Abstract

We theoretically introduce a new type of optical all-pass filter based on guided resonance in coupled photonic crystal slabs. The filter exhibits near-complete transmission for both on- and off-resonant frequencies and yet generates large resonant group delay. We further show that such a filter can be mechanically switched into a flat-top band rejection filter.

© 2003 Optical Society of America

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References

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  1. D. K. Jacob, S. C. Dunn, and M. G. Moharam, Appl. Opt. 41, 1241 (2002).
    [CrossRef] [PubMed]
  2. C. K. Madsen, J. A. Walker, J. E. Ford, K. W. Goossen, T. N. Nielsen, and G. Lenz, IEEE Photon. Technol. Lett. 12, 651 (2000).
    [CrossRef]
  3. F. Gires and P. Tournois, C. R. Hebd. Seances Acad. Sci. B Sci. Phys. (France) 268, 313 (1969).
  4. M. Kanskar, P. Paddon, V. Pacradouni, R. Morin, A. Busch, J. F. Young, S. R. Johnson, J. Mackenzie, and T. Tiedje, Appl. Phys. Lett. 70, 1438 (1997).
    [CrossRef]
  5. S. Fan and J. D. Joannopoulos, Phys. Rev. B 65, 235112 (2002).
    [CrossRef]
  6. R. Magnusson and S. S. Wang, Appl. Phys. Lett. 61, 1022 (1992).
    [CrossRef]
  7. S. Fan, W. Suh, and J. D. Joannopoulos, J. Opt. Soc. Am. A 20, 569 (2003).
    [CrossRef]
  8. E. D. Palik, Handbook of Optical Constants of Solids (Academic, San Diego, Calif., 1985), p. 439.
  9. W. Suh, M. F. Yanik, O. Solgaard, and S. Fan, Appl. Phys. Lett. 82, 1999 (2003).
    [CrossRef]
  10. S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and H. A. Haus, Phys. Rev. Lett. 80, 960 (1998).
    [CrossRef]
  11. H. A. Haus, Waves and Fields in Optoelectronics (Prentice-Hall, Englewood Cliffs, N.J., 1984).
  12. K. S. Kunz and R. J. Luebbers, The Finite-Difference Time-Domain Methods for Electromagnetics (CRC, Boca Raton, Fla., 1993).
  13. A. Taflove and S. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Methods (Artech House, Boston, Mass., 2000).
  14. Similar flat-top behavior in one-dimensional grating structures was reported in Ref. .

2003

S. Fan, W. Suh, and J. D. Joannopoulos, J. Opt. Soc. Am. A 20, 569 (2003).
[CrossRef]

W. Suh, M. F. Yanik, O. Solgaard, and S. Fan, Appl. Phys. Lett. 82, 1999 (2003).
[CrossRef]

2002

2000

C. K. Madsen, J. A. Walker, J. E. Ford, K. W. Goossen, T. N. Nielsen, and G. Lenz, IEEE Photon. Technol. Lett. 12, 651 (2000).
[CrossRef]

A. Taflove and S. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Methods (Artech House, Boston, Mass., 2000).

1998

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and H. A. Haus, Phys. Rev. Lett. 80, 960 (1998).
[CrossRef]

1997

M. Kanskar, P. Paddon, V. Pacradouni, R. Morin, A. Busch, J. F. Young, S. R. Johnson, J. Mackenzie, and T. Tiedje, Appl. Phys. Lett. 70, 1438 (1997).
[CrossRef]

1993

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

1992

R. Magnusson and S. S. Wang, Appl. Phys. Lett. 61, 1022 (1992).
[CrossRef]

1985

E. D. Palik, Handbook of Optical Constants of Solids (Academic, San Diego, Calif., 1985), p. 439.

1984

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

1969

F. Gires and P. Tournois, C. R. Hebd. Seances Acad. Sci. B Sci. Phys. (France) 268, 313 (1969).

Busch, A.

M. Kanskar, P. Paddon, V. Pacradouni, R. Morin, A. Busch, J. F. Young, S. R. Johnson, J. Mackenzie, and T. Tiedje, Appl. Phys. Lett. 70, 1438 (1997).
[CrossRef]

Dunn, S. C.

Fan, S.

S. Fan, W. Suh, and J. D. Joannopoulos, J. Opt. Soc. Am. A 20, 569 (2003).
[CrossRef]

W. Suh, M. F. Yanik, O. Solgaard, and S. Fan, Appl. Phys. Lett. 82, 1999 (2003).
[CrossRef]

S. Fan and J. D. Joannopoulos, Phys. Rev. B 65, 235112 (2002).
[CrossRef]

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and H. A. Haus, Phys. Rev. Lett. 80, 960 (1998).
[CrossRef]

Ford, J. E.

C. K. Madsen, J. A. Walker, J. E. Ford, K. W. Goossen, T. N. Nielsen, and G. Lenz, IEEE Photon. Technol. Lett. 12, 651 (2000).
[CrossRef]

Gires, F.

F. Gires and P. Tournois, C. R. Hebd. Seances Acad. Sci. B Sci. Phys. (France) 268, 313 (1969).

Goossen, K. W.

C. K. Madsen, J. A. Walker, J. E. Ford, K. W. Goossen, T. N. Nielsen, and G. Lenz, IEEE Photon. Technol. Lett. 12, 651 (2000).
[CrossRef]

Hagness, S.

A. Taflove and S. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Methods (Artech House, Boston, Mass., 2000).

Haus, H. A.

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and H. A. Haus, Phys. Rev. Lett. 80, 960 (1998).
[CrossRef]

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

Jacob, D. K.

Joannopoulos, J. D.

S. Fan, W. Suh, and J. D. Joannopoulos, J. Opt. Soc. Am. A 20, 569 (2003).
[CrossRef]

S. Fan and J. D. Joannopoulos, Phys. Rev. B 65, 235112 (2002).
[CrossRef]

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and H. A. Haus, Phys. Rev. Lett. 80, 960 (1998).
[CrossRef]

Johnson, S. R.

M. Kanskar, P. Paddon, V. Pacradouni, R. Morin, A. Busch, J. F. Young, S. R. Johnson, J. Mackenzie, and T. Tiedje, Appl. Phys. Lett. 70, 1438 (1997).
[CrossRef]

Kanskar, M.

M. Kanskar, P. Paddon, V. Pacradouni, R. Morin, A. Busch, J. F. Young, S. R. Johnson, J. Mackenzie, and T. Tiedje, Appl. Phys. Lett. 70, 1438 (1997).
[CrossRef]

Kunz, K. S.

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

Lenz, G.

C. K. Madsen, J. A. Walker, J. E. Ford, K. W. Goossen, T. N. Nielsen, and G. Lenz, IEEE Photon. Technol. Lett. 12, 651 (2000).
[CrossRef]

Luebbers, R. J.

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

Mackenzie, J.

M. Kanskar, P. Paddon, V. Pacradouni, R. Morin, A. Busch, J. F. Young, S. R. Johnson, J. Mackenzie, and T. Tiedje, Appl. Phys. Lett. 70, 1438 (1997).
[CrossRef]

Madsen, C. K.

C. K. Madsen, J. A. Walker, J. E. Ford, K. W. Goossen, T. N. Nielsen, and G. Lenz, IEEE Photon. Technol. Lett. 12, 651 (2000).
[CrossRef]

Magnusson, R.

R. Magnusson and S. S. Wang, Appl. Phys. Lett. 61, 1022 (1992).
[CrossRef]

Moharam, M. G.

Morin, R.

M. Kanskar, P. Paddon, V. Pacradouni, R. Morin, A. Busch, J. F. Young, S. R. Johnson, J. Mackenzie, and T. Tiedje, Appl. Phys. Lett. 70, 1438 (1997).
[CrossRef]

Nielsen, T. N.

C. K. Madsen, J. A. Walker, J. E. Ford, K. W. Goossen, T. N. Nielsen, and G. Lenz, IEEE Photon. Technol. Lett. 12, 651 (2000).
[CrossRef]

Pacradouni, V.

M. Kanskar, P. Paddon, V. Pacradouni, R. Morin, A. Busch, J. F. Young, S. R. Johnson, J. Mackenzie, and T. Tiedje, Appl. Phys. Lett. 70, 1438 (1997).
[CrossRef]

Paddon, P.

M. Kanskar, P. Paddon, V. Pacradouni, R. Morin, A. Busch, J. F. Young, S. R. Johnson, J. Mackenzie, and T. Tiedje, Appl. Phys. Lett. 70, 1438 (1997).
[CrossRef]

Palik, E. D.

E. D. Palik, Handbook of Optical Constants of Solids (Academic, San Diego, Calif., 1985), p. 439.

Solgaard, O.

W. Suh, M. F. Yanik, O. Solgaard, and S. Fan, Appl. Phys. Lett. 82, 1999 (2003).
[CrossRef]

Suh, W.

W. Suh, M. F. Yanik, O. Solgaard, and S. Fan, Appl. Phys. Lett. 82, 1999 (2003).
[CrossRef]

S. Fan, W. Suh, and J. D. Joannopoulos, J. Opt. Soc. Am. A 20, 569 (2003).
[CrossRef]

Taflove, A.

A. Taflove and S. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Methods (Artech House, Boston, Mass., 2000).

Tiedje, T.

M. Kanskar, P. Paddon, V. Pacradouni, R. Morin, A. Busch, J. F. Young, S. R. Johnson, J. Mackenzie, and T. Tiedje, Appl. Phys. Lett. 70, 1438 (1997).
[CrossRef]

Tournois, P.

F. Gires and P. Tournois, C. R. Hebd. Seances Acad. Sci. B Sci. Phys. (France) 268, 313 (1969).

Villeneuve, P. R.

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and H. A. Haus, Phys. Rev. Lett. 80, 960 (1998).
[CrossRef]

Walker, J. A.

C. K. Madsen, J. A. Walker, J. E. Ford, K. W. Goossen, T. N. Nielsen, and G. Lenz, IEEE Photon. Technol. Lett. 12, 651 (2000).
[CrossRef]

Wang, S. S.

R. Magnusson and S. S. Wang, Appl. Phys. Lett. 61, 1022 (1992).
[CrossRef]

Yanik, M. F.

W. Suh, M. F. Yanik, O. Solgaard, and S. Fan, Appl. Phys. Lett. 82, 1999 (2003).
[CrossRef]

Young, J. F.

M. Kanskar, P. Paddon, V. Pacradouni, R. Morin, A. Busch, J. F. Young, S. R. Johnson, J. Mackenzie, and T. Tiedje, Appl. Phys. Lett. 70, 1438 (1997).
[CrossRef]

Appl. Opt.

Appl. Phys. Lett.

M. Kanskar, P. Paddon, V. Pacradouni, R. Morin, A. Busch, J. F. Young, S. R. Johnson, J. Mackenzie, and T. Tiedje, Appl. Phys. Lett. 70, 1438 (1997).
[CrossRef]

W. Suh, M. F. Yanik, O. Solgaard, and S. Fan, Appl. Phys. Lett. 82, 1999 (2003).
[CrossRef]

Appl. Phys. Lett.

R. Magnusson and S. S. Wang, Appl. Phys. Lett. 61, 1022 (1992).
[CrossRef]

C. R. Hebd. Seances Acad. Sci. B Sci. Phys. (France)

F. Gires and P. Tournois, C. R. Hebd. Seances Acad. Sci. B Sci. Phys. (France) 268, 313 (1969).

IEEE Photon. Technol. Lett.

C. K. Madsen, J. A. Walker, J. E. Ford, K. W. Goossen, T. N. Nielsen, and G. Lenz, IEEE Photon. Technol. Lett. 12, 651 (2000).
[CrossRef]

J. Opt. Soc. Am. A

Phys. Rev. B

S. Fan and J. D. Joannopoulos, Phys. Rev. B 65, 235112 (2002).
[CrossRef]

Phys. Rev. Lett.

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and H. A. Haus, Phys. Rev. Lett. 80, 960 (1998).
[CrossRef]

Other

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

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

A. Taflove and S. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Methods (Artech House, Boston, Mass., 2000).

Similar flat-top behavior in one-dimensional grating structures was reported in Ref. .

E. D. Palik, Handbook of Optical Constants of Solids (Academic, San Diego, Calif., 1985), p. 439.

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Figures (4)

Fig. 1
Fig. 1

Schematic of a mechanically tunable photonic crystal filter consisting of two photonic crystal slabs. The arrow represents the direction of the incident light. The spectral response function of the filter is tunable by varying the distances between the two slabs.

Fig. 2
Fig. 2

Transmission spectrum through a single photonic crystal slab for normally incident light. The crystal structure shown in the inset consists of a square lattice of air holes of radius 0.1a, where a is the lattice constant. The slab has a dielectric constant of 11.4 and a thickness of 1.05a. The open circles are the numerical results from a FDTD simulation. The solid curve is from the analytical theory in Ref. 7.

Fig. 3
Fig. 3

Spectral response functions for the two-slab structure shown in Fig. 1, with an edge-to-edge distance of 0.4a. (a) Resonance amplitudes of the even mode (dashed curve) and the odd mode (solid curve). (b) Transmission spectrum for normally incident light. (c) Group delay. In both (b) and (c), the solid curve represents the theory and the open circles correspond to FDTD simulations.

Fig. 4
Fig. 4

Transmission spectra through the two-slab structure shown in Fig. 1 as we vary the distance between the slabs to be (a) 0.5a, (b) 1.1a. The solid curves represent the theory, and the open circles correspond to FDTD simulations.

Equations (6)

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

dadt=jω0-1τa+j1τS1++j1τS2++jκb,
S1-=S2++j1τa,    S2-=S1++j1τa,
dbdt=jω0-1τb+j1τP1++j1τP2++jκa,
P1-=P2++j1τb,    P2-=P1++j1τb,
P1+=exp-jϕS2-,    P1-=expjϕS2+,
t=exp-jϕjω-ω0-1/τjω-ω0+1/τ,

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