Abstract

We propose a structure for ideal 3-dB splitters 1×2–combiners 2×1 in photonic crystals. In photonic crystals, ideal 3-dB splitters based on a three-port system are achievable in principle, but it is impossible to achieve ideal 3-dB combiners based on the three-port system because there is no path for a loss, owing to strong confinement of photons. The proposed structure is based on a four-port system in which the concept of a microwave circuit, the so-called rat-race circuit is adopted. Design conditions for two-dimensional photonic-crystal-based rat-race circuits have been investigated by use of the coupled-mode theory in time. With the proposed structure, a 3-dB splitter–combiner has been designed. The performance of the device was numerically calculated by the finite-difference time-domain method.

© 2005 Optical Society of America

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References

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  1. J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals (Princeton U. Press, Princeton, N.J., 1995).
  2. P. R. Villeneuve, S. Fan, and J. D. Joannopoulos, Phys. Rev. B 54, 7837 (1996).
    [CrossRef]
  3. S. Fan, S. G. Johnson, and J. D. Joannopoulos, J. Opt. Soc. Am. B 18, 162 (2001).
    [CrossRef]
  4. M. Bayindir, B. Temelkuran, and E. Ozbay, Appl. Phy. Lett. 77, 3902 (2000).
    [CrossRef]
  5. S. Boscolo, M. Midrio, and T. F. Krauss, Opt. Lett. 27, 1001 (2002).
    [CrossRef]
  6. D. M. Pozar, Microwave Engineering (Wiley, New York, 1998).
  7. H. A. Haus, Waves and Fields in Optoelectronics (Prentice-Hall, Englewood Cliffs, N.J., 1984).
  8. M. Koshiba, Y. Tsuji, and S. Sasaki, IEEE Microwave Wireless Compon. Lett. 11, 152 (2001).
    [CrossRef]

2002

2001

M. Koshiba, Y. Tsuji, and S. Sasaki, IEEE Microwave Wireless Compon. Lett. 11, 152 (2001).
[CrossRef]

S. Fan, S. G. Johnson, and J. D. Joannopoulos, J. Opt. Soc. Am. B 18, 162 (2001).
[CrossRef]

2000

M. Bayindir, B. Temelkuran, and E. Ozbay, Appl. Phy. Lett. 77, 3902 (2000).
[CrossRef]

1996

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

Bayindir, M.

M. Bayindir, B. Temelkuran, and E. Ozbay, Appl. Phy. Lett. 77, 3902 (2000).
[CrossRef]

Boscolo, S.

Fan, S.

S. Fan, S. G. Johnson, and J. D. Joannopoulos, J. Opt. Soc. Am. B 18, 162 (2001).
[CrossRef]

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

Haus, H. A.

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

Joannopoulos, J. D.

S. Fan, S. G. Johnson, and J. D. Joannopoulos, J. Opt. Soc. Am. B 18, 162 (2001).
[CrossRef]

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

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals (Princeton U. Press, Princeton, N.J., 1995).

Johnson, S. G.

Koshiba, M.

M. Koshiba, Y. Tsuji, and S. Sasaki, IEEE Microwave Wireless Compon. Lett. 11, 152 (2001).
[CrossRef]

Krauss, T. F.

Meade, R. D.

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals (Princeton U. Press, Princeton, N.J., 1995).

Midrio, M.

Ozbay, E.

M. Bayindir, B. Temelkuran, and E. Ozbay, Appl. Phy. Lett. 77, 3902 (2000).
[CrossRef]

Pozar, D. M.

D. M. Pozar, Microwave Engineering (Wiley, New York, 1998).

Sasaki, S.

M. Koshiba, Y. Tsuji, and S. Sasaki, IEEE Microwave Wireless Compon. Lett. 11, 152 (2001).
[CrossRef]

Temelkuran, B.

M. Bayindir, B. Temelkuran, and E. Ozbay, Appl. Phy. Lett. 77, 3902 (2000).
[CrossRef]

Tsuji, Y.

M. Koshiba, Y. Tsuji, and S. Sasaki, IEEE Microwave Wireless Compon. Lett. 11, 152 (2001).
[CrossRef]

Villeneuve, P. R.

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

Winn, J. N.

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals (Princeton U. Press, Princeton, N.J., 1995).

Appl. Phy. Lett.

M. Bayindir, B. Temelkuran, and E. Ozbay, Appl. Phy. Lett. 77, 3902 (2000).
[CrossRef]

IEEE Microwave Wireless Compon. Lett.

M. Koshiba, Y. Tsuji, and S. Sasaki, IEEE Microwave Wireless Compon. Lett. 11, 152 (2001).
[CrossRef]

J. Opt. Soc. Am. B

Opt. Lett.

Phys. Rev. B

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

Other

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals (Princeton U. Press, Princeton, N.J., 1995).

D. M. Pozar, Microwave Engineering (Wiley, New York, 1998).

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

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Figures (3)

Fig. 1
Fig. 1

Structure of a rat-race circuit based on a two-dimensional PC.

Fig. 2
Fig. 2

Conceptual diagram of the rat-race circuit, in which each junction is treated as a resonator.

Fig. 3
Fig. 3

(a) Structure of the rat-race circuit in a two-dimensional (2D) PC made from a triangular lattice of dielectric rods r=0.2a,r=11.56 in air. (b) Reflection and transmission spectra calculated by the finite-difference time-domain method when a broadband pulse is launched into port 1. Inset, wave propagation at f=0.3497 c/a.

Equations (6)

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

daidt=jω0ai-1τ1+2τ2ai+2τ1s+i+2τ2si+1,i+2τ2si-1,i,
s-=-s++2/τa.
daidt=jω0ai-1τ1ai+exp-jϕi,i-11τ2ai-1+exp-jϕi,i+11τ2ai+1+2τ1s+i.
s˜-1s˜+12=-jω-ω0+1/τ12+jω-ω0+1/τ12/τ1-21/τ22jω-ω0+1/τ12+21/τ222,
s˜-2s˜+12=s˜-4s˜+12=-2j/τ1τ2jω-ω0+1/τ12+21/τ222,
s˜-3s˜+12=0.

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