Abstract

We propose a new type of pass-band filter, in this case designed to operate in the terahertz frequency regime, possessing two separate pass-bands utilizing the distinction between positive and negative refraction in a photonic crystal prism. The prism is formed from a two-dimensional hexagonal arrangement of metallic rods. In order to understand the operation of the filter we both consider the photonic bandstructure of the associated infinite photonic structure and carry out simulations of the refraction properties of the prism using finite-difference time-domain software.

© 2008 Optical Society of America

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  1. V. G. Veselago, "The electrodynamics of substances with simultaneously negative values of ε and μ," Sov. Phys. Usp. 10, 509-514 (1968).
    [CrossRef]
  2. C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, "All-angle negative refraction without negative effective index," Phys. Rev. B65, 201104(R) (2002).
  3. E. Ozbay, I. Bulu, K. Guven, H. Caglayan, and K. Aydin, "Observation of negative refraction and focusing in two-dimensional photonic crystals," Jpn. J. Appl. Phys. 45, 6064-6070 (2006).
    [CrossRef]
  4. S-T Wu, M. S. Li, and Y-G Fuh, "Unusual refractions in photonic crystals based on polymer-dispersed liquid crystal films," Appl. Phys. Letts. 91, 251117 (2007).
    [CrossRef]
  5. D. Wang, L. Ran, H. Chen, M. Mu, J. A. Kong and B-I. Wu, "Active left-handed material collaborated with microwave varactors," Appl. Phys. Letts. 91, 164101 (2007).
    [CrossRef]
  6. S. Brand, R. A. Abram and M. A. Kaliteevski, "Complex photonic band structure and effective plasma frequency of a two-dimensional array of metal rods," Phys. Rev. B 75, 035102 (2007).
  7. A. J. Gallant, M. A. Kaliteevski, S. Brand, D. Wood, M. Petty, R. A. Abram and J. M. Chamberlain, "Terahertz frequency passband filters," J. Appl. Phys. 102, 023102 (2007).
    [CrossRef]
  8. 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. Letts 91, 161115 (2007).
    [CrossRef]
  9. FDTD simulations were carried out using the Omnisim© software package.

2007 (5)

S-T Wu, M. S. Li, and Y-G Fuh, "Unusual refractions in photonic crystals based on polymer-dispersed liquid crystal films," Appl. Phys. Letts. 91, 251117 (2007).
[CrossRef]

D. Wang, L. Ran, H. Chen, M. Mu, J. A. Kong and B-I. Wu, "Active left-handed material collaborated with microwave varactors," Appl. Phys. Letts. 91, 164101 (2007).
[CrossRef]

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

A. J. Gallant, M. A. Kaliteevski, S. Brand, D. Wood, M. Petty, R. A. Abram and J. M. Chamberlain, "Terahertz frequency passband filters," J. Appl. Phys. 102, 023102 (2007).
[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. Letts 91, 161115 (2007).
[CrossRef]

2006 (1)

E. Ozbay, I. Bulu, K. Guven, H. Caglayan, and K. Aydin, "Observation of negative refraction and focusing in two-dimensional photonic crystals," Jpn. J. Appl. Phys. 45, 6064-6070 (2006).
[CrossRef]

1968 (1)

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

Abram, R. A.

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

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

Aydin, K.

E. Ozbay, I. Bulu, K. Guven, H. Caglayan, and K. Aydin, "Observation of negative refraction and focusing in two-dimensional photonic crystals," Jpn. J. Appl. Phys. 45, 6064-6070 (2006).
[CrossRef]

Brand, S.

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

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

Bulu, I.

E. Ozbay, I. Bulu, K. Guven, H. Caglayan, and K. Aydin, "Observation of negative refraction and focusing in two-dimensional photonic crystals," Jpn. J. Appl. Phys. 45, 6064-6070 (2006).
[CrossRef]

Caglayan, H.

E. Ozbay, I. Bulu, K. Guven, H. Caglayan, and K. Aydin, "Observation of negative refraction and focusing in two-dimensional photonic crystals," Jpn. J. Appl. Phys. 45, 6064-6070 (2006).
[CrossRef]

Chamberlain, J. M.

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

Chen, H.

D. Wang, L. Ran, H. Chen, M. Mu, J. A. Kong and B-I. Wu, "Active left-handed material collaborated with microwave varactors," Appl. Phys. Letts. 91, 164101 (2007).
[CrossRef]

Fuh, Y-G

S-T Wu, M. S. Li, and Y-G Fuh, "Unusual refractions in photonic crystals based on polymer-dispersed liquid crystal films," Appl. Phys. Letts. 91, 251117 (2007).
[CrossRef]

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. Letts 91, 161115 (2007).
[CrossRef]

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

Guven, K.

E. Ozbay, I. Bulu, K. Guven, H. Caglayan, and K. Aydin, "Observation of negative refraction and focusing in two-dimensional photonic crystals," Jpn. J. Appl. Phys. 45, 6064-6070 (2006).
[CrossRef]

Kaliteevski, M. A.

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

S. Brand, R. A. Abram and M. A. Kaliteevski, "Complex photonic band structure 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. Letts 91, 161115 (2007).
[CrossRef]

Kong, J. A.

D. Wang, L. Ran, H. Chen, M. Mu, J. A. Kong and B-I. Wu, "Active left-handed material collaborated with microwave varactors," Appl. Phys. Letts. 91, 164101 (2007).
[CrossRef]

Li, M. S.

S-T Wu, M. S. Li, and Y-G Fuh, "Unusual refractions in photonic crystals based on polymer-dispersed liquid crystal films," Appl. Phys. Letts. 91, 251117 (2007).
[CrossRef]

Mu, M.

D. Wang, L. Ran, H. Chen, M. Mu, J. A. Kong and B-I. Wu, "Active left-handed material collaborated with microwave varactors," Appl. Phys. Letts. 91, 164101 (2007).
[CrossRef]

Ozbay, E.

E. Ozbay, I. Bulu, K. Guven, H. Caglayan, and K. Aydin, "Observation of negative refraction and focusing in two-dimensional photonic crystals," Jpn. J. Appl. Phys. 45, 6064-6070 (2006).
[CrossRef]

Petty, M.

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

Ran, L.

D. Wang, L. Ran, H. Chen, M. Mu, J. A. Kong and B-I. Wu, "Active left-handed material collaborated with microwave varactors," Appl. Phys. Letts. 91, 164101 (2007).
[CrossRef]

Veselago, V. G.

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

Wang, D.

D. Wang, L. Ran, H. Chen, M. Mu, J. A. Kong and B-I. Wu, "Active left-handed material collaborated with microwave varactors," Appl. Phys. Letts. 91, 164101 (2007).
[CrossRef]

Wood, D.

A. J. Gallant, M. A. Kaliteevski, S. Brand, D. Wood, M. Petty, R. A. Abram and J. M. Chamberlain, "Terahertz frequency passband filters," J. Appl. Phys. 102, 023102 (2007).
[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. Letts 91, 161115 (2007).
[CrossRef]

Wu, B-I.

D. Wang, L. Ran, H. Chen, M. Mu, J. A. Kong and B-I. Wu, "Active left-handed material collaborated with microwave varactors," Appl. Phys. Letts. 91, 164101 (2007).
[CrossRef]

Wu, S-T

S-T Wu, M. S. Li, and Y-G Fuh, "Unusual refractions in photonic crystals based on polymer-dispersed liquid crystal films," Appl. Phys. Letts. 91, 251117 (2007).
[CrossRef]

Appl. Phys. Letts (1)

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. Letts 91, 161115 (2007).
[CrossRef]

Appl. Phys. Letts. (2)

S-T Wu, M. S. Li, and Y-G Fuh, "Unusual refractions in photonic crystals based on polymer-dispersed liquid crystal films," Appl. Phys. Letts. 91, 251117 (2007).
[CrossRef]

D. Wang, L. Ran, H. Chen, M. Mu, J. A. Kong and B-I. Wu, "Active left-handed material collaborated with microwave varactors," Appl. Phys. Letts. 91, 164101 (2007).
[CrossRef]

J. Appl. Phys. (1)

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

Jpn. J. Appl. Phys. (1)

E. Ozbay, I. Bulu, K. Guven, H. Caglayan, and K. Aydin, "Observation of negative refraction and focusing in two-dimensional photonic crystals," Jpn. J. Appl. Phys. 45, 6064-6070 (2006).
[CrossRef]

Phys. Rev. B (1)

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

Sov. Phys. Usp. (1)

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

Other (2)

C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, "All-angle negative refraction without negative effective index," Phys. Rev. B65, 201104(R) (2002).

FDTD simulations were carried out using the Omnisim© software package.

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Figures (6)

Fig. 1.
Fig. 1.

The dispersion relation for an E-polarized electromagnetic wave in the hexagonal photonic crystal.

Fig. 2.
Fig. 2.

The arrows indicate the wavevectors of the incident radiation (at angle α), the corresponding wavevectors in the photonic crystal (at angle β), and their component parallel to the interface (kτ ). The hexagon denotes the first Brillouin zone in the photonic crystal. (a) At frequency, f=1.136 THz, within band 1 part of the near-isotropic equifrequency surface (EFS) in the photonic crystal and the spherical EFS in the vacuum (upper half-space) are shown. The group velocity in the photonic crystal is in the same direction as the wavevector. In (b) in band 2 with f=1.344 THz the EFS in the photonic crystal bandstructure is anisotropic and νg is in the direction of the dashed arrow, giving negative refraction.

Fig. 3.
Fig. 3.

Band 2 equifrequency plot indicating the situation at cutoff.

Fig. 4.
Fig. 4.

Simulations of the electric field intensity when a plane-wave with α=20° is incident on the photonic crystal prism. The boundaries of the prism are highlighted. (a) For frequency f=1.136 THz positive refraction occurs and light emerges from the PRF while in (b), with f=1.344 THz the wave is negatively refracted and emerges from the NRF.

Fig. 5.
Fig. 5.

Spectral dependence of the radiation flux emergent from the PRF (solid line) and the NRF (dashed line) normalized to the flux of the incident beam when α=20°. The flux is calculated at the respective exit surfaces of the prism.

Fig. 6.
Fig. 6.

Solid lines show the boundaries of the PRF band as a function of α, while dashed lines show the boundaries of the NRF band.

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