## Terahertz epsilon-near-zero graded-index lens |

Optics Express, Vol. 21, Issue 7, pp. 9156-9166 (2013)

http://dx.doi.org/10.1364/OE.21.009156

Acrobat PDF (1882 KB)

### Abstract

An epsilon-near-zero graded-index converging lens with planar faces is proposed and analyzed. Each perfectly-electric conducting (PEC) waveguide comprising the lens operates slightly above its cut-off frequency and has the same length but different cross-sectional dimensions. This allows controlling individually the propagation constant and the normalized characteristic impedance of each waveguide for the desired phase front at the lens output while Fresnel reflection losses are minimized. A complete theoretical analysis based on the waveguide theory and Fermat’s principle is provided. This is complemented with numerical simulation results of two-dimensional and three-dimensional lenses, made of PEC and aluminum, respectively, and working in the terahertz regime, which show good agreement with the analytical work.

© 2013 OSA

## 1. Introduction

3. D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. **84**(18), 4184–4187 (2000). [CrossRef] [PubMed]

*n*→ 0) [4

4. R. W. Ziolkowski, “Propagation in and scattering from a matched metamaterial having a zero index of refraction,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. **70**(4), 046608 (2004). [CrossRef] [PubMed]

5. M. G. Silveirinha and N. Engheta, “Tunneling of electromagnetic energy through subwavelength channels and bends using ε-near-zero materials,” Phys. Rev. Lett. **97**(15), 157403 (2006). [CrossRef] [PubMed]

6. A. Alù, M. G. Silveirinha, A. Salandrino, and N. Engheta, “Epsilon-near-zero metamaterials and electromagnetic sources: tailoring the radiation phase pattern,” Phys. Rev. B **75**(15), 155410 (2007). [CrossRef]

9. J. Gómez Rivas, C. Janke, P. Bolivar, and H. Kurz, “Transmission of THz radiation through InSb gratings of subwavelength apertures,” Opt. Express **13**(3), 847–859 (2005). [CrossRef] [PubMed]

10. P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B **6**(12), 4370–4379 (1972). [CrossRef]

11. A. Alù, M. G. Silveirinha, and N. Engheta, “Transmission-line analysis of ε -near-zero-filled narrow channels,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. **78**(1), 016604 (2008). [CrossRef] [PubMed]

11. A. Alù, M. G. Silveirinha, and N. Engheta, “Transmission-line analysis of ε -near-zero-filled narrow channels,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. **78**(1), 016604 (2008). [CrossRef] [PubMed]

12. H. Shi, C. Wang, C. Du, X. Luo, X. Dong, and H. Gao, “Beam manipulating by metallic nano-slits with variant widths,” Opt. Express **13**(18), 6815–6820 (2005). [CrossRef] [PubMed]

20. S. Ishii, V. M. Shalaev, and A. V. Kildishev, “Holey-metal lenses: sieving single modes with proper phases,” Nano Lett. **13**(1), 159–163 (2013). [CrossRef] [PubMed]

## 2. Analytical formulation

*h*and

_{x}*h*with

_{y}*h*>

_{y}*h*and E-field oriented in the

_{x}*x*-direction, the fundamental mode is the TE

_{01}whose cut-off frequency is

*c*is the velocity of light in free space and it is assumed that the guide is filled with free space (or air). The propagation constant of this mode can be written aswhere

11. A. Alù, M. G. Silveirinha, and N. Engheta, “Transmission-line analysis of ε -near-zero-filled narrow channels,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. **78**(1), 016604 (2008). [CrossRef] [PubMed]

22. B. Edwards, A. Alù, M. E. Young, M. Silveirinha, and N. Engheta, “Experimental verification of epsilon-near-zero metamaterial coupling and energy squeezing using a microwave waveguide,” Phys. Rev. Lett. **100**(3), 033903 (2008). [CrossRef] [PubMed]

_{w_eff}is very close to zero, since:where it has been assumed that the effective permeability of the waveguide is

*μ*. From here we can obtain an expression for the accumulated phase variation within the ENZ in terms of the waveguide dimensions:where

_{0}*L*is the waveguide length. Due to the low propagation constant of the guided mode (

*β*), a small phase variation occurs even over a physically long distance. Moreover, with slight variations in the

*h*dimension, we are able to control with high accuracy the propagation constant and consequently the phase of the mode. Thus, we have the basic ingredients for a graded-index lens, where the phase variation of each waveguide is carefully tuned to transform an incident plane wave into a spherical wave. Figure 1(a) illustrates this idea.

_{y}*f*=

*f*, leads to the effective permittivity is near zero,

_{c}*i*is an integer number

*i*= 1,2,…;

*r*-

_{i}*r*), and

_{0}*x*=

_{i}*i·d*represents the

_{x}*x*-coordinate of the center of each aperture. It is worth mentioning that

5. M. G. Silveirinha and N. Engheta, “Tunneling of electromagnetic energy through subwavelength channels and bends using ε-near-zero materials,” Phys. Rev. Lett. **97**(15), 157403 (2006). [CrossRef] [PubMed]

23. M. G. Silveirinha and N. Engheta, “Theory of supercoupling, squeezing wave energy, and field confinement in narrow channels and tight bends using ε near-zero metamaterials,” Phys. Rev. B **76**(24), 245109 (2007). [CrossRef]

*h*can be obtained by analyzing the structure from a transmission line perspective [24] and matching the normalized characteristic line impedance of free space

_{x}*η*and the waveguide

_{air}*η*. Reducing the problem to the single unit cell detailed in the Fig. 1(b),

_{w}*η*is defined in the air volume surrounding an artificial waveguide of dimensions

_{air}*d*and

_{x}*d*with electric and magnetic walls in

_{y}*x*-direction and

*y*-direction, respectively [25

25. M. Beruete, I. Campillo, M. Navarro-Cia, F. Falcone, and M. Sorolla Ayza, “Molding left- or right-handed metamaterials by stacked cutoff metallic hole arrays,” IEEE Trans. Antenn. Propag. **55**(6), 1514–1521 (2007). [CrossRef]

*η*in the narrow channel of the ENZ waveguide of dimensions

_{w}*h*and

_{x}*h*. Thus, matching the impedances, we obtain:

_{y}## 3. Two-dimensional lens

*y*-direction and is excited by an incident plane wave that propagates in the

*z*direction and whose electric field vector is polarized along the

*x*axis. For a design frequency

*f*equal to 1 THz (λ

_{0}_{0}= 300 μm), the thickness of the lens is assumed to be

*L*= 2λ

_{0}, the total width in the

*x*-direction is equal to 10.2λ

_{0}and the dimensions of the unit cell are

*d*= 60 μm and

_{x}*d*= 180 μm. The dimensions of the narrow channels have been chosen to have the focus at

_{y}*r*= 1.5 mm = 5λ

_{0}_{0}from the exit face. The material of the lens is assumed to be PEC and the boundary conditions have been fixed as open (perfectly matched layer) in the

*x*-direction and magnetic walls in the upper and lower faces in order to make the structure infinitely periodic in the

*y*-direction. For the numerical simulation the structure is meshed with accuracy equal to λ

_{0}/20. For all the numerical results, we have used the finite-integration-technique software CST Microwave Studio

^{TM}.

*x*-direction. The abrupt changes in the dimensions of adjacent waveguides correspond to phase changes equal to 2π. Note in the figure that the values for

*Δθ*have been calculated taking into account the fact that we really work at a frequency slightly above 1 THz, exactly at 1.0035 THz. The relative effective permittivity

_{w}*z*-direction) equal to 861.37 μm = 2.87λ

_{0}and a full-width at half-maximum (FWHM) at the focal plane (

*x*-direction) of 174.86 μm = 0.58λ

_{0}. It must be highlighted that with this completely flat graded-index ENZ lens, a reduction of 36.51% of the total volume of the lens is achieved with respect to an ENZ waveguide lens with a convex profile and same dimensions [26

26. M. Navarro-Cía, M. Beruete, M. Sorolla, and N. Engheta, “Lensing system and Fourier transformation using epsilon-near-zero metamaterials,” Phys. Rev. B **86**(16), 165130 (2012). [CrossRef]

_{0}.

26. M. Navarro-Cía, M. Beruete, M. Sorolla, and N. Engheta, “Lensing system and Fourier transformation using epsilon-near-zero metamaterials,” Phys. Rev. B **86**(16), 165130 (2012). [CrossRef]

*n·sinθ*where

*n*is the index of refraction of the medium surrounding the lens, air in this case; and

*θ*the half-angle of the maximum cone of incident wave that can enter or exit the lens, is equal to 0.472. The angle of the maximum cone of incidence is calculated as the angle for which the transmitted power at the focus is half the transmitted power at the focus under normal incident.

*r*-

_{i}*r*) is enforced to be reduced, which happens when the focal length increases. The table also shows a general degradation of the performance of the lens compared to the optimal frequency 1.0035 THz (highlighted in bold in Table 2). This degradation is more severe for frequencies below the optimal frequency because the waveguides with lower values of

_{0}*h*start to operate at cut-off. The bandwidth of operation, estimated as a −3 dB from the optimum enhancement factor, is 0.27 THz, corresponding to a fractional bandwidth of 26.9%. Moreover, the reflection coefficient increases as the frequency of operation deviates from the optimal frequency: we obtain |Γ| = 0.48 at 0.98 THz and |Γ| = 0.65 at 1.2 THz. Therefore, this lens works in a narrow band, which is limited by the frequency dispersion of the effective permittivity and the impedance matching.

_{y}## 4. Three-dimensional lens

12. H. Shi, C. Wang, C. Du, X. Luo, X. Dong, and H. Gao, “Beam manipulating by metallic nano-slits with variant widths,” Opt. Express **13**(18), 6815–6820 (2005). [CrossRef] [PubMed]

20. S. Ishii, V. M. Shalaev, and A. V. Kildishev, “Holey-metal lenses: sieving single modes with proper phases,” Nano Lett. **13**(1), 159–163 (2013). [CrossRef] [PubMed]

*f*= 1 THz so the dimensions of the unit cell are the same:

_{0}*d*= 60 μm and

_{x}*d*= 180 μm. The total dimensions of the full structure are

_{y}*L*

_{x}=

*L*

_{y}= 10.2λ

_{0}= 3.06 mm and the thickness

*L*= 600 μm. Moreover, in order to take into account metal losses, the structure is made of aluminium, with conductivity equal to 3.56 × 10

_{z}^{7}S/m. Figure 5(b) depicts the simulation results for the power distribution in the

*xz*and

*yz*-planes when the lens is excited with a plane wave with TM polarization, i.e. electric field polarized along

*x*. It can be seen in both planes that the energy is focused demonstrating the performance of the lens. The enhancement factor is 62.3, and the focal length and depth of focus are equal to 1312.50 μm = 4.38λ

_{0}and 614.04 μm = 2.05λ

_{0}respectively. The cross section of the power along the focal plane in the

*x*-direction and

*y*-direction is shown in the inset of the Fig. 5(b). The FWHM is 184.04 μm, resulting in a resolution of 1.23λ

_{0}/2, very close to half wavelength. Along the

*y*-direction, the FWHM obtained is 190.60 μm equal to 1.27λ

_{0}/2. It is important to note that this design has been done to get the focus at 5λ

_{0}. It is worth mentioning that the flexibility of tailoring the phase difference between waveguides allows us to modify the focal length and/or to get different phase fronts at the output such as plane waves radiating in other directions or convex phase patterns, by just properly changing the dimensions of the individual waveguide cross section. Finally, the simulation results for the extinction ratio between copolar and crosspolar polarization at the focal distance is 51.32 dB allowing us to use this lens as a polarization analyzer as well.

_{y}for

*xz*and

*yz*-planes, respectively. The focus is clearly observed in both planes but more interesting is that the intensity of the field on the edges is lower than in the middle of the structure thanks to the Gaussian beam excitation, and thus spurious diffraction effects are reduced. This can be observed in further detail in Figs. 6(c) and 6(d), where the power distribution is shown on the

*xz*- and

*yz*-plane. With this new excitation the enhancement factor (now calculated with respect to the beam maximum value) is 24.3. The obtained value of depth of focus is 700.41 μm = 2.33λ

_{0}/2 and the values of FWHM along

*x*and

*y*-direction are 210.8 μm = 1.41λ

_{0}/2 and 218.4 μm = 1.46λ

_{0}/2, respectively. Note that the performance of the focus is slightly worse than that of the plane wave excitation, as expected, since the contribution of the external waveguides is less effective.

32. W. Kock, “Metal-lens antennas,” Proceedings of the IRE **34**(11), 828–836 (1946). [CrossRef]

34. M. Navarro-Cía, M. Beruete, I. Campillo, and M. Sorolla Ayza, “Beamforming by left-handed extraordinary transmission metamaterial bi- and plano-concave lens at millimeter-waves,” IEEE Trans. Antenn. Propag. **59**(6), 2141–2151 (2011). [CrossRef]

^{+}. Consequently, attending to Fermat’s principle [1], classical lenses always have ellipsoidal profiles and ENZ lenses cylindrical profiles if the graded-index techniques are not used. Furthermore, constrained lenses tend to display undesired grating lobes given the large in-plane periodicities, whereas the lens analyzed here prevents them in both planes, due to the subwavelength periodicity along the direction of the incident E-field and approximately λ

_{0}/2 periodicity along the other in-plane direction. In addition, classical metallic lenses display Fresnel reflection losses given the mismatch between the normalized characteristic line impedance of free space and the waveguides. However, as we have shown here, ENZ lens based on near cut-off waveguides can be designed to be approximately impedance-matched. On the other hand, it exists other kind of metallic lenses based on stacked subwavelength hole arrays, called extraordinary transmission lenses [34

34. M. Navarro-Cía, M. Beruete, I. Campillo, and M. Sorolla Ayza, “Beamforming by left-handed extraordinary transmission metamaterial bi- and plano-concave lens at millimeter-waves,” IEEE Trans. Antenn. Propag. **59**(6), 2141–2151 (2011). [CrossRef]

36. M. Navarro-Cía, M. Beruete, I. Campillo, and M. Sorolla, “Enhanced lens by *ε* and *μ* near-zero metamaterial boosted by extraordinary optical transmission,” Phys. Rev. B **83**(11), 115112 (2011). [CrossRef]

_{20}or TM

_{02}(depending on the unit cell dimensions) modes, whereas the lens proposed here supports only a TE

_{01}.

## 5. Conclusions

_{0}to obtain an acceptable performance. In addition, the chromatic dispersion is studied showing a narrow bandwidth of operation equal to 0.27 THz (26.9% fractional bandwidth). Also a full three-dimensional prototype made of aluminum, in order to consider losses as well, is simulated obtaining a clear focus spot with an enhancement factor of 62.3, a FWHM equal to 1.23λ

_{0}/2 and a depth of focus of 2.05λ

_{0}. This technique may be applied to develop devices that require precise phase control, with low losses, good robustness and small size.

## Acknowledgments

*In memoriam*Prof. Mario Sorolla.

## References and links

1. | L. Solymar and E. Shamonina, |

2. | N. Engheta and R. W. Ziolkowski, |

3. | D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. |

4. | R. W. Ziolkowski, “Propagation in and scattering from a matched metamaterial having a zero index of refraction,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. |

5. | M. G. Silveirinha and N. Engheta, “Tunneling of electromagnetic energy through subwavelength channels and bends using ε-near-zero materials,” Phys. Rev. Lett. |

6. | A. Alù, M. G. Silveirinha, A. Salandrino, and N. Engheta, “Epsilon-near-zero metamaterials and electromagnetic sources: tailoring the radiation phase pattern,” Phys. Rev. B |

7. | C. Bohren and D. Huffmann, |

8. | J. D. Jackson, |

9. | J. Gómez Rivas, C. Janke, P. Bolivar, and H. Kurz, “Transmission of THz radiation through InSb gratings of subwavelength apertures,” Opt. Express |

10. | P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B |

11. | A. Alù, M. G. Silveirinha, and N. Engheta, “Transmission-line analysis of ε -near-zero-filled narrow channels,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. |

12. | H. Shi, C. Wang, C. Du, X. Luo, X. Dong, and H. Gao, “Beam manipulating by metallic nano-slits with variant widths,” Opt. Express |

13. | L. Verslegers, P. B. Catrysse, Z. Yu, J. S. White, E. S. Barnard, M. L. Brongersma, and S. Fan, “Planar lenses Based on Nanoscale Slit Arrays in a metallic film,” Nano Lett. |

14. | Z. Sun and H. K. Kim, “Refractive transmission of light and beam shaping with metallic nano-optic lenses,” Appl. Phys. Lett. |

15. | C. Ma, M. Escobar, and Z. Liu, “Extraordinary light focusing and Fourier transform properties of gradient-index metalenses,” Phys. Rev. B |

16. | C. Ma and Z. Liu, “A super resolution metalens with phase compensation mechanism,” Appl. Phys. Lett. |

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. |

18. | S. Ishii, A. V. Kildishev, V. M. Shalaev, K. P. Chen, and V. P. Drachev, “Metal nanoslit lenses with polarization-selective design,” Opt. Lett. |

19. | S. Ishii, A. V. Kildishev, V. M. Shalaev, and V. P. Drachev, “Controlling the wave focal structure of metallic nanoslit lenses with liquid crystals,” Laser Phys. Lett. |

20. | S. Ishii, V. M. Shalaev, and A. V. Kildishev, “Holey-metal lenses: sieving single modes with proper phases,” Nano Lett. |

21. | D. M. Pozar, |

22. | B. Edwards, A. Alù, M. E. Young, M. Silveirinha, and N. Engheta, “Experimental verification of epsilon-near-zero metamaterial coupling and energy squeezing using a microwave waveguide,” Phys. Rev. Lett. |

23. | M. G. Silveirinha and N. Engheta, “Theory of supercoupling, squeezing wave energy, and field confinement in narrow channels and tight bends using ε near-zero metamaterials,” Phys. Rev. B |

24. | R. E. Collin, |

25. | M. Beruete, I. Campillo, M. Navarro-Cia, F. Falcone, and M. Sorolla Ayza, “Molding left- or right-handed metamaterials by stacked cutoff metallic hole arrays,” IEEE Trans. Antenn. Propag. |

26. | M. Navarro-Cía, M. Beruete, M. Sorolla, and N. Engheta, “Lensing system and Fourier transformation using epsilon-near-zero metamaterials,” Phys. Rev. B |

27. | D. Filipovic, S. Gearhart, and G. Rebeiz, “Double-slot antennas on extended hemispherical and elliptical silicon dielectric lenses,” IEEE T. Microw. Theory |

28. | N. Llombart, G. Chattopadhyay, A. Skalare, and I. Mehdi, “Novel terahertz antenna based on a silicon lens fed by a leaky wave enhanced waveguide,” IEEE Trans. Antenn. Propag. |

29. | Microtech Instruments Inc, http://mtinstruments.com |

30. | Thorlabs Inc, http://www.thorlabs.com |

31. | J. W. Goodman, |

32. | W. Kock, “Metal-lens antennas,” Proceedings of the IRE |

33. | J. Ruze, “Wide-angle metal-plate optics,” Proceedings of the IRE |

34. | M. Navarro-Cía, M. Beruete, I. Campillo, and M. Sorolla Ayza, “Beamforming by left-handed extraordinary transmission metamaterial bi- and plano-concave lens at millimeter-waves,” IEEE Trans. Antenn. Propag. |

35. | H. D. Hristov, |

36. | M. Navarro-Cía, M. Beruete, I. Campillo, and M. Sorolla, “Enhanced lens by |

**OCIS Codes**

(070.0070) Fourier optics and signal processing : Fourier optics and signal processing

(080.3630) Geometric optics : Lenses

(160.1245) Materials : Artificially engineered materials

(160.3918) Materials : Metamaterials

**ToC Category:**

Metamaterials

**History**

Original Manuscript: January 22, 2013

Revised Manuscript: March 7, 2013

Manuscript Accepted: March 7, 2013

Published: April 5, 2013

**Citation**

Víctor Torres, Víctor Pacheco-Peña, Pablo Rodríguez-Ulibarri, Miguel Navarro-Cía, Miguel Beruete, Mario Sorolla, and Nader Engheta, "Terahertz epsilon-near-zero graded-index lens," Opt. Express **21**, 9156-9166 (2013)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-7-9156

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### References

- L. Solymar and E. Shamonina, Waves in Metamaterials (Oxford, 2009).
- N. Engheta and R. W. Ziolkowski, Metamaterials: Physics and Engineering Explorations (Wiley, 2006).
- D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett.84(18), 4184–4187 (2000). [CrossRef] [PubMed]
- R. W. Ziolkowski, “Propagation in and scattering from a matched metamaterial having a zero index of refraction,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.70(4), 046608 (2004). [CrossRef] [PubMed]
- M. G. Silveirinha and N. Engheta, “Tunneling of electromagnetic energy through subwavelength channels and bends using ε-near-zero materials,” Phys. Rev. Lett.97(15), 157403 (2006). [CrossRef] [PubMed]
- A. Alù, M. G. Silveirinha, A. Salandrino, and N. Engheta, “Epsilon-near-zero metamaterials and electromagnetic sources: tailoring the radiation phase pattern,” Phys. Rev. B75(15), 155410 (2007). [CrossRef]
- C. Bohren and D. Huffmann, Absorption and Scattering of Light by Small Particles (Wiley, 1983).
- J. D. Jackson, Classical Electrodynamics (Wiley, 1999).
- J. Gómez Rivas, C. Janke, P. Bolivar, and H. Kurz, “Transmission of THz radiation through InSb gratings of subwavelength apertures,” Opt. Express13(3), 847–859 (2005). [CrossRef] [PubMed]
- P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B6(12), 4370–4379 (1972). [CrossRef]
- A. Alù, M. G. Silveirinha, and N. Engheta, “Transmission-line analysis of ε -near-zero-filled narrow channels,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.78(1), 016604 (2008). [CrossRef] [PubMed]
- H. Shi, C. Wang, C. Du, X. Luo, X. Dong, and H. Gao, “Beam manipulating by metallic nano-slits with variant widths,” Opt. Express13(18), 6815–6820 (2005). [CrossRef] [PubMed]
- L. Verslegers, P. B. Catrysse, Z. Yu, J. S. White, E. S. Barnard, M. L. Brongersma, and S. Fan, “Planar lenses Based on Nanoscale Slit Arrays in a metallic film,” Nano Lett.9(1), 235–238 (2009). [CrossRef] [PubMed]
- Z. Sun and H. K. Kim, “Refractive transmission of light and beam shaping with metallic nano-optic lenses,” Appl. Phys. Lett.85(4), 642–644 (2004). [CrossRef]
- C. Ma, M. Escobar, and Z. Liu, “Extraordinary light focusing and Fourier transform properties of gradient-index metalenses,” Phys. Rev. B84(19), 195142 (2011). [CrossRef]
- C. Ma and Z. Liu, “A super resolution metalens with phase compensation mechanism,” Appl. Phys. Lett.96(18), 183103 (2010). [CrossRef]
- 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 (2009). [CrossRef] [PubMed]
- S. Ishii, A. V. Kildishev, V. M. Shalaev, K. P. Chen, and V. P. Drachev, “Metal nanoslit lenses with polarization-selective design,” Opt. Lett.36(4), 451–453 (2011). [CrossRef] [PubMed]
- S. Ishii, A. V. Kildishev, V. M. Shalaev, and V. P. Drachev, “Controlling the wave focal structure of metallic nanoslit lenses with liquid crystals,” Laser Phys. Lett.8(11), 828–832 (2011). [CrossRef]
- S. Ishii, V. M. Shalaev, and A. V. Kildishev, “Holey-metal lenses: sieving single modes with proper phases,” Nano Lett.13(1), 159–163 (2013). [CrossRef] [PubMed]
- D. M. Pozar, Microwave Engineering (Wiley, 2005).
- B. Edwards, A. Alù, M. E. Young, M. Silveirinha, and N. Engheta, “Experimental verification of epsilon-near-zero metamaterial coupling and energy squeezing using a microwave waveguide,” Phys. Rev. Lett.100(3), 033903 (2008). [CrossRef] [PubMed]
- M. G. Silveirinha and N. Engheta, “Theory of supercoupling, squeezing wave energy, and field confinement in narrow channels and tight bends using ε near-zero metamaterials,” Phys. Rev. B76(24), 245109 (2007). [CrossRef]
- R. E. Collin, Foundations for Microwave Engineering (Wiley, 2000).
- M. Beruete, I. Campillo, M. Navarro-Cia, F. Falcone, and M. Sorolla Ayza, “Molding left- or right-handed metamaterials by stacked cutoff metallic hole arrays,” IEEE Trans. Antenn. Propag.55(6), 1514–1521 (2007). [CrossRef]
- M. Navarro-Cía, M. Beruete, M. Sorolla, and N. Engheta, “Lensing system and Fourier transformation using epsilon-near-zero metamaterials,” Phys. Rev. B86(16), 165130 (2012). [CrossRef]
- D. Filipovic, S. Gearhart, and G. Rebeiz, “Double-slot antennas on extended hemispherical and elliptical silicon dielectric lenses,” IEEE T. Microw. Theory41(10), 1738–1749 (1993). [CrossRef]
- N. Llombart, G. Chattopadhyay, A. Skalare, and I. Mehdi, “Novel terahertz antenna based on a silicon lens fed by a leaky wave enhanced waveguide,” IEEE Trans. Antenn. Propag.59(6), 2160–2168 (2011). [CrossRef]
- Microtech Instruments Inc, http://mtinstruments.com
- Thorlabs Inc, http://www.thorlabs.com
- J. W. Goodman, Introduction to Fourier Optics (Roberts & Company Publishers, 2004).
- W. Kock, “Metal-lens antennas,” Proceedings of the IRE34(11), 828–836 (1946). [CrossRef]
- J. Ruze, “Wide-angle metal-plate optics,” Proceedings of the IRE38(1), 853–855 (1950). [CrossRef]
- M. Navarro-Cía, M. Beruete, I. Campillo, and M. Sorolla Ayza, “Beamforming by left-handed extraordinary transmission metamaterial bi- and plano-concave lens at millimeter-waves,” IEEE Trans. Antenn. Propag.59(6), 2141–2151 (2011). [CrossRef]
- H. D. Hristov, Fresnel Zones in Wireless Links, Zone Plate Lenses and Antennas (Artech House, 2000).
- M. Navarro-Cía, M. Beruete, I. Campillo, and M. Sorolla, “Enhanced lens by ε and μ near-zero metamaterial boosted by extraordinary optical transmission,” Phys. Rev. B83(11), 115112 (2011). [CrossRef]

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