Abstract

We theoretically deduce the Bragg gap vanishing conditions in one-dimensional photonic crystals and experimentally demonstrate the m=0 band-gap vanishing phenomena at microwave frequencies. In the case of mismatched impedance, the Bragg gap will vanish as long as the discrete modes appear in photonic crystals containing dispersive materials, while for the matched impedance cases, Bragg gaps will always disappear. The experimental results and the simulations agree extremely well with the theoretical expectation.

© 2009 Optical Society of America

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  1. V. G. Veselago, "The electrodynamics of substances with simultaneously negative values of permittivity and permeability," Sov. Phys. Usp. 10, 509-514 (1968).
    [CrossRef]
  2. D. R. Smith, W. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, "A composite medium with simultaneously negative permeability and permittivity," Phys. Rev. Lett. 84, 4184-4187 (2000).
    [CrossRef] [PubMed]
  3. J. B. Pendry, "Electromagnetic materials enter the negative age," Physics World. 14, 47 (2001).
  4. R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental Verification of a Negative Index of Refraction," Science 292, 77-79 (2001).
    [CrossRef] [PubMed]
  5. M. W. Feise, I. V. Shadrivov, and Y. S. Kivshar, "Tunable transmission and bistability in left-handed band-gap structures," Appl. Phys. Lett. 85, 1451 (2004).
    [CrossRef]
  6. S. Enoch, G. Tayeb, P. Sabouroux, N. Guerin, and P. Vincent, "A Metamaterial for Directive Emission," Phys. Rev. Lett. 89, 213902 (2002).
    [CrossRef] [PubMed]
  7. L. Sungjoon; C. Caloz, T. Itoh, "Metamaterial-based electronically controlled transmission-line structure as a novel leaky-wave antenna with tunable radiation angle and beamwidth," IEEE Trans. Microwave Theory Tech. 53, 161-172 (2005).
    [CrossRef]
  8. 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]
  9. Y. Weng, Z. G. Wang, and H. Chen, "Band structures of one-dimensional subwavelength photonic crystals containing metamaterials," Phys. Rev. E. 75, 046601 (2007).
    [CrossRef]
  10. 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 (2003).
    [CrossRef]
  11. C. Caloz and T. Itoh, "Transmission line approach of Left-Handed (LH) materials and microstrip implementation of an artificial LH transmission Line," IEEE Trans. Antennas Propag. 52, 1159 (2004).
    [CrossRef]
  12. G. V. Eleftheriades, A.K. Iyer and P.C. Kremer,"Planar negative refractive index media using periodically L-C loaded transmission lines," IEEE Trans. Microwave Theory Tech. 50, 2702-2712 (2002).
    [CrossRef]
  13. A. Sanada, C. Caloz, and T. Itoh, "Characteristics of the composite right/left-handed transmission lines," IEEE Microwave Wireless Components Lett. 14, 68-71, 2004.
    [CrossRef]

2007

Y. Weng, Z. G. Wang, and H. Chen, "Band structures of one-dimensional subwavelength photonic crystals containing metamaterials," Phys. Rev. E. 75, 046601 (2007).
[CrossRef]

2005

L. Sungjoon; C. Caloz, T. Itoh, "Metamaterial-based electronically controlled transmission-line structure as a novel leaky-wave antenna with tunable radiation angle and beamwidth," IEEE Trans. Microwave Theory Tech. 53, 161-172 (2005).
[CrossRef]

2004

M. W. Feise, I. V. Shadrivov, and Y. S. Kivshar, "Tunable transmission and bistability in left-handed band-gap structures," Appl. Phys. Lett. 85, 1451 (2004).
[CrossRef]

C. Caloz and T. Itoh, "Transmission line approach of Left-Handed (LH) materials and microstrip implementation of an artificial LH transmission Line," IEEE Trans. Antennas Propag. 52, 1159 (2004).
[CrossRef]

A. Sanada, C. Caloz, and T. Itoh, "Characteristics of the composite right/left-handed transmission lines," IEEE Microwave Wireless Components Lett. 14, 68-71, 2004.
[CrossRef]

2003

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 (2003).
[CrossRef]

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]

2002

S. Enoch, G. Tayeb, P. Sabouroux, N. Guerin, and P. Vincent, "A Metamaterial for Directive Emission," Phys. Rev. Lett. 89, 213902 (2002).
[CrossRef] [PubMed]

G. V. Eleftheriades, A.K. Iyer and P.C. Kremer,"Planar negative refractive index media using periodically L-C loaded transmission lines," IEEE Trans. Microwave Theory Tech. 50, 2702-2712 (2002).
[CrossRef]

2001

J. B. Pendry, "Electromagnetic materials enter the negative age," Physics World. 14, 47 (2001).

R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental Verification of a Negative Index of Refraction," Science 292, 77-79 (2001).
[CrossRef] [PubMed]

2000

D. R. Smith, W. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, "A composite medium with simultaneously negative permeability and permittivity," Phys. Rev. Lett. 84, 4184-4187 (2000).
[CrossRef] [PubMed]

1968

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

Caloz, C.

L. Sungjoon; C. Caloz, T. Itoh, "Metamaterial-based electronically controlled transmission-line structure as a novel leaky-wave antenna with tunable radiation angle and beamwidth," IEEE Trans. Microwave Theory Tech. 53, 161-172 (2005).
[CrossRef]

C. Caloz and T. Itoh, "Transmission line approach of Left-Handed (LH) materials and microstrip implementation of an artificial LH transmission Line," IEEE Trans. Antennas Propag. 52, 1159 (2004).
[CrossRef]

A. Sanada, C. Caloz, and T. Itoh, "Characteristics of the composite right/left-handed transmission lines," IEEE Microwave Wireless Components Lett. 14, 68-71, 2004.
[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]

Chen, H.

Y. Weng, Z. G. Wang, and H. Chen, "Band structures of one-dimensional subwavelength photonic crystals containing metamaterials," Phys. Rev. E. 75, 046601 (2007).
[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 (2003).
[CrossRef]

Eleftheriades, G. V.

G. V. Eleftheriades, A.K. Iyer and P.C. Kremer,"Planar negative refractive index media using periodically L-C loaded transmission lines," IEEE Trans. Microwave Theory Tech. 50, 2702-2712 (2002).
[CrossRef]

Enoch, S.

S. Enoch, G. Tayeb, P. Sabouroux, N. Guerin, and P. Vincent, "A Metamaterial for Directive Emission," Phys. Rev. Lett. 89, 213902 (2002).
[CrossRef] [PubMed]

Feise, M. W.

M. W. Feise, I. V. Shadrivov, and Y. S. Kivshar, "Tunable transmission and bistability in left-handed band-gap structures," Appl. Phys. Lett. 85, 1451 (2004).
[CrossRef]

Guerin, N.

S. Enoch, G. Tayeb, P. Sabouroux, N. Guerin, and P. Vincent, "A Metamaterial for Directive Emission," Phys. Rev. Lett. 89, 213902 (2002).
[CrossRef] [PubMed]

Itoh, T.

L. Sungjoon; C. Caloz, T. Itoh, "Metamaterial-based electronically controlled transmission-line structure as a novel leaky-wave antenna with tunable radiation angle and beamwidth," IEEE Trans. Microwave Theory Tech. 53, 161-172 (2005).
[CrossRef]

C. Caloz and T. Itoh, "Transmission line approach of Left-Handed (LH) materials and microstrip implementation of an artificial LH transmission Line," IEEE Trans. Antennas Propag. 52, 1159 (2004).
[CrossRef]

A. Sanada, C. Caloz, and T. Itoh, "Characteristics of the composite right/left-handed transmission lines," IEEE Microwave Wireless Components Lett. 14, 68-71, 2004.
[CrossRef]

Iyer, A.K.

G. V. Eleftheriades, A.K. Iyer and P.C. Kremer,"Planar negative refractive index media using periodically L-C loaded transmission lines," IEEE Trans. Microwave Theory Tech. 50, 2702-2712 (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 (2003).
[CrossRef]

Kivshar, Y. S.

M. W. Feise, I. V. Shadrivov, and Y. S. Kivshar, "Tunable transmission and bistability in left-handed band-gap structures," Appl. Phys. Lett. 85, 1451 (2004).
[CrossRef]

Kremer, P.C.

G. V. Eleftheriades, A.K. Iyer and P.C. Kremer,"Planar negative refractive index media using periodically L-C loaded transmission lines," IEEE Trans. Microwave Theory Tech. 50, 2702-2712 (2002).
[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 (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]

Nemat-Nasser, S. C.

D. R. Smith, W. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, "A composite medium with simultaneously negative permeability and permittivity," Phys. Rev. Lett. 84, 4184-4187 (2000).
[CrossRef] [PubMed]

Padilla, W.

D. R. Smith, W. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, "A composite medium with simultaneously negative permeability and permittivity," Phys. Rev. Lett. 84, 4184-4187 (2000).
[CrossRef] [PubMed]

Pendry, J. B.

J. B. Pendry, "Electromagnetic materials enter the negative age," Physics World. 14, 47 (2001).

Sabouroux, P.

S. Enoch, G. Tayeb, P. Sabouroux, N. Guerin, and P. Vincent, "A Metamaterial for Directive Emission," Phys. Rev. Lett. 89, 213902 (2002).
[CrossRef] [PubMed]

Sanada, A.

A. Sanada, C. Caloz, and T. Itoh, "Characteristics of the composite right/left-handed transmission lines," IEEE Microwave Wireless Components Lett. 14, 68-71, 2004.
[CrossRef]

Schultz, S.

R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental Verification of a Negative Index of Refraction," Science 292, 77-79 (2001).
[CrossRef] [PubMed]

D. R. Smith, W. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, "A composite medium with simultaneously negative permeability and permittivity," Phys. Rev. Lett. 84, 4184-4187 (2000).
[CrossRef] [PubMed]

Shadrivov, I. V.

M. W. Feise, I. V. Shadrivov, and Y. S. Kivshar, "Tunable transmission and bistability in left-handed band-gap structures," Appl. Phys. Lett. 85, 1451 (2004).
[CrossRef]

Shelby, R. A.

R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental Verification of a Negative Index of Refraction," Science 292, 77-79 (2001).
[CrossRef] [PubMed]

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]

Smith, D. R.

R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental Verification of a Negative Index of Refraction," Science 292, 77-79 (2001).
[CrossRef] [PubMed]

D. R. Smith, W. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, "A composite medium with simultaneously negative permeability and permittivity," Phys. Rev. Lett. 84, 4184-4187 (2000).
[CrossRef] [PubMed]

Sungjoon, L.

L. Sungjoon; C. Caloz, T. Itoh, "Metamaterial-based electronically controlled transmission-line structure as a novel leaky-wave antenna with tunable radiation angle and beamwidth," IEEE Trans. Microwave Theory Tech. 53, 161-172 (2005).
[CrossRef]

Tayeb, G.

S. Enoch, G. Tayeb, P. Sabouroux, N. Guerin, and P. Vincent, "A Metamaterial for Directive Emission," Phys. Rev. Lett. 89, 213902 (2002).
[CrossRef] [PubMed]

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]

Vier, D. C.

D. R. Smith, W. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, "A composite medium with simultaneously negative permeability and permittivity," Phys. Rev. Lett. 84, 4184-4187 (2000).
[CrossRef] [PubMed]

Vincent, P.

S. Enoch, G. Tayeb, P. Sabouroux, N. Guerin, and P. Vincent, "A Metamaterial for Directive Emission," Phys. Rev. Lett. 89, 213902 (2002).
[CrossRef] [PubMed]

Wang, Z. G.

Y. Weng, Z. G. Wang, and H. Chen, "Band structures of one-dimensional subwavelength photonic crystals containing metamaterials," Phys. Rev. E. 75, 046601 (2007).
[CrossRef]

Weng, Y.

Y. Weng, Z. G. Wang, and H. Chen, "Band structures of one-dimensional subwavelength photonic crystals containing metamaterials," Phys. Rev. E. 75, 046601 (2007).
[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 (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 (2003).
[CrossRef]

Appl. Phys. Lett.

M. W. Feise, I. V. Shadrivov, and Y. S. Kivshar, "Tunable transmission and bistability in left-handed band-gap structures," Appl. Phys. Lett. 85, 1451 (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 (2003).
[CrossRef]

IEEE Microwave Wireless Components Lett.

A. Sanada, C. Caloz, and T. Itoh, "Characteristics of the composite right/left-handed transmission lines," IEEE Microwave Wireless Components Lett. 14, 68-71, 2004.
[CrossRef]

IEEE Trans. Antennas Propag.

C. Caloz and T. Itoh, "Transmission line approach of Left-Handed (LH) materials and microstrip implementation of an artificial LH transmission Line," IEEE Trans. Antennas Propag. 52, 1159 (2004).
[CrossRef]

IEEE Trans. Microwave Theory Tech.

G. V. Eleftheriades, A.K. Iyer and P.C. Kremer,"Planar negative refractive index media using periodically L-C loaded transmission lines," IEEE Trans. Microwave Theory Tech. 50, 2702-2712 (2002).
[CrossRef]

L. Sungjoon; C. Caloz, T. Itoh, "Metamaterial-based electronically controlled transmission-line structure as a novel leaky-wave antenna with tunable radiation angle and beamwidth," IEEE Trans. Microwave Theory Tech. 53, 161-172 (2005).
[CrossRef]

Phys. Rev. E.

Y. Weng, Z. G. Wang, and H. Chen, "Band structures of one-dimensional subwavelength photonic crystals containing metamaterials," Phys. Rev. E. 75, 046601 (2007).
[CrossRef]

Phys. Rev. Lett.

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]

S. Enoch, G. Tayeb, P. Sabouroux, N. Guerin, and P. Vincent, "A Metamaterial for Directive Emission," Phys. Rev. Lett. 89, 213902 (2002).
[CrossRef] [PubMed]

D. R. Smith, W. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, "A composite medium with simultaneously negative permeability and permittivity," Phys. Rev. Lett. 84, 4184-4187 (2000).
[CrossRef] [PubMed]

Physics World.

J. B. Pendry, "Electromagnetic materials enter the negative age," Physics World. 14, 47 (2001).

Science

R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental Verification of a Negative Index of Refraction," Science 292, 77-79 (2001).
[CrossRef] [PubMed]

Sov. Phys. Usp.

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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Figures (8)

Fig. 1.
Fig. 1.

A 1-D infinite periodic structure with alternating layers of two materials.

Fig. 2.
Fig. 2.

The circuit model of (a) CRLH-TL unit by loading series capacitors CL and shunt inductors LL on the transmission line and (b) CRH unit by loading shunt capacitors CR and series inductors LR on the transmission line.

Fig. 3.
Fig. 3.

The calculated dispersion relations of the CRLH-TL and the CRH-TL.

Fig. 4.
Fig. 4.

Photograph of the fabricated periodic structure (CRLH3CRH3)7.

Fig. 5.
Fig. 5.

The simulated and measured results of (a) the transmission properties of the photonic crystal (CRLH3CRH3)7 (b) the simulated unit cell phase delay of CRLH3 (-ψ 1), CRH3(-ψ 2) and a period CRLH3CRH3 (-ψ).

Fig. 6.
Fig. 6.

The calculated dispersion relation of infinite periodic structure CRLH3CRH3-TL

Fig. 7.
Fig. 7.

The photonic crystal in the matched impedance case. (a) Photograph of the fabricated periodic structure (RH/LH)12, (b)the circuit model of LH unit with the loading lumped elements: series capacitors CL and shunt inductors LL , and (c) the circuit model of RH-TL.

Fig. 8.
Fig. 8.

The simulated and measured transmission properties of the photonic crystals (LH/RH)12, and the simulated unit cell phase delay of LH/RH (-ψ) with dash line.

Equations (11)

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

ψperoid=ψ1+ψ2 =
cos(βa)=cos(α1d1+α2d2)12(F1F2+F2F12) sin(α1d1) sin(α2d2)
ψperoidω0=(α1d1+α2d2)ω0=
cos(βa)ω=cos(α1d1+α2d2)ω0=1
F1F2ωF1F2ω0=1
cos(βa)ω0=1+12(F1F2+F2F12)sin2(α1d1)1
α1d1ωdα1ω0d1(ωω0)+A+
α2d2ωdα2ω0d2(ωω0)+(ml)πB+(ml)π
cos(βa)ω112[A2+B2+(F1F2+F2F1)AB]<112(A+B)2
cos(βCRLHd1)=cos(k1d1)(114ω2LLCL)+sin(k1d1)(12ωCLZ1+Z12ωLL)14ω2LLCL
cos(βCRHd2)=cos(k2d2)(1ω2LRCR4)+sin(k2d2)(ωCRZ22+ωLR2Z2)ω2LRCR4

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