# Gradient Index Metasurface Lens for Microwave Imaging

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## Abstract

**:**

## 1. Introduction

## 2. Theory

## 3. Design

#### 3.1. Unit Cell

_{21}magnitude and phase results for 10 representative cases obtained using HFSS. 8 GHz was chosen as the frequency of operation from the parametric results to maximize transmission through the lens (S

_{21}magnitude) and achieve high phase shift between the individual unit cells (S

_{21}phase) simultaneously.

#### 3.2. Metasurface Lens

_{o}in Equation (1) at the center of the GRIN lens is 27.91 for the proposed design at 8GHz. The simulated refractive index profile is plotted in Figure 5b. The theoretical refractive index profile according to (2) is plotted as well to demonstrate the correlation between geometric optics and full-wave electromagnetism. The difference in the theoretical and simulated gradient index profile is due to the approximations of EM waves as straight rays in geometric optics, which does not consider effects such as scattering and diffraction. Although it has been argued that assigning bulk material properties to metasurfaces using a variant of Nicholson Ross Weir method may produce ambiguous results [55,56], they can still be used to characterize metasurfaces if the thickness of the metasurface remains constant [19].

## 4. Experiment

#### 4.1. Focusing

#### 4.2. Microwave NDE

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**GRIN Lens operation. Shading of the lens indicates the gradient in the index: darker shading corresponds to a higher refractive index value.

**Figure 2.**(

**a**) ELC unit cell of proposed GRIN Metasurface lens (

**b**) Equivalent circuit of ELC resonator unit cell.

**Figure 5.**(

**a**) Theoretical and simulated phase gradient (

**b**) Theoretical and extracted refractive index gradient (

**c**) Proposed 1D GRIN metasurface lens design.

**Figure 6.**(

**a**) HFSS setup for focusing simulation of 1D GRIN lens. (

**b**) Simulated $E$ field distribution with lens. (

**c**) Simulated $E$ field distribution without lens.

**Figure 8.**(

**a**) Ansys HFSS setup for proposed 2D GRIN Metasurface Lens. (

**b**) Azimuthal plane electric field distribution with lens and (

**c**) without lens. (

**d**) Vertical plane electric field distribution with lens and (

**e**) without lens.

**Figure 9.**(

**a**) Fabricated GRIN Metasurface Lens. (

**b**) Experiment setup using homodyne imaging system. (

**c**) Measured field distribution with lens. (

**d**) Measured field distribution without lens. (

**e**) Normalized measured field at focal plane.

**Figure 10.**(

**a**) Fabricated 2D GRIN Metasurface Lens. (

**b**) Field distribution in horizontal plane with lens and (

**c**) without lens. (

**d**) Field distribution in vertical (focal) plane with lens and (

**e**) without lens. (

**f**) Cross- range intensity profile comparison of lens and free space at focal plane.

**Figure 11.**(

**a**) Microwave NDE experiment setup. (

**b**) Schematic of Teflon sample under test with machined groove. (

**c**) Microwave imaging results of groove defect with lens and (

**d**) without lens.

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Datta, S.; Tamburrino, A.; Udpa, L.
Gradient Index Metasurface Lens for Microwave Imaging. *Sensors* **2022**, *22*, 8319.
https://doi.org/10.3390/s22218319

**AMA Style**

Datta S, Tamburrino A, Udpa L.
Gradient Index Metasurface Lens for Microwave Imaging. *Sensors*. 2022; 22(21):8319.
https://doi.org/10.3390/s22218319

**Chicago/Turabian Style**

Datta, Srijan, Antonello Tamburrino, and Lalita Udpa.
2022. "Gradient Index Metasurface Lens for Microwave Imaging" *Sensors* 22, no. 21: 8319.
https://doi.org/10.3390/s22218319