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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 3 — Jan. 30, 2012
  • pp: 2581–2586
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Breaking the imaging symmetry in negative refraction lenses

Changbao Ma and Zhaowei Liu  »View Author Affiliations


Optics Express, Vol. 20, Issue 3, pp. 2581-2586 (2012)
http://dx.doi.org/10.1364/OE.20.002581


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Abstract

Optical lenses are pervasive in various areas of sciences and technologies. It is well known that conventional lenses have symmetrical imaging properties along forward and backward directions. In this letter, we show that hyperbolic plasmonic metamaterial based negative refraction lenses perform as either converging lenses or diverging lenses depending on the illumination directions. New imaging equations and properties that are different from those of all the existing optical lenses are also presented. These new imaging properties, including symmetry breaking as well as the super resolving power, significantly expand the horizon of imaging optics and optical system design.

© 2012 OSA

1. Introduction

Lenses are the most fundamental and widely used elements in optics. The configuration of a lens is determined by the type of wavefront conversion to perform; basic conversions include transformation among diverging waves, converging waves and plane waves. As an object can be considered as an accumulation of point sources, a lens that converts a diverging wave to a converging one is capable to form an image of the object.

Imaging is one of the most basic functions of a lens, of which the imaging properties have been well established since the first elaboration by Kepler in 1611 [1

1. J. Kepler, Dioptrice (Augsburg: Franci, 1611).

]. As is illustrated in Fig. 1
Fig. 1 Imaging behaviors of a conventional converging lens. An object is placed beyond 2f in (a), at 2f in (b), between f and 2f in (c), and within f in (d). f is the focal length of the lens.
and summarized in Table 1

Table 1. Imaging Properties of a Conventional Converging Lens.

table-icon
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[2

2. E. Hecht, Optics, 4th ed. (Addison-Wesley, 2002).

], the image shows various characteristics when an object is placed at different locations with respect to the focal length f of a lens. Such imaging rules, which are governed by the imaging Eq. (1)/s0 + 1/si = 1/f with s0 and si being the object and image distances, respectively, are the foundations for ray optics and optical system design.

Based on the basic properties of a single lens, systems comprising multiple lenses can be conveniently designed. The resolution of an optical system is however beyond the scope of ray optics and has to be examined by wave optics. Owing to the diffractive nature of light, the best resolution of a lens system is limited to about half of the working wavelength ~λ/2 [3

3. E. Abbe, “Beitrage zur Theorie des Mikroskops und der mikroskopischen Wahrnehmung,” Arch. Mikrosc. Anat. Entwicklungsmech. 9(1), 413–418 (1873). [CrossRef]

]. Using the immersion technique, the resolution can be improved up to ~λ/(2n), but such enhancement however is quite modest due to the low refractive index n of natural materials [4

4. Q. Wu, G. D. Feke, R. D. Grober, and L. P. Ghislain, “Realization of numerical aperture 2.0 using a gallium phosphide solid immersion lens,” Appl. Phys. Lett. 75(26), 4064–4066 (1999). [CrossRef]

, 5

5. S. B. Ippolito, B. B. Goldberg, and M. S. Unlu, “High spatial resolution subsurface microscopy,” Appl. Phys. Lett. 78(26), 4071–4073 (2001). [CrossRef]

]. To achieve higher resolution, a material that can support the propagation of light with higher k-vectors is needed. Metamaterials, which are artificially engineered nanocomposites possessing extraordinary material properties, provide new opportunities for this purpose [6

6. D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, “Metamaterials and negative refractive index,” Science 305(5685), 788–792 (2004). [CrossRef] [PubMed]

8

8. V. M. Shalaev, “Optical negative-index metamaterials,” Nat. Photonics 1(1), 41–48 (2007). [CrossRef]

]. Various metamaterial based lenses have been proposed and demonstrated within the last decade [9

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

21

21. C. Ma, R. Aguinaldo, and Z. Liu, “Advances in the hyperlens,” Chin. Sci. Bull. 55(24), 2618–2624 (2010). [CrossRef]

]. Despite their success in achieving super resolution, such superlenses behave distinctively to their conventional counterpart. For instance, they cannot focus a plane wave, which represents a significant defect from both theoretical and practical points of view.

2. Theory

By introducing various phase compensation mechanisms in metamaterials, the plane wave focusing function has been realized recently [22

22. C. Ma and Z. Liu, “Focusing light into deep subwavelength using metamaterial immersion lenses,” Opt. Express 18(5), 4838–4844 (2010). [CrossRef] [PubMed]

, 23

23. C. Ma and Z. Liu, “A super resolution metalens with phase compensation mechanism,” Appl. Phys. Lett. 96(18), 183103 (2010). [CrossRef]

]. In this paper, we first provide a generalized imaging equation for the phase compensated metamaterials lenses, in which focal lengths can be defined from either direction. We further illustrate the unprecedented imaging properties if such lenses also experience negative refraction at the lens/air interfaces.

By convenience, we use the hyperbolic metalens, which comprises a metal plasmonic waveguide coupler (PWC) (gray structure in Fig. 2(a)
Fig. 2 Focusing behaviors of a hyperbolic metalens. (a) Plane wave from air converges to a focus (Fm) in metamaterial. (c) Plane wave from metamaterial diverges in air, resulting in a virtual focus (Fd) also in metamaterial. The arrows in (a) and (c) are eye-guiding rays. (b) and (d) Symbolized representation of (a) and (c). The dashed vertical lines represent phase compensating elements at the interfaces, i.e. the PWC.
and 2(c)) and plasmonic metamaterials with hyperbolic dispersion (εx >0, εz <0), as a specific example to illustrate the new imaging paradigm. Such a hyperbolic metalens can be designed to focus an incident p-polarized plane wave from the air side to the focus Fm at the focal length fm in the metamaterial by given εx and εz. The details of the PWC design follows similar principles described in literatures [23

23. C. Ma and Z. Liu, “A super resolution metalens with phase compensation mechanism,” Appl. Phys. Lett. 96(18), 183103 (2010). [CrossRef]

25

25. S. Thongrattanasiri and V. A. Podolskiy, “Hypergratings: nanophotonics in planar anisotropic metamaterials,” Opt. Lett. 34(7), 890–892 (2009). [CrossRef] [PubMed]

]. Due to the hyperbolic dispersion of the metalens, a plane wave comes from the metamaterial side, instead of being focused, diverges after the metalens, resulting in a virtual focus at Fd also in the metamaterial (Fig. 2(c)). It is well known that a conventional converging lens has two foci: one on each side; i.e., a plane wave coming from one side focuses to the other, and vice versa. In stark contrast, a hyperbolic metalens works like a converging lens from one side but a diverging lens from the other. Similar to a recent “Janus device” [26

26. T. Zentgraf, J. Valentine, N. Tapia, J. Li, and X. Zhang, “An optical “Janus” device for integrated photonics,” Adv. Mater. (Deerfield Beach Fla.) 22(23), 2561–2564 (2010). [CrossRef] [PubMed]

] showing different functions along multiple directions based on transformation optics [27

27. J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006). [CrossRef] [PubMed]

, 28

28. U. Leonhardt, “Optical conformal mapping,” Science 312(5781), 1777–1780 (2006). [CrossRef] [PubMed]

], a hyperbolic metalens is a “Janus lens” having two different focusing behaviors in opposite directions. Interestingly, although both focal lengths can be clearly defined, different signs must be taken accordingly. This distinctive focusing behavior leads to extraordinary imaging properties that do not exist in common lenses.

3. Formulations and simulations

An image Pd in air is formed by an object Pm in the metamaterial, and vice versa, as schematically shown in Fig. 3(a)
Fig. 3 (a) Schematic representation of forming an image by a hyperbolic metalens. Imaging behavior of a hyperbolic metalens for an object in air: (b) Ray diagram, (b) Numerical result.
. The optical path length (OPL) from Pd to Pm is given by(φd+φm+φc)/k0, whereϕd=k0vd2+x2is the phase delay in air, ϕm=k0εx'vm2+εz'x2is the phase delay in the metamaterial, and ϕc=ϕconstk0εx'fm2+εz'x2is the designed phase delay profile of the PWC according to the metalens design principle. εx and εz are the real part of the metamaterial permittivity in x and z directions respectively. vd and vm are the image/object distances in air and metamaterial, andϕconstis a constant.

According to the Fermat’s Principle, the OPL remains stationary; that is, its derivative with respect to the position variable x is zero, i.e., d[OPL]/dx = 0. So we have

1vd2+x2+εz'εx'vm2+εz'x2=εz'εx'fm2+εz'x2
(1)

This relationship must hold true for all the rays from Pm to Pd. Considering the paraxial approximation (x is negligible), Eq. (1) can be reduced to

1vd+εz'/εx'vm=εz'/εx'fm
(2)

It can be seen from Eq. (2) that when vm, i.e., the incident beam is a plane wave from the metamaterial, the focal length in air is resulted asfd=fmεx'/εz'. Replacing fd into Eq. (2), we obtain another form of metalens imaging equation

1vd+εz'/εx'vm=1fd
(3)

Because of the hyperbolic dispersion of the metamaterial, the relation between fd and fm indicates they always have different signs. According to the sign convention, if fm>0 represents Fm in the metamaterial (Fig. 2 (a)), fd<0 means that the Fd is not in air but also in the metamaterial. Through an analogy to the typical symbolic notation of a focusing lens by using a double arrowed line, we symbolize the hyperbolic metalens with both foci in the metamaterial, as shown in Fig. 2(b) and 2(d).

As is analyzed above, a hyperbolic metalens breaks the forward/backward symmetry preserved in conventional lenses, leading to exceptional focusing behaviors. In the following, we examine the imaging formation for an object placed at various locations with respect to its focal lengths. The specific hyperbolic metalens was designed with fm = 2.0 μm at the wavelength of 690 nm. The metamaterial is assumed to have εx = 6.4 + 0.03i and εz = −10.3 + 0.2i. This specific metamaterial can be constructed by silver nanowires in a dielectric host with a refractive index of 1.3. The silver nanowires are orientated in the z direction and their volumetric filling ratio is 0.5.

Figure 3(a) schematically depicts the imaging behavior of such a hyperbolic metalens for an object in air. Two characteristic rays can be used to determine the image: the one parallel to the optical axis is “refracted” toward the focus Fm in the metamaterial; another one towards the focus Fd is “refracted” to the direction parallel to the optical axis in the metamaterial. The crossing point of these two rays determines the location of the image. Particularly, in the case of an object in air, the image in the metamaterial is always minified, erect, real and within the first focal length, regardless of the distance of the object in air to the metalens. This is completely different from a conventional lens, in which the image properties are dependent on the position of the object (see Table 1). Another special ray, which is the one passing the optical center O, may also be used to determine the location of the image through the calculation of its refraction angle in the metamaterial θmRe(εx/εz)sinθd, withθdbeing the incident angle andθmbeing the refracted angle of that ray with respect to the optical axis. Figure 3(b) shows the numerical verification for such a case using full wave simulation. Because the image cannot go beyond the focal plane in the metamaterial, the entire half space in air is mapped into a highly confined region in metamaterial.

Similarly, through schematic and geometric analysis, the image of an object in metamaterial can also be analyzed: the property of the image is dependent on the position of the object relative to the focus fm. The image location can also be determined using characteristic rays: the one connecting the object and the focus Fm is “refracted” to the direction parallel to the optical axis; another one parallel to the optical axis is “refracted” to the direction whose backward extension passes the focus Fd, because Fd is not in air but in the metamaterial. Figure 4(a)
Fig. 4 Imaging behavior of a hyperbolic metalens for an object in metamaterial. (a) Object is inside point Fm. (c) Object is between points Fm and 2Fm. (e) Object is at point 2Fm. (g) Object is outside point 2Fm. (b), (d), (f), (h), Numerical verifications of (a), (c), (e), (g), respectively.
shows the imaging behavior of an object within the first focal length in the metamaterial, i.e., vm < fm: the image in air is always magnified, erect and real. The image is real because the “refracted” rays converge in air. This case is simply the reciprocal of the case shown in Fig. 3(b). When the object is outside the first focal length, i.e., vm > fm the rays in air diverge, but their backward extensions converge into a point on the other side of the optical axis in the metamaterial space, thus the image is always virtual and inverted. Depending on the relative position of the object, the image may be different in size; when the object is outside the first but inside the second focal length, i.e., fm < vm < 2fm, the image is magnified, as shown in Fig. 4(c); when the object is at the second focal length, i.e., vm = 2fm, the image has the same size as the object, as shown in Fig. 4(e); when the object is outside the second focal length, i.e., vm > 2fm, the image is minified, as shown in Fig. 4(g). All the four cases above for an object in the metamaterial are numerically verified, as shown in Fig. 4(b)-(h). These extraordinary properties of a hyperbolic metalens are summarized in Table 2

Table 2. Imaging Properties of a Hyperbolic Metalens. fm>0 and fd < 0.

table-icon
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, which can also be directly derived from the metalens imaging equations (Eq. (2) and (3)).

As shown in Fig. 3 and Fig. 4, the magnification of the metalens can also be determined analytically through the transverse magnification MT
MT=umud=gmfm=fdgd
(4)
where um and ud are the object/image height, i.e., the distance from the object/image to the optical axis, in the metamaterial and air space respectively; gm and gd are the object/image distance reckoned from their focus in the metamaterial and air space respectively.

4. Discussions and conclusions

Although illustrated using hyperbolic metalenses with fm>0, fm can also be designed to be negative (fm<0), meaning a plane wave from the air side diverges in the hyperbolically dispersive metamaterial. In this case, a plane wave from the metamaterial side will be focused in air, resulting in a positive fd. Analyses show that all the above equations remain valid and the hyperbolic metalens with fm<0 is also a “Janus lens”. The imaging properties of such a hyperbolic metalens with fm<0 can also be deduced through a similar method mentioned above.

We finally emphasize that the new set of imaging properties in the exampled hyperbolic metalens is a result of the hyperbolic dispersion of the metamaterials. The hyperbolic metalenses also possess super resolution capabilities as demonstrated before [23

23. C. Ma and Z. Liu, “A super resolution metalens with phase compensation mechanism,” Appl. Phys. Lett. 96(18), 183103 (2010). [CrossRef]

, 24

24. C. Ma and Z. Liu, “Designing super-resolution metalenses by the combination of metamaterials and nanoscale plasmonic waveguide couplers,” J. Nanophotonics 5(1), 051604 (2011). [CrossRef]

]. The rules are applicable to any other type of phase compensated lenses that experiences negative refraction at the air/lens interface. These exotic imaging properties are impossible to realize by conventional lenses, thus extending the imaging properties and the capabilities of lenses, and the imaging optics in general, to a new horizon. A practical usage of such lenses is to truncate the metamaterial to the focal/image plane so that the optical near field can be accessed from air [29

29. C. Ma, M. A. Escobar, and Z. Liu, “Extraordinary light focusing and Fourier transform propertties of gradient-index metalenses,” Phys. Rev. B 84(19), 195142 (2011). [CrossRef]

]. The new found imaging behaviors and the super resolving power of hyperbolic metalenses provide new opportunities to explore novel optical devices and systems and will profoundly affect the advancement of optics.

Acknowledgment

This work was partially supported by the startup fund of the University of California at San Diego and the NSF-ECCS under Grant No. 0969405.

References and links

1.

J. Kepler, Dioptrice (Augsburg: Franci, 1611).

2.

E. Hecht, Optics, 4th ed. (Addison-Wesley, 2002).

3.

E. Abbe, “Beitrage zur Theorie des Mikroskops und der mikroskopischen Wahrnehmung,” Arch. Mikrosc. Anat. Entwicklungsmech. 9(1), 413–418 (1873). [CrossRef]

4.

Q. Wu, G. D. Feke, R. D. Grober, and L. P. Ghislain, “Realization of numerical aperture 2.0 using a gallium phosphide solid immersion lens,” Appl. Phys. Lett. 75(26), 4064–4066 (1999). [CrossRef]

5.

S. B. Ippolito, B. B. Goldberg, and M. S. Unlu, “High spatial resolution subsurface microscopy,” Appl. Phys. Lett. 78(26), 4071–4073 (2001). [CrossRef]

6.

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, “Metamaterials and negative refractive index,” Science 305(5685), 788–792 (2004). [CrossRef] [PubMed]

7.

J. Yao, Z. Liu, Y. Liu, Y. Wang, C. Sun, G. Bartal, A. M. Stacy, and X. Zhang, “Optical negative refraction in bulk metamaterials of nanowires,” Science 321(5891), 930 (2008). [CrossRef] [PubMed]

8.

V. M. Shalaev, “Optical negative-index metamaterials,” Nat. Photonics 1(1), 41–48 (2007). [CrossRef]

9.

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

10.

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]

11.

Z. Liu, S. Durant, H. Lee, Y. Pikus, N. Fang, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical superlens,” Nano Lett. 7(2), 403–408 (2007). [CrossRef] [PubMed]

12.

E. E. Narimanov, “Far-field superlens: optical nanoscope,” Nat. Photonics 1(5), 260–261 (2007). [CrossRef]

13.

Z. Jacob, L. V. Alekseyev, and E. Narimanov, “Optical Hyperlens: Far-field imaging beyond the diffraction limit,” Opt. Express 14(18), 8247–8256 (2006). [CrossRef] [PubMed]

14.

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science 315(5819), 1686 (2007). [CrossRef] [PubMed]

15.

Y. Xiong, Z. Liu, and X. Zhang, “A simple design of flat hyperlens for lithography and imaging with half-pitch resolution down to 20 nm,” Appl. Phys. Lett. 94(20), 203108 (2009). [CrossRef]

16.

I. I. Smolyaninov, Y. J. Hung, and C. C. Davis, “Magnifying superlens in the visible frequency range,” Science 315(5819), 1699–1701 (2007). [CrossRef] [PubMed]

17.

S. Vedantam, H. Lee, J. Tang, J. Conway, M. Staffaroni, and E. Yablonovitch, “A plasmonic dimple lens for nanoscale focusing of light,” Nano Lett. 9(10), 3447–3452 (2009). [CrossRef] [PubMed]

18.

F. M. Huang and N. I. Zheludev, “Super-resolution without evanescent waves,” Nano Lett. 9(3), 1249–1254 (2009). [CrossRef] [PubMed]

19.

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(3), 033902–033904 (2009). [CrossRef] [PubMed]

20.

X. Zhang and Z. Liu, “Superlenses to overcome the diffraction limit,” Nat. Mater. 7(6), 435–441 (2008). [CrossRef] [PubMed]

21.

C. Ma, R. Aguinaldo, and Z. Liu, “Advances in the hyperlens,” Chin. Sci. Bull. 55(24), 2618–2624 (2010). [CrossRef]

22.

C. Ma and Z. Liu, “Focusing light into deep subwavelength using metamaterial immersion lenses,” Opt. Express 18(5), 4838–4844 (2010). [CrossRef] [PubMed]

23.

C. Ma and Z. Liu, “A super resolution metalens with phase compensation mechanism,” Appl. Phys. Lett. 96(18), 183103 (2010). [CrossRef]

24.

C. Ma and Z. Liu, “Designing super-resolution metalenses by the combination of metamaterials and nanoscale plasmonic waveguide couplers,” J. Nanophotonics 5(1), 051604 (2011). [CrossRef]

25.

S. Thongrattanasiri and V. A. Podolskiy, “Hypergratings: nanophotonics in planar anisotropic metamaterials,” Opt. Lett. 34(7), 890–892 (2009). [CrossRef] [PubMed]

26.

T. Zentgraf, J. Valentine, N. Tapia, J. Li, and X. Zhang, “An optical “Janus” device for integrated photonics,” Adv. Mater. (Deerfield Beach Fla.) 22(23), 2561–2564 (2010). [CrossRef] [PubMed]

27.

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006). [CrossRef] [PubMed]

28.

U. Leonhardt, “Optical conformal mapping,” Science 312(5781), 1777–1780 (2006). [CrossRef] [PubMed]

29.

C. Ma, M. A. Escobar, and Z. Liu, “Extraordinary light focusing and Fourier transform propertties of gradient-index metalenses,” Phys. Rev. B 84(19), 195142 (2011). [CrossRef]

OCIS Codes
(110.2990) Imaging systems : Image formation theory
(220.3630) Optical design and fabrication : Lenses
(160.3918) Materials : Metamaterials
(350.4238) Other areas of optics : Nanophotonics and photonic crystals

ToC Category:
Imaging Systems

History
Original Manuscript: November 23, 2011
Revised Manuscript: January 13, 2012
Manuscript Accepted: January 13, 2012
Published: January 20, 2012

Citation
Changbao Ma and Zhaowei Liu, "Breaking the imaging symmetry in negative refraction lenses," Opt. Express 20, 2581-2586 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-3-2581


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References

  1. J. Kepler, Dioptrice (Augsburg: Franci, 1611).
  2. E. Hecht, Optics, 4th ed. (Addison-Wesley, 2002).
  3. E. Abbe, “Beitrage zur Theorie des Mikroskops und der mikroskopischen Wahrnehmung,” Arch. Mikrosc. Anat. Entwicklungsmech.9(1), 413–418 (1873). [CrossRef]
  4. Q. Wu, G. D. Feke, R. D. Grober, and L. P. Ghislain, “Realization of numerical aperture 2.0 using a gallium phosphide solid immersion lens,” Appl. Phys. Lett.75(26), 4064–4066 (1999). [CrossRef]
  5. S. B. Ippolito, B. B. Goldberg, and M. S. Unlu, “High spatial resolution subsurface microscopy,” Appl. Phys. Lett.78(26), 4071–4073 (2001). [CrossRef]
  6. D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, “Metamaterials and negative refractive index,” Science305(5685), 788–792 (2004). [CrossRef] [PubMed]
  7. J. Yao, Z. Liu, Y. Liu, Y. Wang, C. Sun, G. Bartal, A. M. Stacy, and X. Zhang, “Optical negative refraction in bulk metamaterials of nanowires,” Science321(5891), 930 (2008). [CrossRef] [PubMed]
  8. V. M. Shalaev, “Optical negative-index metamaterials,” Nat. Photonics1(1), 41–48 (2007). [CrossRef]
  9. J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett.85(18), 3966–3969 (2000). [CrossRef] [PubMed]
  10. N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens,” Science308(5721), 534–537 (2005). [CrossRef] [PubMed]
  11. Z. Liu, S. Durant, H. Lee, Y. Pikus, N. Fang, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical superlens,” Nano Lett.7(2), 403–408 (2007). [CrossRef] [PubMed]
  12. E. E. Narimanov, “Far-field superlens: optical nanoscope,” Nat. Photonics1(5), 260–261 (2007). [CrossRef]
  13. Z. Jacob, L. V. Alekseyev, and E. Narimanov, “Optical Hyperlens: Far-field imaging beyond the diffraction limit,” Opt. Express14(18), 8247–8256 (2006). [CrossRef] [PubMed]
  14. Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science315(5819), 1686 (2007). [CrossRef] [PubMed]
  15. Y. Xiong, Z. Liu, and X. Zhang, “A simple design of flat hyperlens for lithography and imaging with half-pitch resolution down to 20 nm,” Appl. Phys. Lett.94(20), 203108 (2009). [CrossRef]
  16. I. I. Smolyaninov, Y. J. Hung, and C. C. Davis, “Magnifying superlens in the visible frequency range,” Science315(5819), 1699–1701 (2007). [CrossRef] [PubMed]
  17. S. Vedantam, H. Lee, J. Tang, J. Conway, M. Staffaroni, and E. Yablonovitch, “A plasmonic dimple lens for nanoscale focusing of light,” Nano Lett.9(10), 3447–3452 (2009). [CrossRef] [PubMed]
  18. F. M. Huang and N. I. Zheludev, “Super-resolution without evanescent waves,” Nano Lett.9(3), 1249–1254 (2009). [CrossRef] [PubMed]
  19. 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(3), 033902–033904 (2009). [CrossRef] [PubMed]
  20. X. Zhang and Z. Liu, “Superlenses to overcome the diffraction limit,” Nat. Mater.7(6), 435–441 (2008). [CrossRef] [PubMed]
  21. C. Ma, R. Aguinaldo, and Z. Liu, “Advances in the hyperlens,” Chin. Sci. Bull.55(24), 2618–2624 (2010). [CrossRef]
  22. C. Ma and Z. Liu, “Focusing light into deep subwavelength using metamaterial immersion lenses,” Opt. Express18(5), 4838–4844 (2010). [CrossRef] [PubMed]
  23. C. Ma and Z. Liu, “A super resolution metalens with phase compensation mechanism,” Appl. Phys. Lett.96(18), 183103 (2010). [CrossRef]
  24. C. Ma and Z. Liu, “Designing super-resolution metalenses by the combination of metamaterials and nanoscale plasmonic waveguide couplers,” J. Nanophotonics5(1), 051604 (2011). [CrossRef]
  25. S. Thongrattanasiri and V. A. Podolskiy, “Hypergratings: nanophotonics in planar anisotropic metamaterials,” Opt. Lett.34(7), 890–892 (2009). [CrossRef] [PubMed]
  26. T. Zentgraf, J. Valentine, N. Tapia, J. Li, and X. Zhang, “An optical “Janus” device for integrated photonics,” Adv. Mater. (Deerfield Beach Fla.)22(23), 2561–2564 (2010). [CrossRef] [PubMed]
  27. J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science312(5781), 1780–1782 (2006). [CrossRef] [PubMed]
  28. U. Leonhardt, “Optical conformal mapping,” Science312(5781), 1777–1780 (2006). [CrossRef] [PubMed]
  29. C. Ma, M. A. Escobar, and Z. Liu, “Extraordinary light focusing and Fourier transform propertties of gradient-index metalenses,” Phys. Rev. B84(19), 195142 (2011). [CrossRef]

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