Reduction of Mutual Coupling in Neighboring Strip … · Reduction of Mutual Coupling in...

1

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

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

Reduction of Mutual Coupling in Neighboring Strip Antennas with Elliptical Metasurface Cloaks

Advanced Communications Center Antennas Mini-Symposium

Outline

2

Introduction and Motivation Mantle Cloaking

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

Analytical and Full-wave Simulation Results Dielectric Elliptical Cylinders at Microwave and Terahertz Frequencies PEC Elliptical Cylinders at Microwave and Terahertz Frequencies Strip as a Degenerated Ellipse

Conclusions

Application Reduction of the Mutual Coupling Between Two Strip Dipole Antennas

Cloaking with a Metasurface

3

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

4

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.

Mantle Cloaking using Graphene

5

The thinnest possible mantle cloak Large tunability Applicable for low terahertz (THz) frequencies

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

Dielectric Cylinder

Planar Structure

Graphene Nanopatches

6

Graphene monolayer provides inductive surface impedance A conducting object needs capacitive surface impedance to be cloaked To resolve this issue, a patterned graphene metasurface is proposed, which owns dual capacitive/inductive inductance and can be used to cloak both dielectric and conducting objects

PEC rε

Y. R. Padooru et.al., “Dual capacitive-inductive nature of periodic graphene patches: Transmission characteristics at low-terahertz frequencies”, Phys. Rev. B, vol. 87, pp. 115401, 2013.

: surface resistance per unit cell

: surface reactance per unit cell

: periodicity size

: gap size

: relative permittivity of the dielectric cylinder or the spacer

Cloaking using Graphene Nanopatches

7

Dielectric Cylinder PEC Cylinder

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

8

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

9

10

Scattering from Strips by Mathieu Functions

Elliptical Coordinate System

11

: represents an ellipse

: represents a hyperbola

Scale factors

Focus

Mathieu Equation

12

Two-dimentional Helmholtz Equation: where: Using the method of separation of variables we have:

Radial Mathieu Equation

Angular Mathieu Equation

The radial Mathieu equation has four kinds of solution as: The angular Mathieu equation has the solution as:

p, m can be even or odd

Formulation of the Scattering Problem

13

Incident Electric Field

Scattered Electric Field

Transmitted Magnetic Field

Incident Magnetic Field

Scattered Magnetic Field

Transmitted Electric Field

Boundary Conditions

14

By applying boundary conditions :

Sheet Impedance Boundary Condition

Sheet Impedance Boundary Condition

Matrix Equation for Coefficients

15

Now, we apply the orthogonality property of angular Mathieu function as below:

If :

Matrix Equation for Coefficients

16

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:

It has already been found by solving the matrix equation

Bistatic Scattering Width

17

The two-dimensional bistatic cross section is defined as:

Finally, we have:

Optimum Reactance in terms of Observation Angle

18

To find the optimum reactance versus observation angle, we solve the matrix equation for the dominant scattering mode and require

Finally the optimum required reactance versus observation angle can be found as:

With the same approach we can find the optimum required reactance versus observation angle for the dielectric elliptical cylinder as:

Optimum Reactance in terms of Observation Angle

19

PEC Elliptical Cylinders

Strip !!!

Optimum Required Reactance

20

PEC

Dielectric

Quasi-static Closed-form Condition

21

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

22

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

Surface Conductivity of Graphene

23

G. W. Hanson, “Dyadic Green’s functions and guided surface waves for a surface conductivity model of graphene”, J. Appl. Phys., vol. 103, pp. 064302, 2008.

: charge of electron : temperature : energy : angular frequency : reduced Planck’s constant : chemical potential : momentum relaxation time

Intraband Contributions

Interband Contributions

Kubo Formula

σ1=sZ

Dielectric Elliptical Cylinder at THz Frequencies

24

Geometry parameters are:

The required reactance is found to be:

The design parameters are:

25

Power Flow and Far-field Pattern Uncloaked Cloaked

f= 3 THz

26

Uncloaked

Cloaked

Electric Field Distribution

f= 3 THz

Closely Spaced and Overlapping Dielectric Elliptical Cylinders

27

Uncloaked

Uncloaked

Cloaked

Cloaked

l= 50 µm

l= 48 µm

f= 3 THz

Cluster of Dielectric Elliptical Cylinders I

28

Uncloaked Cloaked

Uncloaked Cloaked

g= 3 µm

f= 3 THz

l= 50 µm= 0.5 λ

Cluster of Dielectric Elliptical Cylinders II

29

Cloaked Uncloaked

Uncloaked Cloaked

f= 3 THz

g= 3 µm

Overlapping of Dielectric Elliptical Cylinders

30

Cloaked Uncloaked

Uncloaked Cloaked

f= 3 THz

l= 140 µm= 1.4 λ

Dielectric Elliptical Cylinder at Microwave Frequencies

31




rεN= 8

E

H θ

Dielectric Elliptical Cylinder at Microwave Frequencies

32


The required reactance is found to be: The design parameters are:

E

H θ

rε

N= 8

N= 3

N= 3 N= 8

33


Uncloaked

Cloaked

f= 3 GHz

rε

N= 8

34




Dielectric Elliptical Cylinder at THz Frequencies

PEC Elliptical Cylinder at THz Frequencies

35




36

Uncloaked

Cloaked


f= 3 THz

PEC Elliptical Cylinder at Microwave Frequencies

37




E

H θPEC

2-D Metasurface Cloak for PEC at Microwaves

38




E

H θ

PEC

N= 10

cε

39

Power Flow and Far-field Pattern Uncloaked Cloaked

f= 3 GHz

N= 10

cε

40

Uncloaked

Cloaked


PEC cε

f= 3 GHz

Strip (Degenerated Ellipse)

41

A strip can be modeled as a degenerated ellipse


42

Power Flow and Far-field Pattern Cloaked Uncloaked

f= 3 THz

43

Uncloaked

Cloaked


Cloaking for Two Strips

44

Uncloaked Cloaked

f= 3 THz

Two Strips Horizontally Oriented

45

Uncloaked Cloaked

f= 3 THz

Two Strips with Overlapping Cloaks

46

Uncloaked Cloaked

Uncloaked Cloaked

f= 3 THz

g= 3.7 µm

Two Connected Strips

47

Cloaked Uncloaked

Uncloaked Cloaked

f= 3 THz

Wire Dipole Antennas

48

Strip Dipole Antennas

49

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

50

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

51

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 II drastically.

f= 1 GHz f= 5 GHz

d= 6 mm

Cloaking 2-D Metallic Strip

52

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

TM-polarized plane-wave excitation.

Cloaking 2-D Metallic Strip

53

Uncloaked Cloaked

How to Cloak Antenna I?

54

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.

55

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

56

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 Antenna I (Case II)

57

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 Antenna II (Case II)

58

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

59

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

60

To reduce the mutual coupling, we cover each dipole antenna with an elliptically shaped mantle cloak structure consisting of inductive vertical strips and a spacer between the strip and the metasurface. The presence of the spacer, and then, the cloak structure, changes the resonance frequency of the antenna. Therefore, we reduce the length of the antenna in order to provide good matching at the desired working frequency. On the other hand, the parameters of the cloak structure should be chosen in a way that each antenna is invisible at the resonance frequency of the other one.

We have performed an appropriate optimization to minimize the 3-D total RCS of each dipole antenna under Transverse Magnetic (TM) plane-wave excitation.

Separated Cloaked Dipole Antennas

61

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

62

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

63

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.


Radiation patterns are:


64

f= 2.9441 GHz

f= 3.3515 GHz

E-Plane H-Plane

f= 2.9441 GHz

f= 3.3515 GHz

Conclusions

65

An analytical approach has been proposed to cloak elliptical cylinders, and also, strips at microwave and low-THz frequencies by using conformal mantle cloak designs.

Although the electromagnetic wave scattering of an elliptical cylinder is pertinent to the angle of incidence, it is shown that the cloak design is robust for any incident angle.

The idea of cloaking strips has been utilized to reduce the mutual coupling between two strip dipole antennas.

Reduction of Mutual Coupling in Neighboring Strip … · Reduction of Mutual Coupling in...

Documents

Transcript of Reduction of Mutual Coupling in Neighboring Strip … · Reduction of Mutual Coupling in...