## Focusing light into deep subwavelength using metamaterial immersion lenses

Optics Express, Vol. 18, Issue 5, pp. 4838-4844 (2010)

http://dx.doi.org/10.1364/OE.18.004838

Acrobat PDF (197 KB)

### Abstract

We propose and demonstrate metamaterial immersion lenses by shaping plasmonic metamaterials. The convex and concave shapes for the elliptically and hyperbolically dispersive metamaterials are designed using phase compensation method. Numerical simulations verify that the metamaterial immersion lenses possess exceptionally large effective numerical apertures thus can achieve deep subwavelength resolution focusing. We also discuss the importance of the losses in modulating the optical transfer function and thus in enhancing the performance of the metamaterial immersion lenses.

© 2010 OSA

## 1. Introduction

*λ*/(2NA), with

*λ*being the wavelength of light and NA being the numerical aperture of the lens [1

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

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

3. 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]

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

6. 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]

9. 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]

10. 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]

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

12. L. Verslegers, P. B. Catrysse, Z. Yu, and S. Fan, “Deep-Subwavelength Focusing and Steering of Light in an Aperiodic Metallic Waveguide Array,” Appl. Phys. Lett. **103**(3), 033902–033904 (2009). [CrossRef]

13. S. M. Mansfield and G. S. Kino, “Solid immersion microscope,” Appl. Phys. Lett. **57**(24), 2615–2616 (1990). [CrossRef]

14. L. P. Ghislain and V. B. Elings, “Near-field scanning solid immersion microscope,” Appl. Phys. Lett. **72**(22), 2779–2781 (1998). [CrossRef]

15. L. P. Ghislain, V. B. Elings, K. B. Crozier, S. R. Manalis, S. C. Minne, K. Wilder, G. S. Kino, and C. F. Quate, “Near-field photolithography with a solid immersion lens,” Appl. Phys. Lett. **74**(4), 501–503 (1999). [CrossRef]

16. M. Rothschild, T. M. Bloomstein, R. R. Kunz, V. Liberman, M. Switkes, S. T. Palmacci, J. H. C. Sedlacek, D. Hardy, and A. Grenville, “Liquid immersion lithography: Why, how, and when?” J. Vac. Sci. Technol. B **22**(6), 2877–2881 (2004). [CrossRef]

17. B. D. Terris, H. J. Mamin, D. Rugar, W. R. Studenmund, and G. S. Kino, “Near-field optical data storage using a solid immersion lens,” Appl. Phys. Lett. **65**(4), 388–390 (1994). [CrossRef]

18. H. F. Hamann, Y. C. Martin, and H. K. Wickramasinghe, “Thermally assisted recording beyond traditional limits,” Appl. Phys. Lett. **84**(5), 810–812 (2004). [CrossRef]

*n*, the corresponding resolution also improves

*n*times. Many efforts have been taken to increase the NA by introducing various high index materials. Wu et al. reported an NA of 2.0 using a Gallium Phosphide solid immersion lens (SIL) in the visible band [19

19. 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]

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

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

23. 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]

## 2. Theory

24. G. Kino, “The solid immersion lens,” Proc. SPIE **3740**, 2–6 (1999). [CrossRef]

*k*-vector waves supported by the SIL can be coupled into the lens from free space. Moreover, the phases of the incident waves are well compensated by the appropriate shape of the SIL, leading to constructive and high resolution focusing. A metamaterial slab may be easily designed to cover high

*k*-vectors, so the small light cone phenomenon maintains similarly as in the high-index isotropic slab discussed above. In analogy to an isotropic high-index SIL, we shape the interface of a metamaterial to achieve the bidirectional coupling between the metamaterial and air with well designed phase compensation. By replacing the isotropic transparent dielectrics with metamaterial, the MIL possesses unprecedented resolving power when compared with conventional SIL.

*ε*> 0,

_{x}′*ε*> 0) or hyperbolic (

_{z}′*ε*> 0,

_{x}′*ε*< 0) dispersion. Here

_{z}′*ε*and

_{x}′*ε*are the real part of the permittivity of the metamaterial in the

_{z}′*x*and

*z*directions, respectively. The wavefront of a line light source inside such a metamaterial slab may be either convex for elliptic dispersion or concave for hyperbolic dispersion. Accordingly, a metamaterial may be shaped to have either a convex surface for elliptic dispersion or a concave surface for hyperbolic dispersion to achieve the coupling and phase compensation, due to the similarity between the interface shape and the dispersion curve of the metamaterial. Figure 1 shows the dispersion curves (Equifrenquency curves, EFCs) of air and the metamaterials. Let us assume that the principle axes of the metamaterials are always along the horizontal (

*k*) and vertical (

_{x}*k*) directions. When the interface of the metamaterial is along the

_{z}*k*axis, only the incident light within a small light cone with the transverse

_{x}*k*-vectors less than

*k*can transmit into and out of the metamaterial, as shown in Fig. 1(a). Figures 1(b) and 1(c) show that the transverse

_{0}*k*-vector coverage can be enlarged from

*k*to

_{0}*k*when the interface of the metamaterial (

_{1}*k*axis) has an angle with respect to the material principle axes. Each point on the curved interface of the metamaterial may be considered having an interface not in the

_{xt}*x*axis direction, thus the transverse

*k*-vector coverage can be extended by a curved interface. As shown in Figs. 1(b) and 1(c), the extended wavevector coverage

*k*can be much larger than

_{1}*k*and even the highest achievable

_{0}*k*-vectors in natural SIL materials, so super resolution can be achieved. In the following, we demonstrate the MIL concept with both elliptic (referred to as an elliptic MIL) and hyperbolic (referred to as a hyperbolic MIL) dispersions based on phase compensation for focusing in the metamaterials and numerically verify the analysis and designs.

## 3. Formulations and simulations

*f*and

_{m}*F*. Phase condition for constructive interference at

_{m}*F*results in the following quadratic equationTherefore,where

_{m}*k*being the wavevector in free space. Note that the other solution of Eq. (1) makes the position of

_{0}*F*outside the metamaterial, and thus not suitable for MIL purpose. With Eq. (2), the interface shape of the elliptic MIL can be calculated. Equations (1) and (2) are derived for an elliptic MIL. Changing

_{m}*ε*to be negative results in the formulas for the hyperbolic MIL, with

_{z}′*ε*for the hyperbolic MIL case can be easily verified using the schematic of the hyperbolic MIL in Fig. 2(b). If measured from the apex of the curved interfaces, then the focal lengths are

_{z}′*f*= (

*f*+

_{m}*h*), with

_{0}*h*is positive for the elliptic MIL and negative for the hyperbolic MIL.

_{0}*ε*= 5.1 + 0.1i and

_{x}*ε*= 16.0 + 0.08i, which is designed using an alternate multilayer [25] of silver and Gallium Phosphide [19

_{z}19. 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]

*p*= 0.2.

*x*direction in the MIL. The focal length of the elliptic MIL is

*f*= 3 um and

_{m}*x*= 3.4 um, and the calculated

_{max}*h*= 6.7 um. This elliptic MIL achieved a focus with an FWHM (full width at half maximum) of 70 nm (~

_{0}*λ*/9) for the normal plane wave incidence, which is equivalent to an effective NA of 4.5.

*θ*is the incident angle with respect to the

*z*axis and Re denotes the real part. In practical designing,

*x*= 310 nm for

*θ*= 14 degrees, which is comparable to the calculated shift Δ

*x*= 331 nm.

*ε*. Figure 4(a) shows the simulated power profile of a hyperbolic MIL with a normal incidence of plane wave. The permittivity of the elliptic metamaterial is

_{z}′*ε*= 8.1 + 0.1i and

_{x}*ε*= −12.5 + 0.3i, which is designed using silver nanowires [27

_{z}27. J. Pendry, A. Holden, D. Robbins, and W. Stewart, “Low frequency plasmons in thin-wire structures,” J.Phys.-Condens. Matter **10**(22), 4785–4809 (1998). [CrossRef]

*p*= 0.7. The silver nanowires of the metamaterial are aligned in the

*z*direction. The focal length of the elliptic MIL is

*f*= 2 um and

_{m}*x*= 1.29 um, and the calculated

_{max}*h*= −1.23 um. This hyperbolic MIL achieved a focus with an FWHM of 66 nm (~

_{0}*λ*/9.6) for the normal plane wave incidence, which is equivalent to an effective NA of 4.8. As in the elliptic MIL, when the incident light is tilted, the focus will be shifted. The simulation in Fig. 4(b) shows a shift of Δ

*x*= −120 nm for

*θ*= 37.8 degrees to the opposite side to the elliptic MIL. This shift is also comparable to the calculated shift Δ

*x*= −108 nm using Eq. (3).

## 4. Discussions and conclusions

*k*-vectors can be coupled into the metamaterial with compensated phase and thus can be focused into deep subwavelength scale. Notice that the concave interface of the hyperbolic MIL in Fig. 4 is flatter than that of the elliptic MIL in Fig. 3. This is due to the higher anisotropy, i.e.,

28. 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]

*k*-vector coverage determined by the dispersion relation

*k*, which limits

_{x}*k*up to

_{x}*k*has no limit in the dispersion relation of a hyperbolically dispersive metamaterial. The losses also play an important role in the performance of the MILs. Different

_{x}*k*-vectors may have different loss coefficients and propagation lengths in an MIL, thus the

*k*-vectors attenuate differently. Furthermore, the curved shapes of the MILs cause different refraction (coupling) efficiencies at different positions due to the different angles of incidence. The

*k*-vector spectrum at the focus of an MIL may be significantly modulated by both the propagation and coupling losses and thus substantially different from that of a conventional SIL. The presented elliptic MIL achieved an effective NA of 4.5, which is even a little larger than

*k*-vectors in the center part propagate longer distances to the focus than the high

*k*-vectors on the edge parts, so the low

*k*-vectors attenuates more than the high

*k*-vectors. Although the coupling efficiencies of at the center part in Fig. 3 are higher than on the edge parts for normal incidence, the coupling loss profile that makes the OTF is overwhelmed by the propagation losses. Therefore, the overall OTF of the elliptical MIL indicates more transmission for higher

*k-*vector waves to the focus, i.e., more high

*k*-vector contributions to the focus than in the case of a conventional lens, finally resulting in a higher resolution focus and a higher effective NA. In principle,

*k*’s of a hyperbolic MIL can be infinitely large as there is no cutoff in its dispersion relation, so extremely large effective NA’s may be obtained. However, in practice, the chosen

_{x}*x*limits the coverage of

_{max}*k*. In the presented hyperbolic MIL above, the maximum

_{x}*k*is 4.72

_{x}*k*. The loss mechanisms affect the performance of the hyperbolic MIL similarly as in the elliptic MIL, resulting in a higher NA of 4.8.

_{0}27. J. Pendry, A. Holden, D. Robbins, and W. Stewart, “Low frequency plasmons in thin-wire structures,” J.Phys.-Condens. Matter **10**(22), 4785–4809 (1998). [CrossRef]

12. L. Verslegers, P. B. Catrysse, Z. Yu, and S. Fan, “Deep-Subwavelength Focusing and Steering of Light in an Aperiodic Metallic Waveguide Array,” Appl. Phys. Lett. **103**(3), 033902–033904 (2009). [CrossRef]

29. W. Srituravanich, L. Pan, Y. Wang, C. Sun, D. B. Bogy, and X. Zhang, “Flying plasmonic lens in the near field for high-speed nanolithography,” Nat. Nanotechnol. **3**(12), 733–737 (2008). [CrossRef] [PubMed]

30. H. I. Smith, R. Menon, A. Patel, D. Chao, M. Walsh, and G. Barbastathis, “Zone-plate-array lithography: A low-cost complement or competitor to scanning-electron-beam lithography,” Microelectron. Eng. **83**(4-9), 956–961 (2006). [CrossRef]

31. R. Völkel, H. P. Herzig, P. Nussbaum, R. Dandliker, and W. B. Hugle, “Microlens array imaging system for photolithography,” Opt. Eng. **35**(11), 3323–3330 (1996). [CrossRef]

## References and links

1. | E. Abbe, “Beitrage zur Theorie des Mikroskops und der mikroskopischen Wahrnehmung,” Arch. Mikroskop. Anat. |

2. | X. Zhang and Z. Liu, “Superlenses to overcome the diffraction limit,” Nat. Mater. |

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

4. | Z. Liu, S. Durant, H. Lee, Y. Pikus, N. Fang, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical superlens,” Nano Lett. |

5. | E. E. Narimanov, “Far-field superlens: Optical Nanoscope,” Nat. Photonics |

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

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

8. | 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. |

9. | I. I. Smolyaninov, Y. J. Hung, and C. C. Davis, “Magnifying superlens in the visible frequency range,” Science |

10. | S. Vedantam, H. Lee, J. Tang, J. Conway, M. Staffaroni, and E. Yablonovitch, “A Plasmonic Dimple Lens for Nanoscale Focusing of Light,” Nano Lett. |

11. | F. M. Huang and N. I. Zheludev, “Super-resolution without evanescent waves,” Nano Lett. |

12. | L. Verslegers, P. B. Catrysse, Z. Yu, and S. Fan, “Deep-Subwavelength Focusing and Steering of Light in an Aperiodic Metallic Waveguide Array,” Appl. Phys. Lett. |

13. | S. M. Mansfield and G. S. Kino, “Solid immersion microscope,” Appl. Phys. Lett. |

14. | L. P. Ghislain and V. B. Elings, “Near-field scanning solid immersion microscope,” Appl. Phys. Lett. |

15. | L. P. Ghislain, V. B. Elings, K. B. Crozier, S. R. Manalis, S. C. Minne, K. Wilder, G. S. Kino, and C. F. Quate, “Near-field photolithography with a solid immersion lens,” Appl. Phys. Lett. |

16. | M. Rothschild, T. M. Bloomstein, R. R. Kunz, V. Liberman, M. Switkes, S. T. Palmacci, J. H. C. Sedlacek, D. Hardy, and A. Grenville, “Liquid immersion lithography: Why, how, and when?” J. Vac. Sci. Technol. B |

17. | B. D. Terris, H. J. Mamin, D. Rugar, W. R. Studenmund, and G. S. Kino, “Near-field optical data storage using a solid immersion lens,” Appl. Phys. Lett. |

18. | H. F. Hamann, Y. C. Martin, and H. K. Wickramasinghe, “Thermally assisted recording beyond traditional limits,” Appl. Phys. Lett. |

19. | 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. |

20. | S. B. Ippolito, B. B. Goldberg, and M. S. Unlu, “High spatial resolution subsurface microscopy,” Appl. Phys. Lett. |

21. | D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, “Metamaterials and negative refractive index,” Science |

22. | V. Shalaev, “Optical negative-index metamaterials,” Nat. Photonics |

23. | 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 |

24. | G. Kino, “The solid immersion lens,” Proc. SPIE |

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

26. | K. Iizuka, |

27. | J. Pendry, A. Holden, D. Robbins, and W. Stewart, “Low frequency plasmons in thin-wire structures,” J.Phys.-Condens. Matter |

28. | 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 |

29. | W. Srituravanich, L. Pan, Y. Wang, C. Sun, D. B. Bogy, and X. Zhang, “Flying plasmonic lens in the near field for high-speed nanolithography,” Nat. Nanotechnol. |

30. | H. I. Smith, R. Menon, A. Patel, D. Chao, M. Walsh, and G. Barbastathis, “Zone-plate-array lithography: A low-cost complement or competitor to scanning-electron-beam lithography,” Microelectron. Eng. |

31. | R. Völkel, H. P. Herzig, P. Nussbaum, R. Dandliker, and W. B. Hugle, “Microlens array imaging system for photolithography,” Opt. Eng. |

**OCIS Codes**

(220.3630) Optical design and fabrication : Lenses

(350.5730) Other areas of optics : Resolution

(160.3918) Materials : Metamaterials

(350.4238) Other areas of optics : Nanophotonics and photonic crystals

**ToC Category:**

Optical Design and Fabrication

**History**

Original Manuscript: January 27, 2010

Revised Manuscript: February 11, 2010

Manuscript Accepted: February 12, 2010

Published: February 23, 2010

**Citation**

Changbao Ma and Zhaowei Liu, "Focusing light into deep subwavelength using metamaterial immersion lenses," Opt. Express **18**, 4838-4844 (2010)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-5-4838

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### References

- E. Abbe, “Beitrage zur Theorie des Mikroskops und der mikroskopischen Wahrnehmung,” Arch. Mikroskop. Anat. 9(1), 413–418 (1873). [CrossRef]
- X. Zhang and Z. Liu, “Superlenses to overcome the diffraction limit,” Nat. Mater. 7(6), 435–441 (2008). [CrossRef] [PubMed]
- 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]
- 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]
- E. E. Narimanov, “Far-field superlens: Optical Nanoscope,” Nat. Photonics 1(5), 260–261 (2007). [CrossRef]
- 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]
- 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]
- 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]
- 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]
- 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]
- F. M. Huang and N. I. Zheludev, “Super-resolution without evanescent waves,” Nano Lett. 9(3), 1249–1254 (2009). [CrossRef] [PubMed]
- L. Verslegers, P. B. Catrysse, Z. Yu, and S. Fan, “Deep-Subwavelength Focusing and Steering of Light in an Aperiodic Metallic Waveguide Array,” Appl. Phys. Lett. 103(3), 033902–033904 (2009). [CrossRef]
- S. M. Mansfield and G. S. Kino, “Solid immersion microscope,” Appl. Phys. Lett. 57(24), 2615–2616 (1990). [CrossRef]
- L. P. Ghislain and V. B. Elings, “Near-field scanning solid immersion microscope,” Appl. Phys. Lett. 72(22), 2779–2781 (1998). [CrossRef]
- L. P. Ghislain, V. B. Elings, K. B. Crozier, S. R. Manalis, S. C. Minne, K. Wilder, G. S. Kino, and C. F. Quate, “Near-field photolithography with a solid immersion lens,” Appl. Phys. Lett. 74(4), 501–503 (1999). [CrossRef]
- M. Rothschild, T. M. Bloomstein, R. R. Kunz, V. Liberman, M. Switkes, S. T. Palmacci, J. H. C. Sedlacek, D. Hardy, and A. Grenville, “Liquid immersion lithography: Why, how, and when?” J. Vac. Sci. Technol. B 22(6), 2877–2881 (2004). [CrossRef]
- B. D. Terris, H. J. Mamin, D. Rugar, W. R. Studenmund, and G. S. Kino, “Near-field optical data storage using a solid immersion lens,” Appl. Phys. Lett. 65(4), 388–390 (1994). [CrossRef]
- H. F. Hamann, Y. C. Martin, and H. K. Wickramasinghe, “Thermally assisted recording beyond traditional limits,” Appl. Phys. Lett. 84(5), 810–812 (2004). [CrossRef]
- 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]
- S. B. Ippolito, B. B. Goldberg, and M. S. Unlu, “High spatial resolution subsurface microscopy,” Appl. Phys. Lett. 78(26), 4071–4073 (2001). [CrossRef]
- D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, “Metamaterials and negative refractive index,” Science 305(5685), 788–792 (2004). [CrossRef] [PubMed]
- V. Shalaev, “Optical negative-index metamaterials,” Nat. Photonics 1(1), 41–48 (2007). [CrossRef]
- 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]
- G. Kino, “The solid immersion lens,” Proc. SPIE 3740, 2–6 (1999). [CrossRef]
- 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).
- K. Iizuka, Elements of Photonics (John Wiley & Sons, New York, 2002), Vol. 1.
- J. Pendry, A. Holden, D. Robbins, and W. Stewart, “Low frequency plasmons in thin-wire structures,” J. Phys.-Condens. Matter 10(22), 4785–4809 (1998). [CrossRef]
- 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]
- W. Srituravanich, L. Pan, Y. Wang, C. Sun, D. B. Bogy, and X. Zhang, “Flying plasmonic lens in the near field for high-speed nanolithography,” Nat. Nanotechnol. 3(12), 733–737 (2008). [CrossRef] [PubMed]
- H. I. Smith, R. Menon, A. Patel, D. Chao, M. Walsh, and G. Barbastathis, “Zone-plate-array lithography: A low-cost complement or competitor to scanning-electron-beam lithography,” Microelectron. Eng. 83(4-9), 956–961 (2006). [CrossRef]
- R. Völkel, H. P. Herzig, P. Nussbaum, R. Dandliker, and W. B. Hugle, “Microlens array imaging system for photolithography,” Opt. Eng. 35(11), 3323–3330 (1996). [CrossRef]

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