Abstract

A novel design for an ultracompact, high-Q notch-rejection filter is presented, and an analytic expression for the transmission properties is derived. This folded directional coupler shares the properties of a Fabry–Perot resonator and a directional coupler. We compare and contrast the device to high-Q Fabry–Perot cavities in photonic crystal waveguides.

© 2003 Optical Society of America

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References

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  1. S. Cho, B. Kim, Y. Moon, and A. Shakouri, Jpn. J. Appl. Phys. 40, 4045 (2001).
    [Crossref]
  2. A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. Villeneuve, and J. D. Joannopoulos, Phys. Rev. Lett. 77, 3787 (1996).
    [Crossref] [PubMed]
  3. A. Martinez, F. Cuesta, and J. Marti, IEEE Photon. Technol. Lett. 15, 694 (2003).
    [Crossref]
  4. M. Koshiba, J. Lightwave Technol. 19, 1970 (2001).
    [Crossref]
  5. A. Safaai-Jazi and C. Chang, IEEE J. Quantum Electron. 32, 1063 (1996).
    [Crossref]
  6. L. C. Botten, A. A. Asatryan, T. N. Langtry, T. P. White, C. M. de Sterke, and R. C. McPhedran, Opt. Lett. 28, 854 (2003).
    [Crossref] [PubMed]
  7. M. Born and E. Wolf, Principles of Optics, 5th ed. (Pergamon, Oxford, 1975), Sec. 7.6.1.

2003 (2)

2001 (2)

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

S. Cho, B. Kim, Y. Moon, and A. Shakouri, Jpn. J. Appl. Phys. 40, 4045 (2001).
[Crossref]

1996 (2)

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. Villeneuve, and J. D. Joannopoulos, Phys. Rev. Lett. 77, 3787 (1996).
[Crossref] [PubMed]

A. Safaai-Jazi and C. Chang, IEEE J. Quantum Electron. 32, 1063 (1996).
[Crossref]

1975 (1)

M. Born and E. Wolf, Principles of Optics, 5th ed. (Pergamon, Oxford, 1975), Sec. 7.6.1.

Asatryan, A. A.

Born, M.

M. Born and E. Wolf, Principles of Optics, 5th ed. (Pergamon, Oxford, 1975), Sec. 7.6.1.

Botten, L. C.

Chang, C.

A. Safaai-Jazi and C. Chang, IEEE J. Quantum Electron. 32, 1063 (1996).
[Crossref]

Chen, J. C.

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. Villeneuve, and J. D. Joannopoulos, Phys. Rev. Lett. 77, 3787 (1996).
[Crossref] [PubMed]

Cho, S.

S. Cho, B. Kim, Y. Moon, and A. Shakouri, Jpn. J. Appl. Phys. 40, 4045 (2001).
[Crossref]

Cuesta, F.

A. Martinez, F. Cuesta, and J. Marti, IEEE Photon. Technol. Lett. 15, 694 (2003).
[Crossref]

de Sterke, C. M.

Fan, S.

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. Villeneuve, and J. D. Joannopoulos, Phys. Rev. Lett. 77, 3787 (1996).
[Crossref] [PubMed]

Joannopoulos, J. D.

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. Villeneuve, and J. D. Joannopoulos, Phys. Rev. Lett. 77, 3787 (1996).
[Crossref] [PubMed]

Kim, B.

S. Cho, B. Kim, Y. Moon, and A. Shakouri, Jpn. J. Appl. Phys. 40, 4045 (2001).
[Crossref]

Koshiba, M.

Kurland, I.

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. Villeneuve, and J. D. Joannopoulos, Phys. Rev. Lett. 77, 3787 (1996).
[Crossref] [PubMed]

Langtry, T. N.

Marti, J.

A. Martinez, F. Cuesta, and J. Marti, IEEE Photon. Technol. Lett. 15, 694 (2003).
[Crossref]

Martinez, A.

A. Martinez, F. Cuesta, and J. Marti, IEEE Photon. Technol. Lett. 15, 694 (2003).
[Crossref]

McPhedran, R. C.

Mekis, A.

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. Villeneuve, and J. D. Joannopoulos, Phys. Rev. Lett. 77, 3787 (1996).
[Crossref] [PubMed]

Moon, Y.

S. Cho, B. Kim, Y. Moon, and A. Shakouri, Jpn. J. Appl. Phys. 40, 4045 (2001).
[Crossref]

Safaai-Jazi, A.

A. Safaai-Jazi and C. Chang, IEEE J. Quantum Electron. 32, 1063 (1996).
[Crossref]

Shakouri, A.

S. Cho, B. Kim, Y. Moon, and A. Shakouri, Jpn. J. Appl. Phys. 40, 4045 (2001).
[Crossref]

Villeneuve, P.

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. Villeneuve, and J. D. Joannopoulos, Phys. Rev. Lett. 77, 3787 (1996).
[Crossref] [PubMed]

White, T. P.

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 5th ed. (Pergamon, Oxford, 1975), Sec. 7.6.1.

IEEE J. Quantum Electron. (1)

A. Safaai-Jazi and C. Chang, IEEE J. Quantum Electron. 32, 1063 (1996).
[Crossref]

IEEE Photon. Technol. Lett. (1)

A. Martinez, F. Cuesta, and J. Marti, IEEE Photon. Technol. Lett. 15, 694 (2003).
[Crossref]

J. Lightwave Technol. (1)

Jpn. J. Appl. Phys. (1)

S. Cho, B. Kim, Y. Moon, and A. Shakouri, Jpn. J. Appl. Phys. 40, 4045 (2001).
[Crossref]

Opt. Lett. (1)

Phys. Rev. Lett. (1)

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. Villeneuve, and J. D. Joannopoulos, Phys. Rev. Lett. 77, 3787 (1996).
[Crossref] [PubMed]

Other (1)

M. Born and E. Wolf, Principles of Optics, 5th ed. (Pergamon, Oxford, 1975), Sec. 7.6.1.

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Figures (3)

Fig. 1
Fig. 1

FDC with guide overlap region M2 of length L=5d and a single line of cylinders separating the two guides. The odd and even supermodes of region M2, |ψ±, are indicated by the dashed and dotted curves, respectively. The left and right modes, |ψL,R, of the single-guide regions are shown as solid curves.

Fig. 2
Fig. 2

Transmission of the FDC in Fig. 1 near resonance at λ=1.55 µm. Solid curve, full numerical calculation; dashed curve, approximate result obtained from Eqs. (3) with numerical input of β¯, Δβ, and L.

Fig. 3
Fig. 3

(a) Field intensity in the FDC at resonance. The intensity peaks at the blocked end of each waveguide correspond to an intensity enhancement of more than 4 orders of magnitude. (b) Field intensity of a photonic crystal FP filter with cavity length L=4. Shading in both figures is on a logarithmic scale.

Equations (4)

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

|ψL=(|ψ++|ψ-)/2,    |ψR=(|ψ+-|ψ-)/2.
R=cos4ΔβLcos4ΔβL+4 sin2ΔβLcos2β¯L.
ρ=-11-iΔω/Δω1/2,    R=11+Δω/Δω1/22,
Δω1/2=cos2Δβ0L/2β¯1L.

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