Abstract

In this paper, off-axis characteristic of subwavelength focusing in anisotropic metamaterials is examined and analyzed numerically. Conditions for reducing aberrations of off-axis focus are presented and demonstrated. Also discussed are geometrical parameters’ influences on the off-axis focusing behavior.

© 2012 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. M. Born and E. Wolf, Principles of Optics (Cambridge University, 1999).
  2. D. R. Smith and D. Schurig, “Electromagnetic wave propagation in media with indefinite permittivity and permeability tensors,” Phys. Rev. Lett. 90, 077405 (2003).
    [CrossRef]
  3. V. A. Podolskiy and E. E. Narimanov, “Strongly anisotropic waveguide as a nonmagnetic left-handed system,” Phys. Rev. B 71, 201101 (2005).
    [CrossRef]
  4. V. A. Podolskiy, L. Alekseyev, and E. E. Narimanov, “Strongly anisotropic media: the THz perspectives of lefthanded materials,” J. Mod. Opt. 52, 2343–2349 (2005).
    [CrossRef]
  5. A. A. Govyadinov and V. A. Podolskiy, “Meta-material photonic funnels for sub-diffraction light compression and propagation,” Phys. Rev. B 73, 155108 (2006).
    [CrossRef]
  6. B. Wood, J. B. Pendry, and D. P. Tsai, “Directed subwavelength imaging using a layered metal-dielectric system,” Phys. Rev. B 74, 115116 (2006).
    [CrossRef]
  7. S. Feng and J. M. Elson, “Diffraction-suppressed high-resolution imaging through metallodielectric nanofilms,” Opt. Express 14, 216–221 (2006).
    [CrossRef]
  8. Z. Jacob, L. Alekseyev, and E. Narimanov, “Optical hyperlens: far-field imaging beyond the diffraction limit,” Opt. Express 14, 8247–8256 (2006).
    [CrossRef]
  9. Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science 315, 1686 (2007).
    [CrossRef]
  10. W. Wang, H. Xing, L. Fang, Y. Liu, J. Ma, L. Lin, C. Wang, and X. Luo, “Far-field imaging device: planar hyperlens with magnification using multi-layer metamaterial,” Opt. Express 16, 21142–21148 (2008).
    [CrossRef]
  11. Y. Xiong, Z. Liu, and X. Zhang, “Projecting deep-subwavelength patterns from diffraction-limited masks using metal-dielectric multilayers,” Appl. Phys. Lett. 93, 111116 (2008).
  12. C. Wang, Y. Zhao, D. Gan, C. Du, and X. Luo, “Subwavelength imaging with anisotropic structure comprising alternately layered metal and dielectric films,” Opt. Express 16, 4217–4227(2008).
    [CrossRef]
  13. J. Yao, K. Tsai, Y. Wang, Z. Liu, G. Bartal, Y. Wang, and X. Zhang, “Imaging visible light using anisotropic metamaterial slab lens,” Opt. Express 17, 22380–22385 (2009).
    [CrossRef]
  14. S. Thongrattanasiri and V. Podolskiy, “Hypergratings: nanophotonics in planar anisotropic metamaterials,” Opt. Lett. 34, 890–892 (2009).
    [CrossRef]
  15. C. Ma and Z. Liu, “A super resolution metalens with phase compensation mechanism,” Appl. Phys. Lett. 96, 183103 (2010).
    [CrossRef]
  16. G. Ren, Z. Lai, C. Wang, Q. Feng, L. Liu, K. Liu, and X. Luo “Subwavelength focusing of light in the planar anisotropic metamaterials with zone plates,” Opt. Express 18, 18151–18157 (2010).
    [CrossRef]
  17. L. Verslegers, P. B. Catrysse, Z. Yu, and S. Fan, “Deep-subwavelength focusing and steering of light in an aperiodic metallic waveguide array,” Phys. Rev. Lett. 103, 033902(2009).
    [CrossRef]
  18. C. Ma and Z. Liu, “Focusing light into deep subwavelength usingmetamaterial immersion lenses,” Opt. Express 18, 4838–4844 (2010).
    [CrossRef]
  19. P. B. Johnson and R. W. Christy, “Optical constants of noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
    [CrossRef]
  20. E. Palik, ed., The Handbook of Optical Constants of Solids (AP, 1985).
  21. S. Tretyakov, Analytical Modeling in Applied Electromagnetics (Artech House, 2000).

2010 (3)

2009 (3)

2008 (3)

2007 (1)

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science 315, 1686 (2007).
[CrossRef]

2006 (4)

A. A. Govyadinov and V. A. Podolskiy, “Meta-material photonic funnels for sub-diffraction light compression and propagation,” Phys. Rev. B 73, 155108 (2006).
[CrossRef]

B. Wood, J. B. Pendry, and D. P. Tsai, “Directed subwavelength imaging using a layered metal-dielectric system,” Phys. Rev. B 74, 115116 (2006).
[CrossRef]

S. Feng and J. M. Elson, “Diffraction-suppressed high-resolution imaging through metallodielectric nanofilms,” Opt. Express 14, 216–221 (2006).
[CrossRef]

Z. Jacob, L. Alekseyev, and E. Narimanov, “Optical hyperlens: far-field imaging beyond the diffraction limit,” Opt. Express 14, 8247–8256 (2006).
[CrossRef]

2005 (2)

V. A. Podolskiy and E. E. Narimanov, “Strongly anisotropic waveguide as a nonmagnetic left-handed system,” Phys. Rev. B 71, 201101 (2005).
[CrossRef]

V. A. Podolskiy, L. Alekseyev, and E. E. Narimanov, “Strongly anisotropic media: the THz perspectives of lefthanded materials,” J. Mod. Opt. 52, 2343–2349 (2005).
[CrossRef]

2003 (1)

D. R. Smith and D. Schurig, “Electromagnetic wave propagation in media with indefinite permittivity and permeability tensors,” Phys. Rev. Lett. 90, 077405 (2003).
[CrossRef]

1972 (1)

P. B. Johnson and R. W. Christy, “Optical constants of noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
[CrossRef]

Alekseyev, L.

Z. Jacob, L. Alekseyev, and E. Narimanov, “Optical hyperlens: far-field imaging beyond the diffraction limit,” Opt. Express 14, 8247–8256 (2006).
[CrossRef]

V. A. Podolskiy, L. Alekseyev, and E. E. Narimanov, “Strongly anisotropic media: the THz perspectives of lefthanded materials,” J. Mod. Opt. 52, 2343–2349 (2005).
[CrossRef]

Bartal, G.

Born, M.

M. Born and E. Wolf, Principles of Optics (Cambridge University, 1999).

Catrysse, P. B.

L. Verslegers, P. B. Catrysse, Z. Yu, and S. Fan, “Deep-subwavelength focusing and steering of light in an aperiodic metallic waveguide array,” Phys. Rev. Lett. 103, 033902(2009).
[CrossRef]

Christy, R. W.

P. B. Johnson and R. W. Christy, “Optical constants of noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
[CrossRef]

Du, C.

Elson, J. M.

Fan, S.

L. Verslegers, P. B. Catrysse, Z. Yu, and S. Fan, “Deep-subwavelength focusing and steering of light in an aperiodic metallic waveguide array,” Phys. Rev. Lett. 103, 033902(2009).
[CrossRef]

Fang, L.

Feng, Q.

Feng, S.

Gan, D.

Govyadinov, A. A.

A. A. Govyadinov and V. A. Podolskiy, “Meta-material photonic funnels for sub-diffraction light compression and propagation,” Phys. Rev. B 73, 155108 (2006).
[CrossRef]

Jacob, Z.

Johnson, P. B.

P. B. Johnson and R. W. Christy, “Optical constants of noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
[CrossRef]

Lai, Z.

Lee, H.

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science 315, 1686 (2007).
[CrossRef]

Lin, L.

Liu, K.

Liu, L.

Liu, Y.

Liu, Z.

C. Ma and Z. Liu, “Focusing light into deep subwavelength usingmetamaterial immersion lenses,” Opt. Express 18, 4838–4844 (2010).
[CrossRef]

C. Ma and Z. Liu, “A super resolution metalens with phase compensation mechanism,” Appl. Phys. Lett. 96, 183103 (2010).
[CrossRef]

J. Yao, K. Tsai, Y. Wang, Z. Liu, G. Bartal, Y. Wang, and X. Zhang, “Imaging visible light using anisotropic metamaterial slab lens,” Opt. Express 17, 22380–22385 (2009).
[CrossRef]

Y. Xiong, Z. Liu, and X. Zhang, “Projecting deep-subwavelength patterns from diffraction-limited masks using metal-dielectric multilayers,” Appl. Phys. Lett. 93, 111116 (2008).

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science 315, 1686 (2007).
[CrossRef]

Luo, X.

Ma, C.

C. Ma and Z. Liu, “A super resolution metalens with phase compensation mechanism,” Appl. Phys. Lett. 96, 183103 (2010).
[CrossRef]

C. Ma and Z. Liu, “Focusing light into deep subwavelength usingmetamaterial immersion lenses,” Opt. Express 18, 4838–4844 (2010).
[CrossRef]

Ma, J.

Narimanov, E.

Narimanov, E. E.

V. A. Podolskiy, L. Alekseyev, and E. E. Narimanov, “Strongly anisotropic media: the THz perspectives of lefthanded materials,” J. Mod. Opt. 52, 2343–2349 (2005).
[CrossRef]

V. A. Podolskiy and E. E. Narimanov, “Strongly anisotropic waveguide as a nonmagnetic left-handed system,” Phys. Rev. B 71, 201101 (2005).
[CrossRef]

Pendry, J. B.

B. Wood, J. B. Pendry, and D. P. Tsai, “Directed subwavelength imaging using a layered metal-dielectric system,” Phys. Rev. B 74, 115116 (2006).
[CrossRef]

Podolskiy, V.

Podolskiy, V. A.

A. A. Govyadinov and V. A. Podolskiy, “Meta-material photonic funnels for sub-diffraction light compression and propagation,” Phys. Rev. B 73, 155108 (2006).
[CrossRef]

V. A. Podolskiy and E. E. Narimanov, “Strongly anisotropic waveguide as a nonmagnetic left-handed system,” Phys. Rev. B 71, 201101 (2005).
[CrossRef]

V. A. Podolskiy, L. Alekseyev, and E. E. Narimanov, “Strongly anisotropic media: the THz perspectives of lefthanded materials,” J. Mod. Opt. 52, 2343–2349 (2005).
[CrossRef]

Ren, G.

Schurig, D.

D. R. Smith and D. Schurig, “Electromagnetic wave propagation in media with indefinite permittivity and permeability tensors,” Phys. Rev. Lett. 90, 077405 (2003).
[CrossRef]

Smith, D. R.

D. R. Smith and D. Schurig, “Electromagnetic wave propagation in media with indefinite permittivity and permeability tensors,” Phys. Rev. Lett. 90, 077405 (2003).
[CrossRef]

Sun, C.

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science 315, 1686 (2007).
[CrossRef]

Thongrattanasiri, S.

Tretyakov, S.

S. Tretyakov, Analytical Modeling in Applied Electromagnetics (Artech House, 2000).

Tsai, D. P.

B. Wood, J. B. Pendry, and D. P. Tsai, “Directed subwavelength imaging using a layered metal-dielectric system,” Phys. Rev. B 74, 115116 (2006).
[CrossRef]

Tsai, K.

Verslegers, L.

L. Verslegers, P. B. Catrysse, Z. Yu, and S. Fan, “Deep-subwavelength focusing and steering of light in an aperiodic metallic waveguide array,” Phys. Rev. Lett. 103, 033902(2009).
[CrossRef]

Wang, C.

Wang, W.

Wang, Y.

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Cambridge University, 1999).

Wood, B.

B. Wood, J. B. Pendry, and D. P. Tsai, “Directed subwavelength imaging using a layered metal-dielectric system,” Phys. Rev. B 74, 115116 (2006).
[CrossRef]

Xing, H.

Xiong, Y.

Y. Xiong, Z. Liu, and X. Zhang, “Projecting deep-subwavelength patterns from diffraction-limited masks using metal-dielectric multilayers,” Appl. Phys. Lett. 93, 111116 (2008).

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science 315, 1686 (2007).
[CrossRef]

Yao, J.

Yu, Z.

L. Verslegers, P. B. Catrysse, Z. Yu, and S. Fan, “Deep-subwavelength focusing and steering of light in an aperiodic metallic waveguide array,” Phys. Rev. Lett. 103, 033902(2009).
[CrossRef]

Zhang, X.

J. Yao, K. Tsai, Y. Wang, Z. Liu, G. Bartal, Y. Wang, and X. Zhang, “Imaging visible light using anisotropic metamaterial slab lens,” Opt. Express 17, 22380–22385 (2009).
[CrossRef]

Y. Xiong, Z. Liu, and X. Zhang, “Projecting deep-subwavelength patterns from diffraction-limited masks using metal-dielectric multilayers,” Appl. Phys. Lett. 93, 111116 (2008).

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science 315, 1686 (2007).
[CrossRef]

Zhao, Y.

Appl. Phys. Lett. (2)

Y. Xiong, Z. Liu, and X. Zhang, “Projecting deep-subwavelength patterns from diffraction-limited masks using metal-dielectric multilayers,” Appl. Phys. Lett. 93, 111116 (2008).

C. Ma and Z. Liu, “A super resolution metalens with phase compensation mechanism,” Appl. Phys. Lett. 96, 183103 (2010).
[CrossRef]

J. Mod. Opt. (1)

V. A. Podolskiy, L. Alekseyev, and E. E. Narimanov, “Strongly anisotropic media: the THz perspectives of lefthanded materials,” J. Mod. Opt. 52, 2343–2349 (2005).
[CrossRef]

Opt. Express (7)

Opt. Lett. (1)

Phys. Rev. B (4)

P. B. Johnson and R. W. Christy, “Optical constants of noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
[CrossRef]

A. A. Govyadinov and V. A. Podolskiy, “Meta-material photonic funnels for sub-diffraction light compression and propagation,” Phys. Rev. B 73, 155108 (2006).
[CrossRef]

B. Wood, J. B. Pendry, and D. P. Tsai, “Directed subwavelength imaging using a layered metal-dielectric system,” Phys. Rev. B 74, 115116 (2006).
[CrossRef]

V. A. Podolskiy and E. E. Narimanov, “Strongly anisotropic waveguide as a nonmagnetic left-handed system,” Phys. Rev. B 71, 201101 (2005).
[CrossRef]

Phys. Rev. Lett. (2)

L. Verslegers, P. B. Catrysse, Z. Yu, and S. Fan, “Deep-subwavelength focusing and steering of light in an aperiodic metallic waveguide array,” Phys. Rev. Lett. 103, 033902(2009).
[CrossRef]

D. R. Smith and D. Schurig, “Electromagnetic wave propagation in media with indefinite permittivity and permeability tensors,” Phys. Rev. Lett. 90, 077405 (2003).
[CrossRef]

Science (1)

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science 315, 1686 (2007).
[CrossRef]

Other (3)

M. Born and E. Wolf, Principles of Optics (Cambridge University, 1999).

E. Palik, ed., The Handbook of Optical Constants of Solids (AP, 1985).

S. Tretyakov, Analytical Modeling in Applied Electromagnetics (Artech House, 2000).

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 (6)

Fig. 1.
Fig. 1.

Schematic of subwavelength focusing structure with two nanoslits.

Fig. 2.
Fig. 2.

Simulated results of subwavelength focusing in metamaterial with double slits with (a) normal illumination and (b) tilted illumination with incident angle θ = 17.5 ° ( sin θ = 0.3 ), respectively. (c) Calculated focus shifts against the incident angle (solid curves) and the simulated focal shift values (dashed line with circle point). Plotted in (d) are electric intensity profiles at the focal plane. All the electric intensity is normalized.

Fig. 3.
Fig. 3.

Simulated results of subwavelength focusing in metamaterials with opposite anisotropy. (a) and (b) are for incidence angle with θ = 0 ° , θ = 17.5 ° , respectively. (c) Electric intensity profiles at the focal plane. (d) Calculated shifts for different axial symmetric points of the slits as a function of the incident angle (solid curves) and the simulated focal spot shifts (dashed red curve).

Fig. 4.
Fig. 4.

Simulated results of subwavelength focusing in metamaterials with multiple slits. (a) and (b) are calculated focus light field for light illumination with incident angle θ = 0 ° and θ = 17.5 ° , respectively. Electric intensity profiles at the focal plane are plotted in (c). (d) Calculated shifts for variant axial symmetric points of the slits as a function of the incident angle (solid curves) and the simulated focal spot shifts (dashed red curve).

Fig. 5.
Fig. 5.

Off-axis subwavelength focusing in the metamaterials of permittivity tensor ( 1 + 0.02 i , 1 + 0.02 i , 10 + 1 i ) (a), (b) and ( 1 + 0.02 i , 1 + 0.02 i , 3 + 1 i ) (c), (d), respectively, with different incident angles. The incident wavelength is 365 nm and the slit width is 200 nm. The focal lengths are about 500 and 200 nm, respectively.

Fig. 6.
Fig. 6.

Calculated shifts for different axial symmetric points in the slit as a function of the incident angle. The metamaterial permittivity tensors are ( 1 + 0.02 i , 1 + 0.02 i , 10 + 1 i ) and ( 1 + 0.02 i , 1 + 0.02 i , 3 + 1 i ), respectively.

Equations (5)

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

ϕ L const + ϕ L slit + ϕ L MM = ϕ R const + ϕ R slit + ϕ R MM
{ ϕ L const ϕ R const = 2 x sin θ · 2 π / λ ϕ L slit = ϕ R slit ϕ L MM = ε x f 2 + ε z ( x + Δ x ) 2 · 2 π / λ ϕ R MM = ε x f 2 + ε z ( x Δ x ) 2 · 2 π / λ ,
| Δ x | = | sin θ | · f 2 ε x / ( ε z 2 ε z sin 2 θ ) + x 2 / ε z .
| d Δ x d x | = sin θ / ( ( f / x ) 2 ε x / ( 1 sin 2 θ / ε z ) + ε z )
| d Δ x d x | = sin θ / ( ε z 2 / ( ε z sin 2 θ ) + ε z ) .

Metrics