Abstract

A dielectric structure with effective permittivity and permeability close to 1 operating for propagative waves at optical wavelengths is proposed. This structure is a two-dimensional photonic crystal with refractive index 1, coated by appropriate antireflection gratings. Numerical simulations involving a flat lens made of this optimized crystal illustrate the improvements that antireflection gratings can bring. In particular, following Veselago’s proposition, this lens “can focus at a point the radiation from a point source” with negligible reflection losses. The proposed design takes into account the fabrication requirements and can be used for optical devices integrated in planar waveguides.

© 2009 Optical Society of America

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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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2009 (1)

2008 (4)

W. Śmigaj and B. Gralak, Phys. Rev. B 77, 235445 (2008).
[CrossRef]

N. Liu, H. Guo, L. Fu, S. Kaiser, H. Schweizer, and H. Giessen, Nature Mater. 7, 31 (2008).
[CrossRef]

N. Fabre, L. Lalouat, B. Cluzel, X. Mélique, D. Lippens, F. de Fornel, and O. Vanbésien, Phys. Rev. Lett. 101, 073901 (2008).
[CrossRef] [PubMed]

R. Pierre and B. Gralak, J. Mod. Opt. 55, 1759 (2008).
[CrossRef]

2007 (5)

K. Aydin, I. Bulu, and E. Ozbay, Appl. Phys. Lett. 90, 254102 (2007).
[CrossRef]

Z. Lu and D. Prather, Opt. Express 15, 8340 (2007).
[CrossRef] [PubMed]

Y. Jin and S. He, Phys. Lett. A 90, 174113 (2007).
[CrossRef]

B. Zhang and M. Li, Eur. Phys. J. D 45, 321 (2007).
[CrossRef]

Z. Li, E. Ozbay, H. Chen, J. Chen, F. Yang, and H. Zheng, J. Phys. D 40, 5873 (2007).
[CrossRef]

2006 (2)

V. Veselago, L. Braginsky, V. Shklover, and C. Hafner, J. Comput. Theor. Nanosci. 3, 1 (2006).

T. Decoopman, G. Tayeb, S. Enoch, D. Maystre, and B. Gralak, Phys. Rev. Lett. 97, 073905 (2006).
[CrossRef] [PubMed]

2005 (1)

2004 (2)

S. Xiao, M. Qiu, Z. Ruan, and S. He, Appl. Phys. Lett. 85, 4269 (2004).
[CrossRef]

G. Tayeb and S. Enoch, J. Opt. Soc. Am. A 21, 1417 (2004).
[CrossRef]

2003 (3)

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

C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, Phys. Rev. B 68, 045115 (2003).
[CrossRef]

S. Foteinopoulou and C. M. Soukoulis, Phys. Rev. B 67, 235107 (2003).
[CrossRef]

2002 (1)

N. Garcia and M. Nieto-Vesperinas, Phys. Rev. Lett. 88, 207403 (2002).
[CrossRef] [PubMed]

2000 (4)

M. Notomi, Phys. Rev. B 62, 10696 (2000).
[CrossRef]

B. Gralak, S. Enoch, and G. Tayeb, J. Opt. Soc. Am. A 17, 1012 (2000).
[CrossRef]

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, Phys. Rev. Lett. 84, 4184 (2000).
[CrossRef] [PubMed]

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

1993 (1)

1968 (1)

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

Aydin, K.

K. Aydin, I. Bulu, and E. Ozbay, Appl. Phys. Lett. 90, 254102 (2007).
[CrossRef]

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

Banyal, R. K.

Braginsky, L.

V. Veselago, L. Braginsky, V. Shklover, and C. Hafner, J. Comput. Theor. Nanosci. 3, 1 (2006).

Bulu, I.

K. Aydin, I. Bulu, and E. Ozbay, Appl. Phys. Lett. 90, 254102 (2007).
[CrossRef]

Casse, B. D. F.

Chen, H.

Z. Li, E. Ozbay, H. Chen, J. Chen, F. Yang, and H. Zheng, J. Phys. D 40, 5873 (2007).
[CrossRef]

Chen, J.

Z. Li, E. Ozbay, H. Chen, J. Chen, F. Yang, and H. Zheng, J. Phys. D 40, 5873 (2007).
[CrossRef]

Cluzel, B.

N. Fabre, L. Lalouat, B. Cluzel, X. Mélique, D. Lippens, F. de Fornel, and O. Vanbésien, Phys. Rev. Lett. 101, 073901 (2008).
[CrossRef] [PubMed]

Cubukcu, E.

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

de Fornel, F.

N. Fabre, L. Lalouat, B. Cluzel, X. Mélique, D. Lippens, F. de Fornel, and O. Vanbésien, Phys. Rev. Lett. 101, 073901 (2008).
[CrossRef] [PubMed]

Decoopman, T.

T. Decoopman, G. Tayeb, S. Enoch, D. Maystre, and B. Gralak, Phys. Rev. Lett. 97, 073905 (2006).
[CrossRef] [PubMed]

Dokmeci, M. R.

Enoch, S.

Fabre, N.

N. Fabre, L. Lalouat, B. Cluzel, X. Mélique, D. Lippens, F. de Fornel, and O. Vanbésien, Phys. Rev. Lett. 101, 073901 (2008).
[CrossRef] [PubMed]

Foteinopoulou, S.

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

S. Foteinopoulou and C. M. Soukoulis, Phys. Rev. B 67, 235107 (2003).
[CrossRef]

Fu, L.

N. Liu, H. Guo, L. Fu, S. Kaiser, H. Schweizer, and H. Giessen, Nature Mater. 7, 31 (2008).
[CrossRef]

Garcia, N.

N. Garcia and M. Nieto-Vesperinas, Phys. Rev. Lett. 88, 207403 (2002).
[CrossRef] [PubMed]

Giessen, H.

N. Liu, H. Guo, L. Fu, S. Kaiser, H. Schweizer, and H. Giessen, Nature Mater. 7, 31 (2008).
[CrossRef]

Gralak, B.

W. Śmigaj and B. Gralak, Phys. Rev. B 77, 235445 (2008).
[CrossRef]

R. Pierre and B. Gralak, J. Mod. Opt. 55, 1759 (2008).
[CrossRef]

T. Decoopman, G. Tayeb, S. Enoch, D. Maystre, and B. Gralak, Phys. Rev. Lett. 97, 073905 (2006).
[CrossRef] [PubMed]

S. Guenneau, B. Gralak, and J. B. Pendry, Opt. Lett. 30, 1204 (2005).
[CrossRef] [PubMed]

B. Gralak, S. Enoch, and G. Tayeb, J. Opt. Soc. Am. A 17, 1012 (2000).
[CrossRef]

W. Śmigaj, R. Pierre, B. Gralak, and G. Tayeb, in SPP4 Surface Plasmon Photonics Conference (2009).

Guenneau, S.

Guo, H.

N. Liu, H. Guo, L. Fu, S. Kaiser, H. Schweizer, and H. Giessen, Nature Mater. 7, 31 (2008).
[CrossRef]

Hafner, C.

V. Veselago, L. Braginsky, V. Shklover, and C. Hafner, J. Comput. Theor. Nanosci. 3, 1 (2006).

He, S.

Y. Jin and S. He, Phys. Lett. A 90, 174113 (2007).
[CrossRef]

S. Xiao, M. Qiu, Z. Ruan, and S. He, Appl. Phys. Lett. 85, 4269 (2004).
[CrossRef]

Huang, Y. J.

Jin, Y.

Y. Jin and S. He, Phys. Lett. A 90, 174113 (2007).
[CrossRef]

Joannopoulos, J. D.

C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, Phys. Rev. B 68, 045115 (2003).
[CrossRef]

Johnson, S. G.

C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, Phys. Rev. B 68, 045115 (2003).
[CrossRef]

Kaiser, S.

N. Liu, H. Guo, L. Fu, S. Kaiser, H. Schweizer, and H. Giessen, Nature Mater. 7, 31 (2008).
[CrossRef]

Lalouat, L.

N. Fabre, L. Lalouat, B. Cluzel, X. Mélique, D. Lippens, F. de Fornel, and O. Vanbésien, Phys. Rev. Lett. 101, 073901 (2008).
[CrossRef] [PubMed]

Li, M.

B. Zhang and M. Li, Eur. Phys. J. D 45, 321 (2007).
[CrossRef]

Li, Z.

Z. Li, E. Ozbay, H. Chen, J. Chen, F. Yang, and H. Zheng, J. Phys. D 40, 5873 (2007).
[CrossRef]

Lippens, D.

N. Fabre, L. Lalouat, B. Cluzel, X. Mélique, D. Lippens, F. de Fornel, and O. Vanbésien, Phys. Rev. Lett. 101, 073901 (2008).
[CrossRef] [PubMed]

Liu, N.

N. Liu, H. Guo, L. Fu, S. Kaiser, H. Schweizer, and H. Giessen, Nature Mater. 7, 31 (2008).
[CrossRef]

Lu, W. T.

Lu, Z.

Luo, C.

C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, Phys. Rev. B 68, 045115 (2003).
[CrossRef]

Maystre, D.

T. Decoopman, G. Tayeb, S. Enoch, D. Maystre, and B. Gralak, Phys. Rev. Lett. 97, 073905 (2006).
[CrossRef] [PubMed]

Mélique, X.

N. Fabre, L. Lalouat, B. Cluzel, X. Mélique, D. Lippens, F. de Fornel, and O. Vanbésien, Phys. Rev. Lett. 101, 073901 (2008).
[CrossRef] [PubMed]

Morris, G.

Nemat-Nasser, S. C.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, Phys. Rev. Lett. 84, 4184 (2000).
[CrossRef] [PubMed]

Nieto-Vesperinas, M.

N. Garcia and M. Nieto-Vesperinas, Phys. Rev. Lett. 88, 207403 (2002).
[CrossRef] [PubMed]

Notomi, M.

M. Notomi, Phys. Rev. B 62, 10696 (2000).
[CrossRef]

Ozbay, E.

K. Aydin, I. Bulu, and E. Ozbay, Appl. Phys. Lett. 90, 254102 (2007).
[CrossRef]

Z. Li, E. Ozbay, H. Chen, J. Chen, F. Yang, and H. Zheng, J. Phys. D 40, 5873 (2007).
[CrossRef]

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

Padilla, W. J.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, Phys. Rev. Lett. 84, 4184 (2000).
[CrossRef] [PubMed]

Pendry, J. B.

S. Guenneau, B. Gralak, and J. B. Pendry, Opt. Lett. 30, 1204 (2005).
[CrossRef] [PubMed]

C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, Phys. Rev. B 68, 045115 (2003).
[CrossRef]

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

Perry, C. H.

Pierre, R.

R. Pierre and B. Gralak, J. Mod. Opt. 55, 1759 (2008).
[CrossRef]

W. Śmigaj, R. Pierre, B. Gralak, and G. Tayeb, in SPP4 Surface Plasmon Photonics Conference (2009).

Prather, D.

Qiu, M.

S. Xiao, M. Qiu, Z. Ruan, and S. He, Appl. Phys. Lett. 85, 4269 (2004).
[CrossRef]

Raguin, D.

Ruan, Z.

S. Xiao, M. Qiu, Z. Ruan, and S. He, Appl. Phys. Lett. 85, 4269 (2004).
[CrossRef]

Schultz, S.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, Phys. Rev. Lett. 84, 4184 (2000).
[CrossRef] [PubMed]

Schweizer, H.

N. Liu, H. Guo, L. Fu, S. Kaiser, H. Schweizer, and H. Giessen, Nature Mater. 7, 31 (2008).
[CrossRef]

Selvarasah, S.

Shklover, V.

V. Veselago, L. Braginsky, V. Shklover, and C. Hafner, J. Comput. Theor. Nanosci. 3, 1 (2006).

Smigaj, W.

W. Śmigaj and B. Gralak, Phys. Rev. B 77, 235445 (2008).
[CrossRef]

W. Śmigaj, R. Pierre, B. Gralak, and G. Tayeb, in SPP4 Surface Plasmon Photonics Conference (2009).

Smith, D. R.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, Phys. Rev. Lett. 84, 4184 (2000).
[CrossRef] [PubMed]

Soukoulis, C. M.

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

S. Foteinopoulou and C. M. Soukoulis, Phys. Rev. B 67, 235107 (2003).
[CrossRef]

Sridhar, S.

Tayeb, G.

T. Decoopman, G. Tayeb, S. Enoch, D. Maystre, and B. Gralak, Phys. Rev. Lett. 97, 073905 (2006).
[CrossRef] [PubMed]

G. Tayeb and S. Enoch, J. Opt. Soc. Am. A 21, 1417 (2004).
[CrossRef]

B. Gralak, S. Enoch, and G. Tayeb, J. Opt. Soc. Am. A 17, 1012 (2000).
[CrossRef]

W. Śmigaj, R. Pierre, B. Gralak, and G. Tayeb, in SPP4 Surface Plasmon Photonics Conference (2009).

Vanbésien, O.

N. Fabre, L. Lalouat, B. Cluzel, X. Mélique, D. Lippens, F. de Fornel, and O. Vanbésien, Phys. Rev. Lett. 101, 073901 (2008).
[CrossRef] [PubMed]

Veselago, V.

V. Veselago, L. Braginsky, V. Shklover, and C. Hafner, J. Comput. Theor. Nanosci. 3, 1 (2006).

Veselago, V. G.

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

Vier, D. C.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, Phys. Rev. Lett. 84, 4184 (2000).
[CrossRef] [PubMed]

Xiao, S.

S. Xiao, M. Qiu, Z. Ruan, and S. He, Appl. Phys. Lett. 85, 4269 (2004).
[CrossRef]

Yang, F.

Z. Li, E. Ozbay, H. Chen, J. Chen, F. Yang, and H. Zheng, J. Phys. D 40, 5873 (2007).
[CrossRef]

Zhang, B.

B. Zhang and M. Li, Eur. Phys. J. D 45, 321 (2007).
[CrossRef]

Zheng, H.

Z. Li, E. Ozbay, H. Chen, J. Chen, F. Yang, and H. Zheng, J. Phys. D 40, 5873 (2007).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (2)

K. Aydin, I. Bulu, and E. Ozbay, Appl. Phys. Lett. 90, 254102 (2007).
[CrossRef]

S. Xiao, M. Qiu, Z. Ruan, and S. He, Appl. Phys. Lett. 85, 4269 (2004).
[CrossRef]

Eur. Phys. J. D (1)

B. Zhang and M. Li, Eur. Phys. J. D 45, 321 (2007).
[CrossRef]

J. Comput. Theor. Nanosci. (1)

V. Veselago, L. Braginsky, V. Shklover, and C. Hafner, J. Comput. Theor. Nanosci. 3, 1 (2006).

J. Mod. Opt. (1)

R. Pierre and B. Gralak, J. Mod. Opt. 55, 1759 (2008).
[CrossRef]

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

J. Phys. D (1)

Z. Li, E. Ozbay, H. Chen, J. Chen, F. Yang, and H. Zheng, J. Phys. D 40, 5873 (2007).
[CrossRef]

Nature (1)

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

Nature Mater. (1)

N. Liu, H. Guo, L. Fu, S. Kaiser, H. Schweizer, and H. Giessen, Nature Mater. 7, 31 (2008).
[CrossRef]

Opt. Express (1)

Opt. Lett. (2)

Phys. Lett. A (1)

Y. Jin and S. He, Phys. Lett. A 90, 174113 (2007).
[CrossRef]

Phys. Rev. B (4)

W. Śmigaj and B. Gralak, Phys. Rev. B 77, 235445 (2008).
[CrossRef]

M. Notomi, Phys. Rev. B 62, 10696 (2000).
[CrossRef]

C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, Phys. Rev. B 68, 045115 (2003).
[CrossRef]

S. Foteinopoulou and C. M. Soukoulis, Phys. Rev. B 67, 235107 (2003).
[CrossRef]

Phys. Rev. Lett. (5)

T. Decoopman, G. Tayeb, S. Enoch, D. Maystre, and B. Gralak, Phys. Rev. Lett. 97, 073905 (2006).
[CrossRef] [PubMed]

N. Fabre, L. Lalouat, B. Cluzel, X. Mélique, D. Lippens, F. de Fornel, and O. Vanbésien, Phys. Rev. Lett. 101, 073901 (2008).
[CrossRef] [PubMed]

N. Garcia and M. Nieto-Vesperinas, Phys. Rev. Lett. 88, 207403 (2002).
[CrossRef] [PubMed]

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, Phys. Rev. Lett. 84, 4184 (2000).
[CrossRef] [PubMed]

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

Sov. Phys. Usp. (1)

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

Other (1)

W. Śmigaj, R. Pierre, B. Gralak, and G. Tayeb, in SPP4 Surface Plasmon Photonics Conference (2009).

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Figures (5)

Fig. 1
Fig. 1

Photonic crystal with its surface covered by an antireflection grating.

Fig. 2
Fig. 2

Reflectivities as functions of the angle of incidence.

Fig. 3
Fig. 3

Modulus of the electric field around (a) the original flat lens and (b) the optimized flat lens with trapezoidal AGs. The flat lenses are embedded in air. Spatial coordinates are in micrometers. Wavelength, λ 0 = 1.55 μ m .

Fig. 4
Fig. 4

Optimized flat lens with an attached object: (a) object in the blind zone, (b) object at focus.

Fig. 5
Fig. 5

Far-field intensity for situations of Fig. 4.

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