Abstract

We demonstrate how micromachined photonic crystals can be used to negatively refract terahertz frequency light. The photonic crystals, which are constructed from conventional dielectric materials, manipulate the incident beam via interaction with their photonic bands. Consequently, we show that different components of a broadband beam incident on the structure may be positively or negatively refracted, depending upon its frequency and that the structure can be used as an effective spectral filter of THz radiation.

© 2011 Optical Society of America

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  1. J. M. Chamberlain, Phil. Trans. R. Soc. Lond. A 362, 199 (2004).
    [CrossRef]
  2. J. B. Jackson, M. Mourou, J. F. Whitaker, J. N. Duling III, S. C. Williamson, M. Menu, and G. A. Mourou, Opt. Commun. 281, 527 (2008).
    [CrossRef]
  3. E. Pickwell and V. P. Wallace, J. Phys. D 39, R301 (2006).
    [CrossRef]
  4. P. H. Siegel, IEEE Microwave Theory Tech. 50, 910 (2002).
    [CrossRef]
  5. P. W. Milonni, Fast Light, Slow Light and Left-Handed Light (Taylor & Francis, 2005).
  6. V. G. Veselago, Sov. Phys. Usp. 10, 509 (1968).
    [CrossRef]
  7. D. O. S. Melville, R. J. Blaikie, and C. R. Wolf, Appl. Phys. Lett. 84, 4403 (2004).
    [CrossRef]
  8. R. A. Shelby, D. R. Smith, and S. Schultz, Science 292, 77 (2001).
    [CrossRef] [PubMed]
  9. P. V. Parimi, W. T. Lu, P. Vodo, J. Sokoloff, J. S. Derov, and S. Sridhar, Phys. Rev. Lett. 92, 127401 (2004).
    [CrossRef] [PubMed]
  10. J. B. Pendry, Phys. Rev. Lett. 85, 3966 (2000).
    [CrossRef] [PubMed]
  11. J. B. Pendry, D. Schurig, and D. R. Smith, Science 312, 1780 (2006).
    [CrossRef] [PubMed]
  12. I. Newton, Opticks: Or, a Treatise of the Reflexions, Refractions, Inflexions and Colours of Light (William and John Innys, 1704).
  13. S. Wang, F. Garet, K. Blary, E. Lheurette, J. L. Coutaz, and D. Lippens, Appl. Phys. Lett. 97, 181902 (2010).
    [CrossRef]
  14. C. Luo, S. G. Johnson, J. D. Joannopolous, and J. B. Pendry, Phys. Rev. B 65, 201104 (2002).
    [CrossRef]
  15. M. A. Kaliteevski, S. Brand, J. Garvie-Cook, R. A. Abram, and J. M. Chamberlain, Opt. Express 16, 7330 (2008).
    [CrossRef] [PubMed]
  16. A. J. Gallant, M. A. Kaliteevski, S. Brand, D. Wood, M. C. Petty, R. A. Abram, and J. M. Chamberlain, J. Appl. Phys. 102, 023102 (2007).
    [CrossRef]
  17. S. Brand, R. A. Abram, and M. A. Kaliteevski, Phys. Rev. B B75, 035102 (2007).
    [CrossRef]
  18. Finite-difference time-domain simulations to model the EM field profiles were carried out using the OmniSim software package.

2010 (1)

S. Wang, F. Garet, K. Blary, E. Lheurette, J. L. Coutaz, and D. Lippens, Appl. Phys. Lett. 97, 181902 (2010).
[CrossRef]

2008 (2)

M. A. Kaliteevski, S. Brand, J. Garvie-Cook, R. A. Abram, and J. M. Chamberlain, Opt. Express 16, 7330 (2008).
[CrossRef] [PubMed]

J. B. Jackson, M. Mourou, J. F. Whitaker, J. N. Duling III, S. C. Williamson, M. Menu, and G. A. Mourou, Opt. Commun. 281, 527 (2008).
[CrossRef]

2007 (2)

A. J. Gallant, M. A. Kaliteevski, S. Brand, D. Wood, M. C. Petty, R. A. Abram, and J. M. Chamberlain, J. Appl. Phys. 102, 023102 (2007).
[CrossRef]

S. Brand, R. A. Abram, and M. A. Kaliteevski, Phys. Rev. B B75, 035102 (2007).
[CrossRef]

2006 (2)

J. B. Pendry, D. Schurig, and D. R. Smith, Science 312, 1780 (2006).
[CrossRef] [PubMed]

E. Pickwell and V. P. Wallace, J. Phys. D 39, R301 (2006).
[CrossRef]

2004 (3)

D. O. S. Melville, R. J. Blaikie, and C. R. Wolf, Appl. Phys. Lett. 84, 4403 (2004).
[CrossRef]

P. V. Parimi, W. T. Lu, P. Vodo, J. Sokoloff, J. S. Derov, and S. Sridhar, Phys. Rev. Lett. 92, 127401 (2004).
[CrossRef] [PubMed]

J. M. Chamberlain, Phil. Trans. R. Soc. Lond. A 362, 199 (2004).
[CrossRef]

2002 (2)

C. Luo, S. G. Johnson, J. D. Joannopolous, and J. B. Pendry, Phys. Rev. B 65, 201104 (2002).
[CrossRef]

P. H. Siegel, IEEE Microwave Theory Tech. 50, 910 (2002).
[CrossRef]

2001 (1)

R. A. Shelby, D. R. Smith, and S. Schultz, Science 292, 77 (2001).
[CrossRef] [PubMed]

2000 (1)

J. B. Pendry, Phys. Rev. Lett. 85, 3966 (2000).
[CrossRef] [PubMed]

1968 (1)

V. G. Veselago, Sov. Phys. Usp. 10, 509 (1968).
[CrossRef]

Abram, R. A.

M. A. Kaliteevski, S. Brand, J. Garvie-Cook, R. A. Abram, and J. M. Chamberlain, Opt. Express 16, 7330 (2008).
[CrossRef] [PubMed]

A. J. Gallant, M. A. Kaliteevski, S. Brand, D. Wood, M. C. Petty, R. A. Abram, and J. M. Chamberlain, J. Appl. Phys. 102, 023102 (2007).
[CrossRef]

S. Brand, R. A. Abram, and M. A. Kaliteevski, Phys. Rev. B B75, 035102 (2007).
[CrossRef]

Blaikie, R. J.

D. O. S. Melville, R. J. Blaikie, and C. R. Wolf, Appl. Phys. Lett. 84, 4403 (2004).
[CrossRef]

Blary, K.

S. Wang, F. Garet, K. Blary, E. Lheurette, J. L. Coutaz, and D. Lippens, Appl. Phys. Lett. 97, 181902 (2010).
[CrossRef]

Brand, S.

M. A. Kaliteevski, S. Brand, J. Garvie-Cook, R. A. Abram, and J. M. Chamberlain, Opt. Express 16, 7330 (2008).
[CrossRef] [PubMed]

A. J. Gallant, M. A. Kaliteevski, S. Brand, D. Wood, M. C. Petty, R. A. Abram, and J. M. Chamberlain, J. Appl. Phys. 102, 023102 (2007).
[CrossRef]

S. Brand, R. A. Abram, and M. A. Kaliteevski, Phys. Rev. B B75, 035102 (2007).
[CrossRef]

Chamberlain, J. M.

M. A. Kaliteevski, S. Brand, J. Garvie-Cook, R. A. Abram, and J. M. Chamberlain, Opt. Express 16, 7330 (2008).
[CrossRef] [PubMed]

A. J. Gallant, M. A. Kaliteevski, S. Brand, D. Wood, M. C. Petty, R. A. Abram, and J. M. Chamberlain, J. Appl. Phys. 102, 023102 (2007).
[CrossRef]

J. M. Chamberlain, Phil. Trans. R. Soc. Lond. A 362, 199 (2004).
[CrossRef]

Coutaz, J. L.

S. Wang, F. Garet, K. Blary, E. Lheurette, J. L. Coutaz, and D. Lippens, Appl. Phys. Lett. 97, 181902 (2010).
[CrossRef]

Derov, J. S.

P. V. Parimi, W. T. Lu, P. Vodo, J. Sokoloff, J. S. Derov, and S. Sridhar, Phys. Rev. Lett. 92, 127401 (2004).
[CrossRef] [PubMed]

Duling, J. N.

J. B. Jackson, M. Mourou, J. F. Whitaker, J. N. Duling III, S. C. Williamson, M. Menu, and G. A. Mourou, Opt. Commun. 281, 527 (2008).
[CrossRef]

Gallant, A. J.

A. J. Gallant, M. A. Kaliteevski, S. Brand, D. Wood, M. C. Petty, R. A. Abram, and J. M. Chamberlain, J. Appl. Phys. 102, 023102 (2007).
[CrossRef]

Garet, F.

S. Wang, F. Garet, K. Blary, E. Lheurette, J. L. Coutaz, and D. Lippens, Appl. Phys. Lett. 97, 181902 (2010).
[CrossRef]

Garvie-Cook, J.

Jackson, J. B.

J. B. Jackson, M. Mourou, J. F. Whitaker, J. N. Duling III, S. C. Williamson, M. Menu, and G. A. Mourou, Opt. Commun. 281, 527 (2008).
[CrossRef]

Joannopolous, J. D.

C. Luo, S. G. Johnson, J. D. Joannopolous, and J. B. Pendry, Phys. Rev. B 65, 201104 (2002).
[CrossRef]

Johnson, S. G.

C. Luo, S. G. Johnson, J. D. Joannopolous, and J. B. Pendry, Phys. Rev. B 65, 201104 (2002).
[CrossRef]

Kaliteevski, M. A.

M. A. Kaliteevski, S. Brand, J. Garvie-Cook, R. A. Abram, and J. M. Chamberlain, Opt. Express 16, 7330 (2008).
[CrossRef] [PubMed]

A. J. Gallant, M. A. Kaliteevski, S. Brand, D. Wood, M. C. Petty, R. A. Abram, and J. M. Chamberlain, J. Appl. Phys. 102, 023102 (2007).
[CrossRef]

S. Brand, R. A. Abram, and M. A. Kaliteevski, Phys. Rev. B B75, 035102 (2007).
[CrossRef]

Lheurette, E.

S. Wang, F. Garet, K. Blary, E. Lheurette, J. L. Coutaz, and D. Lippens, Appl. Phys. Lett. 97, 181902 (2010).
[CrossRef]

Lippens, D.

S. Wang, F. Garet, K. Blary, E. Lheurette, J. L. Coutaz, and D. Lippens, Appl. Phys. Lett. 97, 181902 (2010).
[CrossRef]

Lu, W. T.

P. V. Parimi, W. T. Lu, P. Vodo, J. Sokoloff, J. S. Derov, and S. Sridhar, Phys. Rev. Lett. 92, 127401 (2004).
[CrossRef] [PubMed]

Luo, C.

C. Luo, S. G. Johnson, J. D. Joannopolous, and J. B. Pendry, Phys. Rev. B 65, 201104 (2002).
[CrossRef]

Melville, D. O. S.

D. O. S. Melville, R. J. Blaikie, and C. R. Wolf, Appl. Phys. Lett. 84, 4403 (2004).
[CrossRef]

Menu, M.

J. B. Jackson, M. Mourou, J. F. Whitaker, J. N. Duling III, S. C. Williamson, M. Menu, and G. A. Mourou, Opt. Commun. 281, 527 (2008).
[CrossRef]

Milonni, P. W.

P. W. Milonni, Fast Light, Slow Light and Left-Handed Light (Taylor & Francis, 2005).

Mourou, G. A.

J. B. Jackson, M. Mourou, J. F. Whitaker, J. N. Duling III, S. C. Williamson, M. Menu, and G. A. Mourou, Opt. Commun. 281, 527 (2008).
[CrossRef]

Mourou, M.

J. B. Jackson, M. Mourou, J. F. Whitaker, J. N. Duling III, S. C. Williamson, M. Menu, and G. A. Mourou, Opt. Commun. 281, 527 (2008).
[CrossRef]

Newton, I.

I. Newton, Opticks: Or, a Treatise of the Reflexions, Refractions, Inflexions and Colours of Light (William and John Innys, 1704).

Parimi, P. V.

P. V. Parimi, W. T. Lu, P. Vodo, J. Sokoloff, J. S. Derov, and S. Sridhar, Phys. Rev. Lett. 92, 127401 (2004).
[CrossRef] [PubMed]

Pendry, J. B.

J. B. Pendry, D. Schurig, and D. R. Smith, Science 312, 1780 (2006).
[CrossRef] [PubMed]

C. Luo, S. G. Johnson, J. D. Joannopolous, and J. B. Pendry, Phys. Rev. B 65, 201104 (2002).
[CrossRef]

J. B. Pendry, Phys. Rev. Lett. 85, 3966 (2000).
[CrossRef] [PubMed]

Petty, M. C.

A. J. Gallant, M. A. Kaliteevski, S. Brand, D. Wood, M. C. Petty, R. A. Abram, and J. M. Chamberlain, J. Appl. Phys. 102, 023102 (2007).
[CrossRef]

Pickwell, E.

E. Pickwell and V. P. Wallace, J. Phys. D 39, R301 (2006).
[CrossRef]

Schultz, S.

R. A. Shelby, D. R. Smith, and S. Schultz, Science 292, 77 (2001).
[CrossRef] [PubMed]

Schurig, D.

J. B. Pendry, D. Schurig, and D. R. Smith, Science 312, 1780 (2006).
[CrossRef] [PubMed]

Shelby, R. A.

R. A. Shelby, D. R. Smith, and S. Schultz, Science 292, 77 (2001).
[CrossRef] [PubMed]

Siegel, P. H.

P. H. Siegel, IEEE Microwave Theory Tech. 50, 910 (2002).
[CrossRef]

Smith, D. R.

J. B. Pendry, D. Schurig, and D. R. Smith, Science 312, 1780 (2006).
[CrossRef] [PubMed]

R. A. Shelby, D. R. Smith, and S. Schultz, Science 292, 77 (2001).
[CrossRef] [PubMed]

Sokoloff, J.

P. V. Parimi, W. T. Lu, P. Vodo, J. Sokoloff, J. S. Derov, and S. Sridhar, Phys. Rev. Lett. 92, 127401 (2004).
[CrossRef] [PubMed]

Sridhar, S.

P. V. Parimi, W. T. Lu, P. Vodo, J. Sokoloff, J. S. Derov, and S. Sridhar, Phys. Rev. Lett. 92, 127401 (2004).
[CrossRef] [PubMed]

Veselago, V. G.

V. G. Veselago, Sov. Phys. Usp. 10, 509 (1968).
[CrossRef]

Vodo, P.

P. V. Parimi, W. T. Lu, P. Vodo, J. Sokoloff, J. S. Derov, and S. Sridhar, Phys. Rev. Lett. 92, 127401 (2004).
[CrossRef] [PubMed]

Wallace, V. P.

E. Pickwell and V. P. Wallace, J. Phys. D 39, R301 (2006).
[CrossRef]

Wang, S.

S. Wang, F. Garet, K. Blary, E. Lheurette, J. L. Coutaz, and D. Lippens, Appl. Phys. Lett. 97, 181902 (2010).
[CrossRef]

Whitaker, J. F.

J. B. Jackson, M. Mourou, J. F. Whitaker, J. N. Duling III, S. C. Williamson, M. Menu, and G. A. Mourou, Opt. Commun. 281, 527 (2008).
[CrossRef]

Williamson, S. C.

J. B. Jackson, M. Mourou, J. F. Whitaker, J. N. Duling III, S. C. Williamson, M. Menu, and G. A. Mourou, Opt. Commun. 281, 527 (2008).
[CrossRef]

Wolf, C. R.

D. O. S. Melville, R. J. Blaikie, and C. R. Wolf, Appl. Phys. Lett. 84, 4403 (2004).
[CrossRef]

Wood, D.

A. J. Gallant, M. A. Kaliteevski, S. Brand, D. Wood, M. C. Petty, R. A. Abram, and J. M. Chamberlain, J. Appl. Phys. 102, 023102 (2007).
[CrossRef]

Appl. Phys. Lett. (2)

D. O. S. Melville, R. J. Blaikie, and C. R. Wolf, Appl. Phys. Lett. 84, 4403 (2004).
[CrossRef]

S. Wang, F. Garet, K. Blary, E. Lheurette, J. L. Coutaz, and D. Lippens, Appl. Phys. Lett. 97, 181902 (2010).
[CrossRef]

IEEE Microwave Theory Tech. (1)

P. H. Siegel, IEEE Microwave Theory Tech. 50, 910 (2002).
[CrossRef]

J. Appl. Phys. (1)

A. J. Gallant, M. A. Kaliteevski, S. Brand, D. Wood, M. C. Petty, R. A. Abram, and J. M. Chamberlain, J. Appl. Phys. 102, 023102 (2007).
[CrossRef]

J. Phys. D (1)

E. Pickwell and V. P. Wallace, J. Phys. D 39, R301 (2006).
[CrossRef]

Opt. Commun. (1)

J. B. Jackson, M. Mourou, J. F. Whitaker, J. N. Duling III, S. C. Williamson, M. Menu, and G. A. Mourou, Opt. Commun. 281, 527 (2008).
[CrossRef]

Opt. Express (1)

Phil. Trans. R. Soc. Lond. A (1)

J. M. Chamberlain, Phil. Trans. R. Soc. Lond. A 362, 199 (2004).
[CrossRef]

Phys. Rev. B (2)

S. Brand, R. A. Abram, and M. A. Kaliteevski, Phys. Rev. B B75, 035102 (2007).
[CrossRef]

C. Luo, S. G. Johnson, J. D. Joannopolous, and J. B. Pendry, Phys. Rev. B 65, 201104 (2002).
[CrossRef]

Phys. Rev. Lett. (2)

P. V. Parimi, W. T. Lu, P. Vodo, J. Sokoloff, J. S. Derov, and S. Sridhar, Phys. Rev. Lett. 92, 127401 (2004).
[CrossRef] [PubMed]

J. B. Pendry, Phys. Rev. Lett. 85, 3966 (2000).
[CrossRef] [PubMed]

Science (2)

J. B. Pendry, D. Schurig, and D. R. Smith, Science 312, 1780 (2006).
[CrossRef] [PubMed]

R. A. Shelby, D. R. Smith, and S. Schultz, Science 292, 77 (2001).
[CrossRef] [PubMed]

Sov. Phys. Usp. (1)

V. G. Veselago, Sov. Phys. Usp. 10, 509 (1968).
[CrossRef]

Other (3)

P. W. Milonni, Fast Light, Slow Light and Left-Handed Light (Taylor & Francis, 2005).

I. Newton, Opticks: Or, a Treatise of the Reflexions, Refractions, Inflexions and Colours of Light (William and John Innys, 1704).

Finite-difference time-domain simulations to model the EM field profiles were carried out using the OmniSim software package.

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Figures (4)

Fig. 1
Fig. 1

(a) Schematic diagram of the band structure of a photonic crystal having metallic pillars arranged on a hexagonal lattice. f P and f J denote the effective plasma frequency and frequency at the J symmetry point. If a wave with a frequency within the first band, lying between f P and f J , is incident on the prism, it should be positively refracted. On the other hand, if an incident wave has a frequency higher than f J , and it lies within the second band, it should undergo negative refraction. (b) Scanning electron microscope image of the hexagonal metallic photonic crystal prism. The arrow on the right depicts the incident beam, while the arrows emerging from the surfaces labeled PRF and NRF show the directions of the positively and negatively refracted beams.

Fig. 2
Fig. 2

Schematic diagram of the reflection THz time domain spectrometer used to measure negative refraction. To measure positive refraction, the second pair of parabolic mirrors and detection optics were rotated through an appropriate angle. The inset shows the orientations of the two refracted beams relative to the incident and a (hypothetical) directly transmitted beams. For waves undergoing negative refraction, the beam emerging from the NRF forms an angle of about 70 ° with the incident beam, while for positive refraction, the exit beam is deflected by approximately 15 ° from the incident beam path. Therefore, the two beams are separated by an angle of the order of 120 ° .

Fig. 3
Fig. 3

(a) Reference pulse in the time domain showing system performance. Inset, spectral content of this pulse. (b) THz pulse in the time domain that has interacted with the sample before emerging from the NRF.

Fig. 4
Fig. 4

Spectral intensity of the two components of the THz pulse that are transmitted by the prism, corresponding to positive refraction when emerging from the PRF and negative refraction in the case of the NRF. The horizontal bars indicate the FWHM frequency ranges of the first ( 0.7 0.91 THz ) and second ( 0.91 1.24 THz ) photonic bands as determined experimentally.

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