Conformal and Confocal Mantle Cloaking of Elliptical Cylinders Using Sub-Wavelength Metallic Meshes and Patches

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1 Conformal and Confocal Mantle Cloaking of lliptical Cylinders Using Sub-Wavelength Metallic Meshes and Patches Hossein M. Bernety and Alexander B. Yakovlev Center for Applied lectromagnetic Systems Research (CASR) University of Mississippi 2014 I International Symposium on Antennas and Propagation and USNC-URSI Radio Science Meeting July

2 Outline Introduction and Motivation Mantle Cloaking FSS Mantle Cloaks Formulation of the Scattering Problem Numerical Results 2

3 Mantle Cloaking Based on scattering cancellation An ultrathin metasurface Anti-phase surface currents Suppression of the dominant mode FSS Mantle Cloaks Uncloaked Cloaked lectric field distributions A. Alu, Mantle cloak: Invisibility induced by a surface, Phys. Rev. B. 80, ,

4 FSS Mantle Cloaks The specific design of metasurface has been carried out by optimizing numerically the shape and size of metasurface elements without a clear analytical approach Then, an analytical modeling of cylindrical FSS mantle cloaks have been proposed r PC Y. R. Padooru et.al., Analytical modeling of conformal mantle cloaks for cylindrical objects using sub-wavelength printed and slotted arrays, J. Appl. Phys., vol. 112, pp ,

5 1-D FSS Structures H r w D Vertical Strips H PC g D Capacitive Rings O. Luukkonen, et.al., I Trans. Antennas Propag., Vol. 56, No. 6, pp , C. R. Simovski, et.al., I Trans. Antennas Propag., Vol. 53, no. 3, pp ,

6 2-D FSS Structures r Mesh Grids PC Patch Arrays 6

7 lliptical Cloaks H r H r r H PC H PC c 7

8 lliptical Coordinate Scale factors : represents an ellipse : represents a hyperbola 8

9 Mathieu quation Two-dimentional Helmholtz quation: where: Using the method of separation of variables we have: Radial Mathieu quation The radial Mathieu equation has for kinds of solution as: Angular Mathieu quation The angular Mathieu equation has the solution as: p, m can be even or odd 9

10 Formulation of the Scattering Problem c 10

11 Formulation of the Scattering Problem By applying boundary conditions : 11

12 Formulation of the Scattering Problem Now, we apply the orthogonality property of angular Mathieu function as below: After some manipulation we come to the matrix equation below: Then, unknown coefficients are found 12

13 Formulation of the Scattering Problem The scattered field is represented as: To find the scattered field for farfield region, we use the asymptotic form of the radial Mathieu function: Then, the scattered field can be written as: It has already been found by solving the matrix equation 13

14 Formulation of the Scattering Problem The two-dimensional bistatic cross section is defined as: Therefore: Finally, we have: 14

15 Numerical Results Geometry parameters are: The required reactance is found to be: The design parameters are: N= 8 H r 15

16 Numerical Results N= 8 H r 16

17 lectric Field Distribution Uncloaked Cloaked 17

18 Numerical Results N= 3 Geometry parameters are: The required reactance is found to be: The design parameters are: H r N= 3 N= 8 N= 8 18

19 Power Flow Uncloaked Cloaked N= 8 19

20 lectric Field Distribution Uncloaked N= 8 Cloaked 20

21 Numerical Results Geometry parameters are: The required reactance is found to be: The design parameters are: H PC 21

22 lectric Field Distribution Uncloaked Cloaked 22

23 lectric Field Distribution Uncloaked Cloaked 23

24 Numerical Results Geometry parameters are: H PC The required reactance is found to be: The design parameters are: N= 10 c 24

25 Power Flow and Farfield Pattern Uncloaked Cloaked 25

26 lectric Field Distribution Uncloaked Cloaked 26

27 Conclusions An analytical approach has been proposed to cloak elliptical cylinders at microwave 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 scattering behavior is analyzed by expressing the incident and scattered fields in terms of radial and angular Mathieu functions and applying sheet impedance boundary conditions at the interface of the sub-wavelength elements. Simulation results are in good agreement with analytical results. 27