Abstract

Since the concept of left-handed material has been introduced, many systems have been presented that exhibit similar properties to these materials, such as negative group velocity, negative refraction, or negative diffraction. We propose what we believe to be a new approximation of a slab of left-handed metamaterial by a system containing three lenses in an arrangement of two identical telescopes. We show that the twin telescopes and the negative index slab share the same ray transfer matrix. We discuss the limits of the approximation and present examples for which it is fully valid.

© 2009 Optical Society of America

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  1. D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184-4187 (2000).
    [CrossRef] [PubMed]
  2. G. Dolling, M. Wegener, C. M. Soukoulis, and S. Linden, “Negative-index metamaterial at 780 nm wavelength,” Opt. Lett. 32, 53-55 (2007).
    [CrossRef]
  3. V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of ε and μ,” Sov. Phys. Usp. 10, 509-514 (1968).
    [CrossRef]
  4. M.-C. Yang and K. J. Webb, “Poynting vector analysis of a superlens,” Opt. Lett. 30, 2382-2384 (2005).
    [CrossRef] [PubMed]
  5. V. Klimov, “Novel approach to a perfect lens,” JETP Lett. 89, 229-232 (2009).
    [CrossRef]
  6. J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966-3969 (2000).
    [CrossRef] [PubMed]
  7. K. Aydin, M. Guven, L. Kafesaki, C. Zhang, M. Soukoulis, and M. Ozbay, “Experimental observation of true left-handed transmission peaks in metamaterials,” Opt. Lett. 29, 2623-2625 (2004).
    [CrossRef] [PubMed]
  8. C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic metamaterials at telecommunication and visible frequencies,” Phys. Rev. Lett. 95, 203901 (2005).
    [CrossRef] [PubMed]
  9. T. F. Gundogdu, I. Tsiapa, A. Kostopoulos, G. Konstantinidis, N. Katsarakis, R. S. Penciu, M. Kafesaki, E. N. Economou, T. Koschny, and C. M. Soukoulis, “Experimental demonstration of negative magnetic permeability in the far-infrared frequency regime,” Appl. Phys. Lett. 89, 084103 (2006).
    [CrossRef]
  10. R. Merlin, “Analytical solution of the almost-perfect-lens problem,” Appl. Phys. Lett. 84, 1290-1292 (2004).
    [CrossRef]
  11. N. A. Kuhta, V. A. Podolskiy, and A. L. Efros, “Far-field imaging by a planar lens: diffraction versus superresolution,” Phys. Rev. B 76, 205102 (2007).
    [CrossRef]
  12. R. Merlin, “Metamaterials and the Landau-Lifshitz permeability argument: large permittivity begets high-frequency magnetism,” Proc. Natl. Acad. Sci. U.S.A. 106, 1693-1698 (2009).
    [CrossRef] [PubMed]
  13. R. Iliew, C. Etrich, U. Peschel, F. Lederer, M. Augustin, H.-J. Fuchs, D. Schelle, E.-B. Kley, S. Nolte, and A. Tünnermann, “Diffractionless propagation of light in a low-index photonic-crystal film,” Appl. Phys. Lett. 85, 5854-5856 (2004).
    [CrossRef]
  14. K. Staliunas and R. Herrero, “Nondiffractive propagation of light in photonic crystals,” Phys. Rev. E 73, 016601 (2006).
    [CrossRef]
  15. K. Staliunas, C. Serrat, R. Herrero, C. Cojocaru, and J. Trull, “Subdiffractive light pulses in photonic crystals,” Phys. Rev. E 74, 016605 (2006).
    [CrossRef]
  16. P. Kockaert, P. Tassin, G. van der Sande, I. Veretennicoff, and M. Tlidi, “Negative diffraction pattern dynamics in nonlinear cavities with left-handed materials,” Phys. Rev. A 74, 033822 (2006).
    [CrossRef]
  17. L. Gelens, G. Van der Sande, P. Tassin, M. Tlidi, P. Kockaert, D. Gomila, I. Veretennicoff, and J. Danckaert, “Impact of nonlocal interactions in dissipative systems: towards minimal-sized localized structures,” Phys. Rev. A 75, 063812 (2007).
    [CrossRef]
  18. P. Tassin, L. Gelens, J. Danckaert, I. Veretennicoff, G. Van der Sande, P. Kockaert, and M. Tlidi, “Dissipative structures in left-handed material cavity optics,” Chaos 17, 037116 (2007).
    [CrossRef] [PubMed]
  19. M. Ballav and A. R. Chowdhury, On a Study of Diffraction and Dispersion Managed Soliton in a Cylindrical Media, Vol. PIER-63 of Progress In Electromagnetics Research (EMW, 2006), pp. 33-50.
  20. A. Boardman, N. King, R. Mitchell-Thomas, V. Malnev, and Y. Rapoport, “Gain control and diffraction-managed solitons in metamaterials,” Metamaterials 2, 145-154 (2008).
    [CrossRef]
  21. A. Siegman, Lasers (University Science Books, 1986).
  22. H. Kogelnik, “On the propagation of Gaussian beams of light through lenslike media including those with a loss or gain variation,” Appl. Opt. 4, 1562-1569 (1965).
    [CrossRef]
  23. P. Tassin, I. Veretennicoff, and G. Van der Sande, “Veselago's lens consisting of left-handed materials with arbitrary index of refraction,” Opt. Commun. 264, 130-134 (2006).
    [CrossRef]
  24. X. Liu and K.-H. Brenner, “Minimal optical decomposition of ray transfer matrices,” Appl. Opt. 47, E88-E98 (2008).
    [CrossRef] [PubMed]
  25. C.Krowne and Y.Zhang, eds., Physics of Negative Refraction and Negative Index Materials: Optical and Electronic Aspects and Diversified Approaches (Springer, 2007).
  26. O. E. Martinez, “Design of high-power ultrashort pulse amplifiers by expansion and recompression,” IEEE J. Quantum Electron. 23, 1385-1387 (1987).
    [CrossRef]
  27. P. Tassin, G. Van der Sande, N. Veretenov, P. Kockaert, I. Veretennicoff, and M. Tlidi, “Three-dimensional structures in nonlinear cavities containing left-handed materials,” Opt. Express 14, 9338-9343 (2006).
    [CrossRef] [PubMed]
  28. K. Ikeda and M. Mizuno, “Modeling of nonlinear Fabry-Perot resonators by difference-differential equations,” IEEE J. Quantum Electron. 21, 1429-1434 (1985).
    [CrossRef]
  29. L. A. Lugiato and R. Lefever, “Spatial dissipative structures in passive optical systems,” Phys. Rev. Lett. 58, 2209-2211 (1987).
    [CrossRef] [PubMed]
  30. R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292, 77-79 (2001).
    [CrossRef] [PubMed]

2009

R. Merlin, “Metamaterials and the Landau-Lifshitz permeability argument: large permittivity begets high-frequency magnetism,” Proc. Natl. Acad. Sci. U.S.A. 106, 1693-1698 (2009).
[CrossRef] [PubMed]

V. Klimov, “Novel approach to a perfect lens,” JETP Lett. 89, 229-232 (2009).
[CrossRef]

2008

A. Boardman, N. King, R. Mitchell-Thomas, V. Malnev, and Y. Rapoport, “Gain control and diffraction-managed solitons in metamaterials,” Metamaterials 2, 145-154 (2008).
[CrossRef]

X. Liu and K.-H. Brenner, “Minimal optical decomposition of ray transfer matrices,” Appl. Opt. 47, E88-E98 (2008).
[CrossRef] [PubMed]

2007

G. Dolling, M. Wegener, C. M. Soukoulis, and S. Linden, “Negative-index metamaterial at 780 nm wavelength,” Opt. Lett. 32, 53-55 (2007).
[CrossRef]

L. Gelens, G. Van der Sande, P. Tassin, M. Tlidi, P. Kockaert, D. Gomila, I. Veretennicoff, and J. Danckaert, “Impact of nonlocal interactions in dissipative systems: towards minimal-sized localized structures,” Phys. Rev. A 75, 063812 (2007).
[CrossRef]

P. Tassin, L. Gelens, J. Danckaert, I. Veretennicoff, G. Van der Sande, P. Kockaert, and M. Tlidi, “Dissipative structures in left-handed material cavity optics,” Chaos 17, 037116 (2007).
[CrossRef] [PubMed]

N. A. Kuhta, V. A. Podolskiy, and A. L. Efros, “Far-field imaging by a planar lens: diffraction versus superresolution,” Phys. Rev. B 76, 205102 (2007).
[CrossRef]

2006

T. F. Gundogdu, I. Tsiapa, A. Kostopoulos, G. Konstantinidis, N. Katsarakis, R. S. Penciu, M. Kafesaki, E. N. Economou, T. Koschny, and C. M. Soukoulis, “Experimental demonstration of negative magnetic permeability in the far-infrared frequency regime,” Appl. Phys. Lett. 89, 084103 (2006).
[CrossRef]

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

K. Staliunas, C. Serrat, R. Herrero, C. Cojocaru, and J. Trull, “Subdiffractive light pulses in photonic crystals,” Phys. Rev. E 74, 016605 (2006).
[CrossRef]

P. Kockaert, P. Tassin, G. van der Sande, I. Veretennicoff, and M. Tlidi, “Negative diffraction pattern dynamics in nonlinear cavities with left-handed materials,” Phys. Rev. A 74, 033822 (2006).
[CrossRef]

P. Tassin, I. Veretennicoff, and G. Van der Sande, “Veselago's lens consisting of left-handed materials with arbitrary index of refraction,” Opt. Commun. 264, 130-134 (2006).
[CrossRef]

P. Tassin, G. Van der Sande, N. Veretenov, P. Kockaert, I. Veretennicoff, and M. Tlidi, “Three-dimensional structures in nonlinear cavities containing left-handed materials,” Opt. Express 14, 9338-9343 (2006).
[CrossRef] [PubMed]

2005

M.-C. Yang and K. J. Webb, “Poynting vector analysis of a superlens,” Opt. Lett. 30, 2382-2384 (2005).
[CrossRef] [PubMed]

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic metamaterials at telecommunication and visible frequencies,” Phys. Rev. Lett. 95, 203901 (2005).
[CrossRef] [PubMed]

2004

R. Merlin, “Analytical solution of the almost-perfect-lens problem,” Appl. Phys. Lett. 84, 1290-1292 (2004).
[CrossRef]

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

K. Aydin, M. Guven, L. Kafesaki, C. Zhang, M. Soukoulis, and M. Ozbay, “Experimental observation of true left-handed transmission peaks in metamaterials,” Opt. Lett. 29, 2623-2625 (2004).
[CrossRef] [PubMed]

2001

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

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

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184-4187 (2000).
[CrossRef] [PubMed]

1987

O. E. Martinez, “Design of high-power ultrashort pulse amplifiers by expansion and recompression,” IEEE J. Quantum Electron. 23, 1385-1387 (1987).
[CrossRef]

L. A. Lugiato and R. Lefever, “Spatial dissipative structures in passive optical systems,” Phys. Rev. Lett. 58, 2209-2211 (1987).
[CrossRef] [PubMed]

1985

K. Ikeda and M. Mizuno, “Modeling of nonlinear Fabry-Perot resonators by difference-differential equations,” IEEE J. Quantum Electron. 21, 1429-1434 (1985).
[CrossRef]

1968

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

1965

Augustin, M.

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

Aydin, K.

Ballav, M.

M. Ballav and A. R. Chowdhury, On a Study of Diffraction and Dispersion Managed Soliton in a Cylindrical Media, Vol. PIER-63 of Progress In Electromagnetics Research (EMW, 2006), pp. 33-50.

Boardman, A.

A. Boardman, N. King, R. Mitchell-Thomas, V. Malnev, and Y. Rapoport, “Gain control and diffraction-managed solitons in metamaterials,” Metamaterials 2, 145-154 (2008).
[CrossRef]

Brenner, K. -H.

Burger, S.

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic metamaterials at telecommunication and visible frequencies,” Phys. Rev. Lett. 95, 203901 (2005).
[CrossRef] [PubMed]

Chowdhury, A. R.

M. Ballav and A. R. Chowdhury, On a Study of Diffraction and Dispersion Managed Soliton in a Cylindrical Media, Vol. PIER-63 of Progress In Electromagnetics Research (EMW, 2006), pp. 33-50.

Cojocaru, C.

K. Staliunas, C. Serrat, R. Herrero, C. Cojocaru, and J. Trull, “Subdiffractive light pulses in photonic crystals,” Phys. Rev. E 74, 016605 (2006).
[CrossRef]

Danckaert, J.

P. Tassin, L. Gelens, J. Danckaert, I. Veretennicoff, G. Van der Sande, P. Kockaert, and M. Tlidi, “Dissipative structures in left-handed material cavity optics,” Chaos 17, 037116 (2007).
[CrossRef] [PubMed]

L. Gelens, G. Van der Sande, P. Tassin, M. Tlidi, P. Kockaert, D. Gomila, I. Veretennicoff, and J. Danckaert, “Impact of nonlocal interactions in dissipative systems: towards minimal-sized localized structures,” Phys. Rev. A 75, 063812 (2007).
[CrossRef]

Dolling, G.

Economou, E. N.

T. F. Gundogdu, I. Tsiapa, A. Kostopoulos, G. Konstantinidis, N. Katsarakis, R. S. Penciu, M. Kafesaki, E. N. Economou, T. Koschny, and C. M. Soukoulis, “Experimental demonstration of negative magnetic permeability in the far-infrared frequency regime,” Appl. Phys. Lett. 89, 084103 (2006).
[CrossRef]

Efros, A. L.

N. A. Kuhta, V. A. Podolskiy, and A. L. Efros, “Far-field imaging by a planar lens: diffraction versus superresolution,” Phys. Rev. B 76, 205102 (2007).
[CrossRef]

Enkrich, C.

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic metamaterials at telecommunication and visible frequencies,” Phys. Rev. Lett. 95, 203901 (2005).
[CrossRef] [PubMed]

Etrich, C.

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

Fuchs, H. -J.

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

Gelens, L.

P. Tassin, L. Gelens, J. Danckaert, I. Veretennicoff, G. Van der Sande, P. Kockaert, and M. Tlidi, “Dissipative structures in left-handed material cavity optics,” Chaos 17, 037116 (2007).
[CrossRef] [PubMed]

L. Gelens, G. Van der Sande, P. Tassin, M. Tlidi, P. Kockaert, D. Gomila, I. Veretennicoff, and J. Danckaert, “Impact of nonlocal interactions in dissipative systems: towards minimal-sized localized structures,” Phys. Rev. A 75, 063812 (2007).
[CrossRef]

Gomila, D.

L. Gelens, G. Van der Sande, P. Tassin, M. Tlidi, P. Kockaert, D. Gomila, I. Veretennicoff, and J. Danckaert, “Impact of nonlocal interactions in dissipative systems: towards minimal-sized localized structures,” Phys. Rev. A 75, 063812 (2007).
[CrossRef]

Gundogdu, T. F.

T. F. Gundogdu, I. Tsiapa, A. Kostopoulos, G. Konstantinidis, N. Katsarakis, R. S. Penciu, M. Kafesaki, E. N. Economou, T. Koschny, and C. M. Soukoulis, “Experimental demonstration of negative magnetic permeability in the far-infrared frequency regime,” Appl. Phys. Lett. 89, 084103 (2006).
[CrossRef]

Guven, M.

Herrero, R.

K. Staliunas, C. Serrat, R. Herrero, C. Cojocaru, and J. Trull, “Subdiffractive light pulses in photonic crystals,” Phys. Rev. E 74, 016605 (2006).
[CrossRef]

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

Ikeda, K.

K. Ikeda and M. Mizuno, “Modeling of nonlinear Fabry-Perot resonators by difference-differential equations,” IEEE J. Quantum Electron. 21, 1429-1434 (1985).
[CrossRef]

Iliew, R.

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

Kafesaki, L.

Kafesaki, M.

T. F. Gundogdu, I. Tsiapa, A. Kostopoulos, G. Konstantinidis, N. Katsarakis, R. S. Penciu, M. Kafesaki, E. N. Economou, T. Koschny, and C. M. Soukoulis, “Experimental demonstration of negative magnetic permeability in the far-infrared frequency regime,” Appl. Phys. Lett. 89, 084103 (2006).
[CrossRef]

Katsarakis, N.

T. F. Gundogdu, I. Tsiapa, A. Kostopoulos, G. Konstantinidis, N. Katsarakis, R. S. Penciu, M. Kafesaki, E. N. Economou, T. Koschny, and C. M. Soukoulis, “Experimental demonstration of negative magnetic permeability in the far-infrared frequency regime,” Appl. Phys. Lett. 89, 084103 (2006).
[CrossRef]

King, N.

A. Boardman, N. King, R. Mitchell-Thomas, V. Malnev, and Y. Rapoport, “Gain control and diffraction-managed solitons in metamaterials,” Metamaterials 2, 145-154 (2008).
[CrossRef]

Kley, E. -B.

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

Klimov, V.

V. Klimov, “Novel approach to a perfect lens,” JETP Lett. 89, 229-232 (2009).
[CrossRef]

Kockaert, P.

P. Tassin, L. Gelens, J. Danckaert, I. Veretennicoff, G. Van der Sande, P. Kockaert, and M. Tlidi, “Dissipative structures in left-handed material cavity optics,” Chaos 17, 037116 (2007).
[CrossRef] [PubMed]

L. Gelens, G. Van der Sande, P. Tassin, M. Tlidi, P. Kockaert, D. Gomila, I. Veretennicoff, and J. Danckaert, “Impact of nonlocal interactions in dissipative systems: towards minimal-sized localized structures,” Phys. Rev. A 75, 063812 (2007).
[CrossRef]

P. Tassin, G. Van der Sande, N. Veretenov, P. Kockaert, I. Veretennicoff, and M. Tlidi, “Three-dimensional structures in nonlinear cavities containing left-handed materials,” Opt. Express 14, 9338-9343 (2006).
[CrossRef] [PubMed]

P. Kockaert, P. Tassin, G. van der Sande, I. Veretennicoff, and M. Tlidi, “Negative diffraction pattern dynamics in nonlinear cavities with left-handed materials,” Phys. Rev. A 74, 033822 (2006).
[CrossRef]

Kogelnik, H.

Konstantinidis, G.

T. F. Gundogdu, I. Tsiapa, A. Kostopoulos, G. Konstantinidis, N. Katsarakis, R. S. Penciu, M. Kafesaki, E. N. Economou, T. Koschny, and C. M. Soukoulis, “Experimental demonstration of negative magnetic permeability in the far-infrared frequency regime,” Appl. Phys. Lett. 89, 084103 (2006).
[CrossRef]

Koschny, T.

T. F. Gundogdu, I. Tsiapa, A. Kostopoulos, G. Konstantinidis, N. Katsarakis, R. S. Penciu, M. Kafesaki, E. N. Economou, T. Koschny, and C. M. Soukoulis, “Experimental demonstration of negative magnetic permeability in the far-infrared frequency regime,” Appl. Phys. Lett. 89, 084103 (2006).
[CrossRef]

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic metamaterials at telecommunication and visible frequencies,” Phys. Rev. Lett. 95, 203901 (2005).
[CrossRef] [PubMed]

Kostopoulos, A.

T. F. Gundogdu, I. Tsiapa, A. Kostopoulos, G. Konstantinidis, N. Katsarakis, R. S. Penciu, M. Kafesaki, E. N. Economou, T. Koschny, and C. M. Soukoulis, “Experimental demonstration of negative magnetic permeability in the far-infrared frequency regime,” Appl. Phys. Lett. 89, 084103 (2006).
[CrossRef]

Kuhta, N. A.

N. A. Kuhta, V. A. Podolskiy, and A. L. Efros, “Far-field imaging by a planar lens: diffraction versus superresolution,” Phys. Rev. B 76, 205102 (2007).
[CrossRef]

Lederer, F.

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

Lefever, R.

L. A. Lugiato and R. Lefever, “Spatial dissipative structures in passive optical systems,” Phys. Rev. Lett. 58, 2209-2211 (1987).
[CrossRef] [PubMed]

Linden, S.

G. Dolling, M. Wegener, C. M. Soukoulis, and S. Linden, “Negative-index metamaterial at 780 nm wavelength,” Opt. Lett. 32, 53-55 (2007).
[CrossRef]

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic metamaterials at telecommunication and visible frequencies,” Phys. Rev. Lett. 95, 203901 (2005).
[CrossRef] [PubMed]

Liu, X.

Lugiato, L. A.

L. A. Lugiato and R. Lefever, “Spatial dissipative structures in passive optical systems,” Phys. Rev. Lett. 58, 2209-2211 (1987).
[CrossRef] [PubMed]

Malnev, V.

A. Boardman, N. King, R. Mitchell-Thomas, V. Malnev, and Y. Rapoport, “Gain control and diffraction-managed solitons in metamaterials,” Metamaterials 2, 145-154 (2008).
[CrossRef]

Martinez, O. E.

O. E. Martinez, “Design of high-power ultrashort pulse amplifiers by expansion and recompression,” IEEE J. Quantum Electron. 23, 1385-1387 (1987).
[CrossRef]

Merlin, R.

R. Merlin, “Metamaterials and the Landau-Lifshitz permeability argument: large permittivity begets high-frequency magnetism,” Proc. Natl. Acad. Sci. U.S.A. 106, 1693-1698 (2009).
[CrossRef] [PubMed]

R. Merlin, “Analytical solution of the almost-perfect-lens problem,” Appl. Phys. Lett. 84, 1290-1292 (2004).
[CrossRef]

Mitchell-Thomas, R.

A. Boardman, N. King, R. Mitchell-Thomas, V. Malnev, and Y. Rapoport, “Gain control and diffraction-managed solitons in metamaterials,” Metamaterials 2, 145-154 (2008).
[CrossRef]

Mizuno, M.

K. Ikeda and M. Mizuno, “Modeling of nonlinear Fabry-Perot resonators by difference-differential equations,” IEEE J. Quantum Electron. 21, 1429-1434 (1985).
[CrossRef]

Nemat-Nasser, S. C.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184-4187 (2000).
[CrossRef] [PubMed]

Nolte, S.

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

Ozbay, M.

Padilla, W. J.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184-4187 (2000).
[CrossRef] [PubMed]

Penciu, R. S.

T. F. Gundogdu, I. Tsiapa, A. Kostopoulos, G. Konstantinidis, N. Katsarakis, R. S. Penciu, M. Kafesaki, E. N. Economou, T. Koschny, and C. M. Soukoulis, “Experimental demonstration of negative magnetic permeability in the far-infrared frequency regime,” Appl. Phys. Lett. 89, 084103 (2006).
[CrossRef]

Pendry, J. B.

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

Peschel, U.

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

Podolskiy, V. A.

N. A. Kuhta, V. A. Podolskiy, and A. L. Efros, “Far-field imaging by a planar lens: diffraction versus superresolution,” Phys. Rev. B 76, 205102 (2007).
[CrossRef]

Rapoport, Y.

A. Boardman, N. King, R. Mitchell-Thomas, V. Malnev, and Y. Rapoport, “Gain control and diffraction-managed solitons in metamaterials,” Metamaterials 2, 145-154 (2008).
[CrossRef]

Schelle, D.

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

Schmidt, F.

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic metamaterials at telecommunication and visible frequencies,” Phys. Rev. Lett. 95, 203901 (2005).
[CrossRef] [PubMed]

Schultz, S.

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292, 77-79 (2001).
[CrossRef] [PubMed]

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184-4187 (2000).
[CrossRef] [PubMed]

Serrat, C.

K. Staliunas, C. Serrat, R. Herrero, C. Cojocaru, and J. Trull, “Subdiffractive light pulses in photonic crystals,” Phys. Rev. E 74, 016605 (2006).
[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]

Siegman, A.

A. Siegman, Lasers (University Science Books, 1986).

Smith, D. R.

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292, 77-79 (2001).
[CrossRef] [PubMed]

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184-4187 (2000).
[CrossRef] [PubMed]

Soukoulis, C. M.

G. Dolling, M. Wegener, C. M. Soukoulis, and S. Linden, “Negative-index metamaterial at 780 nm wavelength,” Opt. Lett. 32, 53-55 (2007).
[CrossRef]

T. F. Gundogdu, I. Tsiapa, A. Kostopoulos, G. Konstantinidis, N. Katsarakis, R. S. Penciu, M. Kafesaki, E. N. Economou, T. Koschny, and C. M. Soukoulis, “Experimental demonstration of negative magnetic permeability in the far-infrared frequency regime,” Appl. Phys. Lett. 89, 084103 (2006).
[CrossRef]

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic metamaterials at telecommunication and visible frequencies,” Phys. Rev. Lett. 95, 203901 (2005).
[CrossRef] [PubMed]

Soukoulis, M.

Staliunas, K.

K. Staliunas, C. Serrat, R. Herrero, C. Cojocaru, and J. Trull, “Subdiffractive light pulses in photonic crystals,” Phys. Rev. E 74, 016605 (2006).
[CrossRef]

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

Tassin, P.

L. Gelens, G. Van der Sande, P. Tassin, M. Tlidi, P. Kockaert, D. Gomila, I. Veretennicoff, and J. Danckaert, “Impact of nonlocal interactions in dissipative systems: towards minimal-sized localized structures,” Phys. Rev. A 75, 063812 (2007).
[CrossRef]

P. Tassin, L. Gelens, J. Danckaert, I. Veretennicoff, G. Van der Sande, P. Kockaert, and M. Tlidi, “Dissipative structures in left-handed material cavity optics,” Chaos 17, 037116 (2007).
[CrossRef] [PubMed]

P. Kockaert, P. Tassin, G. van der Sande, I. Veretennicoff, and M. Tlidi, “Negative diffraction pattern dynamics in nonlinear cavities with left-handed materials,” Phys. Rev. A 74, 033822 (2006).
[CrossRef]

P. Tassin, I. Veretennicoff, and G. Van der Sande, “Veselago's lens consisting of left-handed materials with arbitrary index of refraction,” Opt. Commun. 264, 130-134 (2006).
[CrossRef]

P. Tassin, G. Van der Sande, N. Veretenov, P. Kockaert, I. Veretennicoff, and M. Tlidi, “Three-dimensional structures in nonlinear cavities containing left-handed materials,” Opt. Express 14, 9338-9343 (2006).
[CrossRef] [PubMed]

Tlidi, M.

L. Gelens, G. Van der Sande, P. Tassin, M. Tlidi, P. Kockaert, D. Gomila, I. Veretennicoff, and J. Danckaert, “Impact of nonlocal interactions in dissipative systems: towards minimal-sized localized structures,” Phys. Rev. A 75, 063812 (2007).
[CrossRef]

P. Tassin, L. Gelens, J. Danckaert, I. Veretennicoff, G. Van der Sande, P. Kockaert, and M. Tlidi, “Dissipative structures in left-handed material cavity optics,” Chaos 17, 037116 (2007).
[CrossRef] [PubMed]

P. Kockaert, P. Tassin, G. van der Sande, I. Veretennicoff, and M. Tlidi, “Negative diffraction pattern dynamics in nonlinear cavities with left-handed materials,” Phys. Rev. A 74, 033822 (2006).
[CrossRef]

P. Tassin, G. Van der Sande, N. Veretenov, P. Kockaert, I. Veretennicoff, and M. Tlidi, “Three-dimensional structures in nonlinear cavities containing left-handed materials,” Opt. Express 14, 9338-9343 (2006).
[CrossRef] [PubMed]

Trull, J.

K. Staliunas, C. Serrat, R. Herrero, C. Cojocaru, and J. Trull, “Subdiffractive light pulses in photonic crystals,” Phys. Rev. E 74, 016605 (2006).
[CrossRef]

Tsiapa, I.

T. F. Gundogdu, I. Tsiapa, A. Kostopoulos, G. Konstantinidis, N. Katsarakis, R. S. Penciu, M. Kafesaki, E. N. Economou, T. Koschny, and C. M. Soukoulis, “Experimental demonstration of negative magnetic permeability in the far-infrared frequency regime,” Appl. Phys. Lett. 89, 084103 (2006).
[CrossRef]

Tünnermann, A.

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

Van der Sande, G.

P. Tassin, L. Gelens, J. Danckaert, I. Veretennicoff, G. Van der Sande, P. Kockaert, and M. Tlidi, “Dissipative structures in left-handed material cavity optics,” Chaos 17, 037116 (2007).
[CrossRef] [PubMed]

L. Gelens, G. Van der Sande, P. Tassin, M. Tlidi, P. Kockaert, D. Gomila, I. Veretennicoff, and J. Danckaert, “Impact of nonlocal interactions in dissipative systems: towards minimal-sized localized structures,” Phys. Rev. A 75, 063812 (2007).
[CrossRef]

P. Tassin, G. Van der Sande, N. Veretenov, P. Kockaert, I. Veretennicoff, and M. Tlidi, “Three-dimensional structures in nonlinear cavities containing left-handed materials,” Opt. Express 14, 9338-9343 (2006).
[CrossRef] [PubMed]

P. Tassin, I. Veretennicoff, and G. Van der Sande, “Veselago's lens consisting of left-handed materials with arbitrary index of refraction,” Opt. Commun. 264, 130-134 (2006).
[CrossRef]

P. Kockaert, P. Tassin, G. van der Sande, I. Veretennicoff, and M. Tlidi, “Negative diffraction pattern dynamics in nonlinear cavities with left-handed materials,” Phys. Rev. A 74, 033822 (2006).
[CrossRef]

Veretennicoff, I.

P. Tassin, L. Gelens, J. Danckaert, I. Veretennicoff, G. Van der Sande, P. Kockaert, and M. Tlidi, “Dissipative structures in left-handed material cavity optics,” Chaos 17, 037116 (2007).
[CrossRef] [PubMed]

L. Gelens, G. Van der Sande, P. Tassin, M. Tlidi, P. Kockaert, D. Gomila, I. Veretennicoff, and J. Danckaert, “Impact of nonlocal interactions in dissipative systems: towards minimal-sized localized structures,” Phys. Rev. A 75, 063812 (2007).
[CrossRef]

P. Tassin, I. Veretennicoff, and G. Van der Sande, “Veselago's lens consisting of left-handed materials with arbitrary index of refraction,” Opt. Commun. 264, 130-134 (2006).
[CrossRef]

P. Tassin, G. Van der Sande, N. Veretenov, P. Kockaert, I. Veretennicoff, and M. Tlidi, “Three-dimensional structures in nonlinear cavities containing left-handed materials,” Opt. Express 14, 9338-9343 (2006).
[CrossRef] [PubMed]

P. Kockaert, P. Tassin, G. van der Sande, I. Veretennicoff, and M. Tlidi, “Negative diffraction pattern dynamics in nonlinear cavities with left-handed materials,” Phys. Rev. A 74, 033822 (2006).
[CrossRef]

Veretenov, N.

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]

Vier, D. C.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184-4187 (2000).
[CrossRef] [PubMed]

Webb, K. J.

Wegener, M.

G. Dolling, M. Wegener, C. M. Soukoulis, and S. Linden, “Negative-index metamaterial at 780 nm wavelength,” Opt. Lett. 32, 53-55 (2007).
[CrossRef]

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic metamaterials at telecommunication and visible frequencies,” Phys. Rev. Lett. 95, 203901 (2005).
[CrossRef] [PubMed]

Yang, M. -C.

Zhang, C.

Zhou, J. F.

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, T. Koschny, and 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, and C. M. Soukoulis, “Magnetic metamaterials at telecommunication and visible frequencies,” Phys. Rev. Lett. 95, 203901 (2005).
[CrossRef] [PubMed]

Appl. Opt.

Appl. Phys. Lett.

T. F. Gundogdu, I. Tsiapa, A. Kostopoulos, G. Konstantinidis, N. Katsarakis, R. S. Penciu, M. Kafesaki, E. N. Economou, T. Koschny, and C. M. Soukoulis, “Experimental demonstration of negative magnetic permeability in the far-infrared frequency regime,” Appl. Phys. Lett. 89, 084103 (2006).
[CrossRef]

R. Merlin, “Analytical solution of the almost-perfect-lens problem,” Appl. Phys. Lett. 84, 1290-1292 (2004).
[CrossRef]

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

Chaos

P. Tassin, L. Gelens, J. Danckaert, I. Veretennicoff, G. Van der Sande, P. Kockaert, and M. Tlidi, “Dissipative structures in left-handed material cavity optics,” Chaos 17, 037116 (2007).
[CrossRef] [PubMed]

IEEE J. Quantum Electron.

O. E. Martinez, “Design of high-power ultrashort pulse amplifiers by expansion and recompression,” IEEE J. Quantum Electron. 23, 1385-1387 (1987).
[CrossRef]

K. Ikeda and M. Mizuno, “Modeling of nonlinear Fabry-Perot resonators by difference-differential equations,” IEEE J. Quantum Electron. 21, 1429-1434 (1985).
[CrossRef]

JETP Lett.

V. Klimov, “Novel approach to a perfect lens,” JETP Lett. 89, 229-232 (2009).
[CrossRef]

Metamaterials

A. Boardman, N. King, R. Mitchell-Thomas, V. Malnev, and Y. Rapoport, “Gain control and diffraction-managed solitons in metamaterials,” Metamaterials 2, 145-154 (2008).
[CrossRef]

Opt. Commun.

P. Tassin, I. Veretennicoff, and G. Van der Sande, “Veselago's lens consisting of left-handed materials with arbitrary index of refraction,” Opt. Commun. 264, 130-134 (2006).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. A

P. Kockaert, P. Tassin, G. van der Sande, I. Veretennicoff, and M. Tlidi, “Negative diffraction pattern dynamics in nonlinear cavities with left-handed materials,” Phys. Rev. A 74, 033822 (2006).
[CrossRef]

L. Gelens, G. Van der Sande, P. Tassin, M. Tlidi, P. Kockaert, D. Gomila, I. Veretennicoff, and J. Danckaert, “Impact of nonlocal interactions in dissipative systems: towards minimal-sized localized structures,” Phys. Rev. A 75, 063812 (2007).
[CrossRef]

Phys. Rev. B

N. A. Kuhta, V. A. Podolskiy, and A. L. Efros, “Far-field imaging by a planar lens: diffraction versus superresolution,” Phys. Rev. B 76, 205102 (2007).
[CrossRef]

Phys. Rev. E

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

K. Staliunas, C. Serrat, R. Herrero, C. Cojocaru, and J. Trull, “Subdiffractive light pulses in photonic crystals,” Phys. Rev. E 74, 016605 (2006).
[CrossRef]

Phys. Rev. Lett.

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

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184-4187 (2000).
[CrossRef] [PubMed]

L. A. Lugiato and R. Lefever, “Spatial dissipative structures in passive optical systems,” Phys. Rev. Lett. 58, 2209-2211 (1987).
[CrossRef] [PubMed]

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic metamaterials at telecommunication and visible frequencies,” Phys. Rev. Lett. 95, 203901 (2005).
[CrossRef] [PubMed]

Proc. Natl. Acad. Sci. U.S.A.

R. Merlin, “Metamaterials and the Landau-Lifshitz permeability argument: large permittivity begets high-frequency magnetism,” Proc. Natl. Acad. Sci. U.S.A. 106, 1693-1698 (2009).
[CrossRef] [PubMed]

Science

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292, 77-79 (2001).
[CrossRef] [PubMed]

Sov. Phys. Usp.

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

Other

A. Siegman, Lasers (University Science Books, 1986).

M. Ballav and A. R. Chowdhury, On a Study of Diffraction and Dispersion Managed Soliton in a Cylindrical Media, Vol. PIER-63 of Progress In Electromagnetics Research (EMW, 2006), pp. 33-50.

C.Krowne and Y.Zhang, eds., Physics of Negative Refraction and Negative Index Materials: Optical and Electronic Aspects and Diversified Approaches (Springer, 2007).

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Figures (1)

Fig. 1
Fig. 1

(a)–(c) Three different systems corresponding to the same A B C D matrix. (a) LHM with a negative refractive index n = 1 . (b) Any system with an A B C D matrix defined by ( A = D = 1 , B = d , C = 0 ) . (c) Trio of lenses equivalent to the A B C D matrix of (b). (d) Elementary telescope T ( d / 4 ) with lenses of focal length f = d / 4 . Two such telescopes are equivalent to a negative index slab of thickness d.

Tables (1)

Tables Icon

Table 1 Notations Used in This Paper, Similar to Those of [24]

Equations (15)

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P LHM ( d ) = ( A B C D ) = ( 1 d 0 1 ) ,
P LHM ( d ) = P ( d ) = ( 1 0 0 1 ) ( 1 d 0 1 ) ,
T ( d 2 ) = ( 1 d 0 1 ) = L ( d 2 ) P ( d ) L ( d 2 ) ,
P ( d ) = P 2 ( d 2 ) = P t ( d 2 ) P ( d 2 ) = T 2 ( d 4 ) .
P LHM ( d ) = P ( d ) = T 2 ( d 4 ) = [ L ( d 4 ) P ( d 2 ) L ( d 4 ) ] 2 = L ( d 4 ) P ( d 2 ) L ( d 4 ) L ( d 4 ) P ( d 2 ) L ( d 4 ) = L ( d 4 ) P ( d 2 ) L ( d 8 ) P ( d 2 ) L ( d 4 ) .
( 1 d 0 1 ) = ( 1 0 4 d 1 ) ( 1 d 2 0 1 ) ( 1 0 8 d 1 ) ( 1 d 2 0 1 ) ( 1 0 4 d 1 ) .
T 2 ( 2 d ) = P ( 8 d ) = P 2 ( 4 d ) = T 4 ( d ) ,
N F = a 2 L λ ,
NA i = n ϕ i 2 ϕ i 2 + 4 f i 2 .
ϕ 1 , 3 = 2 f 1 , 3 = d 2 ,
N F = ϕ 2 4 L λ = d 32 λ ,
( 1 d n 0 1 )
( 1 0 1 f 1 )
P ( d n )
L ( f )

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