Abstract

Recently, electromagnetic materials with negative permittivity and permeability have been given much attention. Propagation of electromagnetic waves in double negative (DNG) media and also in photonic crystals has been studied analytically and experimentally. The materials’ optical parameters are complex and frequency dependent to account for both dispersion and absorption. Here we have studied theoretically the dispersion as well the transmission and reflection of the visible light on a one-dimensional heterostructure combining anisotropic DNG and isotropic double positive (DPS) materials. Here our center of attention is the study of the non-Bragg band gaps, which are not based on interference, in a one-dimensional photonic crystal composed of alternating layers of DNG and DPS materials. We find that this type of photonic crystal in the visible wavelength range exhibits negative refraction in a wider frequency range than does a single DNG material.

© 2009 Optical Society of America

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References

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  1. E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059-2062 (1987).
    [CrossRef] [PubMed]
  2. S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486-2489 (1987).
    [CrossRef] [PubMed]
  3. V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of ϵ and μ,” Sov. Phys. Usp. 10, 509-514 (1968).
    [CrossRef]
  4. P. Yeh, A. Yariv, and C. Hong, “Electromagnetic propagation in periodic stratified media. General theory,” J. Opt. Soc. Am. 67, 423-438 (1977).
    [CrossRef]
  5. R. A. Depine, M. L. Martínez-Ricci, and E. Silvestre, “Zero permeability and zero permittivity band gaps in 1D metamaterial photonic crystals,” Phys. Lett. A 364, 352-355 (2007).
    [CrossRef]
  6. J. A. Monsoriu and E. Silvestre, “Interaction between non-Bragg band gaps in 1D metamaterial photonic crystals,” Opt. Express 14, 12958-12967 (2006).
    [CrossRef] [PubMed]
  7. A-G. Kussow, A. Akyurtlu, A. Semichaevsky, and N. Angkawisttpan, “MgB2-based negative refraction index metamaterial at visible frequency,” Phys. Rev. B 76, 195123 (2007).
    [CrossRef]

2007 (2)

R. A. Depine, M. L. Martínez-Ricci, and E. Silvestre, “Zero permeability and zero permittivity band gaps in 1D metamaterial photonic crystals,” Phys. Lett. A 364, 352-355 (2007).
[CrossRef]

A-G. Kussow, A. Akyurtlu, A. Semichaevsky, and N. Angkawisttpan, “MgB2-based negative refraction index metamaterial at visible frequency,” Phys. Rev. B 76, 195123 (2007).
[CrossRef]

2006 (1)

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]

1977 (1)

1968 (1)

V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of ϵ and μ,” Sov. Phys. Usp. 10, 509-514 (1968).
[CrossRef]

Akyurtlu, A.

A-G. Kussow, A. Akyurtlu, A. Semichaevsky, and N. Angkawisttpan, “MgB2-based negative refraction index metamaterial at visible frequency,” Phys. Rev. B 76, 195123 (2007).
[CrossRef]

Angkawisttpan, N.

A-G. Kussow, A. Akyurtlu, A. Semichaevsky, and N. Angkawisttpan, “MgB2-based negative refraction index metamaterial at visible frequency,” Phys. Rev. B 76, 195123 (2007).
[CrossRef]

Depine, R. A.

R. A. Depine, M. L. Martínez-Ricci, and E. Silvestre, “Zero permeability and zero permittivity band gaps in 1D metamaterial photonic crystals,” Phys. Lett. A 364, 352-355 (2007).
[CrossRef]

Hong, C.

John, S.

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

Kussow, A-G.

A-G. Kussow, A. Akyurtlu, A. Semichaevsky, and N. Angkawisttpan, “MgB2-based negative refraction index metamaterial at visible frequency,” Phys. Rev. B 76, 195123 (2007).
[CrossRef]

Martínez-Ricci, M. L.

R. A. Depine, M. L. Martínez-Ricci, and E. Silvestre, “Zero permeability and zero permittivity band gaps in 1D metamaterial photonic crystals,” Phys. Lett. A 364, 352-355 (2007).
[CrossRef]

Monsoriu, J. A.

Semichaevsky, A.

A-G. Kussow, A. Akyurtlu, A. Semichaevsky, and N. Angkawisttpan, “MgB2-based negative refraction index metamaterial at visible frequency,” Phys. Rev. B 76, 195123 (2007).
[CrossRef]

Silvestre, E.

R. A. Depine, M. L. Martínez-Ricci, and E. Silvestre, “Zero permeability and zero permittivity band gaps in 1D metamaterial photonic crystals,” Phys. Lett. A 364, 352-355 (2007).
[CrossRef]

J. A. Monsoriu and E. Silvestre, “Interaction between non-Bragg band gaps in 1D metamaterial photonic crystals,” Opt. Express 14, 12958-12967 (2006).
[CrossRef] [PubMed]

Veselago, V. G.

V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of ϵ and μ,” Sov. Phys. Usp. 10, 509-514 (1968).
[CrossRef]

Yablonovitch, E.

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

Yariv, A.

Yeh, P.

J. Opt. Soc. Am. (1)

Opt. Express (1)

Phys. Lett. A (1)

R. A. Depine, M. L. Martínez-Ricci, and E. Silvestre, “Zero permeability and zero permittivity band gaps in 1D metamaterial photonic crystals,” Phys. Lett. A 364, 352-355 (2007).
[CrossRef]

Phys. Rev. B (1)

A-G. Kussow, A. Akyurtlu, A. Semichaevsky, and N. Angkawisttpan, “MgB2-based negative refraction index metamaterial at visible frequency,” Phys. Rev. B 76, 195123 (2007).
[CrossRef]

Phys. Rev. Lett. (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]

Sov. Phys. Usp. (1)

V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of ϵ and μ,” Sov. Phys. Usp. 10, 509-514 (1968).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

Real electric permittivity (blue, solid line) and real magnetic permeability (red, dashed line) of DNG layer (left). Imaginary part of electric permittivity (blue, solid line) and imaginary part of magnetic permeability (red, dashed line) of a DNG layer as a function of frequency (right).

Fig. 2
Fig. 2

Dispersion relation of anisotropic DPS-DNG layers for incident angle of 30° (top), 45° (middle), and 60° (bottom), for both TE- and TM-polarized beams.

Fig. 3
Fig. 3

Reflectance and transmittance of isotropic DPS-DNG layers, for incident angle of 30° (top), 45° (middle), and 60° (bottom), for both TE- and TM-polarized beams. The right columns are R and T for layers with refraction coefficient of DPS n 1 = 1.1 , and the left column has n 1 = 2.5 . Solid curves (red) represent R and dashed curves (blue) represent T.

Fig. 4
Fig. 4

Reflectance and transmittance for TM and TE polarization, for uniaxial DPS-DNG layers for incident angle of 30° (top), 45° (middle), and 60° (bottom). The right columns are R and T for layers and refraction coefficient of DPS n 1 = 1.1 , and the left column has n 1 = 2.5 . Solid curves represent R and dashed curves represent T.

Equations (11)

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cos ( K d ) cos ( k 1 y d 1 ) cos ( k 2 y d 2 ) + 1 2 ( p 2 k 1 y p 1 k 2 y + p 1 k 2 y p 2 k 1 y ) sin ( k 1 y d 1 ) sin ( k 2 y d 2 ) = 0 .
p i = 0 ,
p 2 k 1 k = p 2 k 2 y ,
k 1 y d 1 = k 2 y d 2 ,
ϵ = ( ϵ i i 0 0 0 ϵ j j 0 0 0 ϵ k k ) μ = ( μ i i 0 0 0 μ j j 0 0 0 μ k k ) .
ϵ ( ω ) = 1 + 4.8412 2 2.1101 2 ω 2 ,
μ ( ω ) = 1 + 4.2295 2 3.6698 2 ω 2 ,
R TE = r i j + r j k e 2 i φ 1 + r i j r j k e 2 i φ ,
r i j = k z i k z j k z i + k z j ,
R TM = r i j + r j k e 2 i φ 1 + r i j r j k e 2 i φ ,
r i j = k j cos ( θ i ) k i cos ( θ j ) k i cos ( θ j ) + k j cos ( θ i ) .

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