Abstract

We experimentally demonstrate full two-dimensional focalization of light beams at visible frequencies by a three-dimensional woodpile photonic crystal. The focalization (the flat lensing) with focal distances of the order of 50–70 μm is experimentally demonstrated. Experimental results are compared with numerical calculations and interpreted by harmonic expansion studies.

© 2013 Optical Society of America

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  1. C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, Phys. Rev. B 65, 201104 (2002).
    [CrossRef]
  2. H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, Appl. Phys. Lett. 74, 1212 (1999).
    [CrossRef]
  3. E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopoulou, and C. M. Soukoulis, Nature 423, 604 (2003).
    [CrossRef]
  4. J. Serbin and M. Gu, Opt. Express 14, 3563 (2006).
    [CrossRef]
  5. P. V. Parimi, W. T. Lu, P. Vodo, and S. Sridhar, Nature 426, 404 (2003).
    [CrossRef]
  6. E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopoulou, and C. M. Soukoulis, Phys. Rev. Lett. 91, 207401 (2003).
    [CrossRef]
  7. Z. Lu, J. A. Murakowski, C. A. Shuetz, S. Shi, G. J. Schneider, and D. W. Prather, Phys. Rev. Lett. 95, 153901 (2005).
    [CrossRef]
  8. A. Cebrecos, V. Romero-Garcia, R. Pico, I. Perez-Arjona, V. Espinosa, V. J. Sanchez-Morcillo, and K. Staliunas, J. Appl. Phys. 111, 104910 (2012).
    [CrossRef]
  9. E. Schonburn, T. Yamashita, W. Park, and C. J. Summers, Phys. Rev. B 73, 195117 (2006).
    [CrossRef]
  10. K. Staliunas and R. Herrero, Phys. Rev. E 73, 016601 (2006).
    [CrossRef]
  11. M. Deubel, G. Freymann, M. Wegener, S. Pereira, K. Bush, and C. M. Soukoulis, Nat. Mater. 3, 444 (2004).
    [CrossRef]
  12. A. Ovsianikov, J. Viertl, B. Chickov, M. Oubaha, B. MacCraith, I. Sakellari, A. Guakoumaki, D. Gray, M. Vamvakaki, M. Farsari, and C. Fotakis, ACS Nano 2, 2257 (2008).
    [CrossRef]

2012 (1)

A. Cebrecos, V. Romero-Garcia, R. Pico, I. Perez-Arjona, V. Espinosa, V. J. Sanchez-Morcillo, and K. Staliunas, J. Appl. Phys. 111, 104910 (2012).
[CrossRef]

2008 (1)

A. Ovsianikov, J. Viertl, B. Chickov, M. Oubaha, B. MacCraith, I. Sakellari, A. Guakoumaki, D. Gray, M. Vamvakaki, M. Farsari, and C. Fotakis, ACS Nano 2, 2257 (2008).
[CrossRef]

2006 (3)

E. Schonburn, T. Yamashita, W. Park, and C. J. Summers, Phys. Rev. B 73, 195117 (2006).
[CrossRef]

K. Staliunas and R. Herrero, Phys. Rev. E 73, 016601 (2006).
[CrossRef]

J. Serbin and M. Gu, Opt. Express 14, 3563 (2006).
[CrossRef]

2005 (1)

Z. Lu, J. A. Murakowski, C. A. Shuetz, S. Shi, G. J. Schneider, and D. W. Prather, Phys. Rev. Lett. 95, 153901 (2005).
[CrossRef]

2004 (1)

M. Deubel, G. Freymann, M. Wegener, S. Pereira, K. Bush, and C. M. Soukoulis, Nat. Mater. 3, 444 (2004).
[CrossRef]

2003 (3)

P. V. Parimi, W. T. Lu, P. Vodo, and S. Sridhar, Nature 426, 404 (2003).
[CrossRef]

E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopoulou, and C. M. Soukoulis, Phys. Rev. Lett. 91, 207401 (2003).
[CrossRef]

E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopoulou, and C. M. Soukoulis, Nature 423, 604 (2003).
[CrossRef]

2002 (1)

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

1999 (1)

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

Aydin, K.

E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopoulou, and C. M. Soukoulis, Phys. Rev. Lett. 91, 207401 (2003).
[CrossRef]

E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopoulou, and C. M. Soukoulis, Nature 423, 604 (2003).
[CrossRef]

Bush, K.

M. Deubel, G. Freymann, M. Wegener, S. Pereira, K. Bush, and C. M. Soukoulis, Nat. Mater. 3, 444 (2004).
[CrossRef]

Cebrecos, A.

A. Cebrecos, V. Romero-Garcia, R. Pico, I. Perez-Arjona, V. Espinosa, V. J. Sanchez-Morcillo, and K. Staliunas, J. Appl. Phys. 111, 104910 (2012).
[CrossRef]

Chickov, B.

A. Ovsianikov, J. Viertl, B. Chickov, M. Oubaha, B. MacCraith, I. Sakellari, A. Guakoumaki, D. Gray, M. Vamvakaki, M. Farsari, and C. Fotakis, ACS Nano 2, 2257 (2008).
[CrossRef]

Cubukcu, E.

E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopoulou, and C. M. Soukoulis, Nature 423, 604 (2003).
[CrossRef]

E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopoulou, and C. M. Soukoulis, Phys. Rev. Lett. 91, 207401 (2003).
[CrossRef]

Deubel, M.

M. Deubel, G. Freymann, M. Wegener, S. Pereira, K. Bush, and C. M. Soukoulis, Nat. Mater. 3, 444 (2004).
[CrossRef]

Espinosa, V.

A. Cebrecos, V. Romero-Garcia, R. Pico, I. Perez-Arjona, V. Espinosa, V. J. Sanchez-Morcillo, and K. Staliunas, J. Appl. Phys. 111, 104910 (2012).
[CrossRef]

Farsari, M.

A. Ovsianikov, J. Viertl, B. Chickov, M. Oubaha, B. MacCraith, I. Sakellari, A. Guakoumaki, D. Gray, M. Vamvakaki, M. Farsari, and C. Fotakis, ACS Nano 2, 2257 (2008).
[CrossRef]

Fotakis, C.

A. Ovsianikov, J. Viertl, B. Chickov, M. Oubaha, B. MacCraith, I. Sakellari, A. Guakoumaki, D. Gray, M. Vamvakaki, M. Farsari, and C. Fotakis, ACS Nano 2, 2257 (2008).
[CrossRef]

Foteinopoulou, S.

E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopoulou, and C. M. Soukoulis, Nature 423, 604 (2003).
[CrossRef]

E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopoulou, and C. M. Soukoulis, Phys. Rev. Lett. 91, 207401 (2003).
[CrossRef]

Freymann, G.

M. Deubel, G. Freymann, M. Wegener, S. Pereira, K. Bush, and C. M. Soukoulis, Nat. Mater. 3, 444 (2004).
[CrossRef]

Gray, D.

A. Ovsianikov, J. Viertl, B. Chickov, M. Oubaha, B. MacCraith, I. Sakellari, A. Guakoumaki, D. Gray, M. Vamvakaki, M. Farsari, and C. Fotakis, ACS Nano 2, 2257 (2008).
[CrossRef]

Gu, M.

Guakoumaki, A.

A. Ovsianikov, J. Viertl, B. Chickov, M. Oubaha, B. MacCraith, I. Sakellari, A. Guakoumaki, D. Gray, M. Vamvakaki, M. Farsari, and C. Fotakis, ACS Nano 2, 2257 (2008).
[CrossRef]

Herrero, R.

K. Staliunas and R. Herrero, Phys. Rev. E 73, 016601 (2006).
[CrossRef]

Joannopoulos, J. D.

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

Johnson, S. G.

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

Kawakami, S.

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

Kawashima, T.

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

Kosaka, H.

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

Lu, W. T.

P. V. Parimi, W. T. Lu, P. Vodo, and S. Sridhar, Nature 426, 404 (2003).
[CrossRef]

Lu, Z.

Z. Lu, J. A. Murakowski, C. A. Shuetz, S. Shi, G. J. Schneider, and D. W. Prather, Phys. Rev. Lett. 95, 153901 (2005).
[CrossRef]

Luo, C.

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

MacCraith, B.

A. Ovsianikov, J. Viertl, B. Chickov, M. Oubaha, B. MacCraith, I. Sakellari, A. Guakoumaki, D. Gray, M. Vamvakaki, M. Farsari, and C. Fotakis, ACS Nano 2, 2257 (2008).
[CrossRef]

Murakowski, J. A.

Z. Lu, J. A. Murakowski, C. A. Shuetz, S. Shi, G. J. Schneider, and D. W. Prather, Phys. Rev. Lett. 95, 153901 (2005).
[CrossRef]

Notomi, M.

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

Oubaha, M.

A. Ovsianikov, J. Viertl, B. Chickov, M. Oubaha, B. MacCraith, I. Sakellari, A. Guakoumaki, D. Gray, M. Vamvakaki, M. Farsari, and C. Fotakis, ACS Nano 2, 2257 (2008).
[CrossRef]

Ovsianikov, A.

A. Ovsianikov, J. Viertl, B. Chickov, M. Oubaha, B. MacCraith, I. Sakellari, A. Guakoumaki, D. Gray, M. Vamvakaki, M. Farsari, and C. Fotakis, ACS Nano 2, 2257 (2008).
[CrossRef]

Ozbay, E.

E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopoulou, and C. M. Soukoulis, Phys. Rev. Lett. 91, 207401 (2003).
[CrossRef]

E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopoulou, and C. M. Soukoulis, Nature 423, 604 (2003).
[CrossRef]

Parimi, P. V.

P. V. Parimi, W. T. Lu, P. Vodo, and S. Sridhar, Nature 426, 404 (2003).
[CrossRef]

Park, W.

E. Schonburn, T. Yamashita, W. Park, and C. J. Summers, Phys. Rev. B 73, 195117 (2006).
[CrossRef]

Pendry, J. B.

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

Pereira, S.

M. Deubel, G. Freymann, M. Wegener, S. Pereira, K. Bush, and C. M. Soukoulis, Nat. Mater. 3, 444 (2004).
[CrossRef]

Perez-Arjona, I.

A. Cebrecos, V. Romero-Garcia, R. Pico, I. Perez-Arjona, V. Espinosa, V. J. Sanchez-Morcillo, and K. Staliunas, J. Appl. Phys. 111, 104910 (2012).
[CrossRef]

Pico, R.

A. Cebrecos, V. Romero-Garcia, R. Pico, I. Perez-Arjona, V. Espinosa, V. J. Sanchez-Morcillo, and K. Staliunas, J. Appl. Phys. 111, 104910 (2012).
[CrossRef]

Prather, D. W.

Z. Lu, J. A. Murakowski, C. A. Shuetz, S. Shi, G. J. Schneider, and D. W. Prather, Phys. Rev. Lett. 95, 153901 (2005).
[CrossRef]

Romero-Garcia, V.

A. Cebrecos, V. Romero-Garcia, R. Pico, I. Perez-Arjona, V. Espinosa, V. J. Sanchez-Morcillo, and K. Staliunas, J. Appl. Phys. 111, 104910 (2012).
[CrossRef]

Sakellari, I.

A. Ovsianikov, J. Viertl, B. Chickov, M. Oubaha, B. MacCraith, I. Sakellari, A. Guakoumaki, D. Gray, M. Vamvakaki, M. Farsari, and C. Fotakis, ACS Nano 2, 2257 (2008).
[CrossRef]

Sanchez-Morcillo, V. J.

A. Cebrecos, V. Romero-Garcia, R. Pico, I. Perez-Arjona, V. Espinosa, V. J. Sanchez-Morcillo, and K. Staliunas, J. Appl. Phys. 111, 104910 (2012).
[CrossRef]

Sato, T.

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

Schneider, G. J.

Z. Lu, J. A. Murakowski, C. A. Shuetz, S. Shi, G. J. Schneider, and D. W. Prather, Phys. Rev. Lett. 95, 153901 (2005).
[CrossRef]

Schonburn, E.

E. Schonburn, T. Yamashita, W. Park, and C. J. Summers, Phys. Rev. B 73, 195117 (2006).
[CrossRef]

Serbin, J.

Shi, S.

Z. Lu, J. A. Murakowski, C. A. Shuetz, S. Shi, G. J. Schneider, and D. W. Prather, Phys. Rev. Lett. 95, 153901 (2005).
[CrossRef]

Shuetz, C. A.

Z. Lu, J. A. Murakowski, C. A. Shuetz, S. Shi, G. J. Schneider, and D. W. Prather, Phys. Rev. Lett. 95, 153901 (2005).
[CrossRef]

Soukoulis, C. M.

M. Deubel, G. Freymann, M. Wegener, S. Pereira, K. Bush, and C. M. Soukoulis, Nat. Mater. 3, 444 (2004).
[CrossRef]

E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopoulou, and C. M. Soukoulis, Phys. Rev. Lett. 91, 207401 (2003).
[CrossRef]

E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopoulou, and C. M. Soukoulis, Nature 423, 604 (2003).
[CrossRef]

Sridhar, S.

P. V. Parimi, W. T. Lu, P. Vodo, and S. Sridhar, Nature 426, 404 (2003).
[CrossRef]

Staliunas, K.

A. Cebrecos, V. Romero-Garcia, R. Pico, I. Perez-Arjona, V. Espinosa, V. J. Sanchez-Morcillo, and K. Staliunas, J. Appl. Phys. 111, 104910 (2012).
[CrossRef]

K. Staliunas and R. Herrero, Phys. Rev. E 73, 016601 (2006).
[CrossRef]

Summers, C. J.

E. Schonburn, T. Yamashita, W. Park, and C. J. Summers, Phys. Rev. B 73, 195117 (2006).
[CrossRef]

Tamamura, T.

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

Tomita, A.

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

Vamvakaki, M.

A. Ovsianikov, J. Viertl, B. Chickov, M. Oubaha, B. MacCraith, I. Sakellari, A. Guakoumaki, D. Gray, M. Vamvakaki, M. Farsari, and C. Fotakis, ACS Nano 2, 2257 (2008).
[CrossRef]

Viertl, J.

A. Ovsianikov, J. Viertl, B. Chickov, M. Oubaha, B. MacCraith, I. Sakellari, A. Guakoumaki, D. Gray, M. Vamvakaki, M. Farsari, and C. Fotakis, ACS Nano 2, 2257 (2008).
[CrossRef]

Vodo, P.

P. V. Parimi, W. T. Lu, P. Vodo, and S. Sridhar, Nature 426, 404 (2003).
[CrossRef]

Wegener, M.

M. Deubel, G. Freymann, M. Wegener, S. Pereira, K. Bush, and C. M. Soukoulis, Nat. Mater. 3, 444 (2004).
[CrossRef]

Yamashita, T.

E. Schonburn, T. Yamashita, W. Park, and C. J. Summers, Phys. Rev. B 73, 195117 (2006).
[CrossRef]

ACS Nano (1)

A. Ovsianikov, J. Viertl, B. Chickov, M. Oubaha, B. MacCraith, I. Sakellari, A. Guakoumaki, D. Gray, M. Vamvakaki, M. Farsari, and C. Fotakis, ACS Nano 2, 2257 (2008).
[CrossRef]

Appl. Phys. Lett. (1)

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

J. Appl. Phys. (1)

A. Cebrecos, V. Romero-Garcia, R. Pico, I. Perez-Arjona, V. Espinosa, V. J. Sanchez-Morcillo, and K. Staliunas, J. Appl. Phys. 111, 104910 (2012).
[CrossRef]

Nat. Mater. (1)

M. Deubel, G. Freymann, M. Wegener, S. Pereira, K. Bush, and C. M. Soukoulis, Nat. Mater. 3, 444 (2004).
[CrossRef]

Nature (2)

E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopoulou, and C. M. Soukoulis, Nature 423, 604 (2003).
[CrossRef]

P. V. Parimi, W. T. Lu, P. Vodo, and S. Sridhar, Nature 426, 404 (2003).
[CrossRef]

Opt. Express (1)

Phys. Rev. B (2)

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

E. Schonburn, T. Yamashita, W. Park, and C. J. Summers, Phys. Rev. B 73, 195117 (2006).
[CrossRef]

Phys. Rev. E (1)

K. Staliunas and R. Herrero, Phys. Rev. E 73, 016601 (2006).
[CrossRef]

Phys. Rev. Lett. (2)

E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopoulou, and C. M. Soukoulis, Phys. Rev. Lett. 91, 207401 (2003).
[CrossRef]

Z. Lu, J. A. Murakowski, C. A. Shuetz, S. Shi, G. J. Schneider, and D. W. Prather, Phys. Rev. Lett. 95, 153901 (2005).
[CrossRef]

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Figures (3)

Fig. 1.
Fig. 1.

(a) Flat PhC lensing scheme, (b) schematic representation of a woodpile PhC, (c) reduced 2D structure, and (d) a scanning electron microscope image of the PhC—45° oblique view.

Fig. 2.
Fig. 2.

(a), (c), (e) Field intensity distributions at 532, 570, and 780 nm, inside and behind the PhC, calculated by 2D FDTD; (b), (d), (f) the beam width depending on distance behind the crystal (red) compared to the width of the reference beam (black) (dots, experimental results; lines, numerical results); (g)–(i) 2D distributions of the beams at the plane of 60 μm behind the PhC taken with a CCD camera for the corresponding wavelengths of 532, 570, and 700 nm [corresponding positions are marked by arrows in (b), (d), and (f), respectively].

Fig. 3.
Fig. 3.

Minimum diameter of the beam behind the PhC (red) and the focal distance (blue) versus wavelength calculated by FDTD. The two insets represent isofrequency lines, where the spanning harmonics (see main text) are highlighted in red and global trends of isofrequency are lines highlighted in blue. The left inset is at the frequency of flat lensing (at 570 nm) and the right one at self-collimation (at 610 nm).

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