Abstract

We study numerically the electromagnetic scattering properties of structures with negative indices of refraction. To perform this analysis, we utilize a commercial finite-element based electromagnetic solver (HFSS, Ansoft), in which a negative index material can be formed from mesh elements whose permittivity and permeability are both negative. In particular, we investigate the expected transmission characteristics of a finite beam incident on negative index prisms and lenses. We also confirm numerically the predicted superlens effect of an image formed by a planar slab with index n=-1, using two subwavelength (λ/20) slits as objects.

© 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 ε and µ,” Soviet Physics USPEKI 10, 509 (1968).
    [Crossref]
  2. J. B. Pendry, “Electromagnetic materials enter the negative age,” Physics World 14, 47 (2001).
  3. D. R. Smith and N. Kroll, “Negative refractive index in left-handed materials,” Phys. Rev. Lett. 85, 2933 (2000).
    [Crossref] [PubMed]
  4. D. R. Smith, Willie J. 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 (2000).
    [Crossref] [PubMed]
  5. R. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292, 77 (2001).
    [Crossref] [PubMed]
  6. J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966 (2000).
    [Crossref] [PubMed]
  7. C. Caloz, C.-C. Chang, and T. Itoh, “Full-wave verification of the fundamental properties of left-handed materials in waveguide configurations,” J. App. Phys. 90, 5483 (2001).
    [Crossref]
  8. C. Parazzoli, R. B. Greegor, K. Li, B. E. C. Kotenbah, and M. Tanelian, “Experimental verification and simulation of negative index of refraction using Snell’s law,” Phys. Rev. Lett. submitted (2002).
  9. A. Yariv, Optical electronics in modern communications, fifth Ed. (Oxford Press, 2000), Chap. 2.
  10. N. Garcia and M. Nieto-Vesperinas, “Left-handed materials do not make a perfect lens,” Appl. Phys. Lett. 88, 207403 (2002).
  11. R. W. Ziolkowski and E. Heyman, “Wave propagation in media having negative permittivity and permeability,” Phys. Rev. E 64, 056625 (2001).
    [Crossref]
  12. J. T. Shen and P. M. Platzman, “Near field imaging with negative dielectric constant lenses,” Appl. Phys. Lett. 80, 3286 (2002).
    [Crossref]
  13. D. R. Smithet al., “Limitations on sub-diffraction imaging with a negative index slab,” Appl. Phys. Lett. in press (2003).
    [Crossref]
  14. R. Ruppin, “Surface polaritons of a left-handed materials slab,” J. Phys.: Condens. Matter 13, 1811 (2001).
    [Crossref]

2002 (2)

N. Garcia and M. Nieto-Vesperinas, “Left-handed materials do not make a perfect lens,” Appl. Phys. Lett. 88, 207403 (2002).

J. T. Shen and P. M. Platzman, “Near field imaging with negative dielectric constant lenses,” Appl. Phys. Lett. 80, 3286 (2002).
[Crossref]

2001 (5)

R. Ruppin, “Surface polaritons of a left-handed materials slab,” J. Phys.: Condens. Matter 13, 1811 (2001).
[Crossref]

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

C. Caloz, C.-C. Chang, and T. Itoh, “Full-wave verification of the fundamental properties of left-handed materials in waveguide configurations,” J. App. Phys. 90, 5483 (2001).
[Crossref]

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

R. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292, 77 (2001).
[Crossref] [PubMed]

2000 (3)

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966 (2000).
[Crossref] [PubMed]

D. R. Smith and N. Kroll, “Negative refractive index in left-handed materials,” Phys. Rev. Lett. 85, 2933 (2000).
[Crossref] [PubMed]

D. R. Smith, Willie J. 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 (2000).
[Crossref] [PubMed]

1968 (1)

V. G. Veselago “The electrodynamics of substances with simultaneously negative values of ε and µ,” Soviet Physics USPEKI 10, 509 (1968).
[Crossref]

Caloz, C.

C. Caloz, C.-C. Chang, and T. Itoh, “Full-wave verification of the fundamental properties of left-handed materials in waveguide configurations,” J. App. Phys. 90, 5483 (2001).
[Crossref]

Chang, C.-C.

C. Caloz, C.-C. Chang, and T. Itoh, “Full-wave verification of the fundamental properties of left-handed materials in waveguide configurations,” J. App. Phys. 90, 5483 (2001).
[Crossref]

Garcia, N.

N. Garcia and M. Nieto-Vesperinas, “Left-handed materials do not make a perfect lens,” Appl. Phys. Lett. 88, 207403 (2002).

Greegor, R. B.

C. Parazzoli, R. B. Greegor, K. Li, B. E. C. Kotenbah, and M. Tanelian, “Experimental verification and simulation of negative index of refraction using Snell’s law,” Phys. Rev. Lett. submitted (2002).

Heyman, E.

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

Itoh, T.

C. Caloz, C.-C. Chang, and T. Itoh, “Full-wave verification of the fundamental properties of left-handed materials in waveguide configurations,” J. App. Phys. 90, 5483 (2001).
[Crossref]

Kotenbah, B. E. C.

C. Parazzoli, R. B. Greegor, K. Li, B. E. C. Kotenbah, and M. Tanelian, “Experimental verification and simulation of negative index of refraction using Snell’s law,” Phys. Rev. Lett. submitted (2002).

Kroll, N.

D. R. Smith and N. Kroll, “Negative refractive index in left-handed materials,” Phys. Rev. Lett. 85, 2933 (2000).
[Crossref] [PubMed]

Li, K.

C. Parazzoli, R. B. Greegor, K. Li, B. E. C. Kotenbah, and M. Tanelian, “Experimental verification and simulation of negative index of refraction using Snell’s law,” Phys. Rev. Lett. submitted (2002).

Nemat-Nasser, S. C.

D. R. Smith, Willie J. 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 (2000).
[Crossref] [PubMed]

Nieto-Vesperinas, M.

N. Garcia and M. Nieto-Vesperinas, “Left-handed materials do not make a perfect lens,” Appl. Phys. Lett. 88, 207403 (2002).

Padilla, Willie J.

D. R. Smith, Willie J. 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 (2000).
[Crossref] [PubMed]

Parazzoli, C.

C. Parazzoli, R. B. Greegor, K. Li, B. E. C. Kotenbah, and M. Tanelian, “Experimental verification and simulation of negative index of refraction using Snell’s law,” Phys. Rev. Lett. submitted (2002).

Pendry, J. B.

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

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966 (2000).
[Crossref] [PubMed]

Platzman, P. M.

J. T. Shen and P. M. Platzman, “Near field imaging with negative dielectric constant lenses,” Appl. Phys. Lett. 80, 3286 (2002).
[Crossref]

Ruppin, R.

R. Ruppin, “Surface polaritons of a left-handed materials slab,” J. Phys.: Condens. Matter 13, 1811 (2001).
[Crossref]

Schultz, S.

R. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292, 77 (2001).
[Crossref] [PubMed]

D. R. Smith, Willie J. 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 (2000).
[Crossref] [PubMed]

Shelby, R.

R. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292, 77 (2001).
[Crossref] [PubMed]

Shen, J. T.

J. T. Shen and P. M. Platzman, “Near field imaging with negative dielectric constant lenses,” Appl. Phys. Lett. 80, 3286 (2002).
[Crossref]

Smith, D. R.

R. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292, 77 (2001).
[Crossref] [PubMed]

D. R. Smith and N. Kroll, “Negative refractive index in left-handed materials,” Phys. Rev. Lett. 85, 2933 (2000).
[Crossref] [PubMed]

D. R. Smith, Willie J. 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 (2000).
[Crossref] [PubMed]

D. R. Smithet al., “Limitations on sub-diffraction imaging with a negative index slab,” Appl. Phys. Lett. in press (2003).
[Crossref]

Tanelian, M.

C. Parazzoli, R. B. Greegor, K. Li, B. E. C. Kotenbah, and M. Tanelian, “Experimental verification and simulation of negative index of refraction using Snell’s law,” Phys. Rev. Lett. submitted (2002).

Veselago, V. G.

V. G. Veselago “The electrodynamics of substances with simultaneously negative values of ε and µ,” Soviet Physics USPEKI 10, 509 (1968).
[Crossref]

Vier, D. C.

D. R. Smith, Willie J. 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 (2000).
[Crossref] [PubMed]

Yariv, A.

A. Yariv, Optical electronics in modern communications, fifth Ed. (Oxford Press, 2000), Chap. 2.

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]

Appl. Phys. Lett. (2)

N. Garcia and M. Nieto-Vesperinas, “Left-handed materials do not make a perfect lens,” Appl. Phys. Lett. 88, 207403 (2002).

J. T. Shen and P. M. Platzman, “Near field imaging with negative dielectric constant lenses,” Appl. Phys. Lett. 80, 3286 (2002).
[Crossref]

J. App. Phys. (1)

C. Caloz, C.-C. Chang, and T. Itoh, “Full-wave verification of the fundamental properties of left-handed materials in waveguide configurations,” J. App. Phys. 90, 5483 (2001).
[Crossref]

J. Phys.: Condens. Matter (1)

R. Ruppin, “Surface polaritons of a left-handed materials slab,” J. Phys.: Condens. Matter 13, 1811 (2001).
[Crossref]

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. Lett. (3)

D. R. Smith and N. Kroll, “Negative refractive index in left-handed materials,” Phys. Rev. Lett. 85, 2933 (2000).
[Crossref] [PubMed]

D. R. Smith, Willie J. 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 (2000).
[Crossref] [PubMed]

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966 (2000).
[Crossref] [PubMed]

Physics World (1)

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

Science (1)

R. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292, 77 (2001).
[Crossref] [PubMed]

Soviet Physics USPEKI (1)

V. G. Veselago “The electrodynamics of substances with simultaneously negative values of ε and µ,” Soviet Physics USPEKI 10, 509 (1968).
[Crossref]

Other (3)

C. Parazzoli, R. B. Greegor, K. Li, B. E. C. Kotenbah, and M. Tanelian, “Experimental verification and simulation of negative index of refraction using Snell’s law,” Phys. Rev. Lett. submitted (2002).

A. Yariv, Optical electronics in modern communications, fifth Ed. (Oxford Press, 2000), Chap. 2.

D. R. Smithet al., “Limitations on sub-diffraction imaging with a negative index slab,” Appl. Phys. Lett. in press (2003).
[Crossref]

Supplementary Material (7)

» Media 1: MOV (738 KB)     
» Media 2: MOV (679 KB)     
» Media 3: MOV (771 KB)     
» Media 4: MOV (673 KB)     
» Media 5: MOV (594 KB)     
» Media 6: MOV (656 KB)     
» Media 7: MOV (656 KB)     

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Figures (6)

Fig. 1.
Fig. 1.

(a) (740K) Movie of an incident beam (from below) positively refracted by a wedge sample with ε=2.2 and µ=+1. The darkened regions indicate absorber, in analogy with the experiments. The circle indicates the path along which the field plots in Fig. 2 were taken. (b) (682K) Movie showing negative refraction from a wedge with ε=-1 and µ=-1.

Fig. 2.
Fig. 2.

Angular plots of the field intensity of the refracted wave at a constant radius away from a positive index wedge with ε=2.2 and µ=+1 (black curve), and a negative index wedge with ε=-1 and µ=-1 (red cruve). The dashed lines indicate the expected refraction angles as predicted by Snell’s law based on the refractive index of the materials.

Fig. 3.
Fig. 3.

(a) (779 KB) Movie of an incident beam (from below) positively refracted by a wedge sample with ε=2.2 and µ=+1. (b) (662 KB) Movie showing negative refraction from a wedge with ε=-1 and µ=-1. In both cases, a stepped pattern was introduced along the refracting interface to simulate more closely the samples used in the experimental work.

Fig. 4.
Fig. 4.

(595 KB) Movie of a plane wave (incident from the left) mostly reflected from an absorbing plane. Two slits separated by a distance of λ/10, and of width λ/20, admit a small portion of the radiation, forming a subwavelength source field distribution. (a) With no slab present, all subwavelength information is lost a short distance away from the slits. (b) With a positive index slab (ε=2.2), indicated by the continuous black lines, no subwavelength information is transmitted at the image plane (continuous white line). (c) A slab with ε=-1 and µ=-1 refocuses the field distribution from the object plane, including subwavelength information; however, unwanted surface modes appear on the slab surfaces. (d) (657 KB) Movie showing that the introduction of losses (ε”=µ”=0.001) damps the surface modes while retaining most of the resolution. [Media 7]

Fig. 5.
Fig. 5.

Field intensity plots along the image plane after the slab. Black dashed curve: the object distribution. Gray curve: after insertion of a dielectric slab with ε=2.2. Black solid curve: after insertion of a slab with ε=-1+0.001i and µ=-1+0.001i. Green curve: after insertion of a slab with ε=-1+0.1i and µ=-1+0.1i. Red curve: after insertion of a slab with ε=+1+0.001i and µ=-1+0.001i.

Fig. 6.
Fig. 6.

(a) A wave incident on a positive index (n=+3) converging lens with R=6 cm is focused to a spot 3 cm away. (b) Similarly, a wave incident on a negative index (n=-1, ε=µ=-1) concave lens with R=6 cm is also focused to a spot 3 cm away. The wavelength used in the calculation was λ=3 cm.

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