Abstract

Achromatic doublets made of materials with normal dispersion have been used for decades to minimize the effects of chromatic aberrations inherent to single-glass optical lenses. Here, we propose a fundamentally different solution to correct the chromatic aberrations based on a nanowire metamaterial with low loss broadband anomalous dispersion in the visible domain. It is theoretically and numerically shown that the proposed metamaterial lens practically eliminates the chromatic aberrations for all the colors of light, and may be an interesting alternative to conventional achromatic doublets.

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References

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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2011 (1)

T. A. Morgado, J. S. Marcos, M. G. Silveirinha, and S. I. Maslovski, “Ultraconfined interlaced plasmons,” Phys. Rev. Lett. 107(6), 063903 (2011).
[CrossRef] [PubMed]

2009 (3)

A. Alù and N. Engheta, “Cloaking a sensor,” Phys. Rev. Lett. 102(23), 233901 (2009).
[CrossRef] [PubMed]

M. G. Silveirinha, “Anomalous refraction of light colors by a metamaterial prism,” Phys. Rev. Lett. 102(19), 193903 (2009).
[CrossRef] [PubMed]

J. M. McMahon, S. K. Gray, and G. C. Schatz, “Nonlocal optical response of metal nanostructures with arbitrary shape,” Phys. Rev. Lett. 103(9), 097403 (2009).
[CrossRef] [PubMed]

2008 (1)

M. G. Silveirinha and C. A. Fernandes, “Nonresonant structured material with extreme effective parameters,” Phys. Rev. B 78(3), 033108 (2008).
[CrossRef]

2007 (1)

Y. Zhao, P. A. Belov, and Y. Hao, “Modelling of wave propagation in wire media using spatially dispersive finite-difference time-domain method: numerical aspects,” IEEE Trans. Antenn. Propag. 55(6), 1506–1513 (2007).
[CrossRef]

2005 (1)

N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens,” Science 308(5721), 534–537 (2005).
[CrossRef] [PubMed]

2000 (1)

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85(18), 3966–3969 (2000).
[CrossRef] [PubMed]

1985 (1)

1963 (1)

1951 (1)

1927 (1)

1925 (1)

1671 (1)

. Newton, “A Letter of Mr. Isaac Newton, Professor of the Mathematicks in the University of Cambridge; Containing His New Theory about Light and Colors: Sent by the Author to the Publisher from Cambridge, Febr. 6. 1671/72; In Order to be Communicated to the R. Society,” Philos. Trans. R. Soc. Lond. 6(69-80), 3075–3087 (1671).
[CrossRef]

Alexander,, R. W.

Alù, A.

A. Alù and N. Engheta, “Cloaking a sensor,” Phys. Rev. Lett. 102(23), 233901 (2009).
[CrossRef] [PubMed]

Bell, R. J.

Belov, P. A.

Y. Zhao, P. A. Belov, and Y. Hao, “Modelling of wave propagation in wire media using spatially dispersive finite-difference time-domain method: numerical aspects,” IEEE Trans. Antenn. Propag. 55(6), 1506–1513 (2007).
[CrossRef]

Engheta, N.

A. Alù and N. Engheta, “Cloaking a sensor,” Phys. Rev. Lett. 102(23), 233901 (2009).
[CrossRef] [PubMed]

Fang, N.

N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens,” Science 308(5721), 534–537 (2005).
[CrossRef] [PubMed]

Fernandes, C. A.

M. G. Silveirinha and C. A. Fernandes, “Nonresonant structured material with extreme effective parameters,” Phys. Rev. B 78(3), 033108 (2008).
[CrossRef]

Gray, S. K.

J. M. McMahon, S. K. Gray, and G. C. Schatz, “Nonlocal optical response of metal nanostructures with arbitrary shape,” Phys. Rev. Lett. 103(9), 097403 (2009).
[CrossRef] [PubMed]

Hao, Y.

Y. Zhao, P. A. Belov, and Y. Hao, “Modelling of wave propagation in wire media using spatially dispersive finite-difference time-domain method: numerical aspects,” IEEE Trans. Antenn. Propag. 55(6), 1506–1513 (2007).
[CrossRef]

Herzberger, M.

Lee, H.

N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens,” Science 308(5721), 534–537 (2005).
[CrossRef] [PubMed]

Long, L. L.

Marcos, J. S.

T. A. Morgado, J. S. Marcos, M. G. Silveirinha, and S. I. Maslovski, “Ultraconfined interlaced plasmons,” Phys. Rev. Lett. 107(6), 063903 (2011).
[CrossRef] [PubMed]

Maslovski, S. I.

T. A. Morgado, J. S. Marcos, M. G. Silveirinha, and S. I. Maslovski, “Ultraconfined interlaced plasmons,” Phys. Rev. Lett. 107(6), 063903 (2011).
[CrossRef] [PubMed]

McClure, N. R.

McMahon, J. M.

J. M. McMahon, S. K. Gray, and G. C. Schatz, “Nonlocal optical response of metal nanostructures with arbitrary shape,” Phys. Rev. Lett. 103(9), 097403 (2009).
[CrossRef] [PubMed]

Morgado, T. A.

T. A. Morgado, J. S. Marcos, M. G. Silveirinha, and S. I. Maslovski, “Ultraconfined interlaced plasmons,” Phys. Rev. Lett. 107(6), 063903 (2011).
[CrossRef] [PubMed]

Newton, .

. Newton, “A Letter of Mr. Isaac Newton, Professor of the Mathematicks in the University of Cambridge; Containing His New Theory about Light and Colors: Sent by the Author to the Publisher from Cambridge, Febr. 6. 1671/72; In Order to be Communicated to the R. Society,” Philos. Trans. R. Soc. Lond. 6(69-80), 3075–3087 (1671).
[CrossRef]

Ordal, M. A.

Pendry, J. B.

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85(18), 3966–3969 (2000).
[CrossRef] [PubMed]

Querry, M. R.

Schatz, G. C.

J. M. McMahon, S. K. Gray, and G. C. Schatz, “Nonlocal optical response of metal nanostructures with arbitrary shape,” Phys. Rev. Lett. 103(9), 097403 (2009).
[CrossRef] [PubMed]

Silveirinha, M. G.

T. A. Morgado, J. S. Marcos, M. G. Silveirinha, and S. I. Maslovski, “Ultraconfined interlaced plasmons,” Phys. Rev. Lett. 107(6), 063903 (2011).
[CrossRef] [PubMed]

M. G. Silveirinha, “Anomalous refraction of light colors by a metamaterial prism,” Phys. Rev. Lett. 102(19), 193903 (2009).
[CrossRef] [PubMed]

M. G. Silveirinha and C. A. Fernandes, “Nonresonant structured material with extreme effective parameters,” Phys. Rev. B 78(3), 033108 (2008).
[CrossRef]

Smith, T. T.

Sun, C.

N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens,” Science 308(5721), 534–537 (2005).
[CrossRef] [PubMed]

Treuting, R. G.

Zhang, X.

N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens,” Science 308(5721), 534–537 (2005).
[CrossRef] [PubMed]

Zhao, Y.

Y. Zhao, P. A. Belov, and Y. Hao, “Modelling of wave propagation in wire media using spatially dispersive finite-difference time-domain method: numerical aspects,” IEEE Trans. Antenn. Propag. 55(6), 1506–1513 (2007).
[CrossRef]

Appl. Opt. (2)

IEEE Trans. Antenn. Propag. (1)

Y. Zhao, P. A. Belov, and Y. Hao, “Modelling of wave propagation in wire media using spatially dispersive finite-difference time-domain method: numerical aspects,” IEEE Trans. Antenn. Propag. 55(6), 1506–1513 (2007).
[CrossRef]

J. Opt. Soc. Am. (3)

Philos. Trans. R. Soc. Lond. (1)

. Newton, “A Letter of Mr. Isaac Newton, Professor of the Mathematicks in the University of Cambridge; Containing His New Theory about Light and Colors: Sent by the Author to the Publisher from Cambridge, Febr. 6. 1671/72; In Order to be Communicated to the R. Society,” Philos. Trans. R. Soc. Lond. 6(69-80), 3075–3087 (1671).
[CrossRef]

Phys. Rev. B (1)

M. G. Silveirinha and C. A. Fernandes, “Nonresonant structured material with extreme effective parameters,” Phys. Rev. B 78(3), 033108 (2008).
[CrossRef]

Phys. Rev. Lett. (5)

T. A. Morgado, J. S. Marcos, M. G. Silveirinha, and S. I. Maslovski, “Ultraconfined interlaced plasmons,” Phys. Rev. Lett. 107(6), 063903 (2011).
[CrossRef] [PubMed]

A. Alù and N. Engheta, “Cloaking a sensor,” Phys. Rev. Lett. 102(23), 233901 (2009).
[CrossRef] [PubMed]

M. G. Silveirinha, “Anomalous refraction of light colors by a metamaterial prism,” Phys. Rev. Lett. 102(19), 193903 (2009).
[CrossRef] [PubMed]

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85(18), 3966–3969 (2000).
[CrossRef] [PubMed]

J. M. McMahon, S. K. Gray, and G. C. Schatz, “Nonlocal optical response of metal nanostructures with arbitrary shape,” Phys. Rev. Lett. 103(9), 097403 (2009).
[CrossRef] [PubMed]

Science (1)

N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens,” Science 308(5721), 534–537 (2005).
[CrossRef] [PubMed]

Other (7)

L. D. Landau, E. Lifshitz, and L. Pitaevskii, Electrodynamics of Continuous Media, 2nd ed. (Elsevier Butterworth-Heinemann, 2004).

K. Yasumoto, Electromagnetic Theory and Applications for Photonic Crystals (Taylor and Francis, 2006).

J. T. Costa and M. G. Silveirinha, “Macroscopic electromagnetic response of arbitrarily shaped spatially dispersive bodies formed by metallic wires,” arXiv:1205.1760v1 [physics.comp-ph], (2012).

F. A. Jenkins and H. E. White, Fundamentals of Optics, 4th ed. (McGraw-Hill, 1981).

CST Microwave Studio SuiteTM2010, ( http://www.cst.com ).

OSA, Handbook of Optics, 2nd ed. (McGraw-Hill Professional, 1994), vol. II.

M. Born and M. Wolf, Principles of Optics, 7th (expanded) ed. (Cambridge University Press, 1999).

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Figures (3)

Fig. 1
Fig. 1

(a) Illustration of the chromatic aberration of a conventional thin biconvex glass lens with parameters n 1 = n 2 = n g (ω) . (b) Biconvex optical metamaterial lens that corrects the chromatic aberration for all the colors of light; the compound lens is formed by a thin plano-convex glass lens coated with a thin plano-convex double wire medium. Panels (c) and (d) show cuts of the “double wire medium” slab along the planes xoz and xoy, respectively. The slab has thickness L .

Fig. 2
Fig. 2

(a) refractive indices of dense flint glass SF10 (black curve) and of the nanowire metamaterial (blue curves). Panels (b), (c) and (d): normalized | E z | 2 in the vicinity of a metamaterial prism at: (b) λ=0.38μm .(c) λ=0.56μm . (d) λ=0.75μm . (e) reversed rainbow obtained by blending the different light wavelengths [panels (b), (c) and (d)]. (f) transmission angle θ t as a function of the wavelength λ[ μm ] for a Gaussian beam that illuminates the prism along the normal direction. The blue dashed curve was obtained using the theoretical formula θ t =arcsin( n xw sinα ) and the solid black curve was calculated using a full wave FDFD-SD [18] simulation based on the effective medium model

Fig. 3
Fig. 3

(a) Profile of the normalized squared electric field near the focal region of the single-material glass lens. Solid curves: obtained using Microwave Studio [20]. Dashed curves: obtained with the FDFD simulator. (b) normalized | E z | 2 (obtained using the FDFD-SD full wave simulator [18]) in the vicinity of the compensated biconvex metamaterial lens. (c) analogous to (a), but for the compensated biconvex metamaterial lens. (d) focal plane curve as a function of the wavelength. The yellow stars (FDFD-SD method based on the effective medium model [18]) and the yellow circles (Microwave Studio [20]) represent the position of the foci of the compensated metamaterial lens. The red triangles and the diamond symbols (FDFD) represent the focal curve of a conventional achromatic doublet and of the single-material lens, respectively.

Equations (4)

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1 f =( n 1 1 ) 1 R 1 +( n 2 1 ) 1 R 2 .
n ˙ 1 = R 1 R 2 n ˙ 2 .
ε xw (ω, k x )=1+ 1 [ ( ε m 1) f V ] 1 [ (ω/c) 2 k x 2 /2 ]/ β p 2 ,
n xw = 3 2 ( β p c ω ) 2 1 ( ε m 1) f V + 1 4 +( 2 1 ( ε m 1) f V ) ( β p c ω ) 2 + 1 ( ε m 1) 2 f V 2 ( β p c ω ) 4 .

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