Abstract

The dispersion characteristics of asymmetric double-negative material slab waveguides have been investigated by using normalized parameters. The results show that the dispersion characteristics of these material waveguides differ dramatically from conventional guided waves, and they possess a number of unusual properties, including the absence of fundamental modes, propagation of the first-order mode within narrow frequency ranges, and the existence of modes for imaginary transverse wave numbers, for example. In particular, for one fast wave mode, near cutoff, one normalized frequency corresponds to two possible propagation coefficients.

© 2006 Optical Society of America

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  1. V. G. Veselago, "The electrodynamics of substances with simultaneously negative values of epsi and μ," Sov. Phys. Usp. 10, 509-514 (1968).
    [CrossRef]
  2. R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental verification of a negative index of refraction," Science 292, 77-79 (2001).
    [CrossRef] [PubMed]
  3. J. B. Pendry, "Negative refraction makes a perfect lens," Phys. Rev. Lett. 85, 3966-3969 (2000).
    [CrossRef] [PubMed]
  4. S. Xiao, L. Shen, and S. He, "A novel directional coupler utilizing a left-handed material," IEEE Photon. Technol. Lett. 16, 171-173 (2004).
    [CrossRef]
  5. H. Cory and C. Zach, "Wave propagation in metamaterial multi-layered structures," Microwave Opt. Technol. Lett. 40, 460-465 (2004).
    [CrossRef]
  6. H. Cory and A. Barger, "Surface-wave propagation along a metamaterial slab," Microwave Opt. Technol. Lett. 38, 392-395 (2003).
    [CrossRef]
  7. I. V. Shadrivov, A. A. Sukhorukov, and Y. S. Kivshar, "Guided modes in negative-refractive-index waveguides," Phys. Rev. E 67, 057602 (2003).
    [CrossRef]
  8. B.-l. Wu, T. M. Grzegorczyk, Y. Zhang, and J. A. Kong, "Guided modes with imaginary transverse wave number in a slab waveguide with negative permittivity and permeability," J. Appl. Phys. 93, 9386-9388 (2003).
    [CrossRef]
  9. H. Kogelnik and V. Ramaswamy, "Scaling rules for thin-film optical waveguides," Appl. Opt. 13, 1857-1862 (1974).
    [CrossRef] [PubMed]
  10. H. Salehi, S. K. Chaudhuri, and R. R. Mansour, "Unusual mode propagation characteristics of negative index slab waveguides," in IEEE Antennas and Propagation Society International Symposium (IEEE, 2005), Vol. 1A, pp. 721-724.

2004 (2)

S. Xiao, L. Shen, and S. He, "A novel directional coupler utilizing a left-handed material," IEEE Photon. Technol. Lett. 16, 171-173 (2004).
[CrossRef]

H. Cory and C. Zach, "Wave propagation in metamaterial multi-layered structures," Microwave Opt. Technol. Lett. 40, 460-465 (2004).
[CrossRef]

2003 (3)

H. Cory and A. Barger, "Surface-wave propagation along a metamaterial slab," Microwave Opt. Technol. Lett. 38, 392-395 (2003).
[CrossRef]

I. V. Shadrivov, A. A. Sukhorukov, and Y. S. Kivshar, "Guided modes in negative-refractive-index waveguides," Phys. Rev. E 67, 057602 (2003).
[CrossRef]

B.-l. Wu, T. M. Grzegorczyk, Y. Zhang, and J. A. Kong, "Guided modes with imaginary transverse wave number in a slab waveguide with negative permittivity and permeability," J. Appl. Phys. 93, 9386-9388 (2003).
[CrossRef]

2001 (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]

2000 (1)

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

1974 (1)

1968 (1)

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

Barger, A.

H. Cory and A. Barger, "Surface-wave propagation along a metamaterial slab," Microwave Opt. Technol. Lett. 38, 392-395 (2003).
[CrossRef]

Chaudhuri, S. K.

H. Salehi, S. K. Chaudhuri, and R. R. Mansour, "Unusual mode propagation characteristics of negative index slab waveguides," in IEEE Antennas and Propagation Society International Symposium (IEEE, 2005), Vol. 1A, pp. 721-724.

Cory, H.

H. Cory and C. Zach, "Wave propagation in metamaterial multi-layered structures," Microwave Opt. Technol. Lett. 40, 460-465 (2004).
[CrossRef]

H. Cory and A. Barger, "Surface-wave propagation along a metamaterial slab," Microwave Opt. Technol. Lett. 38, 392-395 (2003).
[CrossRef]

Grzegorczyk, T. M.

B.-l. Wu, T. M. Grzegorczyk, Y. Zhang, and J. A. Kong, "Guided modes with imaginary transverse wave number in a slab waveguide with negative permittivity and permeability," J. Appl. Phys. 93, 9386-9388 (2003).
[CrossRef]

He, S.

S. Xiao, L. Shen, and S. He, "A novel directional coupler utilizing a left-handed material," IEEE Photon. Technol. Lett. 16, 171-173 (2004).
[CrossRef]

Kivshar, Y. S.

I. V. Shadrivov, A. A. Sukhorukov, and Y. S. Kivshar, "Guided modes in negative-refractive-index waveguides," Phys. Rev. E 67, 057602 (2003).
[CrossRef]

Kogelnik, H.

Kong, J. A.

B.-l. Wu, T. M. Grzegorczyk, Y. Zhang, and J. A. Kong, "Guided modes with imaginary transverse wave number in a slab waveguide with negative permittivity and permeability," J. Appl. Phys. 93, 9386-9388 (2003).
[CrossRef]

Mansour, R. R.

H. Salehi, S. K. Chaudhuri, and R. R. Mansour, "Unusual mode propagation characteristics of negative index slab waveguides," in IEEE Antennas and Propagation Society International Symposium (IEEE, 2005), Vol. 1A, pp. 721-724.

Pendry, J. B.

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

Ramaswamy, V.

Salehi, H.

H. Salehi, S. K. Chaudhuri, and R. R. Mansour, "Unusual mode propagation characteristics of negative index slab waveguides," in IEEE Antennas and Propagation Society International Symposium (IEEE, 2005), Vol. 1A, pp. 721-724.

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]

Shadrivov, I. V.

I. V. Shadrivov, A. A. Sukhorukov, and Y. S. Kivshar, "Guided modes in negative-refractive-index waveguides," Phys. Rev. E 67, 057602 (2003).
[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]

Shen, L.

S. Xiao, L. Shen, and S. He, "A novel directional coupler utilizing a left-handed material," IEEE Photon. Technol. Lett. 16, 171-173 (2004).
[CrossRef]

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]

Sukhorukov, A. A.

I. V. Shadrivov, A. A. Sukhorukov, and Y. S. Kivshar, "Guided modes in negative-refractive-index waveguides," Phys. Rev. E 67, 057602 (2003).
[CrossRef]

Veselago, V. G.

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

Wu, B.-l.

B.-l. Wu, T. M. Grzegorczyk, Y. Zhang, and J. A. Kong, "Guided modes with imaginary transverse wave number in a slab waveguide with negative permittivity and permeability," J. Appl. Phys. 93, 9386-9388 (2003).
[CrossRef]

Xiao, S.

S. Xiao, L. Shen, and S. He, "A novel directional coupler utilizing a left-handed material," IEEE Photon. Technol. Lett. 16, 171-173 (2004).
[CrossRef]

Zach, C.

H. Cory and C. Zach, "Wave propagation in metamaterial multi-layered structures," Microwave Opt. Technol. Lett. 40, 460-465 (2004).
[CrossRef]

Zhang, Y.

B.-l. Wu, T. M. Grzegorczyk, Y. Zhang, and J. A. Kong, "Guided modes with imaginary transverse wave number in a slab waveguide with negative permittivity and permeability," J. Appl. Phys. 93, 9386-9388 (2003).
[CrossRef]

Appl. Opt. (1)

IEEE Photon. Technol. Lett. (1)

S. Xiao, L. Shen, and S. He, "A novel directional coupler utilizing a left-handed material," IEEE Photon. Technol. Lett. 16, 171-173 (2004).
[CrossRef]

J. Appl. Phys. (1)

B.-l. Wu, T. M. Grzegorczyk, Y. Zhang, and J. A. Kong, "Guided modes with imaginary transverse wave number in a slab waveguide with negative permittivity and permeability," J. Appl. Phys. 93, 9386-9388 (2003).
[CrossRef]

Microwave Opt. Technol. Lett. (2)

H. Cory and C. Zach, "Wave propagation in metamaterial multi-layered structures," Microwave Opt. Technol. Lett. 40, 460-465 (2004).
[CrossRef]

H. Cory and A. Barger, "Surface-wave propagation along a metamaterial slab," Microwave Opt. Technol. Lett. 38, 392-395 (2003).
[CrossRef]

Phys. Rev. E (1)

I. V. Shadrivov, A. A. Sukhorukov, and Y. S. Kivshar, "Guided modes in negative-refractive-index waveguides," Phys. Rev. E 67, 057602 (2003).
[CrossRef]

Phys. Rev. Lett. (1)

J. B. Pendry, "Negative refraction makes a perfect lens," Phys. Rev. Lett. 85, 3966-3969 (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 epsi and μ," Sov. Phys. Usp. 10, 509-514 (1968).
[CrossRef]

Other (1)

H. Salehi, S. K. Chaudhuri, and R. R. Mansour, "Unusual mode propagation characteristics of negative index slab waveguides," in IEEE Antennas and Propagation Society International Symposium (IEEE, 2005), Vol. 1A, pp. 721-724.

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Figures (6)

Fig. 1
Fig. 1

Geometry for an asymmetric slab waveguide.

Fig. 2
Fig. 2

Dispersion characteristics of TE modes for a conventional slab waveguide. The parameter is μ 1 = μ 2 = μ 3 .

Fig. 3
Fig. 3

Dispersion characteristics of TE modes for a symmetric LHM slab waveguide. The parameters are (a) μ 1 = 0.5 μ 2 = 0.5 μ 3 , (b) μ 1 = μ 2 = μ 3 , and (c) μ 1 = 2 μ 2 = 2 μ 3 .

Fig. 4
Fig. 4

Dispersion characteristics of TE modes for a conventional asymmetric slab waveguide. The parameters are a = 1 , 10 , μ 1 = μ 2 = μ 3 .

Fig. 5
Fig. 5

Dispersion characteristics of TE modes for an asymmetric LHM slab waveguide. The parameters are (a) μ 1 = μ 2 = μ 3 , a = 1 , 10 , (b) μ 1 = 2 μ 2 = 2 μ 3 , a = 1 , 10 .

Fig. 6
Fig. 6

Dispersion characteristics for an imaginary transverse wave in an asymmetric LHM slab waveguide. The parameters are a = 0 , 10 , 20 , 30 , μ 1 = 2 μ 2 = 2 μ 3 .

Equations (10)

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E y 1 ( x , z ) = ( A e j T x + B e j T x ) e j β z , 0 x d ,
E y 2 ( x , z ) = C e α 2 x e j β z , x 0 ,
E y 3 ( x , z ) = d e α 3 ( x + d ) e j β z , x d ,
tan ( T d ) = ( μ 1 μ 2 α 2 T + μ 1 μ 3 α 3 T ) ( 1 μ 1 2 μ 2 μ 3 α 2 α 3 T 2 ) .
tanh ( α 1 d ) = ( μ 1 μ 2 α 2 α 1 + μ 1 μ 3 α 3 α 1 ) ( 1 + μ 1 2 μ 2 μ 3 α 2 α 3 α 1 2 ) ,
V = ω d μ 1 ε 1 μ 3 ε 3 ,
a = ( μ 3 ε 3 μ 2 ε 2 ) ( μ 1 ε 1 μ 3 ε 3 ) ,
b = ( β 2 ω 2 μ 3 ε 3 ) ( ω 2 μ 1 ε 1 ω 2 μ 3 ε 3 ) = ( α 3 d ) 2 V 2 .
tan ( V 1 b ) = ( μ 1 μ 3 b 1 b + μ 1 μ 2 b + a 1 b ) ( 1 μ 1 2 μ 2 μ 3 b ( b + a ) 1 b ) .
tanh ( V b 1 ) = ( μ 1 μ 3 b b 1 + μ 1 μ 2 b + a b 1 ) ( 1 + μ 1 2 μ 2 μ 3 b ( b + a ) b 1 ) .

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