Cloaking of Dielectric and Metallic Elliptical Cylinders with a Nanostructured Graphene Metasurface

Transcription

1 Cloaking of Dielectric and Metallic Elliptical Cylinders with a Nanostructured Graphene Metasurface Hossein M. Bernety and Alexander B. Yakovlev Center for Applied Electromagnetic Systems Research (CAESR) University of Mississippi 2014 IEEE International Symposium on Antennas and Propagation and USNC-URSI Radio Science Meeting July

2 Outline Introduction and Motivation Formulation and Theory Analytical and Full-wave simulation Results A Special Case 2

3 Plasmonic Cloaking Based on scattering cancellation Homogeneous and isotropic materials Low or negative index materials Suppression of the dominant mode Electric field distribution Uncloaked Cloaked A. Alú and N. Engheta, Achieving transparency with plasmonic and metamaterial coatings, Phys. Rev. E. 72, ,

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

5 Mantle Cloaking using Graphene The thinnest possible mantle cloak Large tunability Applicable for low terahertz (THz) frequencies Planar Structure Dielectric Cylinder P. Y. Chen and A. Alú, Atomically thin surface cloak using graphene monolayers, ACS NANO, vol. 5, no. 7, pp ,

6 Kubo formula Surface Conductivity of Graphene Intraband contributions Interband contributions Z s 1 : charge of electron : temperature : energy : angular frequency : reduced Planck s constant : chemical potential : momentum relaxation time G. W. Hanson, J. Appl. Phys., 103, ,

7 Graphene Nanopatches 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 r PEC : the surface resistance per unit cell related to the conduction losses : the surface reactance per unit cell related to the conduction losses : the periodicity size : the gap size : the relative permittivity of the dielectric cylinder or the spacer 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 ,

8 Graphene Nanopatches Dielectric Cylinder PEC Cylinder P. Y. Chen et. al, Nanostructured graphene metasurface for tunable terahertz cloaking, New. J. Phys., vol. 15, pp ,

9 Elliptical Cloaks 9

10 Elliptical Coordinate Scale factors : represents an ellipse : represents a hyperbola 10

11 Mathieu Equation 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 for kinds of solution as: The angular Mathieu equation has the solution as: p, m can be even or odd 11

12 Formulation of the Scattering Problem 12

13 Formulation of the Scattering Problem By applying boundary conditions : 13

14 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 14

15 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 15

16 Formulation of the Scattering Problem The two-dimensional bistatic cross section is defined as: Therefore: Finally, we have: 16

17 Numerical Results Geometry parameters are: The required reactance is found to be: The design parameters are: 17

18 Power Flow Uncloaked Cloaked 18

19 Electric Field Distribution Uncloaked Cloaked 19

20 Electric Field Distribution Uncloaked Cloaked 20

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

22 Electric Field Distribution Uncloaked Cloaked 22

23 Numerical Results Geometry parameters are: The required reactance is found to be: The design parameters are: 23

24 Power Flow Uncloaked Cloaked 24

25 Electric Field Distribution Uncloaked Cloaked 25

26 Strip (Degenerated Ellipse) A strip can be modeled as a degenerated ellipse Geometry parameters are: 26

27 Power Flow and Farfield Pattern Uncloaked Cloaked 27

28 Electric Field Distribution Uncloaked Cloaked 28