Abstract

The theoretical deduction for the frequency variations of the defect mode and its dependence on the incident angle in one-dimensional defective photonic crystals is discussed. Filters with the dual function of narrow frequency passbands and sharp angular pass breadths in visible and near-infrared wave bands, in which both the defect mode and the periodic structure are layers of integral times of quarter-wavelengths, were designed. This kind of filter was fabricated with commonly used coating machines.

© 2005 Optical Society of America

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References

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  1. E. Yablonovitch, T. J. Gmitter, R. D. Meade, A. M. Rappe, K. D. Brommer, J. D. Joannopoulos, “Donor and acceptor modes in photonic band structure,” Phys. Rev. Lett. 67, 3380–3383 (1991).
    [CrossRef] [PubMed]
  2. D. R. Smith, R. Dalichaouch, N. Kroll, S. Schultz, S. L. McCall, P. M. Platzman, “Photonic band structure and defects in one and two dimensions,” J. Opt. Soc. Am. B 10, 314–321 (1993).
    [CrossRef]
  3. X. Wang, X. Hu, Y. Li, W. Jia, C. Xu, X. Liu, J. Zi, “Enlargement of omnidirectional total reflection frequency range in one-dimensional photonic crystals by using photonic heterostructures,” Appl. Phys. Lett. 80, 4291–4293 (2002).
    [CrossRef]
  4. P. St, J. Russell, S. Tredwell, P. J. Roberts, “Full photonic bandgaps and spontaneous emission control in 1D multilayer dielectric structures,” Opt. Commun. 160, 66–71 (1999).
    [CrossRef]
  5. S. Noda, A. Chutinan, M. Imada, “Trapping and emission of photons by a single defect in a photonic bandgap structure,” Nature 407, 608–610 (2000).
    [CrossRef] [PubMed]
  6. B. Shi, Z. M. Jiang, X. Wang, “Defective photonic crystals with greatly enhanced second-harmonic generation,” Opt. Lett. 26, 1194–1196 (2001).
    [CrossRef]
  7. Z. Wang, L. Wang, Y. Wu, L. Chen, “Multiple channeled phenomena in heterostructures with defects mode,” Appl. Phys. Lett. 84, 1629–1631 (2004).
    [CrossRef]
  8. A. Figotin, V. Gorentsveig, “Localized electromagnetic waves in a layered periodic dielectric medium with a defect,” Phys. Rev. B 58, 180–188 (1998).
    [CrossRef]
  9. H. Jiang, H. Chen, H. Li, Y. Zhang, “Omnidirectional gap and defect mode of one-dimensional photonic crystals containing negative-index materials,” Appl. Phys. Lett. 83, 5386–5388 (2003).
    [CrossRef]
  10. G. Q. Liang, P. Han, H. Z. Wang, “Narrow frequency and sharp angular defect mode in one-dimensional photonic crystals from a photonic heterostructure,” Opt. Lett. 29, 192–194 (2004).
    [CrossRef] [PubMed]
  11. H. A. Macleod, Thin-Film Optical Filters, 2nd Ed. (Macmillan, 1986), p. 18.
  12. A. Yariv, P. Yeh, Optical Waves in Crystals: Propagation and Control of Laser Radiation (Wiley-Interscience, 1984), pp. 174–179, 459–469.

2004 (2)

Z. Wang, L. Wang, Y. Wu, L. Chen, “Multiple channeled phenomena in heterostructures with defects mode,” Appl. Phys. Lett. 84, 1629–1631 (2004).
[CrossRef]

G. Q. Liang, P. Han, H. Z. Wang, “Narrow frequency and sharp angular defect mode in one-dimensional photonic crystals from a photonic heterostructure,” Opt. Lett. 29, 192–194 (2004).
[CrossRef] [PubMed]

2003 (1)

H. Jiang, H. Chen, H. Li, Y. Zhang, “Omnidirectional gap and defect mode of one-dimensional photonic crystals containing negative-index materials,” Appl. Phys. Lett. 83, 5386–5388 (2003).
[CrossRef]

2002 (1)

X. Wang, X. Hu, Y. Li, W. Jia, C. Xu, X. Liu, J. Zi, “Enlargement of omnidirectional total reflection frequency range in one-dimensional photonic crystals by using photonic heterostructures,” Appl. Phys. Lett. 80, 4291–4293 (2002).
[CrossRef]

2001 (1)

2000 (1)

S. Noda, A. Chutinan, M. Imada, “Trapping and emission of photons by a single defect in a photonic bandgap structure,” Nature 407, 608–610 (2000).
[CrossRef] [PubMed]

1999 (1)

P. St, J. Russell, S. Tredwell, P. J. Roberts, “Full photonic bandgaps and spontaneous emission control in 1D multilayer dielectric structures,” Opt. Commun. 160, 66–71 (1999).
[CrossRef]

1998 (1)

A. Figotin, V. Gorentsveig, “Localized electromagnetic waves in a layered periodic dielectric medium with a defect,” Phys. Rev. B 58, 180–188 (1998).
[CrossRef]

1993 (1)

1991 (1)

E. Yablonovitch, T. J. Gmitter, R. D. Meade, A. M. Rappe, K. D. Brommer, J. D. Joannopoulos, “Donor and acceptor modes in photonic band structure,” Phys. Rev. Lett. 67, 3380–3383 (1991).
[CrossRef] [PubMed]

Brommer, K. D.

E. Yablonovitch, T. J. Gmitter, R. D. Meade, A. M. Rappe, K. D. Brommer, J. D. Joannopoulos, “Donor and acceptor modes in photonic band structure,” Phys. Rev. Lett. 67, 3380–3383 (1991).
[CrossRef] [PubMed]

Chen, H.

H. Jiang, H. Chen, H. Li, Y. Zhang, “Omnidirectional gap and defect mode of one-dimensional photonic crystals containing negative-index materials,” Appl. Phys. Lett. 83, 5386–5388 (2003).
[CrossRef]

Chen, L.

Z. Wang, L. Wang, Y. Wu, L. Chen, “Multiple channeled phenomena in heterostructures with defects mode,” Appl. Phys. Lett. 84, 1629–1631 (2004).
[CrossRef]

Chutinan, A.

S. Noda, A. Chutinan, M. Imada, “Trapping and emission of photons by a single defect in a photonic bandgap structure,” Nature 407, 608–610 (2000).
[CrossRef] [PubMed]

Dalichaouch, R.

Figotin, A.

A. Figotin, V. Gorentsveig, “Localized electromagnetic waves in a layered periodic dielectric medium with a defect,” Phys. Rev. B 58, 180–188 (1998).
[CrossRef]

Gmitter, T. J.

E. Yablonovitch, T. J. Gmitter, R. D. Meade, A. M. Rappe, K. D. Brommer, J. D. Joannopoulos, “Donor and acceptor modes in photonic band structure,” Phys. Rev. Lett. 67, 3380–3383 (1991).
[CrossRef] [PubMed]

Gorentsveig, V.

A. Figotin, V. Gorentsveig, “Localized electromagnetic waves in a layered periodic dielectric medium with a defect,” Phys. Rev. B 58, 180–188 (1998).
[CrossRef]

Han, P.

Hu, X.

X. Wang, X. Hu, Y. Li, W. Jia, C. Xu, X. Liu, J. Zi, “Enlargement of omnidirectional total reflection frequency range in one-dimensional photonic crystals by using photonic heterostructures,” Appl. Phys. Lett. 80, 4291–4293 (2002).
[CrossRef]

Imada, M.

S. Noda, A. Chutinan, M. Imada, “Trapping and emission of photons by a single defect in a photonic bandgap structure,” Nature 407, 608–610 (2000).
[CrossRef] [PubMed]

Jia, W.

X. Wang, X. Hu, Y. Li, W. Jia, C. Xu, X. Liu, J. Zi, “Enlargement of omnidirectional total reflection frequency range in one-dimensional photonic crystals by using photonic heterostructures,” Appl. Phys. Lett. 80, 4291–4293 (2002).
[CrossRef]

Jiang, H.

H. Jiang, H. Chen, H. Li, Y. Zhang, “Omnidirectional gap and defect mode of one-dimensional photonic crystals containing negative-index materials,” Appl. Phys. Lett. 83, 5386–5388 (2003).
[CrossRef]

Jiang, Z. M.

Joannopoulos, J. D.

E. Yablonovitch, T. J. Gmitter, R. D. Meade, A. M. Rappe, K. D. Brommer, J. D. Joannopoulos, “Donor and acceptor modes in photonic band structure,” Phys. Rev. Lett. 67, 3380–3383 (1991).
[CrossRef] [PubMed]

Kroll, N.

Li, H.

H. Jiang, H. Chen, H. Li, Y. Zhang, “Omnidirectional gap and defect mode of one-dimensional photonic crystals containing negative-index materials,” Appl. Phys. Lett. 83, 5386–5388 (2003).
[CrossRef]

Li, Y.

X. Wang, X. Hu, Y. Li, W. Jia, C. Xu, X. Liu, J. Zi, “Enlargement of omnidirectional total reflection frequency range in one-dimensional photonic crystals by using photonic heterostructures,” Appl. Phys. Lett. 80, 4291–4293 (2002).
[CrossRef]

Liang, G. Q.

Liu, X.

X. Wang, X. Hu, Y. Li, W. Jia, C. Xu, X. Liu, J. Zi, “Enlargement of omnidirectional total reflection frequency range in one-dimensional photonic crystals by using photonic heterostructures,” Appl. Phys. Lett. 80, 4291–4293 (2002).
[CrossRef]

Macleod, H. A.

H. A. Macleod, Thin-Film Optical Filters, 2nd Ed. (Macmillan, 1986), p. 18.

McCall, S. L.

Meade, R. D.

E. Yablonovitch, T. J. Gmitter, R. D. Meade, A. M. Rappe, K. D. Brommer, J. D. Joannopoulos, “Donor and acceptor modes in photonic band structure,” Phys. Rev. Lett. 67, 3380–3383 (1991).
[CrossRef] [PubMed]

Noda, S.

S. Noda, A. Chutinan, M. Imada, “Trapping and emission of photons by a single defect in a photonic bandgap structure,” Nature 407, 608–610 (2000).
[CrossRef] [PubMed]

Platzman, P. M.

Rappe, A. M.

E. Yablonovitch, T. J. Gmitter, R. D. Meade, A. M. Rappe, K. D. Brommer, J. D. Joannopoulos, “Donor and acceptor modes in photonic band structure,” Phys. Rev. Lett. 67, 3380–3383 (1991).
[CrossRef] [PubMed]

Roberts, P. J.

P. St, J. Russell, S. Tredwell, P. J. Roberts, “Full photonic bandgaps and spontaneous emission control in 1D multilayer dielectric structures,” Opt. Commun. 160, 66–71 (1999).
[CrossRef]

Russell, J.

P. St, J. Russell, S. Tredwell, P. J. Roberts, “Full photonic bandgaps and spontaneous emission control in 1D multilayer dielectric structures,” Opt. Commun. 160, 66–71 (1999).
[CrossRef]

Schultz, S.

Shi, B.

Smith, D. R.

St, P.

P. St, J. Russell, S. Tredwell, P. J. Roberts, “Full photonic bandgaps and spontaneous emission control in 1D multilayer dielectric structures,” Opt. Commun. 160, 66–71 (1999).
[CrossRef]

Tredwell, S.

P. St, J. Russell, S. Tredwell, P. J. Roberts, “Full photonic bandgaps and spontaneous emission control in 1D multilayer dielectric structures,” Opt. Commun. 160, 66–71 (1999).
[CrossRef]

Wang, H. Z.

Wang, L.

Z. Wang, L. Wang, Y. Wu, L. Chen, “Multiple channeled phenomena in heterostructures with defects mode,” Appl. Phys. Lett. 84, 1629–1631 (2004).
[CrossRef]

Wang, X.

X. Wang, X. Hu, Y. Li, W. Jia, C. Xu, X. Liu, J. Zi, “Enlargement of omnidirectional total reflection frequency range in one-dimensional photonic crystals by using photonic heterostructures,” Appl. Phys. Lett. 80, 4291–4293 (2002).
[CrossRef]

B. Shi, Z. M. Jiang, X. Wang, “Defective photonic crystals with greatly enhanced second-harmonic generation,” Opt. Lett. 26, 1194–1196 (2001).
[CrossRef]

Wang, Z.

Z. Wang, L. Wang, Y. Wu, L. Chen, “Multiple channeled phenomena in heterostructures with defects mode,” Appl. Phys. Lett. 84, 1629–1631 (2004).
[CrossRef]

Wu, Y.

Z. Wang, L. Wang, Y. Wu, L. Chen, “Multiple channeled phenomena in heterostructures with defects mode,” Appl. Phys. Lett. 84, 1629–1631 (2004).
[CrossRef]

Xu, C.

X. Wang, X. Hu, Y. Li, W. Jia, C. Xu, X. Liu, J. Zi, “Enlargement of omnidirectional total reflection frequency range in one-dimensional photonic crystals by using photonic heterostructures,” Appl. Phys. Lett. 80, 4291–4293 (2002).
[CrossRef]

Yablonovitch, E.

E. Yablonovitch, T. J. Gmitter, R. D. Meade, A. M. Rappe, K. D. Brommer, J. D. Joannopoulos, “Donor and acceptor modes in photonic band structure,” Phys. Rev. Lett. 67, 3380–3383 (1991).
[CrossRef] [PubMed]

Yariv, A.

A. Yariv, P. Yeh, Optical Waves in Crystals: Propagation and Control of Laser Radiation (Wiley-Interscience, 1984), pp. 174–179, 459–469.

Yeh, P.

A. Yariv, P. Yeh, Optical Waves in Crystals: Propagation and Control of Laser Radiation (Wiley-Interscience, 1984), pp. 174–179, 459–469.

Zhang, Y.

H. Jiang, H. Chen, H. Li, Y. Zhang, “Omnidirectional gap and defect mode of one-dimensional photonic crystals containing negative-index materials,” Appl. Phys. Lett. 83, 5386–5388 (2003).
[CrossRef]

Zi, J.

X. Wang, X. Hu, Y. Li, W. Jia, C. Xu, X. Liu, J. Zi, “Enlargement of omnidirectional total reflection frequency range in one-dimensional photonic crystals by using photonic heterostructures,” Appl. Phys. Lett. 80, 4291–4293 (2002).
[CrossRef]

Appl. Phys. Lett. (3)

X. Wang, X. Hu, Y. Li, W. Jia, C. Xu, X. Liu, J. Zi, “Enlargement of omnidirectional total reflection frequency range in one-dimensional photonic crystals by using photonic heterostructures,” Appl. Phys. Lett. 80, 4291–4293 (2002).
[CrossRef]

Z. Wang, L. Wang, Y. Wu, L. Chen, “Multiple channeled phenomena in heterostructures with defects mode,” Appl. Phys. Lett. 84, 1629–1631 (2004).
[CrossRef]

H. Jiang, H. Chen, H. Li, Y. Zhang, “Omnidirectional gap and defect mode of one-dimensional photonic crystals containing negative-index materials,” Appl. Phys. Lett. 83, 5386–5388 (2003).
[CrossRef]

J. Opt. Soc. Am. B (1)

Nature (1)

S. Noda, A. Chutinan, M. Imada, “Trapping and emission of photons by a single defect in a photonic bandgap structure,” Nature 407, 608–610 (2000).
[CrossRef] [PubMed]

Opt. Commun. (1)

P. St, J. Russell, S. Tredwell, P. J. Roberts, “Full photonic bandgaps and spontaneous emission control in 1D multilayer dielectric structures,” Opt. Commun. 160, 66–71 (1999).
[CrossRef]

Opt. Lett. (2)

Phys. Rev. B (1)

A. Figotin, V. Gorentsveig, “Localized electromagnetic waves in a layered periodic dielectric medium with a defect,” Phys. Rev. B 58, 180–188 (1998).
[CrossRef]

Phys. Rev. Lett. (1)

E. Yablonovitch, T. J. Gmitter, R. D. Meade, A. M. Rappe, K. D. Brommer, J. D. Joannopoulos, “Donor and acceptor modes in photonic band structure,” Phys. Rev. Lett. 67, 3380–3383 (1991).
[CrossRef] [PubMed]

Other (2)

H. A. Macleod, Thin-Film Optical Filters, 2nd Ed. (Macmillan, 1986), p. 18.

A. Yariv, P. Yeh, Optical Waves in Crystals: Propagation and Control of Laser Radiation (Wiley-Interscience, 1984), pp. 174–179, 459–469.

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Figures (5)

Fig. 1
Fig. 1

Transmittance of conventional defective PCs [H(LH)52L(HL)5HL]2; nH = 2.35, nL = 1.38.

Fig. 2
Fig. 2

Schematic sketch of the photonic structure.

Fig. 3
Fig. 3

Results of theoretical calculations. Top, frequency-and incident angle-dependent transmittance of structure H(LH)8C1(HL)8HL(HL)8C2(LH)8; C1 = 2L, C2 = 2H, nH = 2.35, nL = 1.38. Bottom, frequency- and incident-angle-dependent transmittance of structure H(LH)8C1(HL)8HLH(LH)8C2(HL)8H; C1 = 2L, C2 = 4L, nH = 2.35, nL = 1.38.

Fig. 4
Fig. 4

Relative sensitivity of structure [H(LH)82L(HL)(HL)82H(LH)8].

Fig. 5
Fig. 5

(a) Calculated transmission spectra for (HL)4HCH(LH)4L(HL)4C2(LH)4; C1 = 2L, C2 = 2H, nH = 2.35, nL = 1.38. (b) Measured transmission spectra for (HL)4HC1 H(LH)4L(HL)4C2(LH)4; C1 = 2L, C2 = 2H, nH = 2.35, nL = 1.38.

Equations (5)

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φ 1 = φ 2 = 2 δ c 2 = k π ,             k = 0 ,     ± 1 , ± 2 , ,
φ 1 + φ 2 + 2 ω c C 0 n c d c cos θ c = 2 k π .
n 0 sin θ 0 = n c sin θ c ,
ω c = C 0 ( 2 k π - φ 1 - φ 2 ) 2 n c d c { 1 £ - [ ( n 0 / n c ) sin θ 0 ] 2 } 1 / 2 .
Δ ω c = ( ω c θ 0 ) Δ θ 0 = C 0 2 n c d c × ( [ 2 k π - φ 1 ( θ 0 ) - φ 2 ( θ 0 ) ] n 0 2 sin θ 0 cos θ 0 n c 2 { [ 1 - ( n 0 sin θ 0 n c ) 2 ] 3 } 1 / 2 Δ θ 0 - 1 [ 1 - ( n 0 sin θ 0 n c ) 2 ] 1 / 2 ( Δ φ 1 + Δ φ 2 ) ) .

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