Abstract

Unusual narrow transmission bands are found in the Bragg reflective region of a multi-layered structure consisting of alternate right-handed material (RHM) and left-handed material (LHM). These unusual narrow transmission bands may exist no matter whether the optical length of a LHM layer completely cancels that of a RHM layer. However, if they can not cancel each other, it is required that the reflection coefficient for each interface is not too small to permit the existence of the unusual transmission bands. A non-ideal model when the LHM is dispersive and lossy is also employed to confirm the unusual transmission phenomenon.

© 2003 Optical Society of America

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References

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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. R. A. Shelby, D. R. Smith, S. C. Nemat-Nasser, and S. Schultz, �??Microwave transmission through a two-dimensional, isotropic, left-handed meta material,�?? Appl. Phys. Lett. 78, 489-491 (2001).
    [CrossRef]
  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. J. B. Pendry, �??Negative Refraction Makes a Perfect Lens,�?? Phys. Rev. Lett. 85, 3966-3969 (2000).
    [CrossRef] [PubMed]
  6. C. Simovsky and S. L. He, �??Frequency range and explicit expressions for negative permittivity and permeability for an isotropic medium formed by a lattice of perfectly conducting particles�??, Phys. Lett. A 311, 254-263 (2003).
    [CrossRef]
  7. J. Gerardin and A. Lakhtakia, �??Negative index of refraction and distributed bragg reflectors,�?? Mirc. and Opt. Tech. Lett. 34, 409-411 (2002).
    [CrossRef]
  8. Z. M. Zhangand C. J. Fu, �??Unusual photon tunneling in the presence of a layer with a negative refractive index,�?? Appl. Phys. Lett. 80, 1097-1099 (2001).
    [CrossRef]
  9. N. Garcia and M. Nieto-Vesperinas, �??Left-Handed Materials Do Not Make a Perfect Lens,�?? Phys. Rev. Lett. 88, 207403-207406 (2002).
    [CrossRef] [PubMed]

Appl. Phys. Lett. (2)

R. A. Shelby, D. R. Smith, S. C. Nemat-Nasser, and S. Schultz, �??Microwave transmission through a two-dimensional, isotropic, left-handed meta material,�?? Appl. Phys. Lett. 78, 489-491 (2001).
[CrossRef]

Z. M. Zhangand C. J. Fu, �??Unusual photon tunneling in the presence of a layer with a negative refractive index,�?? Appl. Phys. Lett. 80, 1097-1099 (2001).
[CrossRef]

Mirc. and Opt. Tech. Lett. (1)

J. Gerardin and A. Lakhtakia, �??Negative index of refraction and distributed bragg reflectors,�?? Mirc. and Opt. Tech. Lett. 34, 409-411 (2002).
[CrossRef]

Phys. Lett. A (1)

C. Simovsky and S. L. He, �??Frequency range and explicit expressions for negative permittivity and permeability for an isotropic medium formed by a lattice of perfectly conducting particles�??, Phys. Lett. A 311, 254-263 (2003).
[CrossRef]

Phys. Rev. Lett. (3)

J. B. Pendry, �??Negative Refraction Makes a Perfect Lens,�?? Phys. Rev. Lett. 85, 3966-3969 (2000).
[CrossRef] [PubMed]

N. Garcia and M. Nieto-Vesperinas, �??Left-Handed Materials Do Not Make a Perfect Lens,�?? Phys. Rev. Lett. 88, 207403-207406 (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]

Science (1)

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. (1)

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 (4)

Fig. 1.
Fig. 1.

A multi-layered periodic structure (with a finite thickness) of two alternate LHM and RHM materials.

Fig. 2.
Fig. 2.

The reflectance as a function of Λ/λ for a DBR (with N=41). (a) Comparison for the case of RHM-LHM period and the case of RHM-RHM period when the transparent wavelength coincides with the reflective Bragg wavelength at λ=Λ. The angle θ 1=0°. The solid line is for the case of RHM-LHM period with n 1=1, µ=1, n 2=-1, µ 2=-2, d 1=d 2=1/2Λ. The dotted line is for the case of RHM-RHM period withn 1=1, µ=1, n 2=1, µ 2=2, d 1=d 2=1/2Λ. (b) The case of RHM-LHM period for different angle θ 1. The parameters are n 1=1, µ=1, n 2=-1, µ 2=-2 and d 1=d 2=1/2Λ.

Fig. 3.
Fig. 3.

The reflectance as a function of Λ/λ for a DBR (N=41) when n 1 d 1+n 2 d 2≠0. The parameters are n 1=1, µ=1, n 2=-2, θ 1=0° and d 1=d 2=1/2Λ. (a) µ 2=-5. (b) µ 2=-3.8.

Fig. 4.
Fig. 4.

(a) and (b) The electromagnetic parameters of the dispersive and lossy LHM as a function of Λ/λ when γ=0.15, t=5 for Eqs. (7) and (8). (c) The reflectance of a DBR (N=41) as a function of Λ/λ. The solid line is for the case when the LHM is dispersive and lossy while the dashed line is for the case when the LHM is non-dispersive and lossless.

Equations (8)

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( A 1 B 1 ) = M ( A N B N ) .
R = M ( 2 , 1 ) M ( 1 , 1 ) ( M ( 2 , 1 ) M ( 1 , 1 ) ) * .
φ 1 2 π λ ( cos θ 1 n 1 d 1 + cos θ 2 n 2 d 2 ) = k 1 z d 1 + k 2 z d 2 = p π ,
φ 2 = 2 π λ cos θ 2 n 2 d 1 = k 2 z d 2 = q π ,
2 = 1 ω p 2 ω e 2 ω 2 ω e 2 j γ ω ,
μ 2 = 1 ω m p 2 ω m 2 ω 2 ω m 2 j γ ω ,
2 = 1 1.5 ( 1 t 2 ) ω 0 2 ω 2 t 2 ω 0 2 j γ ω ,
μ 2 = 1 3 ( 1 t 2 ) ω 0 2 ω 2 t 2 ω 0 2 j γ ω ,

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