Abstract

We investigate the efficiency of transmission through photonic crystal Y junctions and show the importance of matching mode symmetries. Furthermore, we show that by adding tuning holes to the input waveguide it is possible to achieve almost perfect impedance matching, leading ideally to unitary transmission through the junction. The model system is based on a triangular photonic lattice of holes in dielectrics to reflect experimental reality.

© 2002 Optical Society of America

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References

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  1. J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, Nature 387, 143 (1997).
    [CrossRef]
  2. C. J. M. Smith, H. Benisty, S. Olivier, M. Rattier, C. Weisbuch, T. F. Krauss, R. M. De La Rue, R. Houdré, and U. Oesterle, Appl. Phys. Lett. 77, 2813 (2000).
    [CrossRef]
  3. A. Talneau, L. Le Gouezigou, and N. Bouadma, Opt. Lett. 26, 1259 (2001).
    [CrossRef]
  4. M. Notomi, A. Shinya, K. Yamada, J. Takahashi, C. Takahashi, and I. Yokohama, Electron. Lett. 37, 293 (2001).
    [CrossRef]
  5. M. Loncar, D. Nedejkovic, T. Doll, J. Vuckovic, A. Scherer, and T. P. Pearsall, Appl. Phys. Lett. 77, 1937 (2000).
    [CrossRef]
  6. J. Arentoft, M. Kristensen, T. Sondergaard, and A. Boltasseva, Electron. Lett. 38, 274 (2002).
    [CrossRef]
  7. E. Chow, S. Y. Lin, S. G. Johnson, and J. D. Joannopoulos, Opt. Lett. 26, 286 (2001).
    [CrossRef]
  8. C. J. M. Smith, R. M. De La Rue, M. Rattier, S. Olivier, H. Benisty, C. Weisbuch, T. F. Krauss, R. Houdre, and U. Oesterle, Appl. Phys. Lett. 78, 1487 (2001).
    [CrossRef]
  9. K. Kurokawa, An Introduction to the Theory of Microwave Circuits (Academic, New York, 1969).
  10. S. Boscolo, C. Conti, M. Midrio, and C. G. Someda, J. Lightwave Technol. 20, 304 (2002).
    [CrossRef]
  11. G. Tayeb and D. Maystre, J. Opt. Soc. Am. A 14, 3323 (1997).
    [CrossRef]

2002 (2)

J. Arentoft, M. Kristensen, T. Sondergaard, and A. Boltasseva, Electron. Lett. 38, 274 (2002).
[CrossRef]

S. Boscolo, C. Conti, M. Midrio, and C. G. Someda, J. Lightwave Technol. 20, 304 (2002).
[CrossRef]

2001 (4)

M. Notomi, A. Shinya, K. Yamada, J. Takahashi, C. Takahashi, and I. Yokohama, Electron. Lett. 37, 293 (2001).
[CrossRef]

C. J. M. Smith, R. M. De La Rue, M. Rattier, S. Olivier, H. Benisty, C. Weisbuch, T. F. Krauss, R. Houdre, and U. Oesterle, Appl. Phys. Lett. 78, 1487 (2001).
[CrossRef]

E. Chow, S. Y. Lin, S. G. Johnson, and J. D. Joannopoulos, Opt. Lett. 26, 286 (2001).
[CrossRef]

A. Talneau, L. Le Gouezigou, and N. Bouadma, Opt. Lett. 26, 1259 (2001).
[CrossRef]

2000 (2)

M. Loncar, D. Nedejkovic, T. Doll, J. Vuckovic, A. Scherer, and T. P. Pearsall, Appl. Phys. Lett. 77, 1937 (2000).
[CrossRef]

C. J. M. Smith, H. Benisty, S. Olivier, M. Rattier, C. Weisbuch, T. F. Krauss, R. M. De La Rue, R. Houdré, and U. Oesterle, Appl. Phys. Lett. 77, 2813 (2000).
[CrossRef]

1997 (2)

J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, Nature 387, 143 (1997).
[CrossRef]

G. Tayeb and D. Maystre, J. Opt. Soc. Am. A 14, 3323 (1997).
[CrossRef]

Arentoft, J.

J. Arentoft, M. Kristensen, T. Sondergaard, and A. Boltasseva, Electron. Lett. 38, 274 (2002).
[CrossRef]

Benisty, H.

C. J. M. Smith, R. M. De La Rue, M. Rattier, S. Olivier, H. Benisty, C. Weisbuch, T. F. Krauss, R. Houdre, and U. Oesterle, Appl. Phys. Lett. 78, 1487 (2001).
[CrossRef]

C. J. M. Smith, H. Benisty, S. Olivier, M. Rattier, C. Weisbuch, T. F. Krauss, R. M. De La Rue, R. Houdré, and U. Oesterle, Appl. Phys. Lett. 77, 2813 (2000).
[CrossRef]

Boltasseva, A.

J. Arentoft, M. Kristensen, T. Sondergaard, and A. Boltasseva, Electron. Lett. 38, 274 (2002).
[CrossRef]

Boscolo, S.

Bouadma, N.

Chow, E.

Conti, C.

De La Rue, R. M.

C. J. M. Smith, R. M. De La Rue, M. Rattier, S. Olivier, H. Benisty, C. Weisbuch, T. F. Krauss, R. Houdre, and U. Oesterle, Appl. Phys. Lett. 78, 1487 (2001).
[CrossRef]

C. J. M. Smith, H. Benisty, S. Olivier, M. Rattier, C. Weisbuch, T. F. Krauss, R. M. De La Rue, R. Houdré, and U. Oesterle, Appl. Phys. Lett. 77, 2813 (2000).
[CrossRef]

Doll, T.

M. Loncar, D. Nedejkovic, T. Doll, J. Vuckovic, A. Scherer, and T. P. Pearsall, Appl. Phys. Lett. 77, 1937 (2000).
[CrossRef]

Fan, S.

J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, Nature 387, 143 (1997).
[CrossRef]

Houdre, R.

C. J. M. Smith, R. M. De La Rue, M. Rattier, S. Olivier, H. Benisty, C. Weisbuch, T. F. Krauss, R. Houdre, and U. Oesterle, Appl. Phys. Lett. 78, 1487 (2001).
[CrossRef]

Houdré, R.

C. J. M. Smith, H. Benisty, S. Olivier, M. Rattier, C. Weisbuch, T. F. Krauss, R. M. De La Rue, R. Houdré, and U. Oesterle, Appl. Phys. Lett. 77, 2813 (2000).
[CrossRef]

Joannopoulos, J. D.

E. Chow, S. Y. Lin, S. G. Johnson, and J. D. Joannopoulos, Opt. Lett. 26, 286 (2001).
[CrossRef]

J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, Nature 387, 143 (1997).
[CrossRef]

Johnson, S. G.

Krauss, T. F.

C. J. M. Smith, R. M. De La Rue, M. Rattier, S. Olivier, H. Benisty, C. Weisbuch, T. F. Krauss, R. Houdre, and U. Oesterle, Appl. Phys. Lett. 78, 1487 (2001).
[CrossRef]

C. J. M. Smith, H. Benisty, S. Olivier, M. Rattier, C. Weisbuch, T. F. Krauss, R. M. De La Rue, R. Houdré, and U. Oesterle, Appl. Phys. Lett. 77, 2813 (2000).
[CrossRef]

Kristensen, M.

J. Arentoft, M. Kristensen, T. Sondergaard, and A. Boltasseva, Electron. Lett. 38, 274 (2002).
[CrossRef]

Kurokawa, K.

K. Kurokawa, An Introduction to the Theory of Microwave Circuits (Academic, New York, 1969).

Le Gouezigou, L.

Lin, S. Y.

Loncar, M.

M. Loncar, D. Nedejkovic, T. Doll, J. Vuckovic, A. Scherer, and T. P. Pearsall, Appl. Phys. Lett. 77, 1937 (2000).
[CrossRef]

Maystre, D.

Midrio, M.

Nedejkovic, D.

M. Loncar, D. Nedejkovic, T. Doll, J. Vuckovic, A. Scherer, and T. P. Pearsall, Appl. Phys. Lett. 77, 1937 (2000).
[CrossRef]

Notomi, M.

M. Notomi, A. Shinya, K. Yamada, J. Takahashi, C. Takahashi, and I. Yokohama, Electron. Lett. 37, 293 (2001).
[CrossRef]

Oesterle, U.

C. J. M. Smith, R. M. De La Rue, M. Rattier, S. Olivier, H. Benisty, C. Weisbuch, T. F. Krauss, R. Houdre, and U. Oesterle, Appl. Phys. Lett. 78, 1487 (2001).
[CrossRef]

C. J. M. Smith, H. Benisty, S. Olivier, M. Rattier, C. Weisbuch, T. F. Krauss, R. M. De La Rue, R. Houdré, and U. Oesterle, Appl. Phys. Lett. 77, 2813 (2000).
[CrossRef]

Olivier, S.

C. J. M. Smith, R. M. De La Rue, M. Rattier, S. Olivier, H. Benisty, C. Weisbuch, T. F. Krauss, R. Houdre, and U. Oesterle, Appl. Phys. Lett. 78, 1487 (2001).
[CrossRef]

C. J. M. Smith, H. Benisty, S. Olivier, M. Rattier, C. Weisbuch, T. F. Krauss, R. M. De La Rue, R. Houdré, and U. Oesterle, Appl. Phys. Lett. 77, 2813 (2000).
[CrossRef]

Pearsall, T. P.

M. Loncar, D. Nedejkovic, T. Doll, J. Vuckovic, A. Scherer, and T. P. Pearsall, Appl. Phys. Lett. 77, 1937 (2000).
[CrossRef]

Rattier, M.

C. J. M. Smith, R. M. De La Rue, M. Rattier, S. Olivier, H. Benisty, C. Weisbuch, T. F. Krauss, R. Houdre, and U. Oesterle, Appl. Phys. Lett. 78, 1487 (2001).
[CrossRef]

C. J. M. Smith, H. Benisty, S. Olivier, M. Rattier, C. Weisbuch, T. F. Krauss, R. M. De La Rue, R. Houdré, and U. Oesterle, Appl. Phys. Lett. 77, 2813 (2000).
[CrossRef]

Scherer, A.

M. Loncar, D. Nedejkovic, T. Doll, J. Vuckovic, A. Scherer, and T. P. Pearsall, Appl. Phys. Lett. 77, 1937 (2000).
[CrossRef]

Shinya, A.

M. Notomi, A. Shinya, K. Yamada, J. Takahashi, C. Takahashi, and I. Yokohama, Electron. Lett. 37, 293 (2001).
[CrossRef]

Smith, C. J. M.

C. J. M. Smith, R. M. De La Rue, M. Rattier, S. Olivier, H. Benisty, C. Weisbuch, T. F. Krauss, R. Houdre, and U. Oesterle, Appl. Phys. Lett. 78, 1487 (2001).
[CrossRef]

C. J. M. Smith, H. Benisty, S. Olivier, M. Rattier, C. Weisbuch, T. F. Krauss, R. M. De La Rue, R. Houdré, and U. Oesterle, Appl. Phys. Lett. 77, 2813 (2000).
[CrossRef]

Someda, C. G.

Sondergaard, T.

J. Arentoft, M. Kristensen, T. Sondergaard, and A. Boltasseva, Electron. Lett. 38, 274 (2002).
[CrossRef]

Takahashi, C.

M. Notomi, A. Shinya, K. Yamada, J. Takahashi, C. Takahashi, and I. Yokohama, Electron. Lett. 37, 293 (2001).
[CrossRef]

Takahashi, J.

M. Notomi, A. Shinya, K. Yamada, J. Takahashi, C. Takahashi, and I. Yokohama, Electron. Lett. 37, 293 (2001).
[CrossRef]

Talneau, A.

Tayeb, G.

Villeneuve, P. R.

J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, Nature 387, 143 (1997).
[CrossRef]

Vuckovic, J.

M. Loncar, D. Nedejkovic, T. Doll, J. Vuckovic, A. Scherer, and T. P. Pearsall, Appl. Phys. Lett. 77, 1937 (2000).
[CrossRef]

Weisbuch, C.

C. J. M. Smith, R. M. De La Rue, M. Rattier, S. Olivier, H. Benisty, C. Weisbuch, T. F. Krauss, R. Houdre, and U. Oesterle, Appl. Phys. Lett. 78, 1487 (2001).
[CrossRef]

C. J. M. Smith, H. Benisty, S. Olivier, M. Rattier, C. Weisbuch, T. F. Krauss, R. M. De La Rue, R. Houdré, and U. Oesterle, Appl. Phys. Lett. 77, 2813 (2000).
[CrossRef]

Yamada, K.

M. Notomi, A. Shinya, K. Yamada, J. Takahashi, C. Takahashi, and I. Yokohama, Electron. Lett. 37, 293 (2001).
[CrossRef]

Yokohama, I.

M. Notomi, A. Shinya, K. Yamada, J. Takahashi, C. Takahashi, and I. Yokohama, Electron. Lett. 37, 293 (2001).
[CrossRef]

Appl. Phys. Lett. (3)

M. Loncar, D. Nedejkovic, T. Doll, J. Vuckovic, A. Scherer, and T. P. Pearsall, Appl. Phys. Lett. 77, 1937 (2000).
[CrossRef]

C. J. M. Smith, H. Benisty, S. Olivier, M. Rattier, C. Weisbuch, T. F. Krauss, R. M. De La Rue, R. Houdré, and U. Oesterle, Appl. Phys. Lett. 77, 2813 (2000).
[CrossRef]

C. J. M. Smith, R. M. De La Rue, M. Rattier, S. Olivier, H. Benisty, C. Weisbuch, T. F. Krauss, R. Houdre, and U. Oesterle, Appl. Phys. Lett. 78, 1487 (2001).
[CrossRef]

Electron. Lett. (2)

J. Arentoft, M. Kristensen, T. Sondergaard, and A. Boltasseva, Electron. Lett. 38, 274 (2002).
[CrossRef]

M. Notomi, A. Shinya, K. Yamada, J. Takahashi, C. Takahashi, and I. Yokohama, Electron. Lett. 37, 293 (2001).
[CrossRef]

J. Lightwave Technol. (1)

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

Nature (1)

J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, Nature 387, 143 (1997).
[CrossRef]

Opt. Lett. (2)

Other (1)

K. Kurokawa, An Introduction to the Theory of Microwave Circuits (Academic, New York, 1969).

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Figures (4)

Fig. 1
Fig. 1

(a) Contour plot of the modulus of the magnetic-field amplitude for wavelength a/λ=0.26. (b) Real part of the magnetic field along the dashed line in (a). (c) Same as in (a), with a/λ=0.24. (d) Same as in (b), with a/λ=0.26.

Fig. 2
Fig. 2

Dispersion relations of modes guided by a PhC waveguide with air holes etched in a substrate with refractive index n=3.4. The hole radius-to-pitch ratio is r/a=0.3. Solid curve, dispersion relation for a mode whose one component magnetic field has even symmetry with respect to the guide axis. Dashed curve, dispersion relation for a mode with odd symmetry. Dashed–dotted curve, dispersion relation of a mode guided through total internal reflection.

Fig. 3
Fig. 3

(a) Contour plot of the modulus of the magnetic-field amplitude for wavelength a/λ=0.26 through a suitably designed Y junction. The hole in the middle of the Y junction has radius rY/a=0.2. (b) Spectral dependence of transmission on wavelength. Dotted curve, unmatched junction without the additional hole in the junction center. Dashed curve unmatched junction with the additional hole. Solid curve, matched junction with the additional hole. All curves were calculated numerically (multiple-scattering technique). Filled circles, theoretical results obtained with Eqs. (1)–(3).

Fig. 4
Fig. 4

(a) Dielectric arrangement that produces the matching network. (b) Equivalent circuit.

Equations (3)

Equations on this page are rendered with MathJax. Learn more.

Z1R=ZBZL+iZB tanm1χyaZB+iZL tanm1χya,
Z1L=1iωC1+iωL11+iωC1Z1R1-ω2L1C1+iωC1Z1R,
ϱ=Z2L-ZBZ2L+ZB.

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