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Channel drop filters in photonic crystals

Shanhui Fan, P. R. Villeneuve, J. D. Joannopoulos, and H. A. Haus

Open Access Open Access

Abstract

We present a general analysis of channel drop filter structures composed of two waveguides and an optical resonator system. We show that 100% transfer between the two waveguides can occur by creating resonant states of different symmetry, and by forcing an accidental degeneracy between them. The degeneracy must exist in both the real and imaginary parts of the frequency. Based on the analysis we present novel photonic crystal channel drop filters. Numerical simulations demonstrate that these filters exhibit ideal transfer characteristics.

©1998 Optical Society of America

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References

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  • Publication
  1. R. Adar, C. H. Henry, C. Dragone, R. C. Kistler, and M. A. Milbrodt, “Broad-band array multiplexers made with silica waveguides on silicon,” J. Lightwave Technol. 11, 212 (1993).
    [Crossref]
  2. H. A. Haus and Y. Lai, “Narrow-band optical channel-dropping filter,” J. Lightwave Technol. 10, 57 (1992).
    [Crossref]
  3. B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J. -P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15, 998 (1997).
    [Crossref]
  4. B. E. Little, S. T. Chu, and H. A. Haus, “Estimated surface roughness loss and output coupling in microdisk resonators,” Opt. Lett. 21, 1390 (1996).
    [Crossref] [PubMed]
  5. P. R. Villeneuve, S. Fan, and J. D. Joannopoulos, “Microcavities in photonic crystals: mode symmetry, tunability and coupling efficiency,” Phys. Rev. B 54, 7837 (1996).
    [Crossref]
  6. S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “Theoretical investigation of fabrication-related disorder on the properties of photonic crystals,” J. Appl. Phys. 78, 1415 (1995).
    [Crossref]
  7. S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and H. A. Haus, “Channel drop tunneling through localized states,” Phys. Rev. Lett. 80, 960 (1998).
    [Crossref]
  8. S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and H. A. Haus (unpublished).
  9. For a review, see K. S. Kunz and R. J. Luebbers, The finite-difference time-domain methods (CRC Press, Boca Raton, 1993).
  10. J. C. Chen and K. Li, “Quartic perfectly matched layers for dielectric waveguides and gratings,” Microw. Opt. Technol. Lett. 10, 319 (1995).
    [Crossref]

1998 (1)

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and H. A. Haus, “Channel drop tunneling through localized states,” Phys. Rev. Lett. 80, 960 (1998).
[Crossref]

1997 (1)

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J. -P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15, 998 (1997).
[Crossref]

1996 (2)

B. E. Little, S. T. Chu, and H. A. Haus, “Estimated surface roughness loss and output coupling in microdisk resonators,” Opt. Lett. 21, 1390 (1996).
[Crossref] [PubMed]

P. R. Villeneuve, S. Fan, and J. D. Joannopoulos, “Microcavities in photonic crystals: mode symmetry, tunability and coupling efficiency,” Phys. Rev. B 54, 7837 (1996).
[Crossref]

1995 (2)

S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “Theoretical investigation of fabrication-related disorder on the properties of photonic crystals,” J. Appl. Phys. 78, 1415 (1995).
[Crossref]

J. C. Chen and K. Li, “Quartic perfectly matched layers for dielectric waveguides and gratings,” Microw. Opt. Technol. Lett. 10, 319 (1995).
[Crossref]

1993 (1)

R. Adar, C. H. Henry, C. Dragone, R. C. Kistler, and M. A. Milbrodt, “Broad-band array multiplexers made with silica waveguides on silicon,” J. Lightwave Technol. 11, 212 (1993).
[Crossref]

1992 (1)

H. A. Haus and Y. Lai, “Narrow-band optical channel-dropping filter,” J. Lightwave Technol. 10, 57 (1992).
[Crossref]

Adar, R.

R. Adar, C. H. Henry, C. Dragone, R. C. Kistler, and M. A. Milbrodt, “Broad-band array multiplexers made with silica waveguides on silicon,” J. Lightwave Technol. 11, 212 (1993).
[Crossref]

Chen, J. C.

J. C. Chen and K. Li, “Quartic perfectly matched layers for dielectric waveguides and gratings,” Microw. Opt. Technol. Lett. 10, 319 (1995).
[Crossref]

Chu, S. T.

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J. -P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15, 998 (1997).
[Crossref]

B. E. Little, S. T. Chu, and H. A. Haus, “Estimated surface roughness loss and output coupling in microdisk resonators,” Opt. Lett. 21, 1390 (1996).
[Crossref] [PubMed]

Dragone, C.

R. Adar, C. H. Henry, C. Dragone, R. C. Kistler, and M. A. Milbrodt, “Broad-band array multiplexers made with silica waveguides on silicon,” J. Lightwave Technol. 11, 212 (1993).
[Crossref]

Fan, S.

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and H. A. Haus, “Channel drop tunneling through localized states,” Phys. Rev. Lett. 80, 960 (1998).
[Crossref]

P. R. Villeneuve, S. Fan, and J. D. Joannopoulos, “Microcavities in photonic crystals: mode symmetry, tunability and coupling efficiency,” Phys. Rev. B 54, 7837 (1996).
[Crossref]

S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “Theoretical investigation of fabrication-related disorder on the properties of photonic crystals,” J. Appl. Phys. 78, 1415 (1995).
[Crossref]

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and H. A. Haus (unpublished).

Foresi, J.

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J. -P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15, 998 (1997).
[Crossref]

Haus, H. A.

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and H. A. Haus, “Channel drop tunneling through localized states,” Phys. Rev. Lett. 80, 960 (1998).
[Crossref]

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J. -P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15, 998 (1997).
[Crossref]

B. E. Little, S. T. Chu, and H. A. Haus, “Estimated surface roughness loss and output coupling in microdisk resonators,” Opt. Lett. 21, 1390 (1996).
[Crossref] [PubMed]

H. A. Haus and Y. Lai, “Narrow-band optical channel-dropping filter,” J. Lightwave Technol. 10, 57 (1992).
[Crossref]

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and H. A. Haus (unpublished).

Henry, C. H.

R. Adar, C. H. Henry, C. Dragone, R. C. Kistler, and M. A. Milbrodt, “Broad-band array multiplexers made with silica waveguides on silicon,” J. Lightwave Technol. 11, 212 (1993).
[Crossref]

Joannopoulos, J. D.

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and H. A. Haus, “Channel drop tunneling through localized states,” Phys. Rev. Lett. 80, 960 (1998).
[Crossref]

P. R. Villeneuve, S. Fan, and J. D. Joannopoulos, “Microcavities in photonic crystals: mode symmetry, tunability and coupling efficiency,” Phys. Rev. B 54, 7837 (1996).
[Crossref]

S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “Theoretical investigation of fabrication-related disorder on the properties of photonic crystals,” J. Appl. Phys. 78, 1415 (1995).
[Crossref]

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and H. A. Haus (unpublished).

Kistler, R. C.

R. Adar, C. H. Henry, C. Dragone, R. C. Kistler, and M. A. Milbrodt, “Broad-band array multiplexers made with silica waveguides on silicon,” J. Lightwave Technol. 11, 212 (1993).
[Crossref]

Kunz, K. S.

For a review, see K. S. Kunz and R. J. Luebbers, The finite-difference time-domain methods (CRC Press, Boca Raton, 1993).

Lai, Y.

H. A. Haus and Y. Lai, “Narrow-band optical channel-dropping filter,” J. Lightwave Technol. 10, 57 (1992).
[Crossref]

Laine, J. -P.

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J. -P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15, 998 (1997).
[Crossref]

Li, K.

J. C. Chen and K. Li, “Quartic perfectly matched layers for dielectric waveguides and gratings,” Microw. Opt. Technol. Lett. 10, 319 (1995).
[Crossref]

Little, B. E.

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J. -P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15, 998 (1997).
[Crossref]

B. E. Little, S. T. Chu, and H. A. Haus, “Estimated surface roughness loss and output coupling in microdisk resonators,” Opt. Lett. 21, 1390 (1996).
[Crossref] [PubMed]

Luebbers, R. J.

For a review, see K. S. Kunz and R. J. Luebbers, The finite-difference time-domain methods (CRC Press, Boca Raton, 1993).

Milbrodt, M. A.

R. Adar, C. H. Henry, C. Dragone, R. C. Kistler, and M. A. Milbrodt, “Broad-band array multiplexers made with silica waveguides on silicon,” J. Lightwave Technol. 11, 212 (1993).
[Crossref]

Villeneuve, P. R.

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and H. A. Haus, “Channel drop tunneling through localized states,” Phys. Rev. Lett. 80, 960 (1998).
[Crossref]

P. R. Villeneuve, S. Fan, and J. D. Joannopoulos, “Microcavities in photonic crystals: mode symmetry, tunability and coupling efficiency,” Phys. Rev. B 54, 7837 (1996).
[Crossref]

S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “Theoretical investigation of fabrication-related disorder on the properties of photonic crystals,” J. Appl. Phys. 78, 1415 (1995).
[Crossref]

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and H. A. Haus (unpublished).

J. Appl. Phys. (1)

S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “Theoretical investigation of fabrication-related disorder on the properties of photonic crystals,” J. Appl. Phys. 78, 1415 (1995).
[Crossref]

J. Lightwave Technol. (3)

R. Adar, C. H. Henry, C. Dragone, R. C. Kistler, and M. A. Milbrodt, “Broad-band array multiplexers made with silica waveguides on silicon,” J. Lightwave Technol. 11, 212 (1993).
[Crossref]

H. A. Haus and Y. Lai, “Narrow-band optical channel-dropping filter,” J. Lightwave Technol. 10, 57 (1992).
[Crossref]

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J. -P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15, 998 (1997).
[Crossref]

Microw. Opt. Technol. Lett. (1)

J. C. Chen and K. Li, “Quartic perfectly matched layers for dielectric waveguides and gratings,” Microw. Opt. Technol. Lett. 10, 319 (1995).
[Crossref]

Opt. Lett. (1)

Phys. Rev. B (1)

P. R. Villeneuve, S. Fan, and J. D. Joannopoulos, “Microcavities in photonic crystals: mode symmetry, tunability and coupling efficiency,” Phys. Rev. B 54, 7837 (1996).
[Crossref]

Phys. Rev. Lett. (1)

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and H. A. Haus, “Channel drop tunneling through localized states,” Phys. Rev. Lett. 80, 960 (1998).
[Crossref]

Other (2)

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and H. A. Haus (unpublished).

For a review, see K. S. Kunz and R. J. Luebbers, The finite-difference time-domain methods (CRC Press, Boca Raton, 1993).

Supplementary Material (2)

Media 1: MOV (945 KB)     
Media 2: MOV (1057 KB)     

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Figures (10)
Figure 1.
Figure 1. Schematic of a generic resonant-cavity channel drop filter.

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Figure 2.
Figure 2. Channel drop tunneling process for a resonator system that supports a single resonant state.

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Figure 3.
Figure 3. Channel drop tunneling process for a resonator system that supports two resonant state with different symmetry with respect to the mirror plane perpendicular to the waveguides. These two states are even with respect to the mirror plane parallel to the waveguides.

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Figure 4.
Figure 4. Channel drop tunneling process for a resonator system that supports two resonant states with different symmetry with respect to the mirror plane perpendicular to the waveguides. The states also have different symmetry with respect to the mirror plane parallel to the waveguides.

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Figure 5.
Figure 5. Photonic crystal channel drop filter structure with two waveguides and two cavities. The dark blue circles correspond to rods with a dielectric constant of 11.56, while the light blue circles correspond to rods with a dielectric constant of 9.5. The two smaller rods have a dielectric constant of 6.6, and a radius of 0.05a, where a is the lattice constant.

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Figure 6.
Figure 6. (a) Intensity spectrum of the transmitted signal in the structure shown in Figure 5. (b) Intensity spectrum of the transferred signal in the forward direction. (c) Intensity spectrum of the transferred signal in the backward direction.

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Figure 7
Figure 7 (Quick movie: to be played in a loop mode) Oscillation of the steady-state field distribution at the resonant frequency for the structure shown in Figure 5. Green represents zero field. Red represents positive field maximum. Blue represents negative field maximum. [Media 1]

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Figure 8.
Figure 8. Photonic crystal channel drop filter structure with two waveguides and one cavity that supports two resonant states. The dark blue circle corresponds to a rod with a dielectric constant of 11.56, while the light blue circles correspond to rods with a dielectric constant of 11.90. The bigger rod has a radius of 0.60a, where a is the lattice constant.

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Figure 9.
Figure 9. (a) Intensity spectrum of the transmitted signal in the structure shown in Figure 8. (b)Intensity spectrum of the transferred signal in the forward direction. (c) Intensity spectrum of the transferred signal in the backward direction.

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Figure 10.
Figure 10. (Quicktime movie: to be played in a loop mode) Oscillation of the steady-state field distribution at the resonant frequency for the structure shown in Figure 8. Green represents zero field. Red represents positive field maximum. Blue represents negative field maximum. [Media 2]

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