Abstract

The resonant frequencies of a single cavity embedded in the three-dimensional layer-by-layer photonic crystal are studied with microwave experiments and transfer-scattering matrix method simulations. The effects of the number of cladding layers and the size of the embedded cavity on resonant frequencies and Q values are carefully examined. The fine increments of cavity size indicate a new pattern of relation between resonant frequencies and cavity sizes.

© 2008 Optical Society of America

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References

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  1. E. Yablonovitch, "Inhibited spontaneous emission in solid-state physics and electronics," Phys. Rev. Lett. 58, 2059-2062 (1987).
    [CrossRef] [PubMed]
  2. S. John, "Strong localization of photons in certain disordered dielectric superlattices," Phys. Rev. Lett. 58, 2486-2489 (1987).
    [CrossRef] [PubMed]
  3. K. Ho, C. Chan, and C. Soukoulis, "Existence of a photonic gap in periodic dielectric structures," Phys. Rev. Lett. 65, 3152-3155 (1990).
    [CrossRef] [PubMed]
  4. J. Joannopoulos, R. Meade, and J. Winn, Photonic Crystals (Princeton University Press, 1995).
  5. K. Srinivasan, P. Barclay, O. Painter, J. Chen, A. Cho, and C. Gmachl, "Experimental demonstration of a high quality factor photonic crystal microcavity," Appl. Phys. Lett. 83, 1915-1917 (2003).
    [CrossRef]
  6. S. Ogawa, M. Imada, S. Yoshimoto, M. Okano, and S. Noda, "Control of light emission by 3D photonic crystals," Science 305, 227-229 (2004).
    [CrossRef] [PubMed]
  7. M. Qi, E. Lidorikis, P. Rakich, S. Johnson, J. Joannopoulos, E. Ippen, and H. Smith, "A three-dimensional optical photonic crystal with designed point defects," Nature 429, 538-542 (2004).
    [CrossRef] [PubMed]
  8. K. Ho, C. Chan, C. Soukoulis, R. Biswas, and M. Sigalas, "Photonic band gaps in three dimensions: new layer-by-layer periodic structures," Solid State Commun. 89, 413-416 (1994).
    [CrossRef]
  9. E. Ozbay, A. Abeyta, G. Tuttle, M. Tringides, R. Biswas, and C. Soukoulis, C. Chan, and K. Ho, "Measurement of a three-dimensional photonic band gap in a crystal structure made of dielectric rods," Phys. Rev. B 50, 1945-1948 (1994).
  10. E. Ozbay, G. Tuttle, M. Sigalas, C. Soukoulis, and K. Ho, "Defect structures in a layer-by-layer photonic band-gap crystal," Phys. Rev. B 51, 13961-13965 (1995).
  11. T. Asano, B. Song, and S. Noda, "Analysis of the experimental Q factors (~ 1 million) of photonic crystal nanocavities," Opt. Express 141996-2002 (2006).
    [CrossRef] [PubMed]
  12. S. Tomljenovic-Hanic, C. Sterke, M. Steel, B. Eggleton, Y. Tanaka, and S. Noda, "High-Q cavities in multilayer photonic crystal slabs," Opt. Express 15, 17248-17253 (2007).
    [CrossRef] [PubMed]
  13. Z. Li and L. Lin, "Photonic band structures solved by a plane-wave-based transfer-matrix method," Phys. Rev. E 67, 046607 (2003).
  14. M. Li, Z. Li, K. Ho, J. Cao, and M. Miyawaki, "High-efficiency calculations for three-dimensional photonic crystal cavities," Opt. Lett. 31, 262-264 (2006).
    [CrossRef] [PubMed]
  15. M. Li, X. Hu, Z. Ye, K. Ho, J. Cao, and M. Miyawaki, "Higher-order incidence transfer matrix method used in three-dimensional photonic crystal coupled-resonator array simulation," Opt. Lett. 313498-3500 (2006).
    [CrossRef] [PubMed]
  16. M. Li, X. Hu, Z. Ye, K. Ho, J. Cao, and M. Miyawaki, "Perfectly matched layer absorption boundary condition in planewave based transfer-scattering matrix method for photonic crystal device simulation," Opt. Express 1611548-11554 (2008).
    [PubMed]
  17. C. Sauvan, P. Lalanne, and J. Hugonin, "Slow-wave effect and mode-profile matching in photonic crystal microcavities," Phys. Rev. B 71, 165118 (2005).
  18. Z. Li and K. Ho, "Application of structural symmetries in the plane-wave-based transfer-matrix method for three-dimensional photonic crystal waveguides," Phys. Rev. B 68, 245117 (2003).

2008

2007

2006

2005

C. Sauvan, P. Lalanne, and J. Hugonin, "Slow-wave effect and mode-profile matching in photonic crystal microcavities," Phys. Rev. B 71, 165118 (2005).

2004

S. Ogawa, M. Imada, S. Yoshimoto, M. Okano, and S. Noda, "Control of light emission by 3D photonic crystals," Science 305, 227-229 (2004).
[CrossRef] [PubMed]

M. Qi, E. Lidorikis, P. Rakich, S. Johnson, J. Joannopoulos, E. Ippen, and H. Smith, "A three-dimensional optical photonic crystal with designed point defects," Nature 429, 538-542 (2004).
[CrossRef] [PubMed]

2003

K. Srinivasan, P. Barclay, O. Painter, J. Chen, A. Cho, and C. Gmachl, "Experimental demonstration of a high quality factor photonic crystal microcavity," Appl. Phys. Lett. 83, 1915-1917 (2003).
[CrossRef]

Z. Li and K. Ho, "Application of structural symmetries in the plane-wave-based transfer-matrix method for three-dimensional photonic crystal waveguides," Phys. Rev. B 68, 245117 (2003).

Z. Li and L. Lin, "Photonic band structures solved by a plane-wave-based transfer-matrix method," Phys. Rev. E 67, 046607 (2003).

1995

E. Ozbay, G. Tuttle, M. Sigalas, C. Soukoulis, and K. Ho, "Defect structures in a layer-by-layer photonic band-gap crystal," Phys. Rev. B 51, 13961-13965 (1995).

1994

K. Ho, C. Chan, C. Soukoulis, R. Biswas, and M. Sigalas, "Photonic band gaps in three dimensions: new layer-by-layer periodic structures," Solid State Commun. 89, 413-416 (1994).
[CrossRef]

E. Ozbay, A. Abeyta, G. Tuttle, M. Tringides, R. Biswas, and C. Soukoulis, C. Chan, and K. Ho, "Measurement of a three-dimensional photonic band gap in a crystal structure made of dielectric rods," Phys. Rev. B 50, 1945-1948 (1994).

1990

K. Ho, C. Chan, and C. Soukoulis, "Existence of a photonic gap in periodic dielectric structures," Phys. Rev. Lett. 65, 3152-3155 (1990).
[CrossRef] [PubMed]

1987

E. Yablonovitch, "Inhibited spontaneous emission in solid-state physics and electronics," Phys. Rev. Lett. 58, 2059-2062 (1987).
[CrossRef] [PubMed]

S. John, "Strong localization of photons in certain disordered dielectric superlattices," Phys. Rev. Lett. 58, 2486-2489 (1987).
[CrossRef] [PubMed]

Abeyta, A.

E. Ozbay, A. Abeyta, G. Tuttle, M. Tringides, R. Biswas, and C. Soukoulis, C. Chan, and K. Ho, "Measurement of a three-dimensional photonic band gap in a crystal structure made of dielectric rods," Phys. Rev. B 50, 1945-1948 (1994).

Asano, T.

Barclay, P.

K. Srinivasan, P. Barclay, O. Painter, J. Chen, A. Cho, and C. Gmachl, "Experimental demonstration of a high quality factor photonic crystal microcavity," Appl. Phys. Lett. 83, 1915-1917 (2003).
[CrossRef]

Biswas, R.

E. Ozbay, A. Abeyta, G. Tuttle, M. Tringides, R. Biswas, and C. Soukoulis, C. Chan, and K. Ho, "Measurement of a three-dimensional photonic band gap in a crystal structure made of dielectric rods," Phys. Rev. B 50, 1945-1948 (1994).

K. Ho, C. Chan, C. Soukoulis, R. Biswas, and M. Sigalas, "Photonic band gaps in three dimensions: new layer-by-layer periodic structures," Solid State Commun. 89, 413-416 (1994).
[CrossRef]

Cao, J.

Chan, C.

E. Ozbay, A. Abeyta, G. Tuttle, M. Tringides, R. Biswas, and C. Soukoulis, C. Chan, and K. Ho, "Measurement of a three-dimensional photonic band gap in a crystal structure made of dielectric rods," Phys. Rev. B 50, 1945-1948 (1994).

K. Ho, C. Chan, C. Soukoulis, R. Biswas, and M. Sigalas, "Photonic band gaps in three dimensions: new layer-by-layer periodic structures," Solid State Commun. 89, 413-416 (1994).
[CrossRef]

K. Ho, C. Chan, and C. Soukoulis, "Existence of a photonic gap in periodic dielectric structures," Phys. Rev. Lett. 65, 3152-3155 (1990).
[CrossRef] [PubMed]

Chen, J.

K. Srinivasan, P. Barclay, O. Painter, J. Chen, A. Cho, and C. Gmachl, "Experimental demonstration of a high quality factor photonic crystal microcavity," Appl. Phys. Lett. 83, 1915-1917 (2003).
[CrossRef]

Cho, A.

K. Srinivasan, P. Barclay, O. Painter, J. Chen, A. Cho, and C. Gmachl, "Experimental demonstration of a high quality factor photonic crystal microcavity," Appl. Phys. Lett. 83, 1915-1917 (2003).
[CrossRef]

Eggleton, B.

Gmachl, C.

K. Srinivasan, P. Barclay, O. Painter, J. Chen, A. Cho, and C. Gmachl, "Experimental demonstration of a high quality factor photonic crystal microcavity," Appl. Phys. Lett. 83, 1915-1917 (2003).
[CrossRef]

Ho, K.

M. Li, X. Hu, Z. Ye, K. Ho, J. Cao, and M. Miyawaki, "Perfectly matched layer absorption boundary condition in planewave based transfer-scattering matrix method for photonic crystal device simulation," Opt. Express 1611548-11554 (2008).
[PubMed]

M. Li, X. Hu, Z. Ye, K. Ho, J. Cao, and M. Miyawaki, "Higher-order incidence transfer matrix method used in three-dimensional photonic crystal coupled-resonator array simulation," Opt. Lett. 313498-3500 (2006).
[CrossRef] [PubMed]

M. Li, Z. Li, K. Ho, J. Cao, and M. Miyawaki, "High-efficiency calculations for three-dimensional photonic crystal cavities," Opt. Lett. 31, 262-264 (2006).
[CrossRef] [PubMed]

Z. Li and K. Ho, "Application of structural symmetries in the plane-wave-based transfer-matrix method for three-dimensional photonic crystal waveguides," Phys. Rev. B 68, 245117 (2003).

E. Ozbay, G. Tuttle, M. Sigalas, C. Soukoulis, and K. Ho, "Defect structures in a layer-by-layer photonic band-gap crystal," Phys. Rev. B 51, 13961-13965 (1995).

E. Ozbay, A. Abeyta, G. Tuttle, M. Tringides, R. Biswas, and C. Soukoulis, C. Chan, and K. Ho, "Measurement of a three-dimensional photonic band gap in a crystal structure made of dielectric rods," Phys. Rev. B 50, 1945-1948 (1994).

K. Ho, C. Chan, C. Soukoulis, R. Biswas, and M. Sigalas, "Photonic band gaps in three dimensions: new layer-by-layer periodic structures," Solid State Commun. 89, 413-416 (1994).
[CrossRef]

K. Ho, C. Chan, and C. Soukoulis, "Existence of a photonic gap in periodic dielectric structures," Phys. Rev. Lett. 65, 3152-3155 (1990).
[CrossRef] [PubMed]

Hu, X.

Hugonin, J.

C. Sauvan, P. Lalanne, and J. Hugonin, "Slow-wave effect and mode-profile matching in photonic crystal microcavities," Phys. Rev. B 71, 165118 (2005).

Imada, M.

S. Ogawa, M. Imada, S. Yoshimoto, M. Okano, and S. Noda, "Control of light emission by 3D photonic crystals," Science 305, 227-229 (2004).
[CrossRef] [PubMed]

Ippen, E.

M. Qi, E. Lidorikis, P. Rakich, S. Johnson, J. Joannopoulos, E. Ippen, and H. Smith, "A three-dimensional optical photonic crystal with designed point defects," Nature 429, 538-542 (2004).
[CrossRef] [PubMed]

Joannopoulos, J.

M. Qi, E. Lidorikis, P. Rakich, S. Johnson, J. Joannopoulos, E. Ippen, and H. Smith, "A three-dimensional optical photonic crystal with designed point defects," Nature 429, 538-542 (2004).
[CrossRef] [PubMed]

John, S.

S. John, "Strong localization of photons in certain disordered dielectric superlattices," Phys. Rev. Lett. 58, 2486-2489 (1987).
[CrossRef] [PubMed]

Johnson, S.

M. Qi, E. Lidorikis, P. Rakich, S. Johnson, J. Joannopoulos, E. Ippen, and H. Smith, "A three-dimensional optical photonic crystal with designed point defects," Nature 429, 538-542 (2004).
[CrossRef] [PubMed]

Lalanne, P.

C. Sauvan, P. Lalanne, and J. Hugonin, "Slow-wave effect and mode-profile matching in photonic crystal microcavities," Phys. Rev. B 71, 165118 (2005).

Li, M.

Li, Z.

M. Li, Z. Li, K. Ho, J. Cao, and M. Miyawaki, "High-efficiency calculations for three-dimensional photonic crystal cavities," Opt. Lett. 31, 262-264 (2006).
[CrossRef] [PubMed]

Z. Li and L. Lin, "Photonic band structures solved by a plane-wave-based transfer-matrix method," Phys. Rev. E 67, 046607 (2003).

Z. Li and K. Ho, "Application of structural symmetries in the plane-wave-based transfer-matrix method for three-dimensional photonic crystal waveguides," Phys. Rev. B 68, 245117 (2003).

Lidorikis, E.

M. Qi, E. Lidorikis, P. Rakich, S. Johnson, J. Joannopoulos, E. Ippen, and H. Smith, "A three-dimensional optical photonic crystal with designed point defects," Nature 429, 538-542 (2004).
[CrossRef] [PubMed]

Lin, L.

Z. Li and L. Lin, "Photonic band structures solved by a plane-wave-based transfer-matrix method," Phys. Rev. E 67, 046607 (2003).

Miyawaki, M.

Noda, S.

Ogawa, S.

S. Ogawa, M. Imada, S. Yoshimoto, M. Okano, and S. Noda, "Control of light emission by 3D photonic crystals," Science 305, 227-229 (2004).
[CrossRef] [PubMed]

Okano, M.

S. Ogawa, M. Imada, S. Yoshimoto, M. Okano, and S. Noda, "Control of light emission by 3D photonic crystals," Science 305, 227-229 (2004).
[CrossRef] [PubMed]

Ozbay, E.

E. Ozbay, G. Tuttle, M. Sigalas, C. Soukoulis, and K. Ho, "Defect structures in a layer-by-layer photonic band-gap crystal," Phys. Rev. B 51, 13961-13965 (1995).

E. Ozbay, A. Abeyta, G. Tuttle, M. Tringides, R. Biswas, and C. Soukoulis, C. Chan, and K. Ho, "Measurement of a three-dimensional photonic band gap in a crystal structure made of dielectric rods," Phys. Rev. B 50, 1945-1948 (1994).

Painter, O.

K. Srinivasan, P. Barclay, O. Painter, J. Chen, A. Cho, and C. Gmachl, "Experimental demonstration of a high quality factor photonic crystal microcavity," Appl. Phys. Lett. 83, 1915-1917 (2003).
[CrossRef]

Qi, M.

M. Qi, E. Lidorikis, P. Rakich, S. Johnson, J. Joannopoulos, E. Ippen, and H. Smith, "A three-dimensional optical photonic crystal with designed point defects," Nature 429, 538-542 (2004).
[CrossRef] [PubMed]

Rakich, P.

M. Qi, E. Lidorikis, P. Rakich, S. Johnson, J. Joannopoulos, E. Ippen, and H. Smith, "A three-dimensional optical photonic crystal with designed point defects," Nature 429, 538-542 (2004).
[CrossRef] [PubMed]

Sauvan, C.

C. Sauvan, P. Lalanne, and J. Hugonin, "Slow-wave effect and mode-profile matching in photonic crystal microcavities," Phys. Rev. B 71, 165118 (2005).

Sigalas, M.

E. Ozbay, G. Tuttle, M. Sigalas, C. Soukoulis, and K. Ho, "Defect structures in a layer-by-layer photonic band-gap crystal," Phys. Rev. B 51, 13961-13965 (1995).

K. Ho, C. Chan, C. Soukoulis, R. Biswas, and M. Sigalas, "Photonic band gaps in three dimensions: new layer-by-layer periodic structures," Solid State Commun. 89, 413-416 (1994).
[CrossRef]

Smith, H.

M. Qi, E. Lidorikis, P. Rakich, S. Johnson, J. Joannopoulos, E. Ippen, and H. Smith, "A three-dimensional optical photonic crystal with designed point defects," Nature 429, 538-542 (2004).
[CrossRef] [PubMed]

Song, B.

Soukoulis, C.

E. Ozbay, G. Tuttle, M. Sigalas, C. Soukoulis, and K. Ho, "Defect structures in a layer-by-layer photonic band-gap crystal," Phys. Rev. B 51, 13961-13965 (1995).

K. Ho, C. Chan, C. Soukoulis, R. Biswas, and M. Sigalas, "Photonic band gaps in three dimensions: new layer-by-layer periodic structures," Solid State Commun. 89, 413-416 (1994).
[CrossRef]

E. Ozbay, A. Abeyta, G. Tuttle, M. Tringides, R. Biswas, and C. Soukoulis, C. Chan, and K. Ho, "Measurement of a three-dimensional photonic band gap in a crystal structure made of dielectric rods," Phys. Rev. B 50, 1945-1948 (1994).

K. Ho, C. Chan, and C. Soukoulis, "Existence of a photonic gap in periodic dielectric structures," Phys. Rev. Lett. 65, 3152-3155 (1990).
[CrossRef] [PubMed]

Srinivasan, K.

K. Srinivasan, P. Barclay, O. Painter, J. Chen, A. Cho, and C. Gmachl, "Experimental demonstration of a high quality factor photonic crystal microcavity," Appl. Phys. Lett. 83, 1915-1917 (2003).
[CrossRef]

Steel, M.

Sterke, C.

Tanaka, Y.

Tomljenovic-Hanic, S.

Tringides, M.

E. Ozbay, A. Abeyta, G. Tuttle, M. Tringides, R. Biswas, and C. Soukoulis, C. Chan, and K. Ho, "Measurement of a three-dimensional photonic band gap in a crystal structure made of dielectric rods," Phys. Rev. B 50, 1945-1948 (1994).

Tuttle, G.

E. Ozbay, G. Tuttle, M. Sigalas, C. Soukoulis, and K. Ho, "Defect structures in a layer-by-layer photonic band-gap crystal," Phys. Rev. B 51, 13961-13965 (1995).

E. Ozbay, A. Abeyta, G. Tuttle, M. Tringides, R. Biswas, and C. Soukoulis, C. Chan, and K. Ho, "Measurement of a three-dimensional photonic band gap in a crystal structure made of dielectric rods," Phys. Rev. B 50, 1945-1948 (1994).

Yablonovitch, E.

E. Yablonovitch, "Inhibited spontaneous emission in solid-state physics and electronics," Phys. Rev. Lett. 58, 2059-2062 (1987).
[CrossRef] [PubMed]

Ye, Z.

Yoshimoto, S.

S. Ogawa, M. Imada, S. Yoshimoto, M. Okano, and S. Noda, "Control of light emission by 3D photonic crystals," Science 305, 227-229 (2004).
[CrossRef] [PubMed]

Appl. Phys. Lett.

K. Srinivasan, P. Barclay, O. Painter, J. Chen, A. Cho, and C. Gmachl, "Experimental demonstration of a high quality factor photonic crystal microcavity," Appl. Phys. Lett. 83, 1915-1917 (2003).
[CrossRef]

Nature

M. Qi, E. Lidorikis, P. Rakich, S. Johnson, J. Joannopoulos, E. Ippen, and H. Smith, "A three-dimensional optical photonic crystal with designed point defects," Nature 429, 538-542 (2004).
[CrossRef] [PubMed]

Opt. Express

Opt. Lett.

Phys. Rev. B

C. Sauvan, P. Lalanne, and J. Hugonin, "Slow-wave effect and mode-profile matching in photonic crystal microcavities," Phys. Rev. B 71, 165118 (2005).

Z. Li and K. Ho, "Application of structural symmetries in the plane-wave-based transfer-matrix method for three-dimensional photonic crystal waveguides," Phys. Rev. B 68, 245117 (2003).

E. Ozbay, A. Abeyta, G. Tuttle, M. Tringides, R. Biswas, and C. Soukoulis, C. Chan, and K. Ho, "Measurement of a three-dimensional photonic band gap in a crystal structure made of dielectric rods," Phys. Rev. B 50, 1945-1948 (1994).

E. Ozbay, G. Tuttle, M. Sigalas, C. Soukoulis, and K. Ho, "Defect structures in a layer-by-layer photonic band-gap crystal," Phys. Rev. B 51, 13961-13965 (1995).

Phys. Rev. E

Z. Li and L. Lin, "Photonic band structures solved by a plane-wave-based transfer-matrix method," Phys. Rev. E 67, 046607 (2003).

Phys. Rev. Lett.

E. Yablonovitch, "Inhibited spontaneous emission in solid-state physics and electronics," Phys. Rev. Lett. 58, 2059-2062 (1987).
[CrossRef] [PubMed]

S. John, "Strong localization of photons in certain disordered dielectric superlattices," Phys. Rev. Lett. 58, 2486-2489 (1987).
[CrossRef] [PubMed]

K. Ho, C. Chan, and C. Soukoulis, "Existence of a photonic gap in periodic dielectric structures," Phys. Rev. Lett. 65, 3152-3155 (1990).
[CrossRef] [PubMed]

Science

S. Ogawa, M. Imada, S. Yoshimoto, M. Okano, and S. Noda, "Control of light emission by 3D photonic crystals," Science 305, 227-229 (2004).
[CrossRef] [PubMed]

Solid State Commun.

K. Ho, C. Chan, C. Soukoulis, R. Biswas, and M. Sigalas, "Photonic band gaps in three dimensions: new layer-by-layer periodic structures," Solid State Commun. 89, 413-416 (1994).
[CrossRef]

Other

J. Joannopoulos, R. Meade, and J. Winn, Photonic Crystals (Princeton University Press, 1995).

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Figures (6)

Fig. 1.
Fig. 1.

(a) shows the schematic picture of 3D layer-by-layer PC (not the actual experiment unit); (b) shows the cavity generated by removing portion of the rod material and the stacking sequence along with the polarization direction of electric field; and (c) shows the microwave experiment set up with two horn antennas used for coupling.

Fig. 2.
Fig. 2.

A typical transmission response of a defect cavity for both microwave experiment (red) and numerical simulation (blue), along with the directional band gap of the perfect crystal (gray). The inset is the zoom in view of the transmission around the resonant frequency.

Fig. 3.
Fig. 3.

Comparison of numerical simulation (gray circles with dashed lines) and microwave experiments (black squares with solid lines) for resonant frequency and Q value when the number of cladding layers are increased with fixed cavity size (d/a=1).

Fig. 4.
Fig. 4.

Experimental response of peak resonant frequency for cavities with fine tuned size from 0.5a to 8a. The black square is the highest transmission peak among all resonant peaks for fixed cavity size, the gray square is the relatively low transmission peaks, and the blue line with arrow is the trends of dominant mode if relative larger tuning steps are used.

Fig. 5.
Fig. 5.

Comparison between the microwave experiments (dots) and TMM calculations (lines) with different color representing two different modes (A and B).

Fig. 6.
Fig. 6.

Electric field mode profile from TMM calculation for resonant mode A and B (defined at Fig. 5) of cavity size 2a with the solid rectangle showing the location of the cavity. The x and y scales are in unit of lattice constant a.

Metrics