Abstract

We study light beam propagation in periodic metallic nanostructures—metallic photonic crystals (MPhCs). In particular, we consider a two-dimensional rhombic array of metallic cylinders embedded in air and explore its ability to tailor spatial propagation of light beams. We show that the structure supports self-collimated propagation and negative (anomalous) diffraction. In this later case, flat lensing is observed, leading to the focusing of beams behind the MPhCs. Moreover, the anisotropic attenuation of light provided by the structure enables spatial filtering of noisy beams.

© 2014 Optical Society of America

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References

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  1. J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light, 2nd ed. (Princeton University, 2008).
  2. C. M. Soukoulis, Photonic Crystals and Light Localization in the 21st Century (Springer, 2001), Vol. 563.
  3. R. Zengerle, “Light propagation in singly and doubly periodic planar waveguides,” J. Mod. Opt. 34, 1589–1617 (1987).
    [CrossRef]
  4. H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Self-collimating phenomena in photonic crystals,” Appl. Phys. Lett. 74, 1212–1214 (1999).
    [CrossRef]
  5. R. Illiew, C. Etrich, U. Peschel, F. Lederer, M. Augustin, H. J. Fuchs, D. Schelle, E. B. Kley, S. Nolte, and A. Tunnermann, “Diffractionless propagation of light in a low-index photonic-crystal film,” Appl. Phys. Lett. 85, 5854–5856 (2004).
    [CrossRef]
  6. D. W. Prather, S. Shi, D. M. Pustai, C. Chen, S. Venkataraman, A. Sharkawy, G. J. Schneider, and J. Murakowski, “Dispersion-based optical routing in photonic crystals,” Opt. Lett. 29, 50–52 (2004).
    [CrossRef]
  7. K. Staliunas and R. Herrero, “Nondiffractive propagation of light in photonic crystals,” Phys. Rev. E 73, 016601 (2006).
    [CrossRef]
  8. S. Savo, E. Di Gennaro, and A. Andreone, “Superlensing properties of one-dimensional dielectric photonic crystals,” Opt. Express 17, 19848–19856 (2009).
    [CrossRef]
  9. Q. Wu, E. Schonbrun, and W. Park, “Tunable superlensing by a mechanically controlled photonic crystal,” J. Opt. Soc. Am. B 23, 479–484 (2006).
    [CrossRef]
  10. X. Wang, Z. F. Ren, and K. Kempa, “Unrestricted superlensing in a triangular two dimensional photonic crystal,” Opt. Express 12, 2919–2924 (2004).
    [CrossRef]
  11. L. Maigyte, V. Purlys, J. Trull, M. Peckus, C. Cojocaru, D. Gailevicius, M. Malinauskas, and K. Staliunas, “Flat lensing in the visible frequency range by woodpile photonic crystals,” Opt. Lett. 38, 2376–2378 (2013).
    [CrossRef]
  12. K. Staliunas and V. J. Sánchez-Morcillo, “Spatial filtering of light by chirped photonic crystals,” Phys. Rev. A 79, 053807 (2009).
    [CrossRef]
  13. L. Maigyte, T. Gertus, M. Peckus, J. Trull, C. Cojocaru, V. Sirutkaitis, and K. Staliunas, “Signatures of light-beam spatial filtering in a three-dimensional photonic crystal,” Phys. Rev. A 82, 043819 (2010).
    [CrossRef]
  14. K. Staliunas, R. Herrero, and R. Vilaseca, “Subdiffraction and spatial filtering due to periodic spatial modulation of the gain-loss profile,” Phys. Rev. A 80, 013821 (2009).
    [CrossRef]
  15. M. Botey, R. Herrero, and K. Staliunas, “Light in materials with periodic gain/loss modulation on a wavelength scale,” Phys. Rev. A 82, 013828 (2010).
    [CrossRef]
  16. N. Kumar, M. Botey, R. Herrero, Y. Loiko, and K. Staliunas, “High-directional wave propagation in periodic loss modulated materials,” Photon. Nanostr. Fundam. Appl. 10, 644–650 (2012).
    [CrossRef]
  17. N. Kumar, R. Herrero, M. Botey, and K. Staliunas, “Flat lensing by periodic loss-modulated materials,” J. Opt. Soc. Am. B 30, 2684–2688 (2013).
    [CrossRef]
  18. 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]
  19. G. P. Swift, A. J. Gallant, N. Kaliteevskaya, M. A. Kaliteevski, S. Brand, D. Dai, A. J. Baragwanath, I. Iorsh, R. A. Abram, and J. M. Chamberlain, “Negative refraction and the spectral filtering of terahertz radiation by a photonic crystal prism,” Opt. Lett. 36, 1641–1643 (2011).
    [CrossRef]
  20. We use the commercial CrystalWave software by Photon Design Ltd., http://www.photond.com .

2013 (2)

2012 (1)

N. Kumar, M. Botey, R. Herrero, Y. Loiko, and K. Staliunas, “High-directional wave propagation in periodic loss modulated materials,” Photon. Nanostr. Fundam. Appl. 10, 644–650 (2012).
[CrossRef]

2011 (1)

2010 (2)

L. Maigyte, T. Gertus, M. Peckus, J. Trull, C. Cojocaru, V. Sirutkaitis, and K. Staliunas, “Signatures of light-beam spatial filtering in a three-dimensional photonic crystal,” Phys. Rev. A 82, 043819 (2010).
[CrossRef]

M. Botey, R. Herrero, and K. Staliunas, “Light in materials with periodic gain/loss modulation on a wavelength scale,” Phys. Rev. A 82, 013828 (2010).
[CrossRef]

2009 (3)

K. Staliunas, R. Herrero, and R. Vilaseca, “Subdiffraction and spatial filtering due to periodic spatial modulation of the gain-loss profile,” Phys. Rev. A 80, 013821 (2009).
[CrossRef]

K. Staliunas and V. J. Sánchez-Morcillo, “Spatial filtering of light by chirped photonic crystals,” Phys. Rev. A 79, 053807 (2009).
[CrossRef]

S. Savo, E. Di Gennaro, and A. Andreone, “Superlensing properties of one-dimensional dielectric photonic crystals,” Opt. Express 17, 19848–19856 (2009).
[CrossRef]

2008 (1)

2006 (2)

K. Staliunas and R. Herrero, “Nondiffractive propagation of light in photonic crystals,” Phys. Rev. E 73, 016601 (2006).
[CrossRef]

Q. Wu, E. Schonbrun, and W. Park, “Tunable superlensing by a mechanically controlled photonic crystal,” J. Opt. Soc. Am. B 23, 479–484 (2006).
[CrossRef]

2004 (3)

1999 (1)

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Self-collimating phenomena in photonic crystals,” Appl. Phys. Lett. 74, 1212–1214 (1999).
[CrossRef]

1987 (1)

R. Zengerle, “Light propagation in singly and doubly periodic planar waveguides,” J. Mod. Opt. 34, 1589–1617 (1987).
[CrossRef]

Abram, R. A.

Andreone, A.

Augustin, M.

R. Illiew, C. Etrich, U. Peschel, F. Lederer, M. Augustin, H. J. Fuchs, D. Schelle, E. B. Kley, S. Nolte, and A. Tunnermann, “Diffractionless propagation of light in a low-index photonic-crystal film,” Appl. Phys. Lett. 85, 5854–5856 (2004).
[CrossRef]

Baragwanath, A. J.

Botey, M.

N. Kumar, R. Herrero, M. Botey, and K. Staliunas, “Flat lensing by periodic loss-modulated materials,” J. Opt. Soc. Am. B 30, 2684–2688 (2013).
[CrossRef]

N. Kumar, M. Botey, R. Herrero, Y. Loiko, and K. Staliunas, “High-directional wave propagation in periodic loss modulated materials,” Photon. Nanostr. Fundam. Appl. 10, 644–650 (2012).
[CrossRef]

M. Botey, R. Herrero, and K. Staliunas, “Light in materials with periodic gain/loss modulation on a wavelength scale,” Phys. Rev. A 82, 013828 (2010).
[CrossRef]

Brand, S.

Chamberlain, J. M.

Chen, C.

Cojocaru, C.

L. Maigyte, V. Purlys, J. Trull, M. Peckus, C. Cojocaru, D. Gailevicius, M. Malinauskas, and K. Staliunas, “Flat lensing in the visible frequency range by woodpile photonic crystals,” Opt. Lett. 38, 2376–2378 (2013).
[CrossRef]

L. Maigyte, T. Gertus, M. Peckus, J. Trull, C. Cojocaru, V. Sirutkaitis, and K. Staliunas, “Signatures of light-beam spatial filtering in a three-dimensional photonic crystal,” Phys. Rev. A 82, 043819 (2010).
[CrossRef]

Dai, D.

Di Gennaro, E.

Etrich, C.

R. Illiew, C. Etrich, U. Peschel, F. Lederer, M. Augustin, H. J. Fuchs, D. Schelle, E. B. Kley, S. Nolte, and A. Tunnermann, “Diffractionless propagation of light in a low-index photonic-crystal film,” Appl. Phys. Lett. 85, 5854–5856 (2004).
[CrossRef]

Fuchs, H. J.

R. Illiew, C. Etrich, U. Peschel, F. Lederer, M. Augustin, H. J. Fuchs, D. Schelle, E. B. Kley, S. Nolte, and A. Tunnermann, “Diffractionless propagation of light in a low-index photonic-crystal film,” Appl. Phys. Lett. 85, 5854–5856 (2004).
[CrossRef]

Gailevicius, D.

Gallant, A. J.

Garvie-Cook, J.

Gertus, T.

L. Maigyte, T. Gertus, M. Peckus, J. Trull, C. Cojocaru, V. Sirutkaitis, and K. Staliunas, “Signatures of light-beam spatial filtering in a three-dimensional photonic crystal,” Phys. Rev. A 82, 043819 (2010).
[CrossRef]

Herrero, R.

N. Kumar, R. Herrero, M. Botey, and K. Staliunas, “Flat lensing by periodic loss-modulated materials,” J. Opt. Soc. Am. B 30, 2684–2688 (2013).
[CrossRef]

N. Kumar, M. Botey, R. Herrero, Y. Loiko, and K. Staliunas, “High-directional wave propagation in periodic loss modulated materials,” Photon. Nanostr. Fundam. Appl. 10, 644–650 (2012).
[CrossRef]

M. Botey, R. Herrero, and K. Staliunas, “Light in materials with periodic gain/loss modulation on a wavelength scale,” Phys. Rev. A 82, 013828 (2010).
[CrossRef]

K. Staliunas, R. Herrero, and R. Vilaseca, “Subdiffraction and spatial filtering due to periodic spatial modulation of the gain-loss profile,” Phys. Rev. A 80, 013821 (2009).
[CrossRef]

K. Staliunas and R. Herrero, “Nondiffractive propagation of light in photonic crystals,” Phys. Rev. E 73, 016601 (2006).
[CrossRef]

Illiew, R.

R. Illiew, C. Etrich, U. Peschel, F. Lederer, M. Augustin, H. J. Fuchs, D. Schelle, E. B. Kley, S. Nolte, and A. Tunnermann, “Diffractionless propagation of light in a low-index photonic-crystal film,” Appl. Phys. Lett. 85, 5854–5856 (2004).
[CrossRef]

Iorsh, I.

Joannopoulos, J. D.

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light, 2nd ed. (Princeton University, 2008).

Johnson, S. G.

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light, 2nd ed. (Princeton University, 2008).

Kaliteevskaya, N.

Kaliteevski, M. A.

Kawakami, S.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Self-collimating phenomena in photonic crystals,” 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, “Self-collimating phenomena in photonic crystals,” Appl. Phys. Lett. 74, 1212–1214 (1999).
[CrossRef]

Kempa, K.

Kley, E. B.

R. Illiew, C. Etrich, U. Peschel, F. Lederer, M. Augustin, H. J. Fuchs, D. Schelle, E. B. Kley, S. Nolte, and A. Tunnermann, “Diffractionless propagation of light in a low-index photonic-crystal film,” Appl. Phys. Lett. 85, 5854–5856 (2004).
[CrossRef]

Kosaka, H.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Self-collimating phenomena in photonic crystals,” Appl. Phys. Lett. 74, 1212–1214 (1999).
[CrossRef]

Kumar, N.

N. Kumar, R. Herrero, M. Botey, and K. Staliunas, “Flat lensing by periodic loss-modulated materials,” J. Opt. Soc. Am. B 30, 2684–2688 (2013).
[CrossRef]

N. Kumar, M. Botey, R. Herrero, Y. Loiko, and K. Staliunas, “High-directional wave propagation in periodic loss modulated materials,” Photon. Nanostr. Fundam. Appl. 10, 644–650 (2012).
[CrossRef]

Lederer, F.

R. Illiew, C. Etrich, U. Peschel, F. Lederer, M. Augustin, H. J. Fuchs, D. Schelle, E. B. Kley, S. Nolte, and A. Tunnermann, “Diffractionless propagation of light in a low-index photonic-crystal film,” Appl. Phys. Lett. 85, 5854–5856 (2004).
[CrossRef]

Loiko, Y.

N. Kumar, M. Botey, R. Herrero, Y. Loiko, and K. Staliunas, “High-directional wave propagation in periodic loss modulated materials,” Photon. Nanostr. Fundam. Appl. 10, 644–650 (2012).
[CrossRef]

Maigyte, L.

L. Maigyte, V. Purlys, J. Trull, M. Peckus, C. Cojocaru, D. Gailevicius, M. Malinauskas, and K. Staliunas, “Flat lensing in the visible frequency range by woodpile photonic crystals,” Opt. Lett. 38, 2376–2378 (2013).
[CrossRef]

L. Maigyte, T. Gertus, M. Peckus, J. Trull, C. Cojocaru, V. Sirutkaitis, and K. Staliunas, “Signatures of light-beam spatial filtering in a three-dimensional photonic crystal,” Phys. Rev. A 82, 043819 (2010).
[CrossRef]

Malinauskas, M.

Meade, R. D.

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light, 2nd ed. (Princeton University, 2008).

Murakowski, J.

Nolte, S.

R. Illiew, C. Etrich, U. Peschel, F. Lederer, M. Augustin, H. J. Fuchs, D. Schelle, E. B. Kley, S. Nolte, and A. Tunnermann, “Diffractionless propagation of light in a low-index photonic-crystal film,” Appl. Phys. Lett. 85, 5854–5856 (2004).
[CrossRef]

Notomi, M.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Self-collimating phenomena in photonic crystals,” Appl. Phys. Lett. 74, 1212–1214 (1999).
[CrossRef]

Park, W.

Peckus, M.

L. Maigyte, V. Purlys, J. Trull, M. Peckus, C. Cojocaru, D. Gailevicius, M. Malinauskas, and K. Staliunas, “Flat lensing in the visible frequency range by woodpile photonic crystals,” Opt. Lett. 38, 2376–2378 (2013).
[CrossRef]

L. Maigyte, T. Gertus, M. Peckus, J. Trull, C. Cojocaru, V. Sirutkaitis, and K. Staliunas, “Signatures of light-beam spatial filtering in a three-dimensional photonic crystal,” Phys. Rev. A 82, 043819 (2010).
[CrossRef]

Peschel, U.

R. Illiew, C. Etrich, U. Peschel, F. Lederer, M. Augustin, H. J. Fuchs, D. Schelle, E. B. Kley, S. Nolte, and A. Tunnermann, “Diffractionless propagation of light in a low-index photonic-crystal film,” Appl. Phys. Lett. 85, 5854–5856 (2004).
[CrossRef]

Prather, D. W.

Purlys, V.

Pustai, D. M.

Ren, Z. F.

Sánchez-Morcillo, V. J.

K. Staliunas and V. J. Sánchez-Morcillo, “Spatial filtering of light by chirped photonic crystals,” Phys. Rev. A 79, 053807 (2009).
[CrossRef]

Sato, T.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Self-collimating phenomena in photonic crystals,” Appl. Phys. Lett. 74, 1212–1214 (1999).
[CrossRef]

Savo, S.

Schelle, D.

R. Illiew, C. Etrich, U. Peschel, F. Lederer, M. Augustin, H. J. Fuchs, D. Schelle, E. B. Kley, S. Nolte, and A. Tunnermann, “Diffractionless propagation of light in a low-index photonic-crystal film,” Appl. Phys. Lett. 85, 5854–5856 (2004).
[CrossRef]

Schneider, G. J.

Schonbrun, E.

Sharkawy, A.

Shi, S.

Sirutkaitis, V.

L. Maigyte, T. Gertus, M. Peckus, J. Trull, C. Cojocaru, V. Sirutkaitis, and K. Staliunas, “Signatures of light-beam spatial filtering in a three-dimensional photonic crystal,” Phys. Rev. A 82, 043819 (2010).
[CrossRef]

Soukoulis, C. M.

C. M. Soukoulis, Photonic Crystals and Light Localization in the 21st Century (Springer, 2001), Vol. 563.

Staliunas, K.

L. Maigyte, V. Purlys, J. Trull, M. Peckus, C. Cojocaru, D. Gailevicius, M. Malinauskas, and K. Staliunas, “Flat lensing in the visible frequency range by woodpile photonic crystals,” Opt. Lett. 38, 2376–2378 (2013).
[CrossRef]

N. Kumar, R. Herrero, M. Botey, and K. Staliunas, “Flat lensing by periodic loss-modulated materials,” J. Opt. Soc. Am. B 30, 2684–2688 (2013).
[CrossRef]

N. Kumar, M. Botey, R. Herrero, Y. Loiko, and K. Staliunas, “High-directional wave propagation in periodic loss modulated materials,” Photon. Nanostr. Fundam. Appl. 10, 644–650 (2012).
[CrossRef]

M. Botey, R. Herrero, and K. Staliunas, “Light in materials with periodic gain/loss modulation on a wavelength scale,” Phys. Rev. A 82, 013828 (2010).
[CrossRef]

L. Maigyte, T. Gertus, M. Peckus, J. Trull, C. Cojocaru, V. Sirutkaitis, and K. Staliunas, “Signatures of light-beam spatial filtering in a three-dimensional photonic crystal,” Phys. Rev. A 82, 043819 (2010).
[CrossRef]

K. Staliunas, R. Herrero, and R. Vilaseca, “Subdiffraction and spatial filtering due to periodic spatial modulation of the gain-loss profile,” Phys. Rev. A 80, 013821 (2009).
[CrossRef]

K. Staliunas and V. J. Sánchez-Morcillo, “Spatial filtering of light by chirped photonic crystals,” Phys. Rev. A 79, 053807 (2009).
[CrossRef]

K. Staliunas and R. Herrero, “Nondiffractive propagation of light in photonic crystals,” Phys. Rev. E 73, 016601 (2006).
[CrossRef]

Swift, G. P.

Tamamura, T.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Self-collimating phenomena in photonic crystals,” 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, “Self-collimating phenomena in photonic crystals,” Appl. Phys. Lett. 74, 1212–1214 (1999).
[CrossRef]

Trull, J.

L. Maigyte, V. Purlys, J. Trull, M. Peckus, C. Cojocaru, D. Gailevicius, M. Malinauskas, and K. Staliunas, “Flat lensing in the visible frequency range by woodpile photonic crystals,” Opt. Lett. 38, 2376–2378 (2013).
[CrossRef]

L. Maigyte, T. Gertus, M. Peckus, J. Trull, C. Cojocaru, V. Sirutkaitis, and K. Staliunas, “Signatures of light-beam spatial filtering in a three-dimensional photonic crystal,” Phys. Rev. A 82, 043819 (2010).
[CrossRef]

Tunnermann, A.

R. Illiew, C. Etrich, U. Peschel, F. Lederer, M. Augustin, H. J. Fuchs, D. Schelle, E. B. Kley, S. Nolte, and A. Tunnermann, “Diffractionless propagation of light in a low-index photonic-crystal film,” Appl. Phys. Lett. 85, 5854–5856 (2004).
[CrossRef]

Venkataraman, S.

Vilaseca, R.

K. Staliunas, R. Herrero, and R. Vilaseca, “Subdiffraction and spatial filtering due to periodic spatial modulation of the gain-loss profile,” Phys. Rev. A 80, 013821 (2009).
[CrossRef]

Wang, X.

Winn, J. N.

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light, 2nd ed. (Princeton University, 2008).

Wu, Q.

Zengerle, R.

R. Zengerle, “Light propagation in singly and doubly periodic planar waveguides,” J. Mod. Opt. 34, 1589–1617 (1987).
[CrossRef]

Appl. Phys. Lett. (2)

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Self-collimating phenomena in photonic crystals,” Appl. Phys. Lett. 74, 1212–1214 (1999).
[CrossRef]

R. Illiew, C. Etrich, U. Peschel, F. Lederer, M. Augustin, H. J. Fuchs, D. Schelle, E. B. Kley, S. Nolte, and A. Tunnermann, “Diffractionless propagation of light in a low-index photonic-crystal film,” Appl. Phys. Lett. 85, 5854–5856 (2004).
[CrossRef]

J. Mod. Opt. (1)

R. Zengerle, “Light propagation in singly and doubly periodic planar waveguides,” J. Mod. Opt. 34, 1589–1617 (1987).
[CrossRef]

J. Opt. Soc. Am. B (2)

Opt. Express (3)

Opt. Lett. (3)

Photon. Nanostr. Fundam. Appl. (1)

N. Kumar, M. Botey, R. Herrero, Y. Loiko, and K. Staliunas, “High-directional wave propagation in periodic loss modulated materials,” Photon. Nanostr. Fundam. Appl. 10, 644–650 (2012).
[CrossRef]

Phys. Rev. A (4)

K. Staliunas and V. J. Sánchez-Morcillo, “Spatial filtering of light by chirped photonic crystals,” Phys. Rev. A 79, 053807 (2009).
[CrossRef]

L. Maigyte, T. Gertus, M. Peckus, J. Trull, C. Cojocaru, V. Sirutkaitis, and K. Staliunas, “Signatures of light-beam spatial filtering in a three-dimensional photonic crystal,” Phys. Rev. A 82, 043819 (2010).
[CrossRef]

K. Staliunas, R. Herrero, and R. Vilaseca, “Subdiffraction and spatial filtering due to periodic spatial modulation of the gain-loss profile,” Phys. Rev. A 80, 013821 (2009).
[CrossRef]

M. Botey, R. Herrero, and K. Staliunas, “Light in materials with periodic gain/loss modulation on a wavelength scale,” Phys. Rev. A 82, 013828 (2010).
[CrossRef]

Phys. Rev. E (1)

K. Staliunas and R. Herrero, “Nondiffractive propagation of light in photonic crystals,” Phys. Rev. E 73, 016601 (2006).
[CrossRef]

Other (3)

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light, 2nd ed. (Princeton University, 2008).

C. M. Soukoulis, Photonic Crystals and Light Localization in the 21st Century (Springer, 2001), Vol. 563.

We use the commercial CrystalWave software by Photon Design Ltd., http://www.photond.com .

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Figures (7)

Fig. 1.
Fig. 1.

(a) Schematic representation of a 2D rhombic periodic array of metallic (gold, ωp=12229.7THz, γ=139.7THz) rods in a lattice constant a=0.83μm, with the angle between the lattice vectors θ=75°, and the radius of the rods R=0.2*a. The red arrow indicates the direction of propagation of the beam. (b) Comparison between a 3 μm wide Gaussian beam, generated at a distance of 10 μm from the left facet of the structure, and propagated through a MPhC, and free space propagation of the same beam (thick yellow curve). The considered MPhC structure has seven periods in the longitudinal direction (z), which corresponds to approximately 10 μm. The frequency of the propagated beam is f=307THz, corresponding to a/λ=0.85.

Fig. 2.
Fig. 2.

(a) Band diagram of the structure described in Fig. 1, for the frequency range a/λ=0.51.2. The inset shows the irreducible BZ of the structure. (b), (c) Isofrequency contours for two consecutive bands (fourth and fifth bands): (b) band below the bandgap and (c) band above the bandgap. The side bar indicates frequency in a/λ units. Propagation is considered in the ΓM direction.

Fig. 3.
Fig. 3.

Nondiffractive propagation inside an infinite MPhC with the same structural parameters of Fig. 1: (a) normalized intensity profile of the propagated beam in a length of 70a width 2.5a. at considering an initial beam of a/λ=0.68 and (b) at a/λ=0.79. (c), (d) Horizontal cross-section intensity profile corresponding to x/a=0 for (c) a/λ=0.68 and (d) a/λ=0.79. (e), (f) Transverse cross-section intensity profiles at different propagation distances, z=10a, 20a, 30a, and 40a, normalized to the initial intensity, for (e) a/λ=0.68 and (f) a/λ=0.79.

Fig. 4.
Fig. 4.

Focusing behind a MPhC with the same parameters as in Fig. 1, for a monochromatic Gaussian beam at different frequencies; a/λ=0.85, 0.875, and 0.9 (f=307, 316, and 325 THz). (a)/(b), (c)/(d), and (e)/(f) display the field intensity profile corresponding to on-axis intensity (horizontal cross section) in free space propagation behind the structure at the position x=0, for the first, second, and third frequencies, respectively. (g) Maximum intensity (on the right facet or at the focal point) behind the MPhC depending on frequency.

Fig. 5.
Fig. 5.

(a) Normalized intensity distribution along the horizontal axis, z, depending on frequency. The focal distance from the MPhC is indicated by a dark dashed line, for a/λ>0.8. (b) Beam width depending on frequency along z, normalized to the incident beam width W0 (where W0=3.6a, a being the lattice constant). The bright dashed line indicates the position of the smallest beam width. The normalized intensity maps at z/a=0, i.e., at the exit face of the device and at the focal plane depending on frequency, are depicted in (c) and (d).

Fig. 6.
Fig. 6.

Cross-sectional widths of the beams at the plane of minimum width along propagation plotted as a function of frequency for different initial beam widths, as indicated in the legend. (a) Beam width normalized to the initial beam and (b) focal distance. All normalized to the lattice constant, a.

Fig. 7.
Fig. 7.

(a) Propagation of a random input beam in a MPhC and behind it with frequency a/λ=0.76. (b) Propagation of the same random input beam in free space without the MPhC structure. (c) Fourier spectra of the input beam (red, solid) and Fourier spectra of the beam after propagation through a MPhC (black, solid). The normalized intensity profiles of the same are denoted in (d). The dotted blue curve denotes the intensity profile of the beam in the absence of a MPhC.

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