# Multi-Directional Cloak Design by All-Dielectric Unit-Cell Optimized Structure

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## Abstract

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## 1. Introduction

## 2. Design Steps and Numerical Results

_{x}, E

_{y}) and the magnetic field (H

_{z}) is perpendicular to the xy-plane. In our simulations, perfectly matched layers construct the boundaries of the simulation area to serve as an absorbing boundary condition [65,66]. The corresponding results are gathered in Figure 2. The calculated magnetic field distributions as well as phase distributions for all structures are given in Figure 2a,b (structure types of the corresponding fields are labeled on a vertical axis), respectively. Moreover, cross-sectional field and phase profiles are extracted before (“input”) and after (“output”) structure in the propagation x-direction at a distance of 6.2 λ from the center of the cloak (which corresponds to the radiative near-field region if we consider cloak center as a wave source) [51]. The corresponding input and output cross-sectional profiles indicate the level of distortions in the wave fronts of the propagated light, as seen in Figure 2c. As can be seen from the figure plots, while the bare PEC is a small object compared to the size of its coating structure, it strongly scatters the incident wave. The variations in the output cross-sectional profile are higher than the input side due to the scantiness of back reflections, as seen in Figure 2c. On the other hand, without any optimization process, when the cloaked object is coated with solid PLA material, it is obvious that the scattering effect of bare PEC worsens due to expanding light–matter interactions into the reckless distribution of the covering dielectric material. Moreover, in the case of a randomly distributed cloaking structure, one can see that chaotically superimposed higher-order modes are enhancing back reflections by distorting phase profiles at the input and output locations of the structure. All these undesired effects motivate us to use optimized index modulation of the PEC covering material to design a cloaking structure with negligible scattering characteristics. It is important to note that the calculated transmission efficiencies for only PEC, bare structure with PEC, and randomly generated structure with PEC are 92%, 70%, and 51% at the frequency of 10 GHz, respectively.

## 3. Experimental Verification in Microwave Regime

## 4. Further Discussion: The Concept of Multi-Directional Cloaking

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**(

**a**) Schematic representation and the design approach of the cloaking structure and (

**b**) three-dimensional view of the designed cloaking structure with physical dimensions of each unit cell and the PEC object. The letter “K” indicates applied symmetry effect to the structure.

**Figure 2.**The numerically calculated (

**a**) magnetic field, (

**b**) phase distributions, and (

**c**) their cross-sectional amplitude and phase profiles at the front and back cross sections for the PEC, fully filled structure with PEC and a randomly filled structure with PEC, respectively from top to bottom. The black arrows indicate the incident waves which propagate in the x-direction. The dashed circles represent the boundaries of the PEC material and the obtained structures. The position profiles at the input and output of the cross sections are signified by the vertical dashed lines. All calculations were performed at 10 GHz.

**Figure 3.**The calculated (

**a**) magnetic field and phase distributions, (

**b**) cross-sectional amplitude and phase profiles at the front and back cross sections for x-direction injection for optimized structure. The calculated (

**c**) magnetic field and phase distributions, (

**d**) cross-sectional amplitude and phase profiles at the front and back cross sections for y-direction injection for optimized structure. The black arrows indicate the incident waves. The dashed circles represent the boundaries of the PEC material and the optimized structures. The position profiles at the input and output of the cross sections are signified by the vertical dashed lines. All calculations were performed at 10 GHz.

**Figure 4.**The numerically calculated scattering field of (

**a**) PEC, (

**b**) randomly filled structure with PEC and (

**c**) optimized structure with PEC at 10 GHz in the free space.

**Figure 5.**The plots of cost values with (

**a**) averaged scattered field values and with (

**b**) transmission efficiency values for selected frequency intervals. The numerically calculated magnetic field distributions at (

**c**) 8.7 GHz, (

**d**) 8.8 GHz, (

**e**) 9.2 GHz, (

**f**) 9.6 GHz, (

**g**) 10.48 GHz, (

**h**) 10.52 GHz, (

**i**) 11.3 GHz, and (

**j**) 11.7 GHz.

**Figure 6.**(

**a**) The schematic representation of the experimental setup with a photo of the fabricated cloaking structure and a brass object that is used as PEC. Experimentally measured magnetic field representations of (

**b**) free space, (

**c**) PEC and (

**d**) optimized structure with PEC, respectively. (

**e**) Experimentally measured cross sectional amplitude profile and (

**f**) cross sectional phase profile. (

**g**) Averaged scattering field values for selected frequency intervals. The black vertical dashed lines are signified the positions of the cross sections.

**Figure 7.**(

**a**) Schematic representation and the design approach of the cloaking structure that operates in three directions. Blue arrows demonstrate the incident wave directions with corresponding incident angles. (

**b**) Calculated magnetic field, (

**c**) phase distributions, and (

**d**) scattering field distributions for incident directions of 0°, 60°, and 120°. Black and white dashed lines demonstrate the boundaries of the PEC and cloaking structure. (

**e**) Photographic illustration of the 3D printed cloaking structure and a brass object inside at top and perspective views. Again, red colored arrows demonstrate the incident wave directions.

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## Share and Cite

**MDPI and ACS Style**

Ayik, M.; Kurt, H.; Minin, O.V.; Minin, I.V.; Turduev, M.
Multi-Directional Cloak Design by All-Dielectric Unit-Cell Optimized Structure. *Nanomaterials* **2022**, *12*, 4194.
https://doi.org/10.3390/nano12234194

**AMA Style**

Ayik M, Kurt H, Minin OV, Minin IV, Turduev M.
Multi-Directional Cloak Design by All-Dielectric Unit-Cell Optimized Structure. *Nanomaterials*. 2022; 12(23):4194.
https://doi.org/10.3390/nano12234194

**Chicago/Turabian Style**

Ayik, Muratcan, Hamza Kurt, Oleg V. Minin, Igor V. Minin, and Mirbek Turduev.
2022. "Multi-Directional Cloak Design by All-Dielectric Unit-Cell Optimized Structure" *Nanomaterials* 12, no. 23: 4194.
https://doi.org/10.3390/nano12234194