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Hossein M. Bernety and Alexander B. Yakovlev Department of Electrical Engineering

Center for Applied Electromagnetic Systems Research (CAESR) University of Mississippi

Mutual Coupling Reduction Between Neighboring Strip Dipole Antennas

Using Confocal Elliptical Metasurfaces

The 9th European Conference on Antennas and Propagation (EuCAP 2015)

Outline

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Introduction and Motivation Mantle Cloaking

Formulation and Theory Formulation of the Scattering Problem in terms of Mathieu Functions Optimum Required Reactance

Cloaking of Elliptical Structures and Strips

Conclusions

Reduction of Mutual Coupling Strip Dipole Antennas Strip Monopole Antennas

Cloaking with a Metasurface

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Uncloaked Cloaked

Electric field distributions

A. Alu, “Mantle cloak: Invisibility induced by a surface”, Phys. Rev. B. 80, 245115, 2009.

Metasurface Mantle Cloaks Mantle Cloaking Based on scattering cancellation An ultrathin metasurface Anti-phase surface currents Suppression of the dominant mode

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D

w

E

rε

g

D E

PEC

1-D and 2-D Periodic Structures

Vertical Strips

Capacitive Rings

E

Mesh Grids

Patch Arrays

PEC

E

rε

Y. R. Padooru et.al., J. Appl. Phys. , vol. 112, pp. 0349075, 2012.

Cloaking using Graphene

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Dielectric Cylinder PEC Cylinder

P. Y. Chen et. al, “Nanostructured graphene metasurface for tunable terahertz cloaking,” New. J. Phys., vol. 15, pp. 123029, 2013.

P. Y. Chen and A. Alú, “Atomically thin surface cloak using graphene monolayers”, ACS NANO, vol. 5, no. 7, pp. 5855-5863, 2011.

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rεE

H θ

E

H θ

PEC E

H θ

PEC

cε

rε

Elliptical Cloak Designs at Microwaves

E

H θ

rε

Elliptical Cloak Designs at THz Frequencies

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Formulation of the Scattering Problem

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Incident Electric Field

Scattered Electric Field

Transmitted Magnetic Field

Incident Magnetic Field

Scattered Magnetic Field

Transmitted Electric Field

Boundary Conditions

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By applying boundary conditions :

Sheet Impedance Boundary Condition

Sheet Impedance Boundary Condition

Matrix Equation for Coefficients

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After some manipulation we come to the matrix equation below:

To find the scattered field for farfield region, we use the asymptotic form of the radial Mathieu function and we have:

Finally, the two-dimensional bistatic cross section is :

Quasi-static Closed-form Condition

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In the quasi-static limit( ), the closed-form condition for a PEC elliptical cylinder under TM-polarized illumination can be derived as:

And also, the closed-form condition for a dielectric elliptical cylinder under TM-polarized illumination can be derived as:

Surface Reactance Frequency Dispersion

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Frequency dispersion of the surface reactance for graphene monolayer and nanopatches with respect to the optimum required is found as:

Required Reactance for Dielectric Ellipse

Required Reactance for PEC Ellipse

Required Reactance for Strip

Dielectric Elliptical Cylinder at THz Frequencies

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Geometry parameters are:

The required reactance is found to be:

The design parameters are:

Cluster of Dielectric Elliptical Cylinders

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Cloaked Uncloaked

Uncloaked Cloaked

f= 3 THz

g= 3 µm

Overlapping of Dielectric Elliptical Cylinders

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Cloaked Uncloaked

Uncloaked Cloaked

f= 3 THz

l= 140 µm= 1.4 λ

Dielectric Elliptical Cylinder at Microwave Frequencies

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Geometry parameters are:

The required reactance is found to be:

The design parameters are:

rεN= 8

E

H θ

PEC Elliptical Cylinder at THz Frequencies

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Geometry parameters are:

The required reactance is found to be:

The design parameters are:

PEC Elliptical Cylinder at Microwave Frequencies

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Geometry parameters are:

The required reactance is found to be:

The design parameters are:

E

H θPEC

2-D Metasurface Cloak for PEC at Microwaves

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Geometry parameters are:

The required reactance is found to be:

The design parameters are:

E

H θ

PEC

N= 10

cε

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Uncloaked

Cloaked

Electric Field Distribution

PEC cε

f= 3 GHz

Strip (Degenerated Ellipse)

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A strip can be modeled as a degenerated ellipse

Geometry parameters are:

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Uncloaked

Cloaked

Electric Field Distribution

Two Strips with Overlapping Cloaks

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Uncloaked Cloaked f= 3 THz

g= 3.7 µm Uncloaked Cloaked

f= 3 THz

Cloaking 2-D Metallic Strip at Microwaves

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a 2-D Metallic Strip can be considered as a degenerated ellipse

TM-polarized plane-wave excitation.

Cloaking 2-D Metallic Strip

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Uncloaked Cloaked

Wire Dipole Antennas

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Strip Dipole Antennas

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Here, we present the applicability of elliptically shaped metasurfaces in order to reduce the mutual coupling between two closely spaced antennas. First, we consider two strip dipole antennas resonating at f= 1 GHz and f= 5 GHz, which are separated by a short distance of d= λ/10 (at f= 5 GHz). (Case I)

Second, we consider two strip dipole antennas resonating at f= 3.02 GHz and f= 3.33 GHz, which are separated by a short distance of d= λ/10 (at f= 3 GHz). (Case II)

To present how the mutual blockage is overcome, we consider three different scenarios of isolated, uncloaked, and cloaked for each case.

Case I

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We consider Antenna I (isolated) and Antenna II (isolated) which resonate at f= 1 GHz and f= 5 GHz, respectively, with omni-directional radiation patterns as shown below. Each antenna is matched to a 75-Ω feed.

Antenna I Antenna II

W= 4 mm

L= 130.5.5 mm

Δ= 0.2 mm W= 4 mm

L= 27.5 mm

Δ= 0.2 mm

Neighboring Uncloaked Dipole Antennas

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Now, the antennas are placed in close proximity to each other. The presence of Antenna II does not have much effect on Antenna I since its length is small compared to the wavelength of the resonance frequency of Antenna I, but Antenna I changes the matching characteristics and radiation pattern of Antenna I drastically.

f= 1 GHz f= 5 GHz

d= 6 mm

How to Cloak Antenna I?

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Since the length of Antenna I is 2.5 times the wavelength of Antenna II, therefore, we propose to use the analytical approach for infinite length as a good approximation to find the required metasursurface for this case.

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3-D radiation patterns of Antenna I at 1 GHz (left) and Antenna II at 5 GHz (right) for the scenario, in which Antenna I is cloaked for the resonance frequency of Antenna II and the antennas are in close proximity.

Antenna I

Antenna II

Neighboring Cloaked Dipole Antennas

f= 1 GHz

f= 5 GHz

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Restoration of gain patterns at the first and second resonance frequency of Antenna I (1 GHz, 3 GHz) and resonance frequency of Antenna II

2-D Gain Pattern

E-plane H-plane

Antenna I

Antenna I

H-plane E-plane

E-plane H-plane

Antenna I

f= 1 GHz f= 3 GHz

f= 5 GHz

Isolated Strip Dipole Antenna I

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W= 4 mm f= 3.02 GHz

L

L= 45.8 mm

Δ

Δ= 0.2 mm

First of all, we consider the antenna I (Isolated Case), which resonates at f= 3.02 GHz with an omni-directional radiation pattern as shown below. The S11 of the antenna along with its dimensions are shown below. The antenna is matched to a 75-Ω feed.

Isolated Strip Dipole Antenna II

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f= 3.33 GHz W= 4 mm L= 41.5 mm Δ= 0.2 mm

Then, we consider the antenna II (Isolated Case), which resonates at f= 3.33 GHz with an omni-directional radiation pattern as illustrated below. The S11 of the antenna along with its dimensions are shown below. The antenna is matched to a 75-Ω feed.

L Δ

Neighboring Uncloaked Dipole Antennas

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Now, the antennas are placed in close proximity to each other. As expected, the presence of each of the antennas affects the radiation pattern of the other one drastically because the near-field distribution is changed, and therefore, the input reactance is changed remarkably.

f= 3.02 GHz f= 3.33 GHz

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In this slide, the antenna I covered with the spacer and the metasurface is presented. To achieve a good matching at the desired resonance frequency of 3.02 GHz, we reduced the length of the antenna from L= 45.8 mm to L= 41.4 mm. The S11 parameter, permittivity of the spacer, and also, the dimensions of the cloak structure are shown below.

Cloaked Dipole Antenna I

Rogers RO3006 (Lossy)

L= 41.4 mm

S11

RCS

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In this slide, the antenna II covered with the spacer and the cloak design is presented. To achieve a good matching at the desired resonance frequency of 3.02 GHz, again, we reduced the length of the antenna from L= 41.5 mm to L= 38.8 mm. The S11 parameter, permittivity of the spacer, and also, the dimensions of the cloak structure are shown below.

Cloaked Dipole Antenna II

Rogers TMM 10i (Lossy)

L= 38.8 mm

RCS

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The reflection coefficients at the input port of the Antenna I and the Antenna II in the cloaked case (the antennas are in close proximity to each other) are shown here. As can be seen, the impedance matching of the antennas are good near the resonant frequency of each isolated strip dipole antenna.

Neighboring Cloaked Dipole Antennas

Radiation patterns are:

Neighboring Cloaked Dipole Antennas

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f= 2.9441 GHz

f= 3.3515 GHz

E-Plane H-Plane

f= 2.9441 GHz

f= 3.3515 GHz

Strip Monopole Antennas

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W= 4 mm

f= 3.02 GHz

L

L= 22.75 mm

Δ

Δ= 0.1 mm

First of all, we consider the Antenna I (Isolated) and the Antenna I (Isolated), which resonate at f= 3.02 GHz and f= 3.33 GHz, respectively, with omni-directional radiation patterns as shown below. The antennas are matched to a 37.5-Ω feed.

Δ

L

L= 20.65 mm f= 3.33 GHz

Neighboring Uncloaked Monopole Antennas

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Now, the antennas are placed in close proximity to each other (d= 10 mm). As expected, the presence of each of the antennas affects the radiation pattern of the other one drastically because the near-field distribution is changed, and therefore, the input reactance is changed remarkably.

f= 3.02 GHz f= 3.33 GHz

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The reflection coefficients at the input port of the Antenna I and the Antenna II in the cloaked case (the antennas are in close proximity to each other) are shown here. As can be seen, the impedance matching of the antennas are good near the resonance frequency of each isolated strip monopole antenna.

Neighboring Cloaked Monopole Antennas

d= 10 mm

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Design Parameters for Monopole Antennas L1= 20.7 mm

Δ= 0.1 mm

L2= 19.4 mm

Δ= 0.1 mm

W1= 4 mm

W2= 4 mm

d= 10 mm

Antenna II

Antenna I

Neighboring Cloaked Monopole Antennas

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f= 2.9 GHz

f= 3.3 GHz

E-Plane H-Plane

f= 2.9 GHz

f= 3.3 GHz

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Electric Field Distribution Isolated Uncloaked Cloaked

Isolated Uncloaked Cloaked

Antenna I

Antenna II

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Extension of the idea to different planar antennas!!!

Future Work

Conclusions

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In this presentation, we proposed the idea of utilizing elliptically shaped cloak metasurfaces (which are used to cloak metallic strips) to reduce the mutual coupling between neighboring strip monpole and dipole antennas.

In Case I, the strip monopole/dipole antennas have been designed to resonate at f= 1 GHz and f= 5 GHz and separated by a short distance of d= λ/10 (at f= 5 GHz). In Case II, the strip monopole/dipole antennas have been designed to resonate at f= 3.02 GHz and f= 3.33 GHz and separated by a short distance of d= λ/10 (at f= 3 GHz).

Each antenna’s radiation properties are restored in a way that the radiation patterns are nearly similar to the isolated case.