Abstract

We propose a type of photonic quantum well made of two different photonic crystals with negative- and positive-index materials. It is demonstrated by transfer matrix method that, omnidirectional and multichannel filtering can be achieved. Resonance tunneling modes, or the multichannel filtering modes, are found to exist when a passband of the well photonic crystal is located inside the gap of the barrier photonic crystals. And for each passband of the well photonic crystal in the photonic bandgap of the barrier photonic crystal, the number of modes is the same as the number of periods in the well photonic crystals. Moreover, the modes are insensitive to the incident angle from 0 to 85 degrees and the scaling of the barrier photonic crystals at a certain range. Such structures are useful for all-direction receiving, sending, or linking-up of multi-channel signals in wireless-communication networks. And they can be applied in signal-detection systems to enhance signal-detection sensitivity.

© 2009 Optical Society of America

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  1. V. G. Veselago, "The electrodynamics of substances with simulataneously negative values of permittivity and permeability," Sov. Phys. Usp. 10, 509-514 (1968).
    [CrossRef]
  2. J. B. Pendry, "Negative refraction makes a perfect lens," Phys. Rev. Lett. 85, 3966-3969 (2000).
    [CrossRef] [PubMed]
  3. J. Li, L. Zhou, C. T. Chan, and P. Sheng, "Photonic band gap from a stack of positive and negative index materials," Phys. Rev. Lett. 90, 083901 (2003).
    [CrossRef] [PubMed]
  4. H. T. Jiang, H. Chen, H. Q. Li, Y. W. Zhang, and S. Y. Zhu, "Omnidirectional gap and defect mode of one-dimensional photonic crystals containing negative-index materials," Appl. Phys. Lett. 83, 5386-5388 (2003).
    [CrossRef]
  5. 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]
  6. Y. H. Chen, "Merging of omnidirectional defect modes in one-dimensional photonic crystals with a single-negative material defect," J. Opt. Soc. Am. B 25, 972-975 (2008).
    [CrossRef]
  7. L. Esaki, and R. Tus, "Superlattice and negative diferential conductivity in semiconductors," IBM J. Res. Dev. 14, 61-65 (1970).
    [CrossRef]
  8. S. Y. Lin, V. M. Hietala, S. K. Lyo, and A. Zaslavsky, "Photonic band gap quantum well and quantum box structures: A high-Q resonant cavity," Appl. Phys. Lett. 68, 3233-3235 (1996).
    [CrossRef]
  9. J. Zi, J. Wan, and C. Zhang, "Large frequency range of negligible transmission in one-dimensional photonic quantum well structures," Appl. Phys. Lett. 73, 2084-2086 (1998).
    [CrossRef]
  10. C. Zhang, F. Qiao, J. Wan, and J. Zi, "Enlargement of nontransmission frequency range in photonic crystals by using multiple heterostructures," J. Appl. Phys. 87, 3174-3176 (2000).
    [CrossRef]
  11. F. Qiao, C. Zhang, J. Wan and J. Zi, "Photonic quantum-well structures: Multiple channeled filtering phenomena," Appl. Phys. Lett. 77, 3698-3700 (2000).
    [CrossRef]
  12. 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]
  13. Y. H. Chen, "Frequency response of resonance modes in heterostructures composed of single-negative materials," J. Opt. Soc. Am. B 25,1794-1799 (2008).
    [CrossRef]
  14. L. Liu, C. Caloz, C. C. Chang, and T. Itoh, "Forward coupling phenomena between artifical left-handed transmission lines," J. Appl. Phys. 92, 5560-5565 (2002).
    [CrossRef]
  15. M. Born and E. Wolf, Principles of Optics, 7th (expanded) ed., (Cambridge U. Press, 1999).
  16. L. Feng, X. P. Liu, M. H. Lu, and Y. F. Chen, "Phase compensating effect in left-handed materials," Phys. Lett. A. 332, 449-455 (2004).
    [CrossRef]

2008 (2)

2007 (1)

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]

2006 (1)

2004 (1)

L. Feng, X. P. Liu, M. H. Lu, and Y. F. Chen, "Phase compensating effect in left-handed materials," Phys. Lett. A. 332, 449-455 (2004).
[CrossRef]

2003 (2)

J. Li, L. Zhou, C. T. Chan, and P. Sheng, "Photonic band gap from a stack of positive and negative index materials," Phys. Rev. Lett. 90, 083901 (2003).
[CrossRef] [PubMed]

H. T. Jiang, H. Chen, H. Q. Li, Y. W. Zhang, and S. Y. Zhu, "Omnidirectional gap and defect mode of one-dimensional photonic crystals containing negative-index materials," Appl. Phys. Lett. 83, 5386-5388 (2003).
[CrossRef]

2002 (1)

L. Liu, C. Caloz, C. C. Chang, and T. Itoh, "Forward coupling phenomena between artifical left-handed transmission lines," J. Appl. Phys. 92, 5560-5565 (2002).
[CrossRef]

2000 (3)

C. Zhang, F. Qiao, J. Wan, and J. Zi, "Enlargement of nontransmission frequency range in photonic crystals by using multiple heterostructures," J. Appl. Phys. 87, 3174-3176 (2000).
[CrossRef]

F. Qiao, C. Zhang, J. Wan and J. Zi, "Photonic quantum-well structures: Multiple channeled filtering phenomena," Appl. Phys. Lett. 77, 3698-3700 (2000).
[CrossRef]

J. B. Pendry, "Negative refraction makes a perfect lens," Phys. Rev. Lett. 85, 3966-3969 (2000).
[CrossRef] [PubMed]

1998 (1)

J. Zi, J. Wan, and C. Zhang, "Large frequency range of negligible transmission in one-dimensional photonic quantum well structures," Appl. Phys. Lett. 73, 2084-2086 (1998).
[CrossRef]

1996 (1)

S. Y. Lin, V. M. Hietala, S. K. Lyo, and A. Zaslavsky, "Photonic band gap quantum well and quantum box structures: A high-Q resonant cavity," Appl. Phys. Lett. 68, 3233-3235 (1996).
[CrossRef]

1970 (1)

L. Esaki, and R. Tus, "Superlattice and negative diferential conductivity in semiconductors," IBM J. Res. Dev. 14, 61-65 (1970).
[CrossRef]

1968 (1)

V. G. Veselago, "The electrodynamics of substances with simulataneously negative values of permittivity and permeability," Sov. Phys. Usp. 10, 509-514 (1968).
[CrossRef]

Caloz, C.

L. Liu, C. Caloz, C. C. Chang, and T. Itoh, "Forward coupling phenomena between artifical left-handed transmission lines," J. Appl. Phys. 92, 5560-5565 (2002).
[CrossRef]

Chan, C. T.

J. Li, L. Zhou, C. T. Chan, and P. Sheng, "Photonic band gap from a stack of positive and negative index materials," Phys. Rev. Lett. 90, 083901 (2003).
[CrossRef] [PubMed]

Chang, C. C.

L. Liu, C. Caloz, C. C. Chang, and T. Itoh, "Forward coupling phenomena between artifical left-handed transmission lines," J. Appl. Phys. 92, 5560-5565 (2002).
[CrossRef]

Chen, H.

H. T. Jiang, H. Chen, H. Q. Li, Y. W. Zhang, and S. Y. Zhu, "Omnidirectional gap and defect mode of one-dimensional photonic crystals containing negative-index materials," Appl. Phys. Lett. 83, 5386-5388 (2003).
[CrossRef]

Chen, Y. F.

L. Feng, X. P. Liu, M. H. Lu, and Y. F. Chen, "Phase compensating effect in left-handed materials," Phys. Lett. A. 332, 449-455 (2004).
[CrossRef]

Chen, Y. H.

Dai, X.

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]

Dong, J. W.

Esaki, L.

L. Esaki, and R. Tus, "Superlattice and negative diferential conductivity in semiconductors," IBM J. Res. Dev. 14, 61-65 (1970).
[CrossRef]

Fan, D.

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]

Feng, L.

L. Feng, X. P. Liu, M. H. Lu, and Y. F. Chen, "Phase compensating effect in left-handed materials," Phys. Lett. A. 332, 449-455 (2004).
[CrossRef]

Hietala, V. M.

S. Y. Lin, V. M. Hietala, S. K. Lyo, and A. Zaslavsky, "Photonic band gap quantum well and quantum box structures: A high-Q resonant cavity," Appl. Phys. Lett. 68, 3233-3235 (1996).
[CrossRef]

Itoh, T.

L. Liu, C. Caloz, C. C. Chang, and T. Itoh, "Forward coupling phenomena between artifical left-handed transmission lines," J. Appl. Phys. 92, 5560-5565 (2002).
[CrossRef]

Jiang, H. T.

H. T. Jiang, H. Chen, H. Q. Li, Y. W. Zhang, and S. Y. Zhu, "Omnidirectional gap and defect mode of one-dimensional photonic crystals containing negative-index materials," Appl. Phys. Lett. 83, 5386-5388 (2003).
[CrossRef]

Li, H. Q.

H. T. Jiang, H. Chen, H. Q. Li, Y. W. Zhang, and S. Y. Zhu, "Omnidirectional gap and defect mode of one-dimensional photonic crystals containing negative-index materials," Appl. Phys. Lett. 83, 5386-5388 (2003).
[CrossRef]

Li, J.

J. Li, L. Zhou, C. T. Chan, and P. Sheng, "Photonic band gap from a stack of positive and negative index materials," Phys. Rev. Lett. 90, 083901 (2003).
[CrossRef] [PubMed]

Lin, S. Y.

S. Y. Lin, V. M. Hietala, S. K. Lyo, and A. Zaslavsky, "Photonic band gap quantum well and quantum box structures: A high-Q resonant cavity," Appl. Phys. Lett. 68, 3233-3235 (1996).
[CrossRef]

Liu, L.

L. Liu, C. Caloz, C. C. Chang, and T. Itoh, "Forward coupling phenomena between artifical left-handed transmission lines," J. Appl. Phys. 92, 5560-5565 (2002).
[CrossRef]

Liu, X. P.

L. Feng, X. P. Liu, M. H. Lu, and Y. F. Chen, "Phase compensating effect in left-handed materials," Phys. Lett. A. 332, 449-455 (2004).
[CrossRef]

Lu, M. H.

L. Feng, X. P. Liu, M. H. Lu, and Y. F. Chen, "Phase compensating effect in left-handed materials," Phys. Lett. A. 332, 449-455 (2004).
[CrossRef]

Lyo, S. K.

S. Y. Lin, V. M. Hietala, S. K. Lyo, and A. Zaslavsky, "Photonic band gap quantum well and quantum box structures: A high-Q resonant cavity," Appl. Phys. Lett. 68, 3233-3235 (1996).
[CrossRef]

Pendry, J. B.

J. B. Pendry, "Negative refraction makes a perfect lens," Phys. Rev. Lett. 85, 3966-3969 (2000).
[CrossRef] [PubMed]

Qiao, F.

C. Zhang, F. Qiao, J. Wan, and J. Zi, "Enlargement of nontransmission frequency range in photonic crystals by using multiple heterostructures," J. Appl. Phys. 87, 3174-3176 (2000).
[CrossRef]

F. Qiao, C. Zhang, J. Wan and J. Zi, "Photonic quantum-well structures: Multiple channeled filtering phenomena," Appl. Phys. Lett. 77, 3698-3700 (2000).
[CrossRef]

Sheng, P.

J. Li, L. Zhou, C. T. Chan, and P. Sheng, "Photonic band gap from a stack of positive and negative index materials," Phys. Rev. Lett. 90, 083901 (2003).
[CrossRef] [PubMed]

Tus, R.

L. Esaki, and R. Tus, "Superlattice and negative diferential conductivity in semiconductors," IBM J. Res. Dev. 14, 61-65 (1970).
[CrossRef]

Veselago, V. G.

V. G. Veselago, "The electrodynamics of substances with simulataneously negative values of permittivity and permeability," Sov. Phys. Usp. 10, 509-514 (1968).
[CrossRef]

Wan, J.

F. Qiao, C. Zhang, J. Wan and J. Zi, "Photonic quantum-well structures: Multiple channeled filtering phenomena," Appl. Phys. Lett. 77, 3698-3700 (2000).
[CrossRef]

C. Zhang, F. Qiao, J. Wan, and J. Zi, "Enlargement of nontransmission frequency range in photonic crystals by using multiple heterostructures," J. Appl. Phys. 87, 3174-3176 (2000).
[CrossRef]

J. Zi, J. Wan, and C. Zhang, "Large frequency range of negligible transmission in one-dimensional photonic quantum well structures," Appl. Phys. Lett. 73, 2084-2086 (1998).
[CrossRef]

Wang, H. Z.

Wen, S.

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]

Xiang, Y.

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]

Zaslavsky, A.

S. Y. Lin, V. M. Hietala, S. K. Lyo, and A. Zaslavsky, "Photonic band gap quantum well and quantum box structures: A high-Q resonant cavity," Appl. Phys. Lett. 68, 3233-3235 (1996).
[CrossRef]

Zhang, C.

C. Zhang, F. Qiao, J. Wan, and J. Zi, "Enlargement of nontransmission frequency range in photonic crystals by using multiple heterostructures," J. Appl. Phys. 87, 3174-3176 (2000).
[CrossRef]

F. Qiao, C. Zhang, J. Wan and J. Zi, "Photonic quantum-well structures: Multiple channeled filtering phenomena," Appl. Phys. Lett. 77, 3698-3700 (2000).
[CrossRef]

J. Zi, J. Wan, and C. Zhang, "Large frequency range of negligible transmission in one-dimensional photonic quantum well structures," Appl. Phys. Lett. 73, 2084-2086 (1998).
[CrossRef]

Zhang, Y. W.

H. T. Jiang, H. Chen, H. Q. Li, Y. W. Zhang, and S. Y. Zhu, "Omnidirectional gap and defect mode of one-dimensional photonic crystals containing negative-index materials," Appl. Phys. Lett. 83, 5386-5388 (2003).
[CrossRef]

Zhou, L.

J. Li, L. Zhou, C. T. Chan, and P. Sheng, "Photonic band gap from a stack of positive and negative index materials," Phys. Rev. Lett. 90, 083901 (2003).
[CrossRef] [PubMed]

Zhu, S. Y.

H. T. Jiang, H. Chen, H. Q. Li, Y. W. Zhang, and S. Y. Zhu, "Omnidirectional gap and defect mode of one-dimensional photonic crystals containing negative-index materials," Appl. Phys. Lett. 83, 5386-5388 (2003).
[CrossRef]

Zi, J.

C. Zhang, F. Qiao, J. Wan, and J. Zi, "Enlargement of nontransmission frequency range in photonic crystals by using multiple heterostructures," J. Appl. Phys. 87, 3174-3176 (2000).
[CrossRef]

F. Qiao, C. Zhang, J. Wan and J. Zi, "Photonic quantum-well structures: Multiple channeled filtering phenomena," Appl. Phys. Lett. 77, 3698-3700 (2000).
[CrossRef]

J. Zi, J. Wan, and C. Zhang, "Large frequency range of negligible transmission in one-dimensional photonic quantum well structures," Appl. Phys. Lett. 73, 2084-2086 (1998).
[CrossRef]

Appl. Phys. Lett. (4)

H. T. Jiang, H. Chen, H. Q. Li, Y. W. Zhang, and S. Y. Zhu, "Omnidirectional gap and defect mode of one-dimensional photonic crystals containing negative-index materials," Appl. Phys. Lett. 83, 5386-5388 (2003).
[CrossRef]

S. Y. Lin, V. M. Hietala, S. K. Lyo, and A. Zaslavsky, "Photonic band gap quantum well and quantum box structures: A high-Q resonant cavity," Appl. Phys. Lett. 68, 3233-3235 (1996).
[CrossRef]

J. Zi, J. Wan, and C. Zhang, "Large frequency range of negligible transmission in one-dimensional photonic quantum well structures," Appl. Phys. Lett. 73, 2084-2086 (1998).
[CrossRef]

F. Qiao, C. Zhang, J. Wan and J. Zi, "Photonic quantum-well structures: Multiple channeled filtering phenomena," Appl. Phys. Lett. 77, 3698-3700 (2000).
[CrossRef]

IBM J. Res. Dev. (1)

L. Esaki, and R. Tus, "Superlattice and negative diferential conductivity in semiconductors," IBM J. Res. Dev. 14, 61-65 (1970).
[CrossRef]

J. Appl. Phys. (2)

C. Zhang, F. Qiao, J. Wan, and J. Zi, "Enlargement of nontransmission frequency range in photonic crystals by using multiple heterostructures," J. Appl. Phys. 87, 3174-3176 (2000).
[CrossRef]

L. Liu, C. Caloz, C. C. Chang, and T. Itoh, "Forward coupling phenomena between artifical left-handed transmission lines," J. Appl. Phys. 92, 5560-5565 (2002).
[CrossRef]

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

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]

J. Opt. Soc. Am. B (3)

Phys. Lett. A. (1)

L. Feng, X. P. Liu, M. H. Lu, and Y. F. Chen, "Phase compensating effect in left-handed materials," Phys. Lett. A. 332, 449-455 (2004).
[CrossRef]

Phys. Rev. Lett. (2)

J. B. Pendry, "Negative refraction makes a perfect lens," Phys. Rev. Lett. 85, 3966-3969 (2000).
[CrossRef] [PubMed]

J. Li, L. Zhou, C. T. Chan, and P. Sheng, "Photonic band gap from a stack of positive and negative index materials," Phys. Rev. Lett. 90, 083901 (2003).
[CrossRef] [PubMed]

Sov. Phys. Usp. (1)

V. G. Veselago, "The electrodynamics of substances with simulataneously negative values of permittivity and permeability," Sov. Phys. Usp. 10, 509-514 (1968).
[CrossRef]

Other (1)

M. Born and E. Wolf, Principles of Optics, 7th (expanded) ed., (Cambridge U. Press, 1999).

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Figures (4)

Fig. 1.
Fig. 1.

The PBGs of PhC(AB) and PhC(CD) for the first set of parameters (a) and that for the second set of parameters (b). The solid lines and dashed lines are for PhC(AB) and PhC(CD), respectively. The gray areas are the PBGs of PhC(AB).

Fig. 2.
Fig. 2.

Transmittance spectra of the photonic QW structures (AB) n (CD) m (AB) n (m = 1 ~ 4) for the first set of parameters (a) and that for the second set of parameters (b).

Fig. 3.
Fig. 3.

Influence of incident angle θ on the resonance modes for the first set of parameters (a) and that for the second set of parameters (b), where I, II, III, and IV refer to the modes indicated in Fig. 2.

Fig. 4.
Fig. 4.

Influence of the scaling factor ρ of the barrier PhCs on the relative resonance-frequency shift Δω/ω 0 under θ = 30° for the first set of parameters (a) and that for the second set of parameters (b), where I, II, III, and IV refer to the modes indicated in Fig. 2.

Equations (5)

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

ε NIM = ε α ω 2 ,
μ NIM = μ β ω 2 ,
ρ = d / d 0 ,
M j ( Δ z , ω ) = [ cos ( k zj Δ z ) i q j sin ( k zj Δ z ) i q j sin ( k zj Δ z ) cos ( k zj Δ z ) ] ,
t ( ω ) = 2 cos θ [ x 11 ( ω ) + x 22 ( ω ) ] cos θ + [ x 12 ( ω ) cos 2 θ + x 21 ( ω ) ] ,

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