Abstract

Two choices are possible for the refractive index of a linear, homogeneous, isotropic, active, dielectric material. Either of the choices is adequate for obtaining frequency–domain solutions for (i) scattering by slabs, spheres, and other objects of bounded extent; (ii) guided–wave propagation in homogeneously filled, cross–sectionally uniform, straight waveguide sections with perfectly conducting walls; and (iii) image formation due to flat lenses. The correct choice does matter for the half–space problem, but that problem is not realistic.

© 2007 Optical Society of America

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  4. S. A. Ramakrishna and O. J. F. Martin, "Resolving the wave vector in negative refractive index media," Opt. Lett. 30, 2626-2628 (2005).
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  5. T. G. Mackay and A. Lakhtakia, "Comment on ‘Negative refraction at optical frequencies in nonmagnetic two-component molecular media’," Phys. Rev. Lett. 96, 159701 (2006).
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    [CrossRef]
  8. Y.-F. Chen, P. Fischer, and F. W. Wise, "Sign of the refractive index in a gain medium with negative permittivity and permeability," J. Opt. Soc. Am. B 23, 45-50 (2006).
    [CrossRef]
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    [CrossRef]
  13. B. Nistad and J. Skaar, "Simulations and realizations of active right-handed metamaterials with negative refractive index," Opt. Express 15, 10935-10946 (2007).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  15. J. Skaar, "Fresnel equations and the refractive index of active media," Phys. Rev. E  73, 026605(2006).
    [CrossRef]
  16. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles, pp. 89-101 (Wiley, New York, NY, USA, 1983).
  17. A. Lakhtakia and G.W. Mulholland, "On two numerical techniques for light scattering by dielectric agglomerated structures," J. Res. Nat. Inst. Stand. Technol. 98, 699-716 (1993).
  18. J. Van Bladel, Electromagnetic Fields, Chap. 13 (Hemisphere, Washington, DC, USA, 1985).
  19. C. T. A. Johnk, Engineering Electromagnetic Fields and Waves, Sec. 9-3 (Wiley, New York, NY, USA, 1975).
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    [CrossRef]
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    [CrossRef]

2007 (5)

2006 (4)

2005 (3)

Y.-F. Chen, P. Fischer, and F. W. Wise, "Negative refraction at optical frequencies in nonmagnetic two-component molecular media," Phys. Rev. Lett. 95, 067402 (2005).
[CrossRef] [PubMed]

S. A. Ramakrishna, "Physics of negative refractive index materials," Rep. Prog. Phys. 68, 449-521 (2005).
[CrossRef]

S. A. Ramakrishna and O. J. F. Martin, "Resolving the wave vector in negative refractive index media," Opt. Lett. 30, 2626-2628 (2005).
[CrossRef] [PubMed]

2004 (1)

S. A. Ramakrishna, "On the dual symmetry between absorbing and amplifying random media," Pramana-J. Phys. 62, 1273-1279 (2004).
[CrossRef]

2003 (1)

2001 (1)

R. W. Ziolkowski and E. Heyman, "Wave propagation in media having negative permittivity and permeability," Phys. Rev. E 64, 056625 (2001).
[CrossRef]

1993 (1)

A. Lakhtakia and G.W. Mulholland, "On two numerical techniques for light scattering by dielectric agglomerated structures," J. Res. Nat. Inst. Stand. Technol. 98, 699-716 (1993).

Chang, Y.-C.

Chen, Y.-F.

Y.-F. Chen, P. Fischer, and F. W. Wise, "Sign of the refractive index in a gain medium with negative permittivity and permeability," J. Opt. Soc. Am. B 23, 45-50 (2006).
[CrossRef]

Y.-F. Chen, P. Fischer, and F. W. Wise, "Negative refraction at optical frequencies in nonmagnetic two-component molecular media," Phys. Rev. Lett. 95, 067402 (2005).
[CrossRef] [PubMed]

Dogariu, A.

Fan, J.

Fischer, P.

Y.-F. Chen, P. Fischer, and F. W. Wise, "Sign of the refractive index in a gain medium with negative permittivity and permeability," J. Opt. Soc. Am. B 23, 45-50 (2006).
[CrossRef]

Y.-F. Chen, P. Fischer, and F. W. Wise, "Negative refraction at optical frequencies in nonmagnetic two-component molecular media," Phys. Rev. Lett. 95, 067402 (2005).
[CrossRef] [PubMed]

Geddes, J. B.

J. B. GeddesIII, T. G. Mackay, and A. Lakhtakia, "On the refractive index for a nonmagnetic two-component medium: Resolution of a controversy," Opt. Commun. 280, 120-125 (2007).
[CrossRef]

Grigorenko, A. N.

Heyman, E.

R. W. Ziolkowski and E. Heyman, "Wave propagation in media having negative permittivity and permeability," Phys. Rev. E 64, 056625 (2001).
[CrossRef]

Lakhtakia, A.

J. B. GeddesIII, T. G. Mackay, and A. Lakhtakia, "On the refractive index for a nonmagnetic two-component medium: Resolution of a controversy," Opt. Commun. 280, 120-125 (2007).
[CrossRef]

T. G. Mackay and A. Lakhtakia, "Comment on ‘Negative refraction at optical frequencies in nonmagnetic two-component molecular media’," Phys. Rev. Lett. 96, 159701 (2006).
[CrossRef] [PubMed]

A. Lakhtakia and G.W. Mulholland, "On two numerical techniques for light scattering by dielectric agglomerated structures," J. Res. Nat. Inst. Stand. Technol. 98, 699-716 (1993).

Mackay, T. G.

J. B. GeddesIII, T. G. Mackay, and A. Lakhtakia, "On the refractive index for a nonmagnetic two-component medium: Resolution of a controversy," Opt. Commun. 280, 120-125 (2007).
[CrossRef]

T. G. Mackay and A. Lakhtakia, "Comment on ‘Negative refraction at optical frequencies in nonmagnetic two-component molecular media’," Phys. Rev. Lett. 96, 159701 (2006).
[CrossRef] [PubMed]

Martin, O. J. F.

Mulholland, G.W.

A. Lakhtakia and G.W. Mulholland, "On two numerical techniques for light scattering by dielectric agglomerated structures," J. Res. Nat. Inst. Stand. Technol. 98, 699-716 (1993).

Nazarov, V. U.

Nistad, B.

Ramakrishna, S. A.

S. A. Ramakrishna, "Physics of negative refractive index materials," Rep. Prog. Phys. 68, 449-521 (2005).
[CrossRef]

S. A. Ramakrishna and O. J. F. Martin, "Resolving the wave vector in negative refractive index media," Opt. Lett. 30, 2626-2628 (2005).
[CrossRef] [PubMed]

S. A. Ramakrishna, "On the dual symmetry between absorbing and amplifying random media," Pramana-J. Phys. 62, 1273-1279 (2004).
[CrossRef]

Skaar, J.

Wang, L. J.

Wei, J.

J. Wei and M. Xiao, "Electric and magnetic losses and gains in determining the sign of refractive index," Opt. Commun. 270, 455-464 (2007).
[CrossRef]

Wise, F. W.

Y.-F. Chen, P. Fischer, and F. W. Wise, "Sign of the refractive index in a gain medium with negative permittivity and permeability," J. Opt. Soc. Am. B 23, 45-50 (2006).
[CrossRef]

Y.-F. Chen, P. Fischer, and F. W. Wise, "Negative refraction at optical frequencies in nonmagnetic two-component molecular media," Phys. Rev. Lett. 95, 067402 (2005).
[CrossRef] [PubMed]

Xiao, M.

J. Wei and M. Xiao, "Electric and magnetic losses and gains in determining the sign of refractive index," Opt. Commun. 270, 455-464 (2007).
[CrossRef]

Ziolkowski, R. W.

R. W. Ziolkowski and E. Heyman, "Wave propagation in media having negative permittivity and permeability," Phys. Rev. E 64, 056625 (2001).
[CrossRef]

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

J. Phys. (1)

S. A. Ramakrishna, "On the dual symmetry between absorbing and amplifying random media," Pramana-J. Phys. 62, 1273-1279 (2004).
[CrossRef]

J. Res. Nat. Inst. Stand. Technol. (1)

A. Lakhtakia and G.W. Mulholland, "On two numerical techniques for light scattering by dielectric agglomerated structures," J. Res. Nat. Inst. Stand. Technol. 98, 699-716 (1993).

Opt. Commun. (2)

J. Wei and M. Xiao, "Electric and magnetic losses and gains in determining the sign of refractive index," Opt. Commun. 270, 455-464 (2007).
[CrossRef]

J. B. GeddesIII, T. G. Mackay, and A. Lakhtakia, "On the refractive index for a nonmagnetic two-component medium: Resolution of a controversy," Opt. Commun. 280, 120-125 (2007).
[CrossRef]

Opt. Express (2)

Opt. Lett. (5)

Phys. Rev. E (1)

R. W. Ziolkowski and E. Heyman, "Wave propagation in media having negative permittivity and permeability," Phys. Rev. E 64, 056625 (2001).
[CrossRef]

Phys. Rev. E (1)

J. Skaar, "Fresnel equations and the refractive index of active media," Phys. Rev. E  73, 026605(2006).
[CrossRef]

Phys. Rev. Lett. (2)

Y.-F. Chen, P. Fischer, and F. W. Wise, "Negative refraction at optical frequencies in nonmagnetic two-component molecular media," Phys. Rev. Lett. 95, 067402 (2005).
[CrossRef] [PubMed]

T. G. Mackay and A. Lakhtakia, "Comment on ‘Negative refraction at optical frequencies in nonmagnetic two-component molecular media’," Phys. Rev. Lett. 96, 159701 (2006).
[CrossRef] [PubMed]

Rep. Prog. Phys. (1)

S. A. Ramakrishna, "Physics of negative refractive index materials," Rep. Prog. Phys. 68, 449-521 (2005).
[CrossRef]

Other (4)

M. P. Silverman, And Yet It Moves, pp. 151-163 (Cambridge Univ. Press, New York, NY, USA, 1993).

J. Van Bladel, Electromagnetic Fields, Chap. 13 (Hemisphere, Washington, DC, USA, 1985).

C. T. A. Johnk, Engineering Electromagnetic Fields and Waves, Sec. 9-3 (Wiley, New York, NY, USA, 1975).

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles, pp. 89-101 (Wiley, New York, NY, USA, 1983).

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Equations (20)

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E inc ( r , ω ) = [ a s y ̂ + a p ( α 0 k 0 x ̂ + κ k 0 z ̂ ) ] exp [ i ( κ x + α 0 z ) ] , z 0 ,
E ref ( r , ω ) = [ r s y ̂ + r p ( α 0 k 0 x ̂ + κ k 0 z ̂ ) ] exp [ i ( κ x + α 0 z ) ] , z 0 ,
E tr ( r , ω ) = [ t s y ̂ + t p ( α 0 k 0 x ̂ + κ k 0 z ̂ ) ] exp { i [ κ x + α 0 ( z L ) ] } , z L ,
E int ( r , ω ) = [ c s y ̂ + c p ( α k 0 n x ̂ + κ k 0 n z ̂ ) ] exp [ i ( κ x + α z ) ]
+ [ d s y ̂ + d p ( α k 0 n x ̂ + κ k 0 n z ̂ ) ] exp [ i ( κ x α z ) ] , 0 z L .
r p = a p ( e 2 i α L 1 ) ( α 2 n 4 α 0 2 ) Δ p , t p = 4 n 2 a p e 2 i α L α α 0 / Δ p c p = 2 a p n α 0 ( α + n 2 α 0 ) Δ p , d p = 2 a p n α 0 ( α n 2 α 0 ) Δ p r s = a s ( e 2 i α L 1 ) ( α 2 α 0 2 ) Δ s , t s = 4 a s e 2 i α L α α 0 Δ s c s = 2 a s α 0 ( α + α 0 ) Δ s , d s = 2 a s α 0 ( α α 0 ) Δ s } ,
Δ p = ( e 2 i α L 1 ) ( α 2 + n 4 α 0 2 ) 2 n 2 ( e 2 i α L + 1 ) α α 0 Δ s = ( e 2 i α L 1 ) ( α 2 + α 0 2 ) 2 ( e 2 i α L + 1 ) α α 0 } .
E inc ( r , ω ) = A ν = 1 i ν 2 ν + 1 ν ( ν + 1 ) [ M o 1 ν ( 1 ) ( k 0 r ) i N e 1 ν ( 1 ) ( k 0 r ) ] ,
E sc ( r , ω ) = A ν = 1 i ν 2 ν + 1 ν ( ν + 1 ) [ i a ν N e 1 ν ( 3 ) ( k 0 r ) b ν M o 1 ν ( 3 ) ( k 0 r ) ] , r a
E int ( r , ω ) = A ν = 1 i ν 2 ν + 1 ν ( ν + 1 ) [ i d ν N e 1 ν ( 1 ) ( nk 0 r ) c ν M o 1 ν ( 1 ) ( nk 0 r ) ] , r a ,
a ν = n 2 j ν ( n k 0 a ) ψ ν ( 1 ) ( k 0 a ) j ν ( k 0 a ) ψ ν ( 1 ) ( n k 0 a ) n 2 j ν ( n k 0 a ) ψ ν ( 3 ) ( k 0 a ) h ν ( 1 ) ( k 0 a ) ψ ν ( 1 ) ( n k 0 a ) ,
b ν = j ν ( n k 0 a ) ψ ν ( 1 ) ( k 0 a ) j ν ( k 0 a ) ψ ν ( 1 ) ( n k 0 a ) j ν ( n k 0 a ) ψ ν ( 3 ) ( k 0 a ) h ν ( 1 ) ( k 0 a ) ψ ν ( 1 ) ( n k 0 a ) ,
c ν = i ( k 0 a ) j ν ( n k 0 a ) ψ ν ( 3 ) ( k 0 a ) h ν ( 1 ) ( k 0 a ) ψ ν ( 1 ) ( n k 0 a ) ,
d ν = in ( k 0 a ) n 2 j ν ( n k 0 a ) ψ ν ( 3 ) ( k 0 a ) h ν ( 1 ) ( k 0 a ) ψ ν ( 1 ) ( n k 0 a ) ;
E ( r , ω ) = i ω μ 0 V J G = ( k 0 r , k 0 r ) J so ( r , ω ) d 3 r
+ k 0 2 V ε [ n 2 ( ω ) 1 ] G = ( k 0 r , k 0 r ) E ( r , ω ) d 3 r , r V J V ε V 0 ,
E ( r , ω ) = p q A pq ( TE ) exp ( γ pq z ) i ω μ 0 Δ pq [ q π b cos ( p π a x ) sin ( q π b y ) x ̂
+ p π a sin ( p π a x ) cos ( q π b y ) y ̂ ]
+ p q A pq ( TE ) exp ( γ pq z ) { γ pq Δ pq [ q π a cos ( p π a x ) sin ( q π b y ) x ̂
+ q π b sin ( p π a x ) cos ( q π b y ) y ̂ ] + sin ( p π a x ) sin ( q π b y ) z ̂ } ,

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