Abstract

We evaluate the possibility to focus scanning light beams below the diffraction limit by using the combination of a nonlinear material with a Kerr-type nonlinearity or two-photon absorption to create seed evanescent components of the beam and a negative-refraction material to enhance them. Superfocusing to spots with a FWHM in the range of 0.2λ is theoretically predicted both in the context of the effective-medium theory and by the direct numerical solution of Maxwell equations for an inhomogeneous photonic crystal. The evolution of the transverse spectrum and the dependence of superfocusing on the parameters of the negative-refraction material are also studied. We show that the use of a Kerr-type nonlinear layer for the creation of seed evanescent components yields focused spots with a higher intensity compared with those obtained by the application of a saturable absorber.

© 2006 Optical Society of America

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    [CrossRef] [PubMed]
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2006 (2)

Q. Thommen and P. Mandel, "Electromagnetically Induced Left Handedness in Optically Excited Four-Level Atomic Media", Phys. Rev. Lett. 96, 053601 (2006).
[CrossRef] [PubMed]

A. Husakou and J. Herrmann, "Focusing of Scanning Light Beams below the Diffraction Limit without Near- Field Spatial Control Using a Saturable Absorber and a Negative-Refraction Material," Phys. Rev. Lett. 96, 013902 (2006).
[CrossRef] [PubMed]

2005 (8)

Z. Lu, J.A. Murakowski, C. A. Schuetz, S. Shi, G. J. Schneider, and D. W. Prather, "Three-Dimensional Subwavelength Imaging by a Photonic-Crystal Flat Lens Using Negative Refraction at Microwave Frequencies," Phys. Rev. Lett. 95, 153901 (2005).
[CrossRef] [PubMed]

N. Fang, H. Lee, C. Sun, X. Zhang, "SubDiffraction-Limited Optical Imaging with a Silver Superlens," Science 308, 534-537 (2005).
[CrossRef] [PubMed]

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, T. Koschny, C. M. Soukoulis, "Magnetic Metamaterials at Telecommunication and Visible Frequencies," Phys. Rev. Lett. 95, 203901 (2005).
[CrossRef] [PubMed]

G. Dolling, C. Enkrich, M. Wegener, J. Zhou, C.M. Soukoulis, S. Linden, "Cut-wire pairs and plate pairs as magnetic atoms for optical metamaterials," Opt. Lett 30, 3198-3200 (2005).
[CrossRef] [PubMed]

V. M. Shalaev, W. Cai, U. Chettiar, H. K. Yuan, A.K. Sarychev, V. P. Drachev, and A. V. Kildishev, "Negative index of refraction in optical metamaterials," Opt. Lett 30, 3356-3358 (2005).
[CrossRef]

N. Grigorenko, A. K. Geim, H. F. Gleeson, Y. Zhang, A. A. Firsov, I. Y. Khrushchev, and J. Petrovic, "Nanofabricated media with negative permeability at visible frequencies," Nature 438, 335-338 (2005).
[CrossRef] [PubMed]

L. Lucchetti, M. Gentili, and F. Simoni, "Pretransportal enhancement of the optical nonlinearity of thin dye-doped liquid crystals in the nematic phase," Appl. Phys. Lett. 86, 151117 (2005).
[CrossRef]

D. Melville and R. Blaikie, "Super-resolution imaging through a planar silver layer," Opt. Express 13, 2127-2134 (2005)
[CrossRef] [PubMed]

2004 (3)

A. Husakou and J. Herrmann, "Superfocusing of light below the diffraction limit by photonic crystals with negative refraction," Opt. Express 12, 6491-6497 (2004)
[CrossRef] [PubMed]

A. Berrier, M. Mulot, M. Swillo, M. Qiu, L. Thyln, A. Talneau, and S. Anand, "Negative Refraction at Infrared Wavelengths in a Two-Dimensional Photonic Crystal," Phys. Rev. Lett. 93, 073902 (2004).
[CrossRef] [PubMed]

M. Kolesik and J. V. Moloney, "Nonlinear optical pulse propagation simulation: From Maxwell’s to unidirectional equations," Phys. Rev. E 70, 036604 (2004).
[CrossRef]

2003 (5)

P. V. Parimi, W. T. Lu, P. Vodo and S. Sridhar, "Photonic crystals: Imaging by flat lens using negative refraction," Nature 426, 404-404 (2003).
[CrossRef] [PubMed]

E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopolou, and C. M. Soukoulis, "Subwavelength Resolution in a Two- Dimensional Photonic-Crystal-Based Superlens," Phys. Rev. Lett. 91, 207401 (2003).
[CrossRef] [PubMed]

E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopoulou, and C. M. Soukoulis, "Electromagnetic waves: Negative refraction by photonic crystals," Nature 423, 604-605 (2003).
[CrossRef] [PubMed]

D. R. Smith, D. Schurig, M. Rosenbluth, S. Schultz, S. A. Ramakrishna, and J. B. Pendry, "Limitations on subdiffraction imaging with a negative refractive index slab," Appl. Phys. Lett. 82, 1506-1508 (2003).
[CrossRef]

C. Luo, S. G. Johnson, and J. D. Joannopoulos, "Subwavelength imaging in photonic crystals," Phys. Rev. B 68, 045115 (2003).
[CrossRef]

2001 (1)

R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental Verification of a Negative Index of Refraction," Science 292, 77-79 (2001).
[CrossRef] [PubMed]

2000 (2)

M. Notomi, "Theory of light propagation in strongly modulated photonic crystals: Refractionlike behavior in the vicinity of the photonic band gap," Phys. Rev. B 62, 10696-10705 (2000).
[CrossRef]

J. B. Pendry, "Negative refraction makes perfect lens," Phys. Rev. Lett. 85, 3966-3969 (2000).
[CrossRef] [PubMed]

1999 (1)

1991 (1)

E. Betzig, J. K. Trautmann, T. D. Harris, J. S. Weiner, R. L. Kostelak, "Breaking the diffraction barrier: optical microscopy on a nanometric scale," Science 251, 1468-1450 (1991).
[CrossRef] [PubMed]

1990 (2)

1974 (1)

G. M. Gale and A. Mysyrowicz, "Direct creation of excitonic molecules in CuCl by giant two-photon absorption," Phys. Rev. Lett. 32, 737-740 (1974).
[CrossRef]

1968 (1)

V. G. Veselago, "The electrodynamics of substances with simultaneously negative values of ∑ and ," Soviet Phys. Usp. 10, 509-518 (1968) [Usp. Fiz. Nauk 92, 517-526 (1967).].
[CrossRef]

Anand, S.

A. Berrier, M. Mulot, M. Swillo, M. Qiu, L. Thyln, A. Talneau, and S. Anand, "Negative Refraction at Infrared Wavelengths in a Two-Dimensional Photonic Crystal," Phys. Rev. Lett. 93, 073902 (2004).
[CrossRef] [PubMed]

Aydin, K.

E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopoulou, and C. M. Soukoulis, "Electromagnetic waves: Negative refraction by photonic crystals," Nature 423, 604-605 (2003).
[CrossRef] [PubMed]

E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopolou, and C. M. Soukoulis, "Subwavelength Resolution in a Two- Dimensional Photonic-Crystal-Based Superlens," Phys. Rev. Lett. 91, 207401 (2003).
[CrossRef] [PubMed]

Bennink, R. S.

Berrier, A.

A. Berrier, M. Mulot, M. Swillo, M. Qiu, L. Thyln, A. Talneau, and S. Anand, "Negative Refraction at Infrared Wavelengths in a Two-Dimensional Photonic Crystal," Phys. Rev. Lett. 93, 073902 (2004).
[CrossRef] [PubMed]

Betzig, E.

E. Betzig, J. K. Trautmann, T. D. Harris, J. S. Weiner, R. L. Kostelak, "Breaking the diffraction barrier: optical microscopy on a nanometric scale," Science 251, 1468-1450 (1991).
[CrossRef] [PubMed]

Blaikie, R.

Boyd, R. W.

Burger, S.

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, T. Koschny, C. M. Soukoulis, "Magnetic Metamaterials at Telecommunication and Visible Frequencies," Phys. Rev. Lett. 95, 203901 (2005).
[CrossRef] [PubMed]

Cai, W.

V. M. Shalaev, W. Cai, U. Chettiar, H. K. Yuan, A.K. Sarychev, V. P. Drachev, and A. V. Kildishev, "Negative index of refraction in optical metamaterials," Opt. Lett 30, 3356-3358 (2005).
[CrossRef]

Chettiar, U.

V. M. Shalaev, W. Cai, U. Chettiar, H. K. Yuan, A.K. Sarychev, V. P. Drachev, and A. V. Kildishev, "Negative index of refraction in optical metamaterials," Opt. Lett 30, 3356-3358 (2005).
[CrossRef]

Cubukcu, E.

E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopolou, and C. M. Soukoulis, "Subwavelength Resolution in a Two- Dimensional Photonic-Crystal-Based Superlens," Phys. Rev. Lett. 91, 207401 (2003).
[CrossRef] [PubMed]

E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopoulou, and C. M. Soukoulis, "Electromagnetic waves: Negative refraction by photonic crystals," Nature 423, 604-605 (2003).
[CrossRef] [PubMed]

Ding, Y. J.

Dolling, G.

G. Dolling, C. Enkrich, M. Wegener, J. Zhou, C.M. Soukoulis, S. Linden, "Cut-wire pairs and plate pairs as magnetic atoms for optical metamaterials," Opt. Lett 30, 3198-3200 (2005).
[CrossRef] [PubMed]

Drachev, V. P.

V. M. Shalaev, W. Cai, U. Chettiar, H. K. Yuan, A.K. Sarychev, V. P. Drachev, and A. V. Kildishev, "Negative index of refraction in optical metamaterials," Opt. Lett 30, 3356-3358 (2005).
[CrossRef]

Enkrich, C.

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, T. Koschny, C. M. Soukoulis, "Magnetic Metamaterials at Telecommunication and Visible Frequencies," Phys. Rev. Lett. 95, 203901 (2005).
[CrossRef] [PubMed]

G. Dolling, C. Enkrich, M. Wegener, J. Zhou, C.M. Soukoulis, S. Linden, "Cut-wire pairs and plate pairs as magnetic atoms for optical metamaterials," Opt. Lett 30, 3198-3200 (2005).
[CrossRef] [PubMed]

Fang, N.

N. Fang, H. Lee, C. Sun, X. Zhang, "SubDiffraction-Limited Optical Imaging with a Silver Superlens," Science 308, 534-537 (2005).
[CrossRef] [PubMed]

Firsov, A. A.

N. Grigorenko, A. K. Geim, H. F. Gleeson, Y. Zhang, A. A. Firsov, I. Y. Khrushchev, and J. Petrovic, "Nanofabricated media with negative permeability at visible frequencies," Nature 438, 335-338 (2005).
[CrossRef] [PubMed]

Foteinopolou, S.

E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopolou, and C. M. Soukoulis, "Subwavelength Resolution in a Two- Dimensional Photonic-Crystal-Based Superlens," Phys. Rev. Lett. 91, 207401 (2003).
[CrossRef] [PubMed]

Foteinopoulou, S.

E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopoulou, and C. M. Soukoulis, "Electromagnetic waves: Negative refraction by photonic crystals," Nature 423, 604-605 (2003).
[CrossRef] [PubMed]

Gale, G. M.

G. M. Gale and A. Mysyrowicz, "Direct creation of excitonic molecules in CuCl by giant two-photon absorption," Phys. Rev. Lett. 32, 737-740 (1974).
[CrossRef]

Geim, A. K.

N. Grigorenko, A. K. Geim, H. F. Gleeson, Y. Zhang, A. A. Firsov, I. Y. Khrushchev, and J. Petrovic, "Nanofabricated media with negative permeability at visible frequencies," Nature 438, 335-338 (2005).
[CrossRef] [PubMed]

Gentili, M.

L. Lucchetti, M. Gentili, and F. Simoni, "Pretransportal enhancement of the optical nonlinearity of thin dye-doped liquid crystals in the nematic phase," Appl. Phys. Lett. 86, 151117 (2005).
[CrossRef]

Gleeson, H. F.

N. Grigorenko, A. K. Geim, H. F. Gleeson, Y. Zhang, A. A. Firsov, I. Y. Khrushchev, and J. Petrovic, "Nanofabricated media with negative permeability at visible frequencies," Nature 438, 335-338 (2005).
[CrossRef] [PubMed]

Grigorenko, N.

N. Grigorenko, A. K. Geim, H. F. Gleeson, Y. Zhang, A. A. Firsov, I. Y. Khrushchev, and J. Petrovic, "Nanofabricated media with negative permeability at visible frequencies," Nature 438, 335-338 (2005).
[CrossRef] [PubMed]

Guo, C. L.

Harris, T. D.

E. Betzig, J. K. Trautmann, T. D. Harris, J. S. Weiner, R. L. Kostelak, "Breaking the diffraction barrier: optical microscopy on a nanometric scale," Science 251, 1468-1450 (1991).
[CrossRef] [PubMed]

Herrmann, J.

A. Husakou and J. Herrmann, "Focusing of Scanning Light Beams below the Diffraction Limit without Near- Field Spatial Control Using a Saturable Absorber and a Negative-Refraction Material," Phys. Rev. Lett. 96, 013902 (2006).
[CrossRef] [PubMed]

A. Husakou and J. Herrmann, "Superfocusing of light below the diffraction limit by photonic crystals with negative refraction," Opt. Express 12, 6491-6497 (2004)
[CrossRef] [PubMed]

Husakou, A.

A. Husakou and J. Herrmann, "Focusing of Scanning Light Beams below the Diffraction Limit without Near- Field Spatial Control Using a Saturable Absorber and a Negative-Refraction Material," Phys. Rev. Lett. 96, 013902 (2006).
[CrossRef] [PubMed]

A. Husakou and J. Herrmann, "Superfocusing of light below the diffraction limit by photonic crystals with negative refraction," Opt. Express 12, 6491-6497 (2004)
[CrossRef] [PubMed]

Joannopoulos, J. D.

C. Luo, S. G. Johnson, and J. D. Joannopoulos, "Subwavelength imaging in photonic crystals," Phys. Rev. B 68, 045115 (2003).
[CrossRef]

Johnson, S. G.

C. Luo, S. G. Johnson, and J. D. Joannopoulos, "Subwavelength imaging in photonic crystals," Phys. Rev. B 68, 045115 (2003).
[CrossRef]

Kaplan, A. E.

Khrushchev, I. Y.

N. Grigorenko, A. K. Geim, H. F. Gleeson, Y. Zhang, A. A. Firsov, I. Y. Khrushchev, and J. Petrovic, "Nanofabricated media with negative permeability at visible frequencies," Nature 438, 335-338 (2005).
[CrossRef] [PubMed]

Khurgin, J. B.

Kildishev, A. V.

V. M. Shalaev, W. Cai, U. Chettiar, H. K. Yuan, A.K. Sarychev, V. P. Drachev, and A. V. Kildishev, "Negative index of refraction in optical metamaterials," Opt. Lett 30, 3356-3358 (2005).
[CrossRef]

Kino, G. S.

S. M. Mansfield and G. S. Kino, "Solid immersion microscope," Appl. Phys. Lett. 57, 2615-2626 (1990).
[CrossRef]

Kolesik, M.

M. Kolesik and J. V. Moloney, "Nonlinear optical pulse propagation simulation: From Maxwell’s to unidirectional equations," Phys. Rev. E 70, 036604 (2004).
[CrossRef]

Koschny, T.

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, T. Koschny, C. M. Soukoulis, "Magnetic Metamaterials at Telecommunication and Visible Frequencies," Phys. Rev. Lett. 95, 203901 (2005).
[CrossRef] [PubMed]

Kostelak, R. L.

E. Betzig, J. K. Trautmann, T. D. Harris, J. S. Weiner, R. L. Kostelak, "Breaking the diffraction barrier: optical microscopy on a nanometric scale," Science 251, 1468-1450 (1991).
[CrossRef] [PubMed]

Lee, H.

N. Fang, H. Lee, C. Sun, X. Zhang, "SubDiffraction-Limited Optical Imaging with a Silver Superlens," Science 308, 534-537 (2005).
[CrossRef] [PubMed]

Linden, S.

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, T. Koschny, C. M. Soukoulis, "Magnetic Metamaterials at Telecommunication and Visible Frequencies," Phys. Rev. Lett. 95, 203901 (2005).
[CrossRef] [PubMed]

G. Dolling, C. Enkrich, M. Wegener, J. Zhou, C.M. Soukoulis, S. Linden, "Cut-wire pairs and plate pairs as magnetic atoms for optical metamaterials," Opt. Lett 30, 3198-3200 (2005).
[CrossRef] [PubMed]

Lu, W. T.

P. V. Parimi, W. T. Lu, P. Vodo and S. Sridhar, "Photonic crystals: Imaging by flat lens using negative refraction," Nature 426, 404-404 (2003).
[CrossRef] [PubMed]

Lu, Z.

Z. Lu, J.A. Murakowski, C. A. Schuetz, S. Shi, G. J. Schneider, and D. W. Prather, "Three-Dimensional Subwavelength Imaging by a Photonic-Crystal Flat Lens Using Negative Refraction at Microwave Frequencies," Phys. Rev. Lett. 95, 153901 (2005).
[CrossRef] [PubMed]

Lucchetti, L.

L. Lucchetti, M. Gentili, and F. Simoni, "Pretransportal enhancement of the optical nonlinearity of thin dye-doped liquid crystals in the nematic phase," Appl. Phys. Lett. 86, 151117 (2005).
[CrossRef]

Luo, C.

C. Luo, S. G. Johnson, and J. D. Joannopoulos, "Subwavelength imaging in photonic crystals," Phys. Rev. B 68, 045115 (2003).
[CrossRef]

Mandel, P.

Q. Thommen and P. Mandel, "Electromagnetically Induced Left Handedness in Optically Excited Four-Level Atomic Media", Phys. Rev. Lett. 96, 053601 (2006).
[CrossRef] [PubMed]

Mansfield, S. M.

S. M. Mansfield and G. S. Kino, "Solid immersion microscope," Appl. Phys. Lett. 57, 2615-2626 (1990).
[CrossRef]

Melville, D.

Moloney, J. V.

M. Kolesik and J. V. Moloney, "Nonlinear optical pulse propagation simulation: From Maxwell’s to unidirectional equations," Phys. Rev. E 70, 036604 (2004).
[CrossRef]

Mulot, M.

A. Berrier, M. Mulot, M. Swillo, M. Qiu, L. Thyln, A. Talneau, and S. Anand, "Negative Refraction at Infrared Wavelengths in a Two-Dimensional Photonic Crystal," Phys. Rev. Lett. 93, 073902 (2004).
[CrossRef] [PubMed]

Murakowski, J.A.

Z. Lu, J.A. Murakowski, C. A. Schuetz, S. Shi, G. J. Schneider, and D. W. Prather, "Three-Dimensional Subwavelength Imaging by a Photonic-Crystal Flat Lens Using Negative Refraction at Microwave Frequencies," Phys. Rev. Lett. 95, 153901 (2005).
[CrossRef] [PubMed]

Mysyrowicz, A.

G. M. Gale and A. Mysyrowicz, "Direct creation of excitonic molecules in CuCl by giant two-photon absorption," Phys. Rev. Lett. 32, 737-740 (1974).
[CrossRef]

Notomi, M.

M. Notomi, "Theory of light propagation in strongly modulated photonic crystals: Refractionlike behavior in the vicinity of the photonic band gap," Phys. Rev. B 62, 10696-10705 (2000).
[CrossRef]

Ozbay, E.

E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopolou, and C. M. Soukoulis, "Subwavelength Resolution in a Two- Dimensional Photonic-Crystal-Based Superlens," Phys. Rev. Lett. 91, 207401 (2003).
[CrossRef] [PubMed]

E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopoulou, and C. M. Soukoulis, "Electromagnetic waves: Negative refraction by photonic crystals," Nature 423, 604-605 (2003).
[CrossRef] [PubMed]

Parimi, P. V.

P. V. Parimi, W. T. Lu, P. Vodo and S. Sridhar, "Photonic crystals: Imaging by flat lens using negative refraction," Nature 426, 404-404 (2003).
[CrossRef] [PubMed]

Pendry, J. B.

D. R. Smith, D. Schurig, M. Rosenbluth, S. Schultz, S. A. Ramakrishna, and J. B. Pendry, "Limitations on subdiffraction imaging with a negative refractive index slab," Appl. Phys. Lett. 82, 1506-1508 (2003).
[CrossRef]

J. B. Pendry, "Negative refraction makes perfect lens," Phys. Rev. Lett. 85, 3966-3969 (2000).
[CrossRef] [PubMed]

Petrovic, J.

N. Grigorenko, A. K. Geim, H. F. Gleeson, Y. Zhang, A. A. Firsov, I. Y. Khrushchev, and J. Petrovic, "Nanofabricated media with negative permeability at visible frequencies," Nature 438, 335-338 (2005).
[CrossRef] [PubMed]

Prather, D. W.

Z. Lu, J.A. Murakowski, C. A. Schuetz, S. Shi, G. J. Schneider, and D. W. Prather, "Three-Dimensional Subwavelength Imaging by a Photonic-Crystal Flat Lens Using Negative Refraction at Microwave Frequencies," Phys. Rev. Lett. 95, 153901 (2005).
[CrossRef] [PubMed]

Qiu, M.

A. Berrier, M. Mulot, M. Swillo, M. Qiu, L. Thyln, A. Talneau, and S. Anand, "Negative Refraction at Infrared Wavelengths in a Two-Dimensional Photonic Crystal," Phys. Rev. Lett. 93, 073902 (2004).
[CrossRef] [PubMed]

Ramakrishna, S. A.

D. R. Smith, D. Schurig, M. Rosenbluth, S. Schultz, S. A. Ramakrishna, and J. B. Pendry, "Limitations on subdiffraction imaging with a negative refractive index slab," Appl. Phys. Lett. 82, 1506-1508 (2003).
[CrossRef]

Rosenbluth, M.

D. R. Smith, D. Schurig, M. Rosenbluth, S. Schultz, S. A. Ramakrishna, and J. B. Pendry, "Limitations on subdiffraction imaging with a negative refractive index slab," Appl. Phys. Lett. 82, 1506-1508 (2003).
[CrossRef]

Sarychev, A.K.

V. M. Shalaev, W. Cai, U. Chettiar, H. K. Yuan, A.K. Sarychev, V. P. Drachev, and A. V. Kildishev, "Negative index of refraction in optical metamaterials," Opt. Lett 30, 3356-3358 (2005).
[CrossRef]

Schmidt, F.

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, T. Koschny, C. M. Soukoulis, "Magnetic Metamaterials at Telecommunication and Visible Frequencies," Phys. Rev. Lett. 95, 203901 (2005).
[CrossRef] [PubMed]

Schneider, G. J.

Z. Lu, J.A. Murakowski, C. A. Schuetz, S. Shi, G. J. Schneider, and D. W. Prather, "Three-Dimensional Subwavelength Imaging by a Photonic-Crystal Flat Lens Using Negative Refraction at Microwave Frequencies," Phys. Rev. Lett. 95, 153901 (2005).
[CrossRef] [PubMed]

Schuetz, C. A.

Z. Lu, J.A. Murakowski, C. A. Schuetz, S. Shi, G. J. Schneider, and D. W. Prather, "Three-Dimensional Subwavelength Imaging by a Photonic-Crystal Flat Lens Using Negative Refraction at Microwave Frequencies," Phys. Rev. Lett. 95, 153901 (2005).
[CrossRef] [PubMed]

Schultz, S.

D. R. Smith, D. Schurig, M. Rosenbluth, S. Schultz, S. A. Ramakrishna, and J. B. Pendry, "Limitations on subdiffraction imaging with a negative refractive index slab," Appl. Phys. Lett. 82, 1506-1508 (2003).
[CrossRef]

R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental Verification of a Negative Index of Refraction," Science 292, 77-79 (2001).
[CrossRef] [PubMed]

Schurig, D.

D. R. Smith, D. Schurig, M. Rosenbluth, S. Schultz, S. A. Ramakrishna, and J. B. Pendry, "Limitations on subdiffraction imaging with a negative refractive index slab," Appl. Phys. Lett. 82, 1506-1508 (2003).
[CrossRef]

Shalaev, V. M.

V. M. Shalaev, W. Cai, U. Chettiar, H. K. Yuan, A.K. Sarychev, V. P. Drachev, and A. V. Kildishev, "Negative index of refraction in optical metamaterials," Opt. Lett 30, 3356-3358 (2005).
[CrossRef]

Shelby, R. A.

R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental Verification of a Negative Index of Refraction," Science 292, 77-79 (2001).
[CrossRef] [PubMed]

Shi, S.

Z. Lu, J.A. Murakowski, C. A. Schuetz, S. Shi, G. J. Schneider, and D. W. Prather, "Three-Dimensional Subwavelength Imaging by a Photonic-Crystal Flat Lens Using Negative Refraction at Microwave Frequencies," Phys. Rev. Lett. 95, 153901 (2005).
[CrossRef] [PubMed]

Simoni, F.

L. Lucchetti, M. Gentili, and F. Simoni, "Pretransportal enhancement of the optical nonlinearity of thin dye-doped liquid crystals in the nematic phase," Appl. Phys. Lett. 86, 151117 (2005).
[CrossRef]

Smith, D. R.

D. R. Smith, D. Schurig, M. Rosenbluth, S. Schultz, S. A. Ramakrishna, and J. B. Pendry, "Limitations on subdiffraction imaging with a negative refractive index slab," Appl. Phys. Lett. 82, 1506-1508 (2003).
[CrossRef]

R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental Verification of a Negative Index of Refraction," Science 292, 77-79 (2001).
[CrossRef] [PubMed]

Soukoulis, C. M.

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, T. Koschny, C. M. Soukoulis, "Magnetic Metamaterials at Telecommunication and Visible Frequencies," Phys. Rev. Lett. 95, 203901 (2005).
[CrossRef] [PubMed]

E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopolou, and C. M. Soukoulis, "Subwavelength Resolution in a Two- Dimensional Photonic-Crystal-Based Superlens," Phys. Rev. Lett. 91, 207401 (2003).
[CrossRef] [PubMed]

E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopoulou, and C. M. Soukoulis, "Electromagnetic waves: Negative refraction by photonic crystals," Nature 423, 604-605 (2003).
[CrossRef] [PubMed]

Soukoulis, C.M.

G. Dolling, C. Enkrich, M. Wegener, J. Zhou, C.M. Soukoulis, S. Linden, "Cut-wire pairs and plate pairs as magnetic atoms for optical metamaterials," Opt. Lett 30, 3198-3200 (2005).
[CrossRef] [PubMed]

Sridhar, S.

P. V. Parimi, W. T. Lu, P. Vodo and S. Sridhar, "Photonic crystals: Imaging by flat lens using negative refraction," Nature 426, 404-404 (2003).
[CrossRef] [PubMed]

Sun, C.

N. Fang, H. Lee, C. Sun, X. Zhang, "SubDiffraction-Limited Optical Imaging with a Silver Superlens," Science 308, 534-537 (2005).
[CrossRef] [PubMed]

Swartzlander, G. A.

Swillo, M.

A. Berrier, M. Mulot, M. Swillo, M. Qiu, L. Thyln, A. Talneau, and S. Anand, "Negative Refraction at Infrared Wavelengths in a Two-Dimensional Photonic Crystal," Phys. Rev. Lett. 93, 073902 (2004).
[CrossRef] [PubMed]

Talneau, A.

A. Berrier, M. Mulot, M. Swillo, M. Qiu, L. Thyln, A. Talneau, and S. Anand, "Negative Refraction at Infrared Wavelengths in a Two-Dimensional Photonic Crystal," Phys. Rev. Lett. 93, 073902 (2004).
[CrossRef] [PubMed]

Thommen, Q.

Q. Thommen and P. Mandel, "Electromagnetically Induced Left Handedness in Optically Excited Four-Level Atomic Media", Phys. Rev. Lett. 96, 053601 (2006).
[CrossRef] [PubMed]

Thyln, L.

A. Berrier, M. Mulot, M. Swillo, M. Qiu, L. Thyln, A. Talneau, and S. Anand, "Negative Refraction at Infrared Wavelengths in a Two-Dimensional Photonic Crystal," Phys. Rev. Lett. 93, 073902 (2004).
[CrossRef] [PubMed]

Trautmann, J. K.

E. Betzig, J. K. Trautmann, T. D. Harris, J. S. Weiner, R. L. Kostelak, "Breaking the diffraction barrier: optical microscopy on a nanometric scale," Science 251, 1468-1450 (1991).
[CrossRef] [PubMed]

Veselago, V. G.

V. G. Veselago, "The electrodynamics of substances with simultaneously negative values of ∑ and ," Soviet Phys. Usp. 10, 509-518 (1968) [Usp. Fiz. Nauk 92, 517-526 (1967).].
[CrossRef]

Vodo, P.

P. V. Parimi, W. T. Lu, P. Vodo and S. Sridhar, "Photonic crystals: Imaging by flat lens using negative refraction," Nature 426, 404-404 (2003).
[CrossRef] [PubMed]

Wegener, M.

G. Dolling, C. Enkrich, M. Wegener, J. Zhou, C.M. Soukoulis, S. Linden, "Cut-wire pairs and plate pairs as magnetic atoms for optical metamaterials," Opt. Lett 30, 3198-3200 (2005).
[CrossRef] [PubMed]

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, T. Koschny, C. M. Soukoulis, "Magnetic Metamaterials at Telecommunication and Visible Frequencies," Phys. Rev. Lett. 95, 203901 (2005).
[CrossRef] [PubMed]

Weiner, J. S.

E. Betzig, J. K. Trautmann, T. D. Harris, J. S. Weiner, R. L. Kostelak, "Breaking the diffraction barrier: optical microscopy on a nanometric scale," Science 251, 1468-1450 (1991).
[CrossRef] [PubMed]

Yoon, Y.-K.

Yuan, H. K.

V. M. Shalaev, W. Cai, U. Chettiar, H. K. Yuan, A.K. Sarychev, V. P. Drachev, and A. V. Kildishev, "Negative index of refraction in optical metamaterials," Opt. Lett 30, 3356-3358 (2005).
[CrossRef]

Zhang, X.

N. Fang, H. Lee, C. Sun, X. Zhang, "SubDiffraction-Limited Optical Imaging with a Silver Superlens," Science 308, 534-537 (2005).
[CrossRef] [PubMed]

Zhang, Y.

N. Grigorenko, A. K. Geim, H. F. Gleeson, Y. Zhang, A. A. Firsov, I. Y. Khrushchev, and J. Petrovic, "Nanofabricated media with negative permeability at visible frequencies," Nature 438, 335-338 (2005).
[CrossRef] [PubMed]

Zhou, J.

G. Dolling, C. Enkrich, M. Wegener, J. Zhou, C.M. Soukoulis, S. Linden, "Cut-wire pairs and plate pairs as magnetic atoms for optical metamaterials," Opt. Lett 30, 3198-3200 (2005).
[CrossRef] [PubMed]

Zhou, J. F.

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, T. Koschny, C. M. Soukoulis, "Magnetic Metamaterials at Telecommunication and Visible Frequencies," Phys. Rev. Lett. 95, 203901 (2005).
[CrossRef] [PubMed]

Zschiedrich, L.

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, T. Koschny, C. M. Soukoulis, "Magnetic Metamaterials at Telecommunication and Visible Frequencies," Phys. Rev. Lett. 95, 203901 (2005).
[CrossRef] [PubMed]

Appl. Phys. Lett. (3)

S. M. Mansfield and G. S. Kino, "Solid immersion microscope," Appl. Phys. Lett. 57, 2615-2626 (1990).
[CrossRef]

L. Lucchetti, M. Gentili, and F. Simoni, "Pretransportal enhancement of the optical nonlinearity of thin dye-doped liquid crystals in the nematic phase," Appl. Phys. Lett. 86, 151117 (2005).
[CrossRef]

D. R. Smith, D. Schurig, M. Rosenbluth, S. Schultz, S. A. Ramakrishna, and J. B. Pendry, "Limitations on subdiffraction imaging with a negative refractive index slab," Appl. Phys. Lett. 82, 1506-1508 (2003).
[CrossRef]

Nature (3)

P. V. Parimi, W. T. Lu, P. Vodo and S. Sridhar, "Photonic crystals: Imaging by flat lens using negative refraction," Nature 426, 404-404 (2003).
[CrossRef] [PubMed]

E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopoulou, and C. M. Soukoulis, "Electromagnetic waves: Negative refraction by photonic crystals," Nature 423, 604-605 (2003).
[CrossRef] [PubMed]

N. Grigorenko, A. K. Geim, H. F. Gleeson, Y. Zhang, A. A. Firsov, I. Y. Khrushchev, and J. Petrovic, "Nanofabricated media with negative permeability at visible frequencies," Nature 438, 335-338 (2005).
[CrossRef] [PubMed]

Opt. Express (2)

Opt. Lett (2)

G. Dolling, C. Enkrich, M. Wegener, J. Zhou, C.M. Soukoulis, S. Linden, "Cut-wire pairs and plate pairs as magnetic atoms for optical metamaterials," Opt. Lett 30, 3198-3200 (2005).
[CrossRef] [PubMed]

V. M. Shalaev, W. Cai, U. Chettiar, H. K. Yuan, A.K. Sarychev, V. P. Drachev, and A. V. Kildishev, "Negative index of refraction in optical metamaterials," Opt. Lett 30, 3356-3358 (2005).
[CrossRef]

Opt. Lett. (2)

Phys. Rev. B (2)

C. Luo, S. G. Johnson, and J. D. Joannopoulos, "Subwavelength imaging in photonic crystals," Phys. Rev. B 68, 045115 (2003).
[CrossRef]

M. Notomi, "Theory of light propagation in strongly modulated photonic crystals: Refractionlike behavior in the vicinity of the photonic band gap," Phys. Rev. B 62, 10696-10705 (2000).
[CrossRef]

Phys. Rev. E (1)

M. Kolesik and J. V. Moloney, "Nonlinear optical pulse propagation simulation: From Maxwell’s to unidirectional equations," Phys. Rev. E 70, 036604 (2004).
[CrossRef]

Phys. Rev. Lett. (8)

G. M. Gale and A. Mysyrowicz, "Direct creation of excitonic molecules in CuCl by giant two-photon absorption," Phys. Rev. Lett. 32, 737-740 (1974).
[CrossRef]

E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopolou, and C. M. Soukoulis, "Subwavelength Resolution in a Two- Dimensional Photonic-Crystal-Based Superlens," Phys. Rev. Lett. 91, 207401 (2003).
[CrossRef] [PubMed]

A. Husakou and J. Herrmann, "Focusing of Scanning Light Beams below the Diffraction Limit without Near- Field Spatial Control Using a Saturable Absorber and a Negative-Refraction Material," Phys. Rev. Lett. 96, 013902 (2006).
[CrossRef] [PubMed]

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, T. Koschny, C. M. Soukoulis, "Magnetic Metamaterials at Telecommunication and Visible Frequencies," Phys. Rev. Lett. 95, 203901 (2005).
[CrossRef] [PubMed]

A. Berrier, M. Mulot, M. Swillo, M. Qiu, L. Thyln, A. Talneau, and S. Anand, "Negative Refraction at Infrared Wavelengths in a Two-Dimensional Photonic Crystal," Phys. Rev. Lett. 93, 073902 (2004).
[CrossRef] [PubMed]

Z. Lu, J.A. Murakowski, C. A. Schuetz, S. Shi, G. J. Schneider, and D. W. Prather, "Three-Dimensional Subwavelength Imaging by a Photonic-Crystal Flat Lens Using Negative Refraction at Microwave Frequencies," Phys. Rev. Lett. 95, 153901 (2005).
[CrossRef] [PubMed]

Q. Thommen and P. Mandel, "Electromagnetically Induced Left Handedness in Optically Excited Four-Level Atomic Media", Phys. Rev. Lett. 96, 053601 (2006).
[CrossRef] [PubMed]

J. B. Pendry, "Negative refraction makes perfect lens," Phys. Rev. Lett. 85, 3966-3969 (2000).
[CrossRef] [PubMed]

Science (3)

R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental Verification of a Negative Index of Refraction," Science 292, 77-79 (2001).
[CrossRef] [PubMed]

E. Betzig, J. K. Trautmann, T. D. Harris, J. S. Weiner, R. L. Kostelak, "Breaking the diffraction barrier: optical microscopy on a nanometric scale," Science 251, 1468-1450 (1991).
[CrossRef] [PubMed]

N. Fang, H. Lee, C. Sun, X. Zhang, "SubDiffraction-Limited Optical Imaging with a Silver Superlens," Science 308, 534-537 (2005).
[CrossRef] [PubMed]

Soviet Phys. Usp. (1)

V. G. Veselago, "The electrodynamics of substances with simultaneously negative values of ∑ and ," Soviet Phys. Usp. 10, 509-518 (1968) [Usp. Fiz. Nauk 92, 517-526 (1967).].
[CrossRef]

Other (5)

M. A. Paesler and P. J. Moyer, Near-field optics: theory, instrumentation and applications, John Wiley and Sons, New York (1996).

A. KK. Wong, Resolution enhancement techniques in optical lithography (SPIE Press, Bellingham, Washington, 2001).
[CrossRef]

T. W. McDaniel, Handbook of magneto-optical data recording: materials, subsystems, techniques (Noyes publishing, Westwood, 1997).

C. Luo, S.G. Johnson, J.D. Joannopoulos, and J.B. Pendry, "All-angle negative refraction without negative effective index," Phys. Rev. B 65, 201104(R) (2002).
[CrossRef]

K. Sakoda, Optical properties of photonic crystals, Springer, 2001.

Supplementary Material (1)

» Media 1: MOV (121 KB)     

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Figures (8)

Fig. 1.
Fig. 1.

The general scheme of the proposed setup (a) and the evolution with propagation of evanescent (Eevan ) and propagating (Eprop ) Fourier components (b).

Fig. 2.
Fig. 2.

Superfocusing in the effective-medium theory with a negative refractive index. The spatial spectrum |E(kx , ky )| is shown in (a) after the nonlinear layer (red, surface I) and after the NRM layer (green, surface II). The spatial distribution of the energy density after the slab is shown in (b). The maximum change of the refractive index is ΔnKerrmax/n 0=n2 Imax /n 0=0.033, the linear refractive index of the Kerr medium is n 0=3.0, the thickness of the nonlinear layer is L Kerr=2λ. The thickness of the NRM layer is LNRM =0.6λ, FWHM in =1.5λ and ε=μ=-1-0.0001(i+1).

Fig. 3.
Fig. 3.

Evolution of the transverse spectrum (left panel) and of the spatial shape (right panel) with propagation. Positions Z=0.0..2.0λ correspond to propagation through the nonlinear layer, positions Z=2.0..3.0λ correspond to subsequent propagation through the NRM. The parameters are the same as in Fig. 2. The spatial distribution is normalized to the maximum at each distance position. The animation shows the transverse spectrum and the spatial shape for different positions inside the nonlinear layer and the NRM (121 KB).

Fig. 4.
Fig. 4.

Superfocusing in the effective-medium theory with a negative refractive index, for a weaker nonlinearity. Denotations and parameters are the same as in Fig. 2, except for ΔnKerrmax/n 0=n 2 Imax /n 0=0.003, LNRM =1.3λ, and FWHM in =1.5λ.

Fig. 5.
Fig. 5.

The dependence of the spot area on the deviations δε and δμ of the parameters ε and μ from the ideal case ε=μ=-1. Cyan dash-dotted, green dashed, red solid, and black dotted curves correspond to deviations in Re(ε), Re(μ), Im(ε,μ), and all of the above parameters, correspondingly. The explicit parameters are for the cyan dash-dotted curve: δμ=-0.00001(i+1);δε=-0.00001i-δ; for the green dashed curve: δε=-0.00001(i+1);δμ=-0.00001i-δ; for the red solid curve: δε=δμ=-0.00001-δi; and for the black dotted curve: δε=δμ=-δ (i+1). The NRM length corresponds to the optimum (smallest spot area) in each case. Other parameters are the same as in Fig. 2.

Fig. 6.
Fig. 6.

Photonic crystal structure (a) and transmission into 0th Bragg order as a function of the transverse wavevector (b). The considered design is a silicon substrate having 5 layers of holes as shown in (a), with ε=12.5+0.01i at λ=1000 nm, a=260 nm, d=229 nm, b=110 nm; a, b, d and λ can be scaled by a common factor.

Fig. 7.
Fig. 7.

Superfocusing in a hexagonal air-holes lattice PC with all-angle negative refraction. The transverse spectrum (solid, red) and the phase (dashed, green) of the field Hz is given in (a), and the spatial distribution of the field is shown in (b). The input beam has a Gaussian shape with a FWHM of 1.0λ. The maximum nonlinear change of the refractive index is δnKerrmax/n 0=0.066, the linear refractive index of the Kerr medium is n 0=3.0, the thickness of the nonlinear layer is L Kerr=1.9λ.

Fig. 8.
Fig. 8.

Superfocusing with a two-photon-absorption layer, with (a) aNRMin the framework of the effective-medium theory and (b) provided by a photonic crystal. In both (a) and (b), the spatial distribution of the focused field is shown. The dimensionless parameter βImaxL which characterizes the two-photon absorber is 1.0 in (a) and 1.4 in (b), FWHM in =1.0λ both in (a) and (b). In (a), ε=μ=-1-0.0001(i+1) and LNRM =1.0λ. In (b), the photonic crystal is a 4-layer array of cross-shaped air holes in silicon; for details see [23, 31].

Equations (5)

Equations on this page are rendered with MathJax. Learn more.

2 E ( k x , k y , z ) z 2 = k z 2 E ( k x , k y , z ) + k 0 2 P NL ( k x , k y , z )
E ( k x , k y , z ) = E ( k x , k y , 0 ) exp ( i k z z ) k 0 2 P NL ( k x , k y , 0 ) 2 k z ε 0 [ exp ( i n 0 k 0 z ) exp ( i k z z ) n 0 k 0 k z +
exp ( i n 0 k 0 z ) exp ( i k z z + i k z L + i n 0 k 0 L ) n 0 k 0 + k z ]
E ( k x , k y , z ) z = i k z E ( k x , k y , z ) + i k 0 2 2 k z ε 0 P NL ( k x , k y , z ) .
T s , p = 4 [ ( 2 + κ s , p ) e i q z L + ( 2 κ s , p ) exp i q z L ] 1

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