Abstract

We report the results of simulations relating to the illumination of a structure consisting of a slab constructed from a 2-D hexagonal array of metal rods with a terahertz frequency source. As a consequence of negative refraction an essentially non-divergent beam pattern is observed. Although the results presented relate to the terahertz regime they should also be applicable at other frequencies.

© 2008 Optical Society of America

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  1. K. Dholakia, "Against the spread of the light," Nature 451, 413 (2008)
    [CrossRef] [PubMed]
  2. J .Durnin, J. J. Mieceli, and J. H. Eberly, "Diffraction-free beams," Phys. Rev. Lett. 58, 1499-1501 (1987).
    [CrossRef] [PubMed]
  3. G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, "Observation of accelerating Airy beams," Phys.Rev.Lett. 99, 213901 (2007)
    [CrossRef]
  4. V. G. Veselago, "The electrodynamics of substances with simultaneously negative values of ? and ?," Sov. Phys. Usp. 10, 509-514 (1968)
    [CrossRef]
  5. J. B. Pendry, "Negative refraction makes a perfect lens," Phys.Rev. Lett. 85, 3966-3969 (2000)
    [CrossRef] [PubMed]
  6. R. A. Shelby, D. R. Smith, and S. Shultz, "Experimental verification of a negative index of refraction," Science 292, 77-79 (2002)
    [CrossRef]
  7. V. Patanjali V. Parimi, W. T. Lu, Plarenta Vodo and Srinivas Sridhar, "Photonic crystals: Imaging by flat lens using negative refraction," Nature 426, 404 (2003)
    [CrossRef]
  8. E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopoulou and C. M. Soukoulis, "Electromagnetic waves: Negative refraction by photonic crystals," Nature 423, 604-605 (2003)
    [CrossRef] [PubMed]
  9. M. A. Kaliteevski, S. Brand, J. Garvie-Cook, R. A. Abram, and J. M. Chamberlain, "Terahertz filter based on refractive properties of metallic photonic crystal," Opt. Express 16, 7330-7335 (2008)
    [CrossRef] [PubMed]
  10. D. O. S. Melville, R. J .Blaikie, and C. R. Wolf, "Submicron imaging with a planar silver lens," Appl. Phys. Lett. 84, 4403-4405 (2004)
    [CrossRef]
  11. S. Brand, R. A. Abram and M. A. Kaliteevski, "Complex photonic bandstructure and effective plasma frequency of a two-dimensional array of metal rods," Phys. Rev. B 75, 035102, (2007)
  12. A. J. Gallant, M. A. Kaliteevski, D. Wood, M. C. Petty, .R A. Abram, S. Brand, G. P. Swift, D. A. Zeze and J. M. Chamberlain, "Passband filters for terahertz radiation based on dual metallic photonic structures," Appl. Phys. Lett. 91, 161115 (2007)
    [CrossRef]
  13. Dispersion relations have been calculated using a complex photonic bandstructure method described in [11], and finite difference time domain software OMNISIM© has been employed to simulate the beam propagation. Due to minor convergence problems the frequency scales for the two methods are slightly different. In order to provide matching of the two scales, the bandstructure has been renormalized to provide matching of the frequencies at the J point which can be determined for both calculation techniques.
  14. H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, Appl. Phys. Lett. 74, 1212-1214 (1999)
    [CrossRef]
  15. D. N. Chigrin, S. Enoch, C. M. Sotomayor Torres and G. Tayeb, "Self-guiding in two-dimensional photonic crystals," Opt. Express 11, 1203-1211 (2003).
    [CrossRef] [PubMed]

2008 (2)

2007 (3)

S. Brand, R. A. Abram and M. A. Kaliteevski, "Complex photonic bandstructure and effective plasma frequency of a two-dimensional array of metal rods," Phys. Rev. B 75, 035102, (2007)

A. J. Gallant, M. A. Kaliteevski, D. Wood, M. C. Petty, .R A. Abram, S. Brand, G. P. Swift, D. A. Zeze and J. M. Chamberlain, "Passband filters for terahertz radiation based on dual metallic photonic structures," Appl. Phys. Lett. 91, 161115 (2007)
[CrossRef]

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, "Observation of accelerating Airy beams," Phys.Rev.Lett. 99, 213901 (2007)
[CrossRef]

2004 (1)

D. O. S. Melville, R. J .Blaikie, and C. R. Wolf, "Submicron imaging with a planar silver lens," Appl. Phys. Lett. 84, 4403-4405 (2004)
[CrossRef]

2003 (3)

D. N. Chigrin, S. Enoch, C. M. Sotomayor Torres and G. Tayeb, "Self-guiding in two-dimensional photonic crystals," Opt. Express 11, 1203-1211 (2003).
[CrossRef] [PubMed]

V. Patanjali V. Parimi, W. T. Lu, Plarenta Vodo and Srinivas Sridhar, "Photonic crystals: Imaging by flat lens using negative refraction," Nature 426, 404 (2003)
[CrossRef]

E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopoulou and C. M. Soukoulis, "Electromagnetic waves: Negative refraction by photonic crystals," Nature 423, 604-605 (2003)
[CrossRef] [PubMed]

2002 (1)

R. A. Shelby, D. R. Smith, and S. Shultz, "Experimental verification of a negative index of refraction," Science 292, 77-79 (2002)
[CrossRef]

2000 (1)

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

1999 (1)

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, Appl. Phys. Lett. 74, 1212-1214 (1999)
[CrossRef]

1987 (1)

J .Durnin, J. J. Mieceli, and J. H. Eberly, "Diffraction-free beams," Phys. Rev. Lett. 58, 1499-1501 (1987).
[CrossRef] [PubMed]

1968 (1)

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

Abram, R. A.

M. A. Kaliteevski, S. Brand, J. Garvie-Cook, R. A. Abram, and J. M. Chamberlain, "Terahertz filter based on refractive properties of metallic photonic crystal," Opt. Express 16, 7330-7335 (2008)
[CrossRef] [PubMed]

A. J. Gallant, M. A. Kaliteevski, D. Wood, M. C. Petty, .R A. Abram, S. Brand, G. P. Swift, D. A. Zeze and J. M. Chamberlain, "Passband filters for terahertz radiation based on dual metallic photonic structures," Appl. Phys. Lett. 91, 161115 (2007)
[CrossRef]

S. Brand, R. A. Abram and M. A. Kaliteevski, "Complex photonic bandstructure and effective plasma frequency of a two-dimensional array of metal rods," Phys. Rev. B 75, 035102, (2007)

Aydin, K.

E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopoulou and C. M. Soukoulis, "Electromagnetic waves: Negative refraction by photonic crystals," Nature 423, 604-605 (2003)
[CrossRef] [PubMed]

Blaikie, R. J.

D. O. S. Melville, R. J .Blaikie, and C. R. Wolf, "Submicron imaging with a planar silver lens," Appl. Phys. Lett. 84, 4403-4405 (2004)
[CrossRef]

Brand, S.

M. A. Kaliteevski, S. Brand, J. Garvie-Cook, R. A. Abram, and J. M. Chamberlain, "Terahertz filter based on refractive properties of metallic photonic crystal," Opt. Express 16, 7330-7335 (2008)
[CrossRef] [PubMed]

A. J. Gallant, M. A. Kaliteevski, D. Wood, M. C. Petty, .R A. Abram, S. Brand, G. P. Swift, D. A. Zeze and J. M. Chamberlain, "Passband filters for terahertz radiation based on dual metallic photonic structures," Appl. Phys. Lett. 91, 161115 (2007)
[CrossRef]

S. Brand, R. A. Abram and M. A. Kaliteevski, "Complex photonic bandstructure and effective plasma frequency of a two-dimensional array of metal rods," Phys. Rev. B 75, 035102, (2007)

Broky, J.

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, "Observation of accelerating Airy beams," Phys.Rev.Lett. 99, 213901 (2007)
[CrossRef]

Chamberlain, J. M.

M. A. Kaliteevski, S. Brand, J. Garvie-Cook, R. A. Abram, and J. M. Chamberlain, "Terahertz filter based on refractive properties of metallic photonic crystal," Opt. Express 16, 7330-7335 (2008)
[CrossRef] [PubMed]

A. J. Gallant, M. A. Kaliteevski, D. Wood, M. C. Petty, .R A. Abram, S. Brand, G. P. Swift, D. A. Zeze and J. M. Chamberlain, "Passband filters for terahertz radiation based on dual metallic photonic structures," Appl. Phys. Lett. 91, 161115 (2007)
[CrossRef]

Chigrin, D. N.

Christodoulides, D. N.

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, "Observation of accelerating Airy beams," Phys.Rev.Lett. 99, 213901 (2007)
[CrossRef]

Cubukcu, E.

E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopoulou and C. M. Soukoulis, "Electromagnetic waves: Negative refraction by photonic crystals," Nature 423, 604-605 (2003)
[CrossRef] [PubMed]

Dogariu, A.

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, "Observation of accelerating Airy beams," Phys.Rev.Lett. 99, 213901 (2007)
[CrossRef]

Durnin, J.

J .Durnin, J. J. Mieceli, and J. H. Eberly, "Diffraction-free beams," Phys. Rev. Lett. 58, 1499-1501 (1987).
[CrossRef] [PubMed]

Eberly, J. H.

J .Durnin, J. J. Mieceli, and J. H. Eberly, "Diffraction-free beams," Phys. Rev. Lett. 58, 1499-1501 (1987).
[CrossRef] [PubMed]

Enoch, S.

Foteinopoulou, S.

E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopoulou and C. M. Soukoulis, "Electromagnetic waves: Negative refraction by photonic crystals," Nature 423, 604-605 (2003)
[CrossRef] [PubMed]

Gallant, A. J.

A. J. Gallant, M. A. Kaliteevski, D. Wood, M. C. Petty, .R A. Abram, S. Brand, G. P. Swift, D. A. Zeze and J. M. Chamberlain, "Passband filters for terahertz radiation based on dual metallic photonic structures," Appl. Phys. Lett. 91, 161115 (2007)
[CrossRef]

Garvie-Cook, J.

Kaliteevski, M. A.

M. A. Kaliteevski, S. Brand, J. Garvie-Cook, R. A. Abram, and J. M. Chamberlain, "Terahertz filter based on refractive properties of metallic photonic crystal," Opt. Express 16, 7330-7335 (2008)
[CrossRef] [PubMed]

A. J. Gallant, M. A. Kaliteevski, D. Wood, M. C. Petty, .R A. Abram, S. Brand, G. P. Swift, D. A. Zeze and J. M. Chamberlain, "Passband filters for terahertz radiation based on dual metallic photonic structures," Appl. Phys. Lett. 91, 161115 (2007)
[CrossRef]

S. Brand, R. A. Abram and M. A. Kaliteevski, "Complex photonic bandstructure and effective plasma frequency of a two-dimensional array of metal rods," Phys. Rev. B 75, 035102, (2007)

Kawakami, S.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, Appl. Phys. Lett. 74, 1212-1214 (1999)
[CrossRef]

Kawashima, T.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, Appl. Phys. Lett. 74, 1212-1214 (1999)
[CrossRef]

Kosaka, H.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, Appl. Phys. Lett. 74, 1212-1214 (1999)
[CrossRef]

Melville, D. O. S.

D. O. S. Melville, R. J .Blaikie, and C. R. Wolf, "Submicron imaging with a planar silver lens," Appl. Phys. Lett. 84, 4403-4405 (2004)
[CrossRef]

Mieceli, J. J.

J .Durnin, J. J. Mieceli, and J. H. Eberly, "Diffraction-free beams," Phys. Rev. Lett. 58, 1499-1501 (1987).
[CrossRef] [PubMed]

Notomi, M.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, Appl. Phys. Lett. 74, 1212-1214 (1999)
[CrossRef]

Ozbay, E.

E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopoulou and C. M. Soukoulis, "Electromagnetic waves: Negative refraction by photonic crystals," Nature 423, 604-605 (2003)
[CrossRef] [PubMed]

Pendry, J. B.

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

Petty, M. C.

A. J. Gallant, M. A. Kaliteevski, D. Wood, M. C. Petty, .R A. Abram, S. Brand, G. P. Swift, D. A. Zeze and J. M. Chamberlain, "Passband filters for terahertz radiation based on dual metallic photonic structures," Appl. Phys. Lett. 91, 161115 (2007)
[CrossRef]

Sato, T.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, Appl. Phys. Lett. 74, 1212-1214 (1999)
[CrossRef]

Shelby, R. A.

R. A. Shelby, D. R. Smith, and S. Shultz, "Experimental verification of a negative index of refraction," Science 292, 77-79 (2002)
[CrossRef]

Shultz, S.

R. A. Shelby, D. R. Smith, and S. Shultz, "Experimental verification of a negative index of refraction," Science 292, 77-79 (2002)
[CrossRef]

Siviloglou, G. A.

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, "Observation of accelerating Airy beams," Phys.Rev.Lett. 99, 213901 (2007)
[CrossRef]

Smith, D. R.

R. A. Shelby, D. R. Smith, and S. Shultz, "Experimental verification of a negative index of refraction," Science 292, 77-79 (2002)
[CrossRef]

Soukoulis, C. M.

E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopoulou and C. M. Soukoulis, "Electromagnetic waves: Negative refraction by photonic crystals," Nature 423, 604-605 (2003)
[CrossRef] [PubMed]

Swift, G. P.

A. J. Gallant, M. A. Kaliteevski, D. Wood, M. C. Petty, .R A. Abram, S. Brand, G. P. Swift, D. A. Zeze and J. M. Chamberlain, "Passband filters for terahertz radiation based on dual metallic photonic structures," Appl. Phys. Lett. 91, 161115 (2007)
[CrossRef]

Tamamura, T.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, Appl. Phys. Lett. 74, 1212-1214 (1999)
[CrossRef]

Tomita, A.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, Appl. Phys. Lett. 74, 1212-1214 (1999)
[CrossRef]

Veselago, V. G.

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

Wolf, C. R.

D. O. S. Melville, R. J .Blaikie, and C. R. Wolf, "Submicron imaging with a planar silver lens," Appl. Phys. Lett. 84, 4403-4405 (2004)
[CrossRef]

Wood, D.

A. J. Gallant, M. A. Kaliteevski, D. Wood, M. C. Petty, .R A. Abram, S. Brand, G. P. Swift, D. A. Zeze and J. M. Chamberlain, "Passband filters for terahertz radiation based on dual metallic photonic structures," Appl. Phys. Lett. 91, 161115 (2007)
[CrossRef]

Zeze, D. A.

A. J. Gallant, M. A. Kaliteevski, D. Wood, M. C. Petty, .R A. Abram, S. Brand, G. P. Swift, D. A. Zeze and J. M. Chamberlain, "Passband filters for terahertz radiation based on dual metallic photonic structures," Appl. Phys. Lett. 91, 161115 (2007)
[CrossRef]

Appl. Phys. Lett. (3)

D. O. S. Melville, R. J .Blaikie, and C. R. Wolf, "Submicron imaging with a planar silver lens," Appl. Phys. Lett. 84, 4403-4405 (2004)
[CrossRef]

A. J. Gallant, M. A. Kaliteevski, D. Wood, M. C. Petty, .R A. Abram, S. Brand, G. P. Swift, D. A. Zeze and J. M. Chamberlain, "Passband filters for terahertz radiation based on dual metallic photonic structures," Appl. Phys. Lett. 91, 161115 (2007)
[CrossRef]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, Appl. Phys. Lett. 74, 1212-1214 (1999)
[CrossRef]

Nature (3)

K. Dholakia, "Against the spread of the light," Nature 451, 413 (2008)
[CrossRef] [PubMed]

V. Patanjali V. Parimi, W. T. Lu, Plarenta Vodo and Srinivas Sridhar, "Photonic crystals: Imaging by flat lens using negative refraction," Nature 426, 404 (2003)
[CrossRef]

E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopoulou and C. M. Soukoulis, "Electromagnetic waves: Negative refraction by photonic crystals," Nature 423, 604-605 (2003)
[CrossRef] [PubMed]

Opt. Express (2)

Phys. Rev. B (1)

S. Brand, R. A. Abram and M. A. Kaliteevski, "Complex photonic bandstructure and effective plasma frequency of a two-dimensional array of metal rods," Phys. Rev. B 75, 035102, (2007)

Phys. Rev. Lett. (1)

J .Durnin, J. J. Mieceli, and J. H. Eberly, "Diffraction-free beams," Phys. Rev. Lett. 58, 1499-1501 (1987).
[CrossRef] [PubMed]

Phys.Rev. Lett. (1)

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

Phys.Rev.Lett. (1)

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, "Observation of accelerating Airy beams," Phys.Rev.Lett. 99, 213901 (2007)
[CrossRef]

Science (1)

R. A. Shelby, D. R. Smith, and S. Shultz, "Experimental verification of a negative index of refraction," Science 292, 77-79 (2002)
[CrossRef]

Sov. Phys. Usp. (1)

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

Other (1)

Dispersion relations have been calculated using a complex photonic bandstructure method described in [11], and finite difference time domain software OMNISIM© has been employed to simulate the beam propagation. Due to minor convergence problems the frequency scales for the two methods are slightly different. In order to provide matching of the two scales, the bandstructure has been renormalized to provide matching of the frequencies at the J point which can be determined for both calculation techniques.

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Figures (4)

Fig. 1.
Fig. 1.

Propagation of rays from a 2-D point source through a slab of negatively refracting material.

Fig. 2.
Fig. 2.

Band structure [13] of the hexagonal photonic crystal with lattice constant of 200 µm formed by metallic rods of diameter 80 µm. Horizontal arrows indicate the frequencies for which the modelling of the field pattern is shown in Fig. 3.

Fig. 3.
Fig. 3.

The field patterns formed when a line source irradiates the photonic crystal slab at frequencies of (a) 1.621 THz, (b) 1.667 THz and (c) 1.715 THz. The distance between the source and the edge of the slab is A=1.8 mm.

Fig. 4.
Fig. 4.

Intensity profile of the beam for frequencies (a) 1.621 THz, (b) 1.667 THz and (c) 1.715 THz at distances from the left-hand edge of the slab of 7.5 mm (solid line), 16 mm (dashed line), and for distances of the source from the right-hand edge of the slab of A= 1.8 mm (black), A=4.5 mm (red), A=5.3 mm (green).

Tables (1)

Tables Icon

Table 1. Parameters relating to the results shown in Figs. 3 and 4.

Equations (2)

Equations on this page are rendered with MathJax. Learn more.

sin α = n sin β
D + A = L tan β tan α = L 1 sin 2 α n 2 sin 2 α .

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