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In this work, the fishnet metamaterial is applied to several converging metalenses by combining the zoning, reference phase, and phase reversal techniques. First, the zoning and reference phase techniques are implemented in several metalenses at 55 GHz (_{0}. Then, the phase reversal technique is applied to these metalenses by switching from a concave to a convex profile in order to change the phase distribution inside of them. The designs are evaluated both numerically and experimentally demonstrating that chromatic dispersion (the shift of the position of the focus at different frequencies) is reduced when using the phase-reversed profiles. It is shown how the position of the focus remains at the same location within a relatively broadband frequency range of ~4% around the design frequency without affecting the overall behaviour of the metalenses. The best performance is achieved with the design that combines both reference phase and phase reversal techniques, with an experimental position of the focus of 1.75 _{0}, reduced side lobes, and a power enhancement of 6.5 dB. The metalenses designed here may find applications in situations where a wideband response and low side lobes are required because of the reduced chromatic aberrations of the focus.

Metamaterials (MTMs) are artificial structures engineered to get control of light propagation beyond the possibilities offered by natural materials [

Among the large numbers of MTM structures reported in the past years, the fishnet has proven to provide a good performance for high-frequency and quasioptical applications [

A major drawback of the abovementioned lenses is the large volume occupied by the lens that leads to a considerable weight of the structure. To mitigate this problem, one can apply the zoning technique whereby parts of the lens are removed when their phase variation with respect to free-space propagation is an integer multiple of

In this paper, we continue this study by changing the typical concave profile to a convex profile; that is, we aim to evaluate the performance when the phase distribution inside the lens is reversed compared to the designs shown in [_{0} using

The metalenses considered here use both the zoning technique and the reference phase. These were already explained in detail in [

With the reference phase, an extra phase advance is allowed inside the lens [

The unit cell employed is the same as the one used in our previous paper [

Dispersion diagram of the unit cell and profiles of the metalenses. (a) Refractive index of the fishnet structure used to design the lenses, assuming it to be infinitely periodic. Unit cell (inset) with dimensions:

From these results, we select an operation frequency of 55 GHz because it falls in the range where

Taking into account these factors, two metalenses were designed: without (

The focusing performance of the metalenses was evaluated both numerically and experimentally. The numerical simulations were carried out using the transient solver of CST Microwave Studio. In the first study, the focal position and the operation frequency in the numerical simulations were found by exciting the lens with a plane wave (with linear polarization,

Fabricated prototypes. (a) Sketch of the experimental setup used for characterizing the metalenses. Photographs of the fabricated metalenses with (b)

With this configuration, the results (numerical and experimental) of the normalized power distribution spectra along the _{0}) and _{0}) for _{0}) and _{0}), for each design, respectively. The slight deviation of the FL, ~0.3 _{0} from the designed value (1.5 _{0}), along with the small frequency deviation (0.9%) in all the metalenses could be attributed to experimental misalignments and fabrication tolerances. Additionally, this small error could be due to the fact that the waves emerging from the furthest zones (along the

Spectral response. Numerical (a, c) and experimental results (b, d) of the power distribution spectra along the propagation

For the sake of completeness, the impedance matching between the lenses and free space was numerically evaluated using the frequency domain solver of the commercial software CST Microwave Studio (not shown). In this study, the fishnet metamaterial was modeled using an infinite array of holes along the

In the next study, the power distribution in the

Focusing performance. Numerical (a, c, e) and experimental results (b, d, f) of the power distribution in the

Results of the focusing properties of the metalenses with reference phase and phase reversal. The experimental and numerical values are given at frequencies of 55.5 GHz and 55 GHz, respectively.

Sim | Exp | Sim | Exp | |
---|---|---|---|---|

FL | 1.87 _{0} |
1.94 _{0} |
1.79 _{0} |
1.75 _{0} |

FWHMx | 0.55 _{0} |
0.555 _{0} |
0.54 _{0} |
0.55 _{0} |

DF | 0.93 _{0} |
0.925 _{0} |
0.94 _{0} |
0.97 _{0} |

Enh | 5.7 dB | 4.5 dB | 8.2 dB | 6.5 dB |

As it is shown, the best performance is obtained for the design with

The profile of the zoned fishnet metalenses using the reference phase technique has been changed from a concave profile to a convex profile in order to evaluate their performance when the phase distribution inside of them is reversed. From the results of the spectral response, it has been shown that the chromatic dispersion is reduced with the reversed convex fishnet metalenses compared with the concave profiles. In this respect, it has been demonstrated that the position of the focus does not change for a relatively broadband frequency range of ~4% around the design frequency (considering the intrinsic narrow band response of the fishnet metamaterial) without affecting the overall performance of the metalenses. The best performance in terms of the power enhancement, reduced FWHM, and FL close to the design value has been achieved with the design with

The data used to support the findings of this study are available from the corresponding author upon request.

The authors declare that there is no conflict of interest regarding the publication of this paper.

The authors would like to thank Dr. V. Torres for the fabrication of the prototypes. This communication is based on the research conducted within the PhD thesis developed by Victor Pacheco-Peña. This work was partially supported by the Spanish Ministerio de Economía y Competitividad with European Union Fondo Europeo de Desarrollo Regional (FEDER) funds (TEC2014-51902-C2-2-R). Victor Pacheco-Peña is supported by Newcastle University (Newcastle University Research Fellow). Igor V. Minin and Oleg V. Minin were partially supported by the Mendeleev scientific fund of Tomsk State University.