and Y. Lai, IEEE J. Quantum Electron. 28, 205 (1992).
[CrossRef]

H. A. Haus, Waves and Fields in Optoelectronics (Prentice-Hall, Englewood Cliffs, N.J., 1984), Chap. 7.

Jessop, P. E.

M. G. Daly, P. E. Jessop, and D. Yevick, J. Lightwave Technol. 14, 1695 (1996).
[CrossRef]

Joannopoulos, J. D.

J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, Nature (London) 386, 143 (1997).
[CrossRef]

P. R. Villeneuve, S. Fan, and J. D. Joannopoulos, Phys. Rev. B 54, 7837 (1996).
[CrossRef]

S. Fan, J. N. Winn, A. Devenyi, J. C. Chen, R. D. Meade, and J. D. Joannopoulos, J. Opt. Soc. Am. B 12, 1267 (1995).
[CrossRef]

Kunz, K. S.

See, e.g., K. S. Kunz and R. J. Luebbers, The Finite-Difference Time-Domain Methods (CRC, Boca Raton, Fla., 1993).

Lai, Y.

See, e.g., H. A. Haus and Y. Lai, IEEE J. Quantum Electron. 28, 205 (1992).
[CrossRef]

Luebbers, R. J.

See, e.g., K. S. Kunz and R. J. Luebbers, The Finite-Difference Time-Domain Methods (CRC, Boca Raton, Fla., 1993).

Meade, R. D.

Tinkham, M.

See, e.g., M. Tinkham, Group Theory and Quantum Mechanics (McGraw-Hill, New York, 1964).

Villeneuve, P. R.

J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, Nature (London) 386, 143 (1997).
[CrossRef]

P. R. Villeneuve, S. Fan, and J. D. Joannopoulos, Phys. Rev. B 54, 7837 (1996).
[CrossRef]

Winn, J. N.

Yevick, D.

M. G. Daly, P. E. Jessop, and D. Yevick, J. Lightwave Technol. 14, 1695 (1996).
[CrossRef]

Electron. Lett. (1)

K. Aretz and H. Bülow, Electron. Lett. 25, 730 (1989).
[CrossRef]

IEEE J. Quantum Electron. (1)

See, e.g., H. A. Haus and Y. Lai, IEEE J. Quantum Electron. 28, 205 (1992).
[CrossRef]

J. Lightwave Technol. (1)

M. G. Daly, P. E. Jessop, and D. Yevick, J. Lightwave Technol. 14, 1695 (1996).
[CrossRef]

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

Nature (London) (1)

J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, Nature (London) 386, 143 (1997).
[CrossRef]

Phys. Rev. B (1)

P. R. Villeneuve, S. Fan, and J. D. Joannopoulos, Phys. Rev. B 54, 7837 (1996).
[CrossRef]

Other (3)

See, e.g., K. S. Kunz and R. J. Luebbers, The Finite-Difference Time-Domain Methods (CRC, Boca Raton, Fla., 1993).

H. A. Haus, Waves and Fields in Optoelectronics (Prentice-Hall, Englewood Cliffs, N.J., 1984), Chap. 7.

See, e.g., M. Tinkham, Group Theory and Quantum Mechanics (McGraw-Hill, New York, 1964).

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Figures (5)

Fig. 1
Fig. 1

Abstract diagram of symmetry requirements for waveguide crossing, showing waveguide mode profiles and resonant-cavity mode contours. By symmetry, the solid-line modes cannot couple with the dashed-line modes and vice versa.

Fig. 2
Fig. 2

Waveguide intersections in a two-dimensional photonic crystal consisting of a square lattice of dielectric rods in air.

Fig. 3
Fig. 3

TM transmission spectra for the four intersections shown in Fig. 2: (a) throughput from the input port to the output port and (b) cross talk from the input port to one of the transverse ports.

Fig. 4
Fig. 4

Intersection of two-dimensional, high-index-contrast waveguides in air, both (a) without holes and (b) with air holes added to create a resonant cavity by use of a photonic bandgap.

Fig. 5
Fig. 5

TE transmission spectra for the two intersections shown in Fig. 4.

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