Abstract

Different definitions of the resolution of negative-index-material (NIM) slabs and classical optical lenses with magnification 1 are presented and evaluated for both cases. Several numerical codes—based on domain and boundary discretizations and working in the time and frequency domains—are applied and compared. It is shown that superresolution depends very much on the definition of resolution and that it may be obtained not only for NIM slabs but also for highly refracting classical lenses when the distances of the image and source points from the surface of the lens or slab are shorter than the wavelength.

© 2006 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. V. G. Veselago, 'The electrodynamics of substances with simultaneous negative values of epsilon and μ,' Sov. Phys. Usp. 10, 509-514 (1968).
    [CrossRef]
  2. J. B. Pendry, 'Negative refraction makes a perfect lens,' Phys. Rev. Lett. 85, 3966-3969 (2000).
    [CrossRef] [PubMed]
  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]
  4. J.-S. Lih, Y.-S. Wang, M.-C. Lu, Y.-C. Huang, K.-H. Chen, J.-L. Chern, and L.-E. Li, 'Experimental realization of breaking diffraction limit by planar negative-index metematerials in free space,' Europhys. Lett. 69, 544-548 (2005).
    [CrossRef]
  5. Z. Lu, S. Shi, C. A. Schuetz, J. A. Murakowski, and D. W. Prather, 'Three-dimensional photonic crystal flat lens by full 3D negative refraction,' Opt. Express 13, 5592-5599 (2005).
    [CrossRef] [PubMed]
  6. J. L. Garcia-Pomar and M. Nieto-Vesperinas, 'Imaging of extended objects by a negative refractive index slab,' New J. Phys. 7, 160 (2005); http://www.njp.org.
    [CrossRef]
  7. Viktor A. Podolskiy and Evgenii E. Narimanov, 'Near-sighted superlens,' Opt. Lett. 30, 75-77 (2005).
    [CrossRef] [PubMed]
  8. N. Garcia and M. Nieto-Vesperinas, 'Is there an experimental verification of a negative index of refraction yet?' Opt. Lett. 27, 885-887 (2002).
    [CrossRef]
  9. K. J. Webb, M. Yang, D. W. Ward, and K. A. Nelson, 'Metrics for negative-refractive-index materials,' Phys. Rev. E 70, 035602 (2004).
    [CrossRef]
  10. M. Nieto-Vesperinas, 'Problem of image superresolution with a negative-refractive-index slab,' J. Opt. Soc. Am. A 21, 491-498 (2004).
    [CrossRef]
  11. D. O. S. Melville and R. J. Blaikie, 'Near-field optical lithography using a planar silver lens,' J. Vac. Sci. Technol. B 22, 3470-3474 (2004).
    [CrossRef]
  12. N. Fang, H. Lee, C. Sun, and X. Zhang, 'Sub-diffraction-limited optical imaging with a silver superlens,' Science 308, 534-537 (2005).
    [CrossRef] [PubMed]
  13. J. L. Garcia-Pomar and M. Nieto-Vesperinas, 'Waveguiding, collimation and wavelength concentration in photonic crystals,' Opt. Express 13, 7997-8007 (2005).
    [CrossRef] [PubMed]
  14. D. A. Fletcher, K. E. Goodson, and G. S. Kino, 'Focusing in microlens close to a wavelength in diameter,' Opt. Lett. 26, 399-401 (2001).
    [CrossRef]
  15. http://www.remcom.com/xfdtd6/index.html.
  16. http://www.optiwave.com/2005/products/optifdtd/index.html.
  17. http://www.empire.de.
  18. http://www.cst.de/Content/Products/MWS/Overview.aspx.
  19. P. F. Loschialpo, D. W. Forester, D. L. Smith, and F. J. Rachford, 'Optical properties of an ideal homogeneous causal left-handed material slab,' Phys. Rev. E 70, 036605 (2004).
    [CrossRef]
  20. P. M. So, H. Du, and W. J. R. Hoefer, 'Modeling of metamaterials with negative refractive index using 2-D shunt and 3-D SCN TLM networks,' IEEE Trans. Microwave Theory Tech. 53, 1496-1505 (2005).
    [CrossRef]
  21. http://www.ansoft.com/products/hf/hfss/.
  22. http://www.comsol.com/products/.
  23. http://www.mathworks.com/.
  24. J. L. Garcia-Pomar and M. Nieto-Vesperinas, 'Transmission study of prisms and slabs of lossy negative index media,' Opt. Express 12, 2081-2095 (2004).
    [CrossRef] [PubMed]
  25. Ch. Hafner, Post-modern Electromagnetics: Using Intelligent Maxwell Solvers (Wiley, 1999).
  26. Ch. Hafner, MAX-1, a Visual Electromagnetics Platform for PCs (Wiley, 1999).

2005 (7)

J.-S. Lih, Y.-S. Wang, M.-C. Lu, Y.-C. Huang, K.-H. Chen, J.-L. Chern, and L.-E. Li, 'Experimental realization of breaking diffraction limit by planar negative-index metematerials in free space,' Europhys. Lett. 69, 544-548 (2005).
[CrossRef]

Z. Lu, S. Shi, C. A. Schuetz, J. A. Murakowski, and D. W. Prather, 'Three-dimensional photonic crystal flat lens by full 3D negative refraction,' Opt. Express 13, 5592-5599 (2005).
[CrossRef] [PubMed]

J. L. Garcia-Pomar and M. Nieto-Vesperinas, 'Imaging of extended objects by a negative refractive index slab,' New J. Phys. 7, 160 (2005); http://www.njp.org.
[CrossRef]

Viktor A. Podolskiy and Evgenii E. Narimanov, 'Near-sighted superlens,' Opt. Lett. 30, 75-77 (2005).
[CrossRef] [PubMed]

N. Fang, H. Lee, C. Sun, and X. Zhang, 'Sub-diffraction-limited optical imaging with a silver superlens,' Science 308, 534-537 (2005).
[CrossRef] [PubMed]

J. L. Garcia-Pomar and M. Nieto-Vesperinas, 'Waveguiding, collimation and wavelength concentration in photonic crystals,' Opt. Express 13, 7997-8007 (2005).
[CrossRef] [PubMed]

P. M. So, H. Du, and W. J. R. Hoefer, 'Modeling of metamaterials with negative refractive index using 2-D shunt and 3-D SCN TLM networks,' IEEE Trans. Microwave Theory Tech. 53, 1496-1505 (2005).
[CrossRef]

2004 (5)

J. L. Garcia-Pomar and M. Nieto-Vesperinas, 'Transmission study of prisms and slabs of lossy negative index media,' Opt. Express 12, 2081-2095 (2004).
[CrossRef] [PubMed]

P. F. Loschialpo, D. W. Forester, D. L. Smith, and F. J. Rachford, 'Optical properties of an ideal homogeneous causal left-handed material slab,' Phys. Rev. E 70, 036605 (2004).
[CrossRef]

K. J. Webb, M. Yang, D. W. Ward, and K. A. Nelson, 'Metrics for negative-refractive-index materials,' Phys. Rev. E 70, 035602 (2004).
[CrossRef]

M. Nieto-Vesperinas, 'Problem of image superresolution with a negative-refractive-index slab,' J. Opt. Soc. Am. A 21, 491-498 (2004).
[CrossRef]

D. O. S. Melville and R. J. Blaikie, 'Near-field optical lithography using a planar silver lens,' J. Vac. Sci. Technol. B 22, 3470-3474 (2004).
[CrossRef]

2002 (1)

2001 (2)

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. A. Fletcher, K. E. Goodson, and G. S. Kino, 'Focusing in microlens close to a wavelength in diameter,' Opt. Lett. 26, 399-401 (2001).
[CrossRef]

2000 (1)

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

1968 (1)

V. G. Veselago, 'The electrodynamics of substances with simultaneous negative values of epsilon and μ,' Sov. Phys. Usp. 10, 509-514 (1968).
[CrossRef]

Blaikie, R. J.

D. O. S. Melville and R. J. Blaikie, 'Near-field optical lithography using a planar silver lens,' J. Vac. Sci. Technol. B 22, 3470-3474 (2004).
[CrossRef]

Chen, K.-H.

J.-S. Lih, Y.-S. Wang, M.-C. Lu, Y.-C. Huang, K.-H. Chen, J.-L. Chern, and L.-E. Li, 'Experimental realization of breaking diffraction limit by planar negative-index metematerials in free space,' Europhys. Lett. 69, 544-548 (2005).
[CrossRef]

Chern, J.-L.

J.-S. Lih, Y.-S. Wang, M.-C. Lu, Y.-C. Huang, K.-H. Chen, J.-L. Chern, and L.-E. Li, 'Experimental realization of breaking diffraction limit by planar negative-index metematerials in free space,' Europhys. Lett. 69, 544-548 (2005).
[CrossRef]

Du, H.

P. M. So, H. Du, and W. J. R. Hoefer, 'Modeling of metamaterials with negative refractive index using 2-D shunt and 3-D SCN TLM networks,' IEEE Trans. Microwave Theory Tech. 53, 1496-1505 (2005).
[CrossRef]

Fang, N.

N. Fang, H. Lee, C. Sun, and X. Zhang, 'Sub-diffraction-limited optical imaging with a silver superlens,' Science 308, 534-537 (2005).
[CrossRef] [PubMed]

Fletcher, D. A.

Forester, D. W.

P. F. Loschialpo, D. W. Forester, D. L. Smith, and F. J. Rachford, 'Optical properties of an ideal homogeneous causal left-handed material slab,' Phys. Rev. E 70, 036605 (2004).
[CrossRef]

Garcia, N.

Garcia-Pomar, J. L.

Goodson, K. E.

Hafner, Ch.

Ch. Hafner, Post-modern Electromagnetics: Using Intelligent Maxwell Solvers (Wiley, 1999).

Ch. Hafner, MAX-1, a Visual Electromagnetics Platform for PCs (Wiley, 1999).

Hoefer, W. J. R.

P. M. So, H. Du, and W. J. R. Hoefer, 'Modeling of metamaterials with negative refractive index using 2-D shunt and 3-D SCN TLM networks,' IEEE Trans. Microwave Theory Tech. 53, 1496-1505 (2005).
[CrossRef]

Huang, Y.-C.

J.-S. Lih, Y.-S. Wang, M.-C. Lu, Y.-C. Huang, K.-H. Chen, J.-L. Chern, and L.-E. Li, 'Experimental realization of breaking diffraction limit by planar negative-index metematerials in free space,' Europhys. Lett. 69, 544-548 (2005).
[CrossRef]

Kino, G. S.

Lee, H.

N. Fang, H. Lee, C. Sun, and X. Zhang, 'Sub-diffraction-limited optical imaging with a silver superlens,' Science 308, 534-537 (2005).
[CrossRef] [PubMed]

Li, L.-E.

J.-S. Lih, Y.-S. Wang, M.-C. Lu, Y.-C. Huang, K.-H. Chen, J.-L. Chern, and L.-E. Li, 'Experimental realization of breaking diffraction limit by planar negative-index metematerials in free space,' Europhys. Lett. 69, 544-548 (2005).
[CrossRef]

Lih, J.-S.

J.-S. Lih, Y.-S. Wang, M.-C. Lu, Y.-C. Huang, K.-H. Chen, J.-L. Chern, and L.-E. Li, 'Experimental realization of breaking diffraction limit by planar negative-index metematerials in free space,' Europhys. Lett. 69, 544-548 (2005).
[CrossRef]

Loschialpo, P. F.

P. F. Loschialpo, D. W. Forester, D. L. Smith, and F. J. Rachford, 'Optical properties of an ideal homogeneous causal left-handed material slab,' Phys. Rev. E 70, 036605 (2004).
[CrossRef]

Lu, M.-C.

J.-S. Lih, Y.-S. Wang, M.-C. Lu, Y.-C. Huang, K.-H. Chen, J.-L. Chern, and L.-E. Li, 'Experimental realization of breaking diffraction limit by planar negative-index metematerials in free space,' Europhys. Lett. 69, 544-548 (2005).
[CrossRef]

Lu, Z.

Melville, D. O. S.

D. O. S. Melville and R. J. Blaikie, 'Near-field optical lithography using a planar silver lens,' J. Vac. Sci. Technol. B 22, 3470-3474 (2004).
[CrossRef]

Murakowski, J. A.

Narimanov, Evgenii E.

Nelson, K. A.

K. J. Webb, M. Yang, D. W. Ward, and K. A. Nelson, 'Metrics for negative-refractive-index materials,' Phys. Rev. E 70, 035602 (2004).
[CrossRef]

Nieto-Vesperinas, M.

Pendry, J. B.

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

Podolskiy, Viktor A.

Prather, D. W.

Rachford, F. J.

P. F. Loschialpo, D. W. Forester, D. L. Smith, and F. J. Rachford, 'Optical properties of an ideal homogeneous causal left-handed material slab,' Phys. Rev. E 70, 036605 (2004).
[CrossRef]

Schuetz, C. A.

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]

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.

Smith, D. L.

P. F. Loschialpo, D. W. Forester, D. L. Smith, and F. J. Rachford, 'Optical properties of an ideal homogeneous causal left-handed material slab,' Phys. Rev. E 70, 036605 (2004).
[CrossRef]

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]

So, P. M.

P. M. So, H. Du, and W. J. R. Hoefer, 'Modeling of metamaterials with negative refractive index using 2-D shunt and 3-D SCN TLM networks,' IEEE Trans. Microwave Theory Tech. 53, 1496-1505 (2005).
[CrossRef]

Sun, C.

N. Fang, H. Lee, C. Sun, and X. Zhang, 'Sub-diffraction-limited optical imaging with a silver superlens,' Science 308, 534-537 (2005).
[CrossRef] [PubMed]

Veselago, V. G.

V. G. Veselago, 'The electrodynamics of substances with simultaneous negative values of epsilon and μ,' Sov. Phys. Usp. 10, 509-514 (1968).
[CrossRef]

Wang, Y.-S.

J.-S. Lih, Y.-S. Wang, M.-C. Lu, Y.-C. Huang, K.-H. Chen, J.-L. Chern, and L.-E. Li, 'Experimental realization of breaking diffraction limit by planar negative-index metematerials in free space,' Europhys. Lett. 69, 544-548 (2005).
[CrossRef]

Ward, D. W.

K. J. Webb, M. Yang, D. W. Ward, and K. A. Nelson, 'Metrics for negative-refractive-index materials,' Phys. Rev. E 70, 035602 (2004).
[CrossRef]

Webb, K. J.

K. J. Webb, M. Yang, D. W. Ward, and K. A. Nelson, 'Metrics for negative-refractive-index materials,' Phys. Rev. E 70, 035602 (2004).
[CrossRef]

Yang, M.

K. J. Webb, M. Yang, D. W. Ward, and K. A. Nelson, 'Metrics for negative-refractive-index materials,' Phys. Rev. E 70, 035602 (2004).
[CrossRef]

Zhang, X.

N. Fang, H. Lee, C. Sun, and X. Zhang, 'Sub-diffraction-limited optical imaging with a silver superlens,' Science 308, 534-537 (2005).
[CrossRef] [PubMed]

Europhys. Lett. (1)

J.-S. Lih, Y.-S. Wang, M.-C. Lu, Y.-C. Huang, K.-H. Chen, J.-L. Chern, and L.-E. Li, 'Experimental realization of breaking diffraction limit by planar negative-index metematerials in free space,' Europhys. Lett. 69, 544-548 (2005).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (1)

P. M. So, H. Du, and W. J. R. Hoefer, 'Modeling of metamaterials with negative refractive index using 2-D shunt and 3-D SCN TLM networks,' IEEE Trans. Microwave Theory Tech. 53, 1496-1505 (2005).
[CrossRef]

J. Opt. Soc. Am. A (1)

J. Vac. Sci. Technol. B (1)

D. O. S. Melville and R. J. Blaikie, 'Near-field optical lithography using a planar silver lens,' J. Vac. Sci. Technol. B 22, 3470-3474 (2004).
[CrossRef]

New J. Phys. (1)

J. L. Garcia-Pomar and M. Nieto-Vesperinas, 'Imaging of extended objects by a negative refractive index slab,' New J. Phys. 7, 160 (2005); http://www.njp.org.
[CrossRef]

Opt. Express (3)

Opt. Lett. (3)

Phys. Rev. E (2)

K. J. Webb, M. Yang, D. W. Ward, and K. A. Nelson, 'Metrics for negative-refractive-index materials,' Phys. Rev. E 70, 035602 (2004).
[CrossRef]

P. F. Loschialpo, D. W. Forester, D. L. Smith, and F. J. Rachford, 'Optical properties of an ideal homogeneous causal left-handed material slab,' Phys. Rev. E 70, 036605 (2004).
[CrossRef]

Phys. Rev. Lett. (1)

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

Science (2)

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

N. Fang, H. Lee, C. Sun, and X. Zhang, 'Sub-diffraction-limited optical imaging with a silver superlens,' Science 308, 534-537 (2005).
[CrossRef] [PubMed]

Sov. Phys. Usp. (1)

V. G. Veselago, 'The electrodynamics of substances with simultaneous negative values of epsilon and μ,' Sov. Phys. Usp. 10, 509-514 (1968).
[CrossRef]

Other (9)

http://www.remcom.com/xfdtd6/index.html.

http://www.optiwave.com/2005/products/optifdtd/index.html.

http://www.empire.de.

http://www.cst.de/Content/Products/MWS/Overview.aspx.

Ch. Hafner, Post-modern Electromagnetics: Using Intelligent Maxwell Solvers (Wiley, 1999).

Ch. Hafner, MAX-1, a Visual Electromagnetics Platform for PCs (Wiley, 1999).

http://www.ansoft.com/products/hf/hfss/.

http://www.comsol.com/products/.

http://www.mathworks.com/.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (14)

Fig. 1
Fig. 1

Point source S illuminates a NIM slab. Inside the slab, an internal focus point X is obtained, and on the other side of the slab, the image point (focus point) F is obtained.

Fig. 2
Fig. 2

2D model of a small, conventional lens with refractive index n = 2.5 illuminated by (a) a centered point source and by (b) two symmetric point sources. Time average of the Poynting vector field obtained from the MMP solver in the MAX-1 platform. Coordinates indicated in wavelengths.

Fig. 3
Fig. 3

Illumination (time average of the y component of the Poynting vector field) along the line at y = 2 λ for two sources shown in Fig. 2b, with coordinates ± x , y = 2 λ . The location x is indicated as parameter of the different curves.

Fig. 4
Fig. 4

Same as Fig. 2 but for a lens with a high optical index of n = 10 .

Fig. 5
Fig. 5

Same as in Fig. 3 but for a lens with a high optical index of n = 10 .

Fig. 6
Fig. 6

XFDTD simulation of a 2D rectangular NIM of width 1 λ and length 5 λ illuminated from top by a point source S with electric field E perpendicular to the plane and E field intensity at different times: after (a) 5 periods; (b) 10 periods; (c) 20 periods.

Fig. 7
Fig. 7

MEFISTO3D simulation of an infinite NIM slab of width 1 λ illuminated by a point source S from the left-hand side with electric field E perpendicular to the plane and time-averaged E field intensity at different times: after (a) 10 periods; (b) 25 periods, (c) 50 periods. Only the upper half-plane is shown.

Fig. 8
Fig. 8

(a)–(c) Three FEMLAB meshes for the simulation of a NIM slab of width 1 λ and length 5 λ illuminated by a small circular source S with electric field E perpendicular to the plane. (d) Norm of the electric field along the focus line (horizontal line through the focus point F). The loss tangent of the NIM is 0.01.

Fig. 9
Fig. 9

Same models as in Fig. 8; y component of the time average of the Poynting vector field of the focus line.

Fig. 10
Fig. 10

Same model as in Fig. 8c; y component of the time average of the Poynting vector field along the focus line for different loss tangents of the relative permittivity and permeability of the NIM.

Fig. 11
Fig. 11

MMP simulation of a NIM slab of width 1 λ and length 10 λ illuminated by a small monopole source S with electric field E perpendicular to the plane. Intensity plot of the time-averaged Poynting vector field, logarithmic gray scale. The model is symmetric; only the right half is shown. (a) Rectangular end, (b) circular end.

Fig. 12
Fig. 12

Illumination (negative y component of the time average of the Poynting vector field) of the focus line for a NIM slab with loss tangent 0.01 of width and length 1 λ 10 λ .

Fig. 13
Fig. 13

Resolution R 1 for a NIM slab of width 1 λ and length 6 λ with loss tangent varying from 0.1 to 10 9 . The thick line indicates the optical limit of resolution 0.5 λ . Below this line, superresolution in the sense of R 1 is obtained. (a) Pure NIM slab. (b) A rectangular absorber is placed below the focus line. The size of the absorber is the same as the size of the NIM slab. Its relative permittivity and permeability are 2 + 2 i and 1, respectively. (c) Hypothetical impedance-matched absorber with both relative permittivity and relative permeability equal to 1 + 1 i .

Fig. 14
Fig. 14

NIM slab with loss tangent 0.001 (top) and 0.01 (bottom) of width 2 and length 20 (arbitrary units) illuminated by two symmetric monopole sources located at x = ± x source (horizontal axis) at distance 1 from the slab for different wavelengths ranging from 0.5 to 2.5. Left-hand side, location x max of the maxima detected along the focus line versus x source . Right-hand side, amplitudes (arbitrary units) of the maxima detected along the focus line versus x source .

Metrics