Multi-directional cloak design by all dielectric unit-cell optimized structure Muratcan Ayik12 Hamza Kurt3 Oleg V. Minin4 Igor V. Minin4 and Mirbek Turduev5

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Multi-directional cloak design by all dielectric unit-cell optimized

structure

Muratcan Ayik1,2, Hamza Kurt3, Oleg V. Minin4, Igor V. Minin4 and Mirbek Turduev5,*

1Department of Electrical and Electronics Engineering, Middle East Technical University,

Ankara 06800, Turkey

2Aselsan Inc., Ankara 06200, Turkey

3School of Electrical Engineering, Korea Advanced Institute of Science and Technology

(KAIST), Daejeon, 34141, Republic of Korea

4Nondestructive school, Tomsk Polytechnic University, 634050, Tomsk, Russia

5Department of Electrical and Electronics Engineering, Kyrgyz-Turkish Manas University,

Bishkek 720038, Kyrgyzstan

*Corresponding author: mirbek.turduev@manas.edu.kg

Abstract

In this manuscript, we demonstrate the design and experimental proof of an optical cloaking

structure which multi-directionally conceals a perfectly electric conductor (PEC) object from

an incident plane wave. The dielectric modulation around the highly reflective scattering PEC

object is determined by an optimization process for multi-directional cloaking purposes. And

to obtain the multi-directional effect of the cloaking structure, an optimized slice is mirror

symmetrized through a radial perimeter. Three-dimensional (3D) finite-difference time-domain

method is integrated with genetic optimization to achieve cloaking design. In order to overcome

the technological problems of the corresponding devices in the optical range and to

experimentally demonstrate the proposed concept, our experiments were carried out on a scale

model in the microwave range. The scaled proof-of-concept of proposed structure is fabricated

by 3D printing of polylactide material, and the brass metallic alloy is used as a perfect electrical

conductor for microwave experiments. A good agreement between numerical and experimental

results is achieved. The proposed design approach is not restricted only to multi-directional

optical cloaking but can also be applied for different cloaking scenarios dealing with

electromagnetic waves in nanoscales as well as other types of such as acoustic waves. Using

nanotechnology, our scale proof-of-concept research will take the next step towards the creation

of "optical cloaking" devices.

1. Introduction

One of the most intriguing and mysterious phenomena that have captured researchers’

imaginations for centuries is invisibility. In general, invisibility means that light wave incident

on the object should remain its optical property after passing through an object. In other words,

the scattered and deteriorated field resulting from the object should be reconstructed and

corrected to replicate the incident wave. The first realistic idea of the invisibility cloak has been

introduced to the literature by the pioneering works of Leonhardt and Pendry [1, 2]. Here,

application of conformal mapping concept is proposed and the first application of

transformation optics (TO) into optical cloaking is demonstrated [3-6]. In TO, the incident wave

is guided to follow a curved trajectory by simply bending the coordinate system to obtain the

cloaking of objects.

Along with TO, an interesting approach for concealing an object named as “carpet-cloaking” is

proposed. Here large scatterer object is hidden under a reflective layer named carpet by using

quasi-conformal mapping [7-11]. Similarly, as in TO, this non-Euclidian approach provides an

interesting solution to prevent an object from detection [12]. This approach has been further

developed to design and analyze carpet cloaking methods [13-15]. Lately, different from the

TO concept, new design strategies for optical cloaking are proposed such as metasurfaces

[16,17], zero-refractive-index materials [18], plasmonics [19-21], woodpile photonic structures

[22], graded index structures [23], and superluminal media [24] to operate in different

wavelength regimes including microwave, terahertz, infrared and visible. Also, the mantle

cloaking technique offers scattering cancellation by covering the cylindrical dielectric with

conducting helical sheet [25] or concentric mantle cloak [26] by satisfying surface impedance

condition at designed frequencies.

Moreover, to obtain optical cloaking effect the suppression of scatterings resulting from an

object is realized by using generalized Hilbert transforms [27] and Kramers-Kronig relations

[28]. In addition to these studies, the focusing effect is also used for creating invisible regions

both in ray and wave optics [29, 30]. Finally, the idea of using optimization algorithms for the

generation/reshaping of the cloaking region shows promising results [31-34]. Here, the

optimization methods search for possible designs of cloaking structures in accordance with a

specific objective function. Furthermore, experimental verifications at microwave frequency

regimes of cloaking designs based on optimization methods were reported in Refs. [35] and

[36].

The nanotechnology plays a significant role in the development and creation of new cloaking

devices in nanoscale [37]. Moreover, optical cloaking plays an important role in industry where

the development of nanotechnology makes possible the design of novel camouflage systems

and radar absorbing surfaces for low observable technologies [38 - 41]. In accordance with the

state-of-the-art nanofabrication technology, controlling the flow of light along with their spatial

mapping at the nanoscale in some cases is always not possible. On the other hand, thanks to the

scalability of the Maxwell’s equations [42, 43], one can always analyze the designed prototype

at the microwave region for verification of the proof of the proposed concept [44 - 46].

In this study, we propose the design of all-dielectric, lossless, broadband, and passive multi-

directional cloaking structure which conceals a high reflective perfectly electric conductor

(PEC) material/object from an incident plane wave. The designed cloak is composed of

polylactide (PLA) material which is a low loss biodegradable thermoplastic polymer with a low

permittivity value. This dielectric material is widely used in three-dimensional (3D) additive

printing technology and gives the opportunity for direct and cost-effective fabrication of the

devices. The generalized framework of the proposed design approach with numerical and

experimental analysis of the performance of the designed cloaking structure is provided in the

current study. In addition, experimental verification of numerical results is performed at

microwave frequency regime at around 10 GHz to demonstrate the operating principle of the

design. As it was noted above the scale model of the proposed cloaking structure allow realizing

a “rapid low-cost prototyping” for verification of proof-of-concept in microwave regime. Also,

the physical mechanism of directional concealing effect of the designed optical cloak is

primarily associated with the imperfect conformal mapping and partial suppression of scattered

fields from the object. Since complete cloaking is impossible by conformal mapping with

realistic material parameters, the remaining scattering is eliminated by an intelligent rendering

of the cloaking structure thanks to advanced optimization. In addition, the proposed design

methodology can find various cloaking applications of electromagnetic waves and may enable

the multi-directional concealment of different objects possessing various sizes and shapes.

2. Design steps and numerical results

To optically hide object or to make it invisible, the incident wave should be reconstructed

without distortion after passing through an object. In other words, the scattered field resulting

from the object should be corrected/transformed to replicate the incident wave. For this reason,

one should design such an environment around object that enables suppression of scatterings

and diminishing of back-reflections. Hence, in contrast to forward design approaches the

problem of optical cloaking can be treated as an inverse problem. Here the desired optical

properties of the output electromagnetic field are defined and integrated into the cost function

of the optimization method, and the algorithm iteratively searches for the best structure

(environment) that provides the desired output. Therefore, to obtain desired optical cloaking

effect, we optimally modulated the cloaking region’s effective index distribution.

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.

In this study, to achieve an optical cloaking effect, the concept of covering highly scattering

material by index modulated structure is considered. For this reason, the circular shape is

selected for the covering structure, which is also beneficial for multi-directional optical

concealing in both x- and y- propagation directions. Fig. 1(a) illustrates the schematic

representation of the design approach. As can be seen in Fig. 1(a), the circular region is divided

into 8 slices with 45° internal angles to increase the directional independency. Here, to obtain

bi-directional effect of the cloaking structure, optimized slice is mirror symmetrized through

radial perimeter (the letter “K” shows the symmetry effect). In other words, by this symmetry

concept the proposed structure demonstrates the exact same optical light conveying behavior in

both injection x- and y- directions. The dashed and solid lines superimposed on the schematics

in Fig. 1(a) define the border lines of mirror symmetry and rotational symmetry, respectively.

In other words, the designed structure has 8 mirror symmetry slices which provide 4-fold

rotational symmetry with 90° rotation angles. Here, rotational symmetry border lines define the

injection directions of the cloak which are defined by blue arrows in Fig. 1(a). It should be

noted that it is also possible to increase the number of injection directions (for multi-directional

cloaking) by properly increasing the number of symmetry slices. Symmetry slices considered

to be composed of rectangular shaped unit cells. The unit cells can be in two different states

such as PLA (𝜀𝑃𝐿𝐴-existence of the unit cell) or Air (𝜀𝑎𝑖𝑟-absence of the unit cell) according to

the decision of the applied optimization.

It is important to note that to define the states of those unit cells the genetic algorithm (GA) is

integrated with the 3D finite difference time domain (FDTD) method [47]. GA is used for

optimal distribution of permittivity that reduces observability of the object. GA is an

evolutionary algorithm, i.e., a meta-heuristic, that mainly adapts advantage of the survival of

the fittest in the evolutionary process. As the biological counterparts of evolution theory, GA

comprises mechanisms such as crossover, mutation, and selection. GA iteratively searches the

solution space to find candidate solutions to the problem described as a cost function. Here, GA

decides whether each unit cell inside the optimization region is filled with PLA material or not.

The algorithm fills the unit cell with air if it generates the binary number “0”. Otherwise, for

“1”, it fills the unit cell with PLA. The three-dimensional view of the optimized cloaking

structure with materials’ parameters is demonstrated in Fig. 1(b). All unit cells filled with PLA

are structurally identical and each one emerges as a rectangular prism that has dimensions of

0.1λ×0.1λ×1.5λ as shown as an inset in Fig. 1(b). Throughout the study the dielectric constants

of PLA material and air are fixed to 𝜀𝑃𝐿𝐴 = 2.4, and 𝜀𝑎𝑖𝑟 = 1.0, respectively. In place of the

highly scattered object which intended to be hidden from the incident wave, the cylindrical

shaped perfect electrical conductor (PEC) is considered. The cylindrical PEC has a diameter of

1.15λ and a height of 1.5λ. Additionally, the diameter of the final structure is measured as 5.6λ.

Considering the dimension of the structure we can say that designed structure belongs to the

class of mesotronics [48].

The main goal of the study is to design such a surrounding structure that reduces the scattering

effect of itself and the PEC that located inside the cloaked region. For this reason, before starting

the optimization it is instructive to inspect the incident light scattering effect of bare PEC

without cloaking, PEC coated with a fully filled/solid structure and PEC coated with a randomly

PLA filled 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

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Multi-directionalcloakdesignbyalldielectricunit-celloptimizedstructureMuratcanAyik1,2,HamzaKurt3,OlegV.Minin4,IgorV.Minin4andMirbekTurduev5,*1DepartmentofElectricalandElectronicsEngineering,MiddleEastTechnicalUniversity,Ankara06800,Turkey2AselsanInc.,Ankara06200,Turkey3SchoolofElectricalEngineering,...

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Multi-directional cloak design by all dielectric unit-cell optimized structure Muratcan Ayik12 Hamza Kurt3 Oleg V. Minin4 Igor V. Minin4 and Mirbek Turduev5

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