Abstract

Tunable and omnidirectional filters have been demonstrated theoretically, using one-dimensional photonic crystals composed of single-negative materials. It is seen that a bilayer eight period structure can act as a tunable filter, which is sensitive to incident angle but insensitive to polarization. By increasing the number of periods to 16 and by tailoring the layer thicknesses, the same structure can act as an omnidirectional, polarization-independent filter for angles of incidence between 0° and 75°.

© 2011 Optical Society of America

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  1. H. Y. Lee, S. J. Cho, G. Y. Nam, W. H. Lee, T. Baba, H. Makino, M. W. Cho, and T. Yao, “Multiple-wavelength-transmission filters based on Si-SiO2 one-dimensional photonic crystals,” J. Appl. Phys. 97, 103111 (2005).
    [CrossRef]
  2. N. E. J. Hunt, E. F. Schubert, and G. J. Zydzik, “Resonant-cavity p-i-n photodetector utilizing an electron-beam evaporated Si/SiO2 microcavity,” Appl. Phys. Lett. 63, 391–393 (1993).
    [CrossRef]
  3. Y. Chen, “Tunable omnidirectional multichannel filters based on dual-defective photonic crystals containing negative-index materials,” J. Phys. D 42, 075106 (2009).
    [CrossRef]
  4. X. H. Deng, L. G. Fang, J. T. Liu, L. E. Zou, and N. H. Liu, “Multichannel filtering properties of photonic crystals containing single-negative materials,” Appl. Phys. B 99, 507–511(2010).
    [CrossRef]
  5. Y. Xiang, X. Dai, S. Wen, and D. Fan, “Omnidirectional and multiple-channeled high-quality filters of photonic heterostructures containing single-negative materials,” J. Opt. Soc. Am. A 24, A28–A32 (2007).
    [CrossRef]
  6. X. Hu, Z. Liu, and Q. Gong, “A multichannel filter in a photonic crystal heterostructure containing single-negative materials,” J. Opt. A 9, 877–883 (2007).
    [CrossRef]
  7. X.-H. Deng and N.-H. Liu, “Polarization-dependent angle filters based on one-dimensional photonic crystals using mu-negative materials,” J. Mod. Opt. 56, 482–486 (2009).
    [CrossRef]
  8. Y. H. Chen, J. W. Dong, and H. Z. Wang, “Twin defect modes in one-dimensional photonic crystals with a single-negative material defect,” Appl. Phys. Lett. 89, 141101(2006).
    [CrossRef]
  9. X.-H. Deng and N.-H. Liu, “Resonant tunnelling properties of photonic crystals containing mu-negative materials,” J. Phys. D 42, 045420 (2009).
    [CrossRef]
  10. Y. H. Chen, J. W. Dong, and H. Z. Wang, “Omnidirectional resonance modes in photonic crystal heterostructures containing single-negative materials,” J. Opt. Soc. Am. B 23, 2237–2240(2006).
    [CrossRef]
  11. L.-G. Wang, H. Chen, and S.-Y. Zhu, “Omnidirectional gap and defect mode of one-dimensional photonic crystals with single negative materials,” Phys. Rev. B 70, 245102 (2004).
    [CrossRef]

2010 (1)

X. H. Deng, L. G. Fang, J. T. Liu, L. E. Zou, and N. H. Liu, “Multichannel filtering properties of photonic crystals containing single-negative materials,” Appl. Phys. B 99, 507–511(2010).
[CrossRef]

2009 (3)

X.-H. Deng and N.-H. Liu, “Polarization-dependent angle filters based on one-dimensional photonic crystals using mu-negative materials,” J. Mod. Opt. 56, 482–486 (2009).
[CrossRef]

X.-H. Deng and N.-H. Liu, “Resonant tunnelling properties of photonic crystals containing mu-negative materials,” J. Phys. D 42, 045420 (2009).
[CrossRef]

Y. Chen, “Tunable omnidirectional multichannel filters based on dual-defective photonic crystals containing negative-index materials,” J. Phys. D 42, 075106 (2009).
[CrossRef]

2007 (2)

Y. Xiang, X. Dai, S. Wen, and D. Fan, “Omnidirectional and multiple-channeled high-quality filters of photonic heterostructures containing single-negative materials,” J. Opt. Soc. Am. A 24, A28–A32 (2007).
[CrossRef]

X. Hu, Z. Liu, and Q. Gong, “A multichannel filter in a photonic crystal heterostructure containing single-negative materials,” J. Opt. A 9, 877–883 (2007).
[CrossRef]

2006 (2)

Y. H. Chen, J. W. Dong, and H. Z. Wang, “Omnidirectional resonance modes in photonic crystal heterostructures containing single-negative materials,” J. Opt. Soc. Am. B 23, 2237–2240(2006).
[CrossRef]

Y. H. Chen, J. W. Dong, and H. Z. Wang, “Twin defect modes in one-dimensional photonic crystals with a single-negative material defect,” Appl. Phys. Lett. 89, 141101(2006).
[CrossRef]

2005 (1)

H. Y. Lee, S. J. Cho, G. Y. Nam, W. H. Lee, T. Baba, H. Makino, M. W. Cho, and T. Yao, “Multiple-wavelength-transmission filters based on Si-SiO2 one-dimensional photonic crystals,” J. Appl. Phys. 97, 103111 (2005).
[CrossRef]

2004 (1)

L.-G. Wang, H. Chen, and S.-Y. Zhu, “Omnidirectional gap and defect mode of one-dimensional photonic crystals with single negative materials,” Phys. Rev. B 70, 245102 (2004).
[CrossRef]

1993 (1)

N. E. J. Hunt, E. F. Schubert, and G. J. Zydzik, “Resonant-cavity p-i-n photodetector utilizing an electron-beam evaporated Si/SiO2 microcavity,” Appl. Phys. Lett. 63, 391–393 (1993).
[CrossRef]

Baba, T.

H. Y. Lee, S. J. Cho, G. Y. Nam, W. H. Lee, T. Baba, H. Makino, M. W. Cho, and T. Yao, “Multiple-wavelength-transmission filters based on Si-SiO2 one-dimensional photonic crystals,” J. Appl. Phys. 97, 103111 (2005).
[CrossRef]

Chen, H.

L.-G. Wang, H. Chen, and S.-Y. Zhu, “Omnidirectional gap and defect mode of one-dimensional photonic crystals with single negative materials,” Phys. Rev. B 70, 245102 (2004).
[CrossRef]

Chen, Y.

Y. Chen, “Tunable omnidirectional multichannel filters based on dual-defective photonic crystals containing negative-index materials,” J. Phys. D 42, 075106 (2009).
[CrossRef]

Chen, Y. H.

Y. H. Chen, J. W. Dong, and H. Z. Wang, “Omnidirectional resonance modes in photonic crystal heterostructures containing single-negative materials,” J. Opt. Soc. Am. B 23, 2237–2240(2006).
[CrossRef]

Y. H. Chen, J. W. Dong, and H. Z. Wang, “Twin defect modes in one-dimensional photonic crystals with a single-negative material defect,” Appl. Phys. Lett. 89, 141101(2006).
[CrossRef]

Cho, M. W.

H. Y. Lee, S. J. Cho, G. Y. Nam, W. H. Lee, T. Baba, H. Makino, M. W. Cho, and T. Yao, “Multiple-wavelength-transmission filters based on Si-SiO2 one-dimensional photonic crystals,” J. Appl. Phys. 97, 103111 (2005).
[CrossRef]

Cho, S. J.

H. Y. Lee, S. J. Cho, G. Y. Nam, W. H. Lee, T. Baba, H. Makino, M. W. Cho, and T. Yao, “Multiple-wavelength-transmission filters based on Si-SiO2 one-dimensional photonic crystals,” J. Appl. Phys. 97, 103111 (2005).
[CrossRef]

Dai, X.

Deng, X. H.

X. H. Deng, L. G. Fang, J. T. Liu, L. E. Zou, and N. H. Liu, “Multichannel filtering properties of photonic crystals containing single-negative materials,” Appl. Phys. B 99, 507–511(2010).
[CrossRef]

Deng, X.-H.

X.-H. Deng and N.-H. Liu, “Polarization-dependent angle filters based on one-dimensional photonic crystals using mu-negative materials,” J. Mod. Opt. 56, 482–486 (2009).
[CrossRef]

X.-H. Deng and N.-H. Liu, “Resonant tunnelling properties of photonic crystals containing mu-negative materials,” J. Phys. D 42, 045420 (2009).
[CrossRef]

Dong, J. W.

Y. H. Chen, J. W. Dong, and H. Z. Wang, “Omnidirectional resonance modes in photonic crystal heterostructures containing single-negative materials,” J. Opt. Soc. Am. B 23, 2237–2240(2006).
[CrossRef]

Y. H. Chen, J. W. Dong, and H. Z. Wang, “Twin defect modes in one-dimensional photonic crystals with a single-negative material defect,” Appl. Phys. Lett. 89, 141101(2006).
[CrossRef]

Fan, D.

Fang, L. G.

X. H. Deng, L. G. Fang, J. T. Liu, L. E. Zou, and N. H. Liu, “Multichannel filtering properties of photonic crystals containing single-negative materials,” Appl. Phys. B 99, 507–511(2010).
[CrossRef]

Gong, Q.

X. Hu, Z. Liu, and Q. Gong, “A multichannel filter in a photonic crystal heterostructure containing single-negative materials,” J. Opt. A 9, 877–883 (2007).
[CrossRef]

Hu, X.

X. Hu, Z. Liu, and Q. Gong, “A multichannel filter in a photonic crystal heterostructure containing single-negative materials,” J. Opt. A 9, 877–883 (2007).
[CrossRef]

Hunt, N. E. J.

N. E. J. Hunt, E. F. Schubert, and G. J. Zydzik, “Resonant-cavity p-i-n photodetector utilizing an electron-beam evaporated Si/SiO2 microcavity,” Appl. Phys. Lett. 63, 391–393 (1993).
[CrossRef]

Lee, H. Y.

H. Y. Lee, S. J. Cho, G. Y. Nam, W. H. Lee, T. Baba, H. Makino, M. W. Cho, and T. Yao, “Multiple-wavelength-transmission filters based on Si-SiO2 one-dimensional photonic crystals,” J. Appl. Phys. 97, 103111 (2005).
[CrossRef]

Lee, W. H.

H. Y. Lee, S. J. Cho, G. Y. Nam, W. H. Lee, T. Baba, H. Makino, M. W. Cho, and T. Yao, “Multiple-wavelength-transmission filters based on Si-SiO2 one-dimensional photonic crystals,” J. Appl. Phys. 97, 103111 (2005).
[CrossRef]

Liu, J. T.

X. H. Deng, L. G. Fang, J. T. Liu, L. E. Zou, and N. H. Liu, “Multichannel filtering properties of photonic crystals containing single-negative materials,” Appl. Phys. B 99, 507–511(2010).
[CrossRef]

Liu, N. H.

X. H. Deng, L. G. Fang, J. T. Liu, L. E. Zou, and N. H. Liu, “Multichannel filtering properties of photonic crystals containing single-negative materials,” Appl. Phys. B 99, 507–511(2010).
[CrossRef]

Liu, N.-H.

X.-H. Deng and N.-H. Liu, “Polarization-dependent angle filters based on one-dimensional photonic crystals using mu-negative materials,” J. Mod. Opt. 56, 482–486 (2009).
[CrossRef]

X.-H. Deng and N.-H. Liu, “Resonant tunnelling properties of photonic crystals containing mu-negative materials,” J. Phys. D 42, 045420 (2009).
[CrossRef]

Liu, Z.

X. Hu, Z. Liu, and Q. Gong, “A multichannel filter in a photonic crystal heterostructure containing single-negative materials,” J. Opt. A 9, 877–883 (2007).
[CrossRef]

Makino, H.

H. Y. Lee, S. J. Cho, G. Y. Nam, W. H. Lee, T. Baba, H. Makino, M. W. Cho, and T. Yao, “Multiple-wavelength-transmission filters based on Si-SiO2 one-dimensional photonic crystals,” J. Appl. Phys. 97, 103111 (2005).
[CrossRef]

Nam, G. Y.

H. Y. Lee, S. J. Cho, G. Y. Nam, W. H. Lee, T. Baba, H. Makino, M. W. Cho, and T. Yao, “Multiple-wavelength-transmission filters based on Si-SiO2 one-dimensional photonic crystals,” J. Appl. Phys. 97, 103111 (2005).
[CrossRef]

Schubert, E. F.

N. E. J. Hunt, E. F. Schubert, and G. J. Zydzik, “Resonant-cavity p-i-n photodetector utilizing an electron-beam evaporated Si/SiO2 microcavity,” Appl. Phys. Lett. 63, 391–393 (1993).
[CrossRef]

Wang, H. Z.

Y. H. Chen, J. W. Dong, and H. Z. Wang, “Twin defect modes in one-dimensional photonic crystals with a single-negative material defect,” Appl. Phys. Lett. 89, 141101(2006).
[CrossRef]

Y. H. Chen, J. W. Dong, and H. Z. Wang, “Omnidirectional resonance modes in photonic crystal heterostructures containing single-negative materials,” J. Opt. Soc. Am. B 23, 2237–2240(2006).
[CrossRef]

Wang, L.-G.

L.-G. Wang, H. Chen, and S.-Y. Zhu, “Omnidirectional gap and defect mode of one-dimensional photonic crystals with single negative materials,” Phys. Rev. B 70, 245102 (2004).
[CrossRef]

Wen, S.

Xiang, Y.

Yao, T.

H. Y. Lee, S. J. Cho, G. Y. Nam, W. H. Lee, T. Baba, H. Makino, M. W. Cho, and T. Yao, “Multiple-wavelength-transmission filters based on Si-SiO2 one-dimensional photonic crystals,” J. Appl. Phys. 97, 103111 (2005).
[CrossRef]

Zhu, S.-Y.

L.-G. Wang, H. Chen, and S.-Y. Zhu, “Omnidirectional gap and defect mode of one-dimensional photonic crystals with single negative materials,” Phys. Rev. B 70, 245102 (2004).
[CrossRef]

Zou, L. E.

X. H. Deng, L. G. Fang, J. T. Liu, L. E. Zou, and N. H. Liu, “Multichannel filtering properties of photonic crystals containing single-negative materials,” Appl. Phys. B 99, 507–511(2010).
[CrossRef]

Zydzik, G. J.

N. E. J. Hunt, E. F. Schubert, and G. J. Zydzik, “Resonant-cavity p-i-n photodetector utilizing an electron-beam evaporated Si/SiO2 microcavity,” Appl. Phys. Lett. 63, 391–393 (1993).
[CrossRef]

Appl. Phys. B (1)

X. H. Deng, L. G. Fang, J. T. Liu, L. E. Zou, and N. H. Liu, “Multichannel filtering properties of photonic crystals containing single-negative materials,” Appl. Phys. B 99, 507–511(2010).
[CrossRef]

Appl. Phys. Lett. (2)

N. E. J. Hunt, E. F. Schubert, and G. J. Zydzik, “Resonant-cavity p-i-n photodetector utilizing an electron-beam evaporated Si/SiO2 microcavity,” Appl. Phys. Lett. 63, 391–393 (1993).
[CrossRef]

Y. H. Chen, J. W. Dong, and H. Z. Wang, “Twin defect modes in one-dimensional photonic crystals with a single-negative material defect,” Appl. Phys. Lett. 89, 141101(2006).
[CrossRef]

J. Appl. Phys. (1)

H. Y. Lee, S. J. Cho, G. Y. Nam, W. H. Lee, T. Baba, H. Makino, M. W. Cho, and T. Yao, “Multiple-wavelength-transmission filters based on Si-SiO2 one-dimensional photonic crystals,” J. Appl. Phys. 97, 103111 (2005).
[CrossRef]

J. Mod. Opt. (1)

X.-H. Deng and N.-H. Liu, “Polarization-dependent angle filters based on one-dimensional photonic crystals using mu-negative materials,” J. Mod. Opt. 56, 482–486 (2009).
[CrossRef]

J. Opt. A (1)

X. Hu, Z. Liu, and Q. Gong, “A multichannel filter in a photonic crystal heterostructure containing single-negative materials,” J. Opt. A 9, 877–883 (2007).
[CrossRef]

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

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

J. Phys. D (2)

Y. Chen, “Tunable omnidirectional multichannel filters based on dual-defective photonic crystals containing negative-index materials,” J. Phys. D 42, 075106 (2009).
[CrossRef]

X.-H. Deng and N.-H. Liu, “Resonant tunnelling properties of photonic crystals containing mu-negative materials,” J. Phys. D 42, 045420 (2009).
[CrossRef]

Phys. Rev. B (1)

L.-G. Wang, H. Chen, and S.-Y. Zhu, “Omnidirectional gap and defect mode of one-dimensional photonic crystals with single negative materials,” Phys. Rev. B 70, 245102 (2004).
[CrossRef]

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Figures (8)

Fig. 1
Fig. 1

Depiction of a 1D binary periodic lattice. A (B) are MNG (ENG) materials.

Fig. 2
Fig. 2

Transmission spectra of 1D PC ( A B ) 8 for different incident angles for the case of TE wave. ( d A = 1.6 d , d B = 0.8 d .)

Fig. 3
Fig. 3

Transmission spectra of 1D PC ( A B ) 8 for different incident angles for the case of TM wave. ( d A = 1.6 d , d B = 0.8 d .)

Fig. 4
Fig. 4

Transmission spectra of 1D PC ( A B ) 8 at normal incidence for different thicknesses d A of the MNG layer (thickness d B of the ENG layer is constant).

Fig. 5
Fig. 5

Transmission spectra of 1D PC ( A B ) 8 for different damping factors (a)  10 6 ω o , (b)  5 × 10 6 ω o , and (c)  10 5 ω o . ( d A = 1.6 d , d B = 0.8 d .)

Fig. 6
Fig. 6

Transmission spectra of 1D PC ( A B ) 16 for different incident angles for the case of TE wave. ( d A = 0.4 d , d B = 0.8 d .)

Fig. 7
Fig. 7

Transmission spectra of 1D PC ( A B ) 16 for different incident angles for the case of TM wave. ( d A = 0.4 d , d B = 0.8 d .)

Fig. 8
Fig. 8

Band structure for 1D PC ( A B ) 16 for d A = 0.4 d , d B = 0.8 d . The dark solid curve indicates the polarization-independent omnidirectional transmission mode. The weak transmission mode at the lower-frequency side of the omnidirectional transmission mode is shown by means of crosses. Regions enclosed by the light solid curves (dashed curves) indicate the first (second) passbands on the higher-frequency side of the omnidirectional mode. The lower-frequency edge of the third passband is indicated by the dotted curve.

Equations (4)

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

ε 1 = a , μ 1 = 1 ω mp 2 / ω 2 ,
ε 2 = 1 ω ep 2 / ω 2 , μ 2 = b .
M ( Δ z , ω ) = [ cos ( k z Δ z ) i p z k z sin ( k z Δ z ) i k z p z sin ( k z Δ z ) cos ( k z Δ z ) ] ,
t ( ω ) = 2 q 0 ( q s x 11 + q 0 x 22 ) + ( q 0 q s x 12 + x 21 ) .

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