## Subwavelength image manipulation through an oblique layered system |

Optics Express, Vol. 19, Issue 18, pp. 16809-16820 (2011)

http://dx.doi.org/10.1364/OE.19.016809

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### Abstract

We show in this work an oblique layered system that is capable of manipulating two dimensional subwavelength images. Through properly designed planar layered system, we demonstrate analytically that lateral image shift could be achieved with subwavelength resolution, due to the asymmetry of the dispersion curve of constant frequency. Further, image rotation with arbitrary angle, as well as image magnification could be generated through a concentric geometry of the alternating layered system. In addition, we verify the image mechanism using full wave electromagnetic (EM) simulations. Utilizing the proposed layered system, optical image of an object with subwavelength features can be projected allowing for further optical processing of the image by conventional optics.

© 2011 OSA

## 1. Introduction

1. E. Abbe, “Beitrage zur theorie des mikroskops und der mikroskopischen wahrnehmung,” Arch. Mikrosk. Anat. **9**, 413–468 (1873). [CrossRef]

*λ*/2. The reason is that high spatial frequency information carried by evanescent waves only exists in the near field of an object, only the propagating light reaches the far-field image plane. So collecting the evanescent information directly in the near field has long been considered as the most straightforward and effective way to overcome the diffraction limit.

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

*ɛ*= −1 and

*μ*= −1 can form a perfect copy of an object: all details of the object, even smaller than the wavelength of light are reproduced. This proposed lens can couple incident evanescent waves into resonant surface plasmon, therefore amplify and “restore” evanescent components to exhibit perfect focusing. However, there are no natural NIMs and low-loss isotropic artificial NIMs are difficult to fabricate, especially at the infrared and visible frequencies. So a practical scheme [2

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

3. 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]

4. T. J. Cui, D. R. Smith, and R. Liu, eds., *Metamaterials—Theory, Design, and Applications* (Springer, 2009). [PubMed]

19. R. Kotynski and T. Stefaniuk, “Multiscale analysis of subwavelength imaging with metal-dielectric multilayers,” Opt. Lett. **35**, 1133–1135 (2010). [CrossRef] [PubMed]

7. T. A. Morgado and M. G. Silveirinha, “Transport of an arbitrary near-field component with an array of tilted wires,” New J. Phys. **11**, 083023 (2009). [CrossRef]

9. A. Rahman, P. A. Belov, Y. Hao, and C. Parini, “Periscope-like endoscope for transmission of a near field in the infrared range,” Opt. Lett. **35**, 142–144 (2010). [CrossRef] [PubMed]

11. P. A. Belov and Y. Hao, “Subwavelength imaging at optical frequencies using a transmission device formed by a periodic layered metal-dielectric structure operating in the canalization regime,” Phys. Rev. B **73**, 113110 (2006). [CrossRef]

12. X. Li, S. He, and Y. Jin, “Subwavelength focusing with a multilayered Fabry-Perot structure at optical frequencies,” Phys. Rev. B **75**, 045103 (2007). [CrossRef]

13. Y. Jin, “Improving subwavelength resolution of multilayered structures containing negative-permittivity layers by flatting the transmission curves,” Prog. Electromagn. Res. **105**, 347–364 (2010). [CrossRef]

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

24. M. Yan, W. Yan, and M. Qiu, “Cylindrical superlens by a coordinate transformation,” Phys. Rev. B **78**, 125113 (2008). [CrossRef]

25. H. Lee, Z. Liu, Y. Xiong, C. Sun, and X. Zhang, “Development of optical hyperlens for imaging below the diffraction limit,” Opt. Express **15**, 15886–15891 (2007). [CrossRef] [PubMed]

26. 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] [PubMed]

## 2. Oblique layered systems

*d*

_{1}and

*d*

_{2}and permittivities are

*ɛ*and

_{m}*ɛ*, respectively. We further assume that the magnetic field is perpendicular to

_{d}*x*–

*y*plane (TM polarization, magnetic field in the

*ẑ*direction) and the time harmonic factor is exp(−

*iωt*). According to EMT, when the thickness of the unit cell (

*d*

_{1}+

*d*

_{2}) is far smaller than the operating wavelength, the effective permittivity of this layered system could be approximated as [27

27. 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]

30. H. Chen and C. T. Chan, “Electromagnetic wave manipulation by layered systems using the transformation media concept,” Phys. Rev. B **78**, 054204 (2008). [CrossRef]

*ẑ*direction is homogenous).

*x*

_{1}<

*x*<

*x*

_{2}shown in Fig. 1(a), then the normal direction of the alternating layers is oriented at a fixed angle,

*θ*, from the

*x̂*direction. Such an oblique layered structure in

*x*

_{1}<

*x*<

*x*

_{2}can be described as

*ω*and the wave vector

**k**. We assume that we are dealing with nonmagnetic materials, so that the magnetic permeability

*μ*= 1. Appropriate thickness of the metal and dielectric films in each unit cell could yield positive and negative signs for

*ɛ*,

_{xx}*ɛ*and

_{xy}*ɛ*, which represent different forms of dispersion relation where

_{yy}*c*is the velocity of light in vacuum, and

*k*and

_{x}*k*represent the wavevectors in the normal and transversal directions, respectively. Here, typically the parameter

_{y}*ɛ*,

_{xx}*ɛ*and

_{xy}*ɛ*satisfy the condition

_{yy}*k*is real for a much wider range of values of

_{x}*k*. Even the high spatial frequency components with large |

_{y}*k*, which would normally be evanescent, now correspond to real values of

_{y}|*k*, and hence to propagating waves in the media.

_{x}*v*= ∇

_{g}*(*

_{k}ω*k*) [27

27. 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]

28. B. Stein, J. Y. Laluet, E. Devaux, C. Genet, and T. W. Ebbesen, “Surface plasmon mode steering and negative refraction,” Phys. Rev. Lett. **105**, 266804 (2010). [CrossRef]

*k*| propagate almost in one direction, which is defined by the angle

_{y}*α*with respect to the

*x*axis as Therefore it is clearly seen that

*α*will be approximated as

*θ*, when

*ɛ*≪ |

_{y}*ɛ*|.

_{x}29. A. A. Orlov, P. M. Voroshilov, P. A. Belov, and Y. S. Kivshar, “Engineered optical nonlocality in nanostructured metamaterials,” Phys. Rev. B **84**, 045424 (2011). [CrossRef]

## 3. Mode analysis and transmission through the oblique layered system

*k′*to distinguish the

_{x}*x*component of the wave vector in the surrounding medium from that in the slab. Considering the guided wave inside the slab, the fields outside the slab must be evanescent in the longitudinal direction, i.e.

*k′*=

_{x}*iα*, whereas

*k*in Eqs. (4) can be real or imaginary which stands for bulk modes and surface modes traveling along the slab, respectively.

_{x}*k*+

_{x}*ɛ*/

_{xy}k_{y}*ɛ*, and (+) and (−) correspond to symmetric (even) and antisymmetric (odd) guided modes, respectively. In the above equations,

_{xx}*α*,

*k*can be expressed in terms of

_{x}*ω*and

*k*. We thereby obtain a set of transcendental equations, which may be solved graphically or numerically to yield the

_{y}*ω*vs.

*k*dispersion curves.

_{y}*θ*= 45°. Due to the excitation of the guided modes, transmission resonances appear. It is worthy noting that transmission curves show a wide flat upheaval for small |

*k*|, which is very beneficial for subwavelength imaging. Also, it is noticed that due to mismatched impedance, there is some reflection for |

_{y}*k*| <

_{y}*k*

_{0}on the input interface, but not very large. This may reduce the intensity of the image, but influence little the resolution. In addition, due to the translation invariance of the structure along the y direction, the transmission for negative

*k*is the same as that for positive

_{y}*k*. However, the symmetry will be broken for lossy cases as seen next.

_{y}*ɛ*we used is larger than −

_{d}*Re*(

*ɛ*), otherwise, the incident propagation waves will be reflected strongly, which is not good for imaging. Also we can obtain flat upheavals of transmission curves which can improve the image quality greatly.

_{m}## 4. Shift of subwavelength image

*ɛ*= −3.5 + 0.23

_{m}*i*at a particular optical frequency

*ω*=

*ω*

_{0}. Full wave EM simulation based on the two-dimensional finite element method is performed to verify the subwavelength resolution imaging.

*θ*. Figs. 3(a)–3(e) show the image of a point source through the effective anisotropic medium, when

*θ*changes from 0° to 15°, 30°, 45°, and 60°. Here,

*ɛ*= 4.3 is unchanged. The source is put at

_{d}*y*= 0 at the left of the structure. the imaging point does not locate at

*y*= 0, but makes a displacement, Δ

*y*= (

*x*

_{1}–

*x*

_{2}) tan

*θ*, due to the designed oblique structure. As we expect, as

*θ*increasing from 0° to 15°, 30°, 45°, 60°, the displacements Δ

*y*can be observed as 0, −0.13

*λ*, −0.29

*λ*, −0.51

*λ*, −0.90

*λ*, respectively. To see clearly the image intensity and resolution, we plot in Fig. 4(a) the distribution of magnetic energy density at the image plane. For

*θ*= 0°, the full width at half maximum (FWHM) of image is about 0.08

*λ*, with high intensity. While increasing

*θ*to 60°, the FWHM of image increases to 0.2

*λ*, and the image becomes dimmer. Moreover, strong side-lobes appear and destroy the imaging. This phenomenon of variation of image resolution and intensity as

*θ*increases can be well understood according to transmission curves shown as Fig. 5. With loss introduced, the transmission |

*T*| drops quickly for large |

*k*|. However, fortunately, such dropping of |

_{y}*T*| for large |

*k*| does not influence significantly high resolution imaging. The amplitudes of evanescent wave with small |

_{y}*k*| are usually larger than those with large |

_{y}*k*|. That is, evanescent waves with small |

_{y}*k*| are more important to generate a subwavelength image and evanescent waves with large |

_{y}*k*| are of little importance. Therefore, for

_{y}*θ*= 0°, 15°, 30°, it can still generate a good subwavelength-image through this structure. However, for larger oblique angle, i.e.

*θ*= 45°, 60°, material loss enhances further the quick dropping of the transmission |

*t*|, which influences significantly high-resolution imaging.

*θ*. The distributions of magnetic energy density look quite similar to those shown Figs. 3(a)–3(e) for the corresponding effective anisotropic media. To see clearly, Fig. 4(b) also shows the corresponding distribution at the image plane for the oblique layered system. The comparison between Fig. 4(a) and Fig. 4(b) validates the appropriateness of the EMT, as the layers are made thin enough.

*ɛ*of the corresponding multilayered structure. Figs. 6(a)–6(e) show the distribution of magnetic energy density for the effective anisotropic medium, when

_{d}*ɛ*increases from 3.5 to 4.0, 4.3, 4.8, to 6.0. Here,

_{d}*θ*is fixed, i.e.

*θ*= 30°. For different

*ɛ*, it always indicates the same shift of imaging. However, with

_{d}*ɛ*increasing, the imaging quality will be influenced greatly, as clearly seen from Fig. 7(a). For

_{d}*ɛ*= −

_{d}*Re*(

*ɛ*) = 3.5, the lossy structure can not work well for subwavelength imaging, whereas a high image resolution is obtained for the case of

_{m}*ɛ*= 4.0, 4.3, 4.8, and the FWHM is about

_{d}*λ*/10 for

*ɛ*= 4.3. However, further increasing

_{d}*ɛ*will reduce the image quality, even the location of shift-imaging is changed slightly. The explanation can also be obtained from the transmission curves shown in Fig. 8. From these transmission curves, we can see material loss damps the sharp transmission peaks, but they remain sharp for

_{d}*ɛ*= 3.5, and over-amplification of some evanescent waves can not be eliminated completely, which may deteriorate the image quality. Thus it can not work well for subwavelength imaging, due to the existence of sharp transmission. With

_{d}*ɛ*increasing and deviating away from 3.5, they display a flat pattern near

_{d}*k*

_{0}for

*ɛ*= 4.0, 4.3 and 4.8, which is beneficial for subwavelength imaging. As

_{d}*ɛ*increases further, a new sharp peak is generated near

_{d}*k*

_{0}, and material loss decreases the image resolution. The oblique layered structure is used to confirm the above result. In Figs. 6(f)–6(j) we plot the magnetic energy for the oblique layered structure with

*θ*= 30° in case of

*ɛ*= 3.5, 4.0, 4.3, 4.8 and 6.0. The magnetic energy distributions look quite similar to those shown in Figs. 6(a)–6(e). A detailed comparison between Fig. 7(a) and Fig. 7(b) for the energy distribution at the image plane also shows the accuracy of EMT.

_{d}*x*–

*y*plane, which corresponds to one-dimensional imaging. Actually, we can realize two-dimensional subwavelength imaging in the proposed oblique multilayered structure. To see the two-dimensional imaging effect, we show in Figs. 9(a)–9(b) the image of a point source in the

*x*–

*z*plane through the effective anisotropic medium for

*ɛ*= 4.3, 4.8, respectively. We take other parameters: the oblique angle

_{d}*θ*= 30°,

*ɛ*= −3.5+0.23

_{m}*i*in two cases. Obviously from the simulation the good image quality can also be achieved in x–z plane. The FWHM of image is about

*λ*/10 shown respectively in Figs. 9(e)–9(f). Subsequently, tuning the oblique angle

*θ*= 45°, we still achieve the image with subwavelength resolution in Figs. 9(c)–9(d). The corresponding distributions of magnetic energy density at the image plane are shown in Figs. 9(g)–9(h). Thus we can confirm our proposed structure can work well for two-dimensional subwavelength imaging.

## 5. Rotation effect of subwavelength image

*a*<

*r*<

*b*,

*a*and

*b*are radius of inner and outer radii of the system, respectively) into

*N*layers for the alternating material of dielectric or metals. For these curves, we have the formula in the cylindrical coordinates (

*r*,

*ϕ*,

*z*) [the

*ẑ*direction is homogenous] [30

30. H. Chen and C. T. Chan, “Electromagnetic wave manipulation by layered systems using the transformation media concept,” Phys. Rev. B **78**, 054204 (2008). [CrossRef]

*r*=

*a*and

*ϕ*=

*β*. Here,

*θ*is the oblique angle, and

*β*= 0, 2

*π*/

*N*, 4

*π*/

*N*,...,2(

*N*– 1)

*π*/

*N*. Starting with these

*N*points, we can produce

*N*curves that will divide the concentric shell (

*a*<

*r*<

*b*) into

*N*fan shaped parts [see Fig. 10(a)]. Then if the number of the alternating layers is large enough, the concentric layered structure with alternating layers of dielectric and metal can be used to mimic the anisotropic properties in the

*r̂*and

*directions very precisely. We use these alternating layers of dielectric and metallic (*ϕ ^

*ɛ*and

_{d}*ɛ*) materials the same way as before. According to the EMT, we can obtain the permittivity tensor for an image rotator within the shell region (

_{m}*a*<

*r*<

*b*) in the Cartesian coordinates [30

30. H. Chen and C. T. Chan, “Electromagnetic wave manipulation by layered systems using the transformation media concept,” Phys. Rev. B **78**, 054204 (2008). [CrossRef]

*a*and an outer radius of

*b*. With the material parameter obtained above, 2D subwavelength objects at the inner surface will be imaged at the outer surface of the structure. For example, point sources at

*S*

_{1},

*S*

_{2}, and

*S*

_{3}of the source plane will be restored well at

*I*

_{1},

*I*

_{2}, and

*I*

_{3}of the image plane, respectively. Such a structure acts as an optical image component that makes perfect image between source and image plane with the rotation of tan(

*θ*)ln(

*b/a*) [30

**78**, 054204 (2008). [CrossRef]

*a*= 0.1

*λ*and an outer radius of

*b*= 0.6

*λ*, Three point sources

*S*

_{1},

*S*

_{2}, and

*S*

_{3}are located at the inner boundary (−

*a*, 0), (

*a*/2,

*a*/2,

*θ*= 30°,

*ɛ*= 4.0 and

_{d}*ɛ*= −3.5 + 0.23

_{m}*i*. It is clearly demonstrated that well resolved images of the three point sources appear at the outer surface with positions of (−

*b*/2,

*b*, 0), (−

*b*/2,

*b*/

*a*= 6, the resolution of image is about

*λ*/10, and the rotation angle of image is nearly 60° as clearly shown in Fig. 11. It is worth noting that small material loss does not influence significantly high-resolution imaging. The key is to transmit evanescent waves in a wide range through the lens structure in appropriate proportion. We also give the imaging through the concentric layered metal-dielectric structure with

*N*= 72 in Fig. 10(d). Appropriateness of the EMT is confirmed by similar distributions of magnetic energy density.

## 6. Conclusion

## Acknowledgments

## References and links

1. | E. Abbe, “Beitrage zur theorie des mikroskops und der mikroskopischen wahrnehmung,” Arch. Mikrosk. Anat. |

2. | J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. |

3. | N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens,” Science |

4. | T. J. Cui, D. R. Smith, and R. Liu, eds., |

5. | S. A. Ramakrishna, J. B. Pendry, M. C. K. Wiltshire, and W. J. Stewart, “Imaging the near field,” J. Mod. Opt. |

6. | S. A. Ramakrishna and J. B. Pendry, “Removal of absorption and increase in resolution in a near-field lens via optical gain,” Phys. Rev. B |

7. | T. A. Morgado and M. G. Silveirinha, “Transport of an arbitrary near-field component with an array of tilted wires,” New J. Phys. |

8. | T. A. Morgado, J. S. Marcos, M. G. Silveirinha, and S. I. Maslovski, “Experimental verification of full reconstruction of the near-field with a metamaterial lens,” Appl. Phys. Lett. |

9. | A. Rahman, P. A. Belov, Y. Hao, and C. Parini, “Periscope-like endoscope for transmission of a near field in the infrared range,” Opt. Lett. |

10. | P. A. Belov, C. R. Simovski, and P. Ikonen, “Canalization of subwavelength images by electromagnetic crystals,” Phys. Rev. B |

11. | P. A. Belov and Y. Hao, “Subwavelength imaging at optical frequencies using a transmission device formed by a periodic layered metal-dielectric structure operating in the canalization regime,” Phys. Rev. B |

12. | X. Li, S. He, and Y. Jin, “Subwavelength focusing with a multilayered Fabry-Perot structure at optical frequencies,” Phys. Rev. B |

13. | Y. Jin, “Improving subwavelength resolution of multilayered structures containing negative-permittivity layers by flatting the transmission curves,” Prog. Electromagn. Res. |

14. | A. Salandrino and N. Engheta, “Far-field subdiffraction optical microscopy using metamaterial crystals: theory and simulations,” Phys. Rev. B |

15. | K. J. Webb and M. Yang, “Subwavelength imaging with a multilayer silver film structure,” Opt. Lett. |

16. | B. Wang, L. Shen, and S. He, “Superlens formed by a one-dimensional dielectric photonic crystal,” J. Opt. Soc. Am. B |

17. | B. Zeng, X. Yang, C. Wang, Q. Feng, and X. Luo, “Super-resolution imaging at different wavelengths by using a one-dimensional metamaterial structure,” J. Opt. |

18. | R. Kotynski, T. Stefaniuk, and A. Pastuszczak, “Sub-wavelength diffraction-free imaging with low-loss metal-dielectric multilayers,” arXiv:1002.0658v1. |

19. | R. Kotynski and T. Stefaniuk, “Multiscale analysis of subwavelength imaging with metal-dielectric multilayers,” Opt. Lett. |

20. | Z. Jacob, L. V. Alekseyev, and E. Narimanov, “Optical hyperlens: far-field imaging beyond the diffraction limit,” Opt. Express |

21. | Z. Jacob, L. V. Alekseyev, and E. Narimanov, “Semiclassical theory of the hyperlens,” J. Opt. Soc. Am. A |

22. | A. V. Kildishev and E. E. Narimanov, “Impedance-matched hyperlens,” Opt. Lett. |

23. | 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 |

24. | M. Yan, W. Yan, and M. Qiu, “Cylindrical superlens by a coordinate transformation,” Phys. Rev. B |

25. | H. Lee, Z. Liu, Y. Xiong, C. Sun, and X. Zhang, “Development of optical hyperlens for imaging below the diffraction limit,” Opt. Express |

26. | Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science |

27. | B. Wood, J. B. Pendry, and D. P. Tsai, “Directed subwavelength imaging using a layered metal-dielectric system,” Phys. Rev. B |

28. | B. Stein, J. Y. Laluet, E. Devaux, C. Genet, and T. W. Ebbesen, “Surface plasmon mode steering and negative refraction,” Phys. Rev. Lett. |

29. | A. A. Orlov, P. M. Voroshilov, P. A. Belov, and Y. S. Kivshar, “Engineered optical nonlocality in nanostructured metamaterials,” Phys. Rev. B |

30. | H. Chen and C. T. Chan, “Electromagnetic wave manipulation by layered systems using the transformation media concept,” Phys. Rev. B |

**OCIS Codes**

(110.0180) Imaging systems : Microscopy

(160.1190) Materials : Anisotropic optical materials

**ToC Category:**

Imaging Systems

**History**

Original Manuscript: May 17, 2011

Revised Manuscript: July 5, 2011

Manuscript Accepted: August 1, 2011

Published: August 15, 2011

**Virtual Issues**

Vol. 6, Iss. 9 *Virtual Journal for Biomedical Optics*

**Citation**

Jin Wang, Hui Yuan Dong, Kin Hung Fung, Tie Jun Cui, and Nicholas X. Fang, "Subwavelength image manipulation through an oblique layered system," Opt. Express **19**, 16809-16820 (2011)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-18-16809

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### References

- E. Abbe, “Beitrage zur theorie des mikroskops und der mikroskopischen wahrnehmung,” Arch. Mikrosk. Anat. 9, 413–468 (1873). [CrossRef]
- J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966–3969 (2000). [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]
- T. J. Cui, D. R. Smith, and R. Liu, eds., Metamaterials—Theory, Design, and Applications (Springer, 2009). [PubMed]
- S. A. Ramakrishna, J. B. Pendry, M. C. K. Wiltshire, and W. J. Stewart, “Imaging the near field,” J. Mod. Opt. 50, 1419–1430 (2003).
- S. A. Ramakrishna and J. B. Pendry, “Removal of absorption and increase in resolution in a near-field lens via optical gain,” Phys. Rev. B 67, 201101(R) (2003).
- T. A. Morgado and M. G. Silveirinha, “Transport of an arbitrary near-field component with an array of tilted wires,” New J. Phys. 11, 083023 (2009). [CrossRef]
- T. A. Morgado, J. S. Marcos, M. G. Silveirinha, and S. I. Maslovski, “Experimental verification of full reconstruction of the near-field with a metamaterial lens,” Appl. Phys. Lett. 97, 144102 (2010). [CrossRef]
- A. Rahman, P. A. Belov, Y. Hao, and C. Parini, “Periscope-like endoscope for transmission of a near field in the infrared range,” Opt. Lett. 35, 142–144 (2010). [CrossRef] [PubMed]
- P. A. Belov, C. R. Simovski, and P. Ikonen, “Canalization of subwavelength images by electromagnetic crystals,” Phys. Rev. B 71, 193105 (2005).
- P. A. Belov and Y. Hao, “Subwavelength imaging at optical frequencies using a transmission device formed by a periodic layered metal-dielectric structure operating in the canalization regime,” Phys. Rev. B 73, 113110 (2006). [CrossRef]
- X. Li, S. He, and Y. Jin, “Subwavelength focusing with a multilayered Fabry-Perot structure at optical frequencies,” Phys. Rev. B 75, 045103 (2007). [CrossRef]
- Y. Jin, “Improving subwavelength resolution of multilayered structures containing negative-permittivity layers by flatting the transmission curves,” Prog. Electromagn. Res. 105, 347–364 (2010). [CrossRef]
- A. Salandrino and N. Engheta, “Far-field subdiffraction optical microscopy using metamaterial crystals: theory and simulations,” Phys. Rev. B 74, 075103 (2006). [CrossRef]
- K. J. Webb and M. Yang, “Subwavelength imaging with a multilayer silver film structure,” Opt. Lett. 31, 2130–2132 (2006). [CrossRef] [PubMed]
- B. Wang, L. Shen, and S. He, “Superlens formed by a one-dimensional dielectric photonic crystal,” J. Opt. Soc. Am. B 25, 391–395 (2008). [CrossRef]
- B. Zeng, X. Yang, C. Wang, Q. Feng, and X. Luo, “Super-resolution imaging at different wavelengths by using a one-dimensional metamaterial structure,” J. Opt. 12, 035104 (2010). [CrossRef]
- R. Kotynski, T. Stefaniuk, and A. Pastuszczak, “Sub-wavelength diffraction-free imaging with low-loss metal-dielectric multilayers,” arXiv:1002.0658v1.
- R. Kotynski and T. Stefaniuk, “Multiscale analysis of subwavelength imaging with metal-dielectric multilayers,” Opt. Lett. 35, 1133–1135 (2010). [CrossRef] [PubMed]
- Z. Jacob, L. V. Alekseyev, and E. Narimanov, “Optical hyperlens: far-field imaging beyond the diffraction limit,” Opt. Express 14, 8247–8256 (2006). [CrossRef] [PubMed]
- Z. Jacob, L. V. Alekseyev, and E. Narimanov, “Semiclassical theory of the hyperlens,” J. Opt. Soc. Am. A 24, A52–A59 (2007). [CrossRef]
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