Abstract

The design and application of omnidirectional and multiple-channeled filters with high-quality (high-Q) factors applied by using photonic heterostructures containing single-negative materials is demonstrated. Through adjusting the period number of the heterostructures, the number of the resonance modes can be controlled, and the resonance modes are then insensitive to the incident angle. With perfect transmission, controllable mode, and omnidirectional channel, this structure opens a promising way to fabricate omnidirectional and multiple-channeled filters for future dense wavelength division multiplexing applications. The effect of the losses of single-negative materials on the filters is also considered.

© 2007 Optical Society of America

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  3. A. Sharkawy, S. Shi, and D. W. Prather, "Heterostructure photonic crystals: theory and applications," Appl. Opt. 41, 7245-7253 (2002).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  6. Q. Qin, H. Lu, S. N. Zhu, C. S. Yuan, Y. Y. Zhu, and N. B. Ming, "Resonance transmission modes in dual-periodical dielectric multilayer films," Appl. Phys. Lett. 82, 4654-4656 (2003).
    [CrossRef]
  7. V. G. Veselago, "The electrodynamics of substances with simultaneously negative values of permittivity and permeability," Sov. Phys. Usp. 10, 509-514 (1968).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  11. A. Alù and N. Engheta, "Pairing an epsilon-negative slab with a mu-negative slab: resonance, tunneling and transparency," IEEE Trans. Antennas Propag. 51, 2558-2570 (2003).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  15. G. S. Guan, H. T. Jiang, H. Q. Li, Y. W. Zhang, H. Chen, and S. Y. Zhu, "Tunneling modes of photonic heterostructures consisting of single-negative materials," Appl. Phys. Lett. 88, 211112 (2006).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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  21. V. M. Shalaev, "Optical negative-index metamaterials," Nat. Photonics 1, 41-48 (2006).
    [CrossRef]

2006 (4)

G. S. Guan, H. T. Jiang, H. Q. Li, Y. W. Zhang, H. Chen, and S. Y. Zhu, "Tunneling modes of photonic heterostructures consisting of single-negative materials," Appl. Phys. Lett. 88, 211112 (2006).
[CrossRef]

V. M. Shalaev, "Optical negative-index metamaterials," Nat. Photonics 1, 41-48 (2006).
[CrossRef]

G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, "Low-loss negative-index metamaterial at telecommunication wavelengths," Opt. Lett. 31, 1800-1802 (2006).
[CrossRef] [PubMed]

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]

2005 (2)

V. M. Shalaev, W. Cai, U. K. Chettiar, H.-K. Yuan, A. K. Sarychev, V. P. Drachev, and A. V. Kildishev, "Negative index of refraction in optical metamaterials," Opt. Lett. 30, 3356-3358 (2005).
[CrossRef]

K. Y. Xu, X. Zheng, C. L. Li, and W. L. She, "Design of omnidirectional and multiple channeled filters using one-dimensional photonic crystals containing a defect layer with a negative refractive index," Phys. Rev. E 71, 066604 (2005).
[CrossRef]

2004 (3)

H. T. Jiang, H. Chen, H. Q. Li, Y. W. Zhang, J. Zi, and S. Y. Zhu, "Properties of one-dimensional photonic crystals containing single-negative materials," Phys. Rev. E 69, 066607 (2004).
[CrossRef]

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]

E. L. Ivchenko, M. M. Voronov, M. V. Erementchouk, L. I. Deych, and A. A. Lisyansky, "Multiple-quantum-well-based photonic crystals with simple and compound elementary supercells," Phys. Rev. B 70, 195106 (2004).
[CrossRef]

2003 (4)

Q. Qin, H. Lu, S. N. Zhu, C. S. Yuan, Y. Y. Zhu, and N. B. Ming, "Resonance transmission modes in dual-periodical dielectric multilayer films," Appl. Phys. Lett. 82, 4654-4656 (2003).
[CrossRef]

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]

A. Alù and N. Engheta, "Pairing an epsilon-negative slab with a mu-negative slab: resonance, tunneling and transparency," IEEE Trans. Antennas Propag. 51, 2558-2570 (2003).
[CrossRef]

A. Lakhtakia and J. A. Sherwin, "Orthorhombic materials and perfect lenses," Int. J. Infrared Millim. Waves 24, 19-23 (2003).
[CrossRef]

2002 (2)

D. R. Fredkin and A. Ron, "Effectively left-handed (negative index) composite material," Appl. Phys. Lett. 81, 1753-1755 (2002).
[CrossRef]

A. Sharkawy, S. Shi, and D. W. Prather, "Heterostructure photonic crystals: theory and applications," Appl. Opt. 41, 7245-7253 (2002).
[CrossRef] [PubMed]

2001 (1)

M. Bayindir, C. Kural, and E. Ozbay, "Coupled optical microcavities in one dimensional photonic bandgap structures," J. Opt. A, Pure Appl. Opt. 3, 184-188 (2001).
[CrossRef]

2000 (1)

D. R. Smith, and N. Kroll, "Negative refractive index in left-handed materials," Phys. Rev. Lett. 85, 2933-2936 (2000).
[CrossRef] [PubMed]

1987 (2)

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]

1968 (1)

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

Alù, A.

A. Alù and N. Engheta, "Pairing an epsilon-negative slab with a mu-negative slab: resonance, tunneling and transparency," IEEE Trans. Antennas Propag. 51, 2558-2570 (2003).
[CrossRef]

Bayindir, M.

M. Bayindir, C. Kural, and E. Ozbay, "Coupled optical microcavities in one dimensional photonic bandgap structures," J. Opt. A, Pure Appl. Opt. 3, 184-188 (2001).
[CrossRef]

Born, M.

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

Cai, W.

Chen, H.

G. S. Guan, H. T. Jiang, H. Q. Li, Y. W. Zhang, H. Chen, and S. Y. Zhu, "Tunneling modes of photonic heterostructures consisting of single-negative materials," Appl. Phys. Lett. 88, 211112 (2006).
[CrossRef]

H. T. Jiang, H. Chen, H. Q. Li, Y. W. Zhang, J. Zi, and S. Y. Zhu, "Properties of one-dimensional photonic crystals containing single-negative materials," Phys. Rev. E 69, 066607 (2004).
[CrossRef]

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]

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. H.

Chettiar, U. K.

Deych, L. I.

E. L. Ivchenko, M. M. Voronov, M. V. Erementchouk, L. I. Deych, and A. A. Lisyansky, "Multiple-quantum-well-based photonic crystals with simple and compound elementary supercells," Phys. Rev. B 70, 195106 (2004).
[CrossRef]

Dolling, G.

Dong, J. W.

Drachev, V. P.

Engheta, N.

A. Alù and N. Engheta, "Pairing an epsilon-negative slab with a mu-negative slab: resonance, tunneling and transparency," IEEE Trans. Antennas Propag. 51, 2558-2570 (2003).
[CrossRef]

Enkrich, C.

Erementchouk, M. V.

E. L. Ivchenko, M. M. Voronov, M. V. Erementchouk, L. I. Deych, and A. A. Lisyansky, "Multiple-quantum-well-based photonic crystals with simple and compound elementary supercells," Phys. Rev. B 70, 195106 (2004).
[CrossRef]

Fredkin, D. R.

D. R. Fredkin and A. Ron, "Effectively left-handed (negative index) composite material," Appl. Phys. Lett. 81, 1753-1755 (2002).
[CrossRef]

Guan, G. S.

G. S. Guan, H. T. Jiang, H. Q. Li, Y. W. Zhang, H. Chen, and S. Y. Zhu, "Tunneling modes of photonic heterostructures consisting of single-negative materials," Appl. Phys. Lett. 88, 211112 (2006).
[CrossRef]

Ivchenko, E. L.

E. L. Ivchenko, M. M. Voronov, M. V. Erementchouk, L. I. Deych, and A. A. Lisyansky, "Multiple-quantum-well-based photonic crystals with simple and compound elementary supercells," Phys. Rev. B 70, 195106 (2004).
[CrossRef]

Jiang, H. T.

G. S. Guan, H. T. Jiang, H. Q. Li, Y. W. Zhang, H. Chen, and S. Y. Zhu, "Tunneling modes of photonic heterostructures consisting of single-negative materials," Appl. Phys. Lett. 88, 211112 (2006).
[CrossRef]

H. T. Jiang, H. Chen, H. Q. Li, Y. W. Zhang, J. Zi, and S. Y. Zhu, "Properties of one-dimensional photonic crystals containing single-negative materials," Phys. Rev. E 69, 066607 (2004).
[CrossRef]

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]

John, S.

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

Kildishev, A. V.

Kroll, N.

D. R. Smith, and N. Kroll, "Negative refractive index in left-handed materials," Phys. Rev. Lett. 85, 2933-2936 (2000).
[CrossRef] [PubMed]

Kural, C.

M. Bayindir, C. Kural, and E. Ozbay, "Coupled optical microcavities in one dimensional photonic bandgap structures," J. Opt. A, Pure Appl. Opt. 3, 184-188 (2001).
[CrossRef]

Lakhtakia, A.

A. Lakhtakia and J. A. Sherwin, "Orthorhombic materials and perfect lenses," Int. J. Infrared Millim. Waves 24, 19-23 (2003).
[CrossRef]

Li, C. L.

K. Y. Xu, X. Zheng, C. L. Li, and W. L. She, "Design of omnidirectional and multiple channeled filters using one-dimensional photonic crystals containing a defect layer with a negative refractive index," Phys. Rev. E 71, 066604 (2005).
[CrossRef]

Li, H. Q.

G. S. Guan, H. T. Jiang, H. Q. Li, Y. W. Zhang, H. Chen, and S. Y. Zhu, "Tunneling modes of photonic heterostructures consisting of single-negative materials," Appl. Phys. Lett. 88, 211112 (2006).
[CrossRef]

H. T. Jiang, H. Chen, H. Q. Li, Y. W. Zhang, J. Zi, and S. Y. Zhu, "Properties of one-dimensional photonic crystals containing single-negative materials," Phys. Rev. E 69, 066607 (2004).
[CrossRef]

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]

Linden, S.

Lisyansky, A. A.

E. L. Ivchenko, M. M. Voronov, M. V. Erementchouk, L. I. Deych, and A. A. Lisyansky, "Multiple-quantum-well-based photonic crystals with simple and compound elementary supercells," Phys. Rev. B 70, 195106 (2004).
[CrossRef]

Lu, H.

Q. Qin, H. Lu, S. N. Zhu, C. S. Yuan, Y. Y. Zhu, and N. B. Ming, "Resonance transmission modes in dual-periodical dielectric multilayer films," Appl. Phys. Lett. 82, 4654-4656 (2003).
[CrossRef]

Ming, N. B.

Q. Qin, H. Lu, S. N. Zhu, C. S. Yuan, Y. Y. Zhu, and N. B. Ming, "Resonance transmission modes in dual-periodical dielectric multilayer films," Appl. Phys. Lett. 82, 4654-4656 (2003).
[CrossRef]

Ozbay, E.

M. Bayindir, C. Kural, and E. Ozbay, "Coupled optical microcavities in one dimensional photonic bandgap structures," J. Opt. A, Pure Appl. Opt. 3, 184-188 (2001).
[CrossRef]

Prather, D. W.

Qin, Q.

Q. Qin, H. Lu, S. N. Zhu, C. S. Yuan, Y. Y. Zhu, and N. B. Ming, "Resonance transmission modes in dual-periodical dielectric multilayer films," Appl. Phys. Lett. 82, 4654-4656 (2003).
[CrossRef]

Ron, A.

D. R. Fredkin and A. Ron, "Effectively left-handed (negative index) composite material," Appl. Phys. Lett. 81, 1753-1755 (2002).
[CrossRef]

Sarychev, A. K.

Shalaev, V. M.

Sharkawy, A.

She, W. L.

K. Y. Xu, X. Zheng, C. L. Li, and W. L. She, "Design of omnidirectional and multiple channeled filters using one-dimensional photonic crystals containing a defect layer with a negative refractive index," Phys. Rev. E 71, 066604 (2005).
[CrossRef]

Sherwin, J. A.

A. Lakhtakia and J. A. Sherwin, "Orthorhombic materials and perfect lenses," Int. J. Infrared Millim. Waves 24, 19-23 (2003).
[CrossRef]

Shi, S.

Smith, D. R.

D. R. Smith, and N. Kroll, "Negative refractive index in left-handed materials," Phys. Rev. Lett. 85, 2933-2936 (2000).
[CrossRef] [PubMed]

Soukoulis, C. M.

Veselago, V. G.

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

Voronov, M. M.

E. L. Ivchenko, M. M. Voronov, M. V. Erementchouk, L. I. Deych, and A. A. Lisyansky, "Multiple-quantum-well-based photonic crystals with simple and compound elementary supercells," Phys. Rev. B 70, 195106 (2004).
[CrossRef]

Wang, H. Z.

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]

Wegener, M.

Wolf, E.

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

Xu, K. Y.

K. Y. Xu, X. Zheng, C. L. Li, and W. L. She, "Design of omnidirectional and multiple channeled filters using one-dimensional photonic crystals containing a defect layer with a negative refractive index," Phys. Rev. E 71, 066604 (2005).
[CrossRef]

Yablonovitch, E.

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

Yuan, C. S.

Q. Qin, H. Lu, S. N. Zhu, C. S. Yuan, Y. Y. Zhu, and N. B. Ming, "Resonance transmission modes in dual-periodical dielectric multilayer films," Appl. Phys. Lett. 82, 4654-4656 (2003).
[CrossRef]

Yuan, H.-K.

Zhang, Y. W.

G. S. Guan, H. T. Jiang, H. Q. Li, Y. W. Zhang, H. Chen, and S. Y. Zhu, "Tunneling modes of photonic heterostructures consisting of single-negative materials," Appl. Phys. Lett. 88, 211112 (2006).
[CrossRef]

H. T. Jiang, H. Chen, H. Q. Li, Y. W. Zhang, J. Zi, and S. Y. Zhu, "Properties of one-dimensional photonic crystals containing single-negative materials," Phys. Rev. E 69, 066607 (2004).
[CrossRef]

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]

Zheng, X.

K. Y. Xu, X. Zheng, C. L. Li, and W. L. She, "Design of omnidirectional and multiple channeled filters using one-dimensional photonic crystals containing a defect layer with a negative refractive index," Phys. Rev. E 71, 066604 (2005).
[CrossRef]

Zhu, S. N.

Q. Qin, H. Lu, S. N. Zhu, C. S. Yuan, Y. Y. Zhu, and N. B. Ming, "Resonance transmission modes in dual-periodical dielectric multilayer films," Appl. Phys. Lett. 82, 4654-4656 (2003).
[CrossRef]

Zhu, S. Y.

G. S. Guan, H. T. Jiang, H. Q. Li, Y. W. Zhang, H. Chen, and S. Y. Zhu, "Tunneling modes of photonic heterostructures consisting of single-negative materials," Appl. Phys. Lett. 88, 211112 (2006).
[CrossRef]

H. T. Jiang, H. Chen, H. Q. Li, Y. W. Zhang, J. Zi, and S. Y. Zhu, "Properties of one-dimensional photonic crystals containing single-negative materials," Phys. Rev. E 69, 066607 (2004).
[CrossRef]

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]

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]

Zhu, Y. Y.

Q. Qin, H. Lu, S. N. Zhu, C. S. Yuan, Y. Y. Zhu, and N. B. Ming, "Resonance transmission modes in dual-periodical dielectric multilayer films," Appl. Phys. Lett. 82, 4654-4656 (2003).
[CrossRef]

Zi, J.

H. T. Jiang, H. Chen, H. Q. Li, Y. W. Zhang, J. Zi, and S. Y. Zhu, "Properties of one-dimensional photonic crystals containing single-negative materials," Phys. Rev. E 69, 066607 (2004).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (4)

G. S. Guan, H. T. Jiang, H. Q. Li, Y. W. Zhang, H. Chen, and S. Y. Zhu, "Tunneling modes of photonic heterostructures consisting of single-negative materials," Appl. Phys. Lett. 88, 211112 (2006).
[CrossRef]

Q. Qin, H. Lu, S. N. Zhu, C. S. Yuan, Y. Y. Zhu, and N. B. Ming, "Resonance transmission modes in dual-periodical dielectric multilayer films," Appl. Phys. Lett. 82, 4654-4656 (2003).
[CrossRef]

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]

D. R. Fredkin and A. Ron, "Effectively left-handed (negative index) composite material," Appl. Phys. Lett. 81, 1753-1755 (2002).
[CrossRef]

IEEE Trans. Antennas Propag. (1)

A. Alù and N. Engheta, "Pairing an epsilon-negative slab with a mu-negative slab: resonance, tunneling and transparency," IEEE Trans. Antennas Propag. 51, 2558-2570 (2003).
[CrossRef]

Int. J. Infrared Millim. Waves (1)

A. Lakhtakia and J. A. Sherwin, "Orthorhombic materials and perfect lenses," Int. J. Infrared Millim. Waves 24, 19-23 (2003).
[CrossRef]

J. Opt. A, Pure Appl. Opt. (1)

M. Bayindir, C. Kural, and E. Ozbay, "Coupled optical microcavities in one dimensional photonic bandgap structures," J. Opt. A, Pure Appl. Opt. 3, 184-188 (2001).
[CrossRef]

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

Nat. Photonics (1)

V. M. Shalaev, "Optical negative-index metamaterials," Nat. Photonics 1, 41-48 (2006).
[CrossRef]

Opt. Lett. (2)

Phys. Rev. B (2)

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]

E. L. Ivchenko, M. M. Voronov, M. V. Erementchouk, L. I. Deych, and A. A. Lisyansky, "Multiple-quantum-well-based photonic crystals with simple and compound elementary supercells," Phys. Rev. B 70, 195106 (2004).
[CrossRef]

Phys. Rev. E (2)

H. T. Jiang, H. Chen, H. Q. Li, Y. W. Zhang, J. Zi, and S. Y. Zhu, "Properties of one-dimensional photonic crystals containing single-negative materials," Phys. Rev. E 69, 066607 (2004).
[CrossRef]

K. Y. Xu, X. Zheng, C. L. Li, and W. L. She, "Design of omnidirectional and multiple channeled filters using one-dimensional photonic crystals containing a defect layer with a negative refractive index," Phys. Rev. E 71, 066604 (2005).
[CrossRef]

Phys. Rev. Lett. (3)

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]

D. R. Smith, and N. Kroll, "Negative refractive index in left-handed materials," Phys. Rev. Lett. 85, 2933-2936 (2000).
[CrossRef] [PubMed]

Sov. Phys. Usp. (1)

V. G. Veselago, "The electrodynamics of substances with simultaneously 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 (7)

Fig. 1
Fig. 1

Schematic of a heterostructure constituted by two different 1D photonic crystals, PC 1 [ ( A B ) m ] and PC 2 [ ( A B ) n ] , with single-negative materials.

Fig. 2
Fig. 2

Comparison of PBGs of PC1, PC2, and a photonic heterostructure when ε ¯ = 0 , μ ¯ = 0 . (a) PBG of PC1, (b) PBG of PC2, and (c) PBG of the heterostructure ( PC 1 PC 2 ) .

Fig. 3
Fig. 3

Transmission spectra of PBGs of multiple heterostructures ( PC 1 PC 2 ) N that show the splitting of the midgap mode as the number N increases at normal incidence. (a) N = 2 , (b) N = 3 , (c) N = 4 .

Fig. 4
Fig. 4

Transmission spectra of structure ( PC 1 PC 2 ) 2 at different incident angles for TE and TM modes. (a) θ = 0 ° , (b) θ = 30 ° for TE modes, (c) θ = 30 ° for TM modes, (d) θ = 60 ° for TE modes, and (e) θ = 60 ° for TM modes.

Fig. 5
Fig. 5

Dependence of the resonance transmission peaks on incident angle for structure ( PC 1 PC 2 ) 2 for TE and TM modes. The parameters are the same as those in Fig. 4a.

Fig. 6
Fig. 6

Transmission spectra of PBGs of multiple heterostructures ( PC 1 PC 2 ) 2 with different damping factors γ.

Fig. 7
Fig. 7

Q factor of multiple-channeled filters for multiple heterostructures ( PC 1 PC 2 ) 2 with different damping factors. The solid curve with squares (I) indicates the Q factor of channel I in Fig. 3a, the solid curve with circles (II) for channeled II, and the solid curve with triangles (III) for channel III.

Equations (6)

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ϵ 1 = a , μ 1 = 1 ω m p 2 ω 2 ,
ϵ 2 = 1 ω e p 2 ω 2 , μ 2 = b ,
ϵ ¯ = ϵ 1 ( m d A + n d A ) + ϵ 2 ( m d B + n d B ) m ( d A + d B ) + n ( d A + d B ) = 0 ,
μ ¯ = μ 1 ( m d A + n d A ) + μ 2 ( m d B + n d B ) m ( d A + d B ) + n ( d A + d B ) = 0 .
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 0 q s x 12 + x 21 ) .

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