1 The University of Mississippi Department of Electrical Engineering Center of Applied Electromagnetic Systems Research (CAESR) Atef Z. Elsherbeni The University of Mississippi Electromagnetic Scattering From Chiral Media Mohamed H. Al Sharkawy The University of Mississippi Veysel Demir Syracuse University Ercument Arvas Syracuse University Samir Mahmoud Kuwait University

2 The University of Mississippi Department of Electrical Engineering Center of Applied Electromagnetic Systems Research (CAESR) Outline n Objectives n Properties of Chiral material Example of Chiral Objects n Problem Geometry n Solution Techniques FDTD Solution Boundary Value Solution Iterative Solution n Verifications n Numerical Results and Applications  Conclusion

3 The University of Mississippi Department of Electrical Engineering Center of Applied Electromagnetic Systems Research (CAESR) Objectives  Techniques for the scattering from arbitrary shaped two-dimensional chiral, dielectric and conducting scatterers.  RCS reduction and field focusing using composite scatterers.

4 The University of Mississippi Department of Electrical Engineering Center of Applied Electromagnetic Systems Research (CAESR) Properties of Chiral Material  Unlike dielectric or conducting cylinders, chiral scatterers produce both co-polarized and cross-polarized scattered fields.  A chiral medium is therefore characterized by right-hand circularly polarized waves (RCP) and left-hand circularly polarized waves (LCP).  Coating with chiral material can reduce or enhance the radar cross-section of targets. A short metallic helix as a chiral object and its enantiomorphism.

5 The University of Mississippi Department of Electrical Engineering Center of Applied Electromagnetic Systems Research (CAESR) A sample of chiral material manufactured by a Finnish company. The sample measures 15 cm in diameters. A closer view of the individual helices and their orientation. Example of Chiral Objects

6 The University of Mississippi Department of Electrical Engineering Center of Applied Electromagnetic Systems Research (CAESR) Chiral Media Parameters is the chiral admittance is the wave number, depending on the chirality material is the chirality parameter

7 The University of Mississippi Department of Electrical Engineering Center of Applied Electromagnetic Systems Research (CAESR) Constitutive Relation for the Chiral Material e j  t is assumed Waves in a chiral medium can be expressed as a superposition of RCP (R) and LCP (L) waves Maxwell’s equations in chiral medium:

8 The University of Mississippi Department of Electrical Engineering Center of Applied Electromagnetic Systems Research (CAESR) Time Domain Solution Technique

9 The University of Mississippi Department of Electrical Engineering Center of Applied Electromagnetic Systems Research (CAESR) Multiple Frequency FDTD Formulation for Chiral Media Using Maxwell’s equations and applying the 2 nd order central difference approximation for the e j  t time harmonic variation, we get Where M x and N x are defined in terms of field components at previous time.

10 The University of Mississippi Department of Electrical Engineering Center of Applied Electromagnetic Systems Research (CAESR) Multiple Frequency FDTD Formulation for Chiral Media

11 The University of Mississippi Department of Electrical Engineering Center of Applied Electromagnetic Systems Research (CAESR) Reflection and Transmission from a One Dimensional Chiral Slab of  r = 2 and  = 0.3 Co-Polarized Field. Cr-Polarized Field.

12 The University of Mississippi Department of Electrical Engineering Center of Applied Electromagnetic Systems Research (CAESR) Scattering from a Chiral Sphere using the FDTD at 1 GHz with  r = 4

13 The University of Mississippi Department of Electrical Engineering Center of Applied Electromagnetic Systems Research (CAESR) Scattering from a Chiral Sphere using the FDTD at four different frequencies of  r = 4 and  = 0.5

14 The University of Mississippi Department of Electrical Engineering Center of Applied Electromagnetic Systems Research (CAESR) Scattering from a Chiral Sphere using the FDTD at four different frequencies of  r = 4 &  = 0.5

15 The University of Mississippi Department of Electrical Engineering Center of Applied Electromagnetic Systems Research (CAESR) Frequency Domain Solution Techniques

16 The University of Mississippi Department of Electrical Engineering Center of Applied Electromagnetic Systems Research (CAESR) Problem Geometry Conducting Cylinder Dielectric Cylinder Chiral Cylinder yMyM xMxM M 1 x y 0 yjyj xjxj yiyi xixi y1y1 x1x1 d ij  ji

17 The University of Mississippi Department of Electrical Engineering Center of Applied Electromagnetic Systems Research (CAESR) Plane Wave Excitation-Incident E & H n E-polarized incident wave TM z n The corresponding  component of the H-polarized incident wave 0

18 The University of Mississippi Department of Electrical Engineering Center of Applied Electromagnetic Systems Research (CAESR) Scattered and Internal Co-Polarized Fields C in, A in and B in are unknown coefficients. 0

19 The University of Mississippi Department of Electrical Engineering Center of Applied Electromagnetic Systems Research (CAESR) Scattered and Internal Cross-Polarized Fields D in, A in and B in are unknown coefficients. 0

20 The University of Mississippi Department of Electrical Engineering Center of Applied Electromagnetic Systems Research (CAESR) Boundary Value Solution (BVS)

21 The University of Mississippi Department of Electrical Engineering Center of Applied Electromagnetic Systems Research (CAESR) Boundary Conditions at the Surface of One Chiral Cylinder (Cylinder “i”,  i = a i ) To solve for the unknown coefficients, the boundary conditions must be applied on cylinder i These four equations are repeated for all M cylinders.

22 The University of Mississippi Department of Electrical Engineering Center of Applied Electromagnetic Systems Research (CAESR) Transformation of Scattered Fields The scattered field components from the g th cylinder in terms of the local coordinates of the i th cylinder x y 0 ygyg xgxg yiyi xixi d ig  gi

23 The University of Mississippi Department of Electrical Engineering Center of Applied Electromagnetic Systems Research (CAESR) Transformation of Scattered Fields The scattered field components from the g th cylinder in terms of the local coordinates of the i th cylinder 0

24 The University of Mississippi Department of Electrical Engineering Center of Applied Electromagnetic Systems Research (CAESR) Determining the External Coefficients C gn and D gn From the application of the boundary conditions on all M cylinders Where

25 The University of Mississippi Department of Electrical Engineering Center of Applied Electromagnetic Systems Research (CAESR) 00 Solving for the External Coefficients C gn and D gn

26 The University of Mississippi Department of Electrical Engineering Center of Applied Electromagnetic Systems Research (CAESR) Solving for the Internal Coefficients A gn and B gn

27 The University of Mississippi Department of Electrical Engineering Center of Applied Electromagnetic Systems Research (CAESR) Used Variables:

28 The University of Mississippi Department of Electrical Engineering Center of Applied Electromagnetic Systems Research (CAESR) Iterative Solution (IS)

29 The University of Mississippi Department of Electrical Engineering Center of Applied Electromagnetic Systems Research (CAESR) Algorithm for Iterative Solution Stage 1: Apply the boundary condition on the surface of each cylinder, as the incident field is due to an external source. Stage 2: The incident field on each cylinder is produced by the scattered field from all other cylinders.

30 The University of Mississippi Department of Electrical Engineering Center of Applied Electromagnetic Systems Research (CAESR) Algorithm for Iterative Solution

31 The University of Mississippi Department of Electrical Engineering Center of Applied Electromagnetic Systems Research (CAESR) Matrix Formulation where

32 The University of Mississippi Department of Electrical Engineering Center of Applied Electromagnetic Systems Research (CAESR) Bistatic Scattering Cross Section of Five Perfectly Conducting Cylinders Each cylinder has radius = 0.1 and their centers are separated by 0.5 due to a TM plane wave incident at  0 =180 y x * Atef Z. Elsherbeni, “A comparative study of two-dimensional multiple scattering techniques,” Radio Science, vol. 29, pp , July-August  (degrees)  / 0 (dB) BVS ITS

33 The University of Mississippi Department of Electrical Engineering Center of Applied Electromagnetic Systems Research (CAESR) Echo-Width of a Homogenous Chiral Strip Echo Width (dB/m) * Michael S. Kluskens and Edward H. Newman, “Scattering by a Chiral Cylinder of Arbitrary Cross Section,” IEEE Trans. Antennas Propagate., vol. 38, pp , Sept

34 The University of Mississippi Department of Electrical Engineering Center of Applied Electromagnetic Systems Research (CAESR) Echo-Width of an Inhomogeneous Chiral Strip (degrees) Echo Width (dB/m) * Michael S. Kluskens and Edward H. Newman, “Scattering by a Chiral Cylinder of Arbitrary Cross Section,” IEEE Trans. Antennas Propagate., vol. 38, pp , Sept

35 The University of Mississippi Department of Electrical Engineering Center of Applied Electromagnetic Systems Research (CAESR)  = Co-Polarized X-Polarized Dielectric  r = 5 r = 0.1 d = 0.75 Normalized Scattered Field Using BVS and IS

36 The University of Mississippi Department of Electrical Engineering Center of Applied Electromagnetic Systems Research (CAESR)  = Co-Polarized X-Polarized Dielectric F. RCS max_Diel = 18.3 dB F. RCS max_Chi_Co = 11.8 dB F. RCS max_Chi_X = dB B. RCS max_Diel = 17 dB B. RCS max_Chi_Co = -20 dB B. RCS max_Chi_X = -8 dB  r = 5 r = 0.1 d = 0.75 RCS Radiation Pattern in dB Using BVS and IS

37 The University of Mississippi Department of Electrical Engineering Center of Applied Electromagnetic Systems Research (CAESR) Parametric Study for a vertical Inhomogeneous Strip Back-ward Scattered field for different Chiral admittance values For-ward Scattered field for different Chiral admittance values

38 The University of Mississippi Department of Electrical Engineering Center of Applied Electromagnetic Systems Research (CAESR)  =  Co-Polarized X-Polarized Dielectric F. RCS max_Diel = 20 dB F. RCS max_Chi_Co = 26 dB F. RCS max_Chi_X = -5 dB B. RCS max_Diel = 15.5 dB B. RCS max_Chi_Co = 2 dB B. RCS max_Chi_X = -10 dB RCS Radiation Pattern in dB for a TM z Plane Wave  c =  c =  c =  c =  c =  c =

39 The University of Mississippi Department of Electrical Engineering Center of Applied Electromagnetic Systems Research (CAESR)  =  Co-Polarized X-Polarized Dielectric F. RCS max_Diel = 20 dB F. RCS max_Chi_Co = 25 dB F. RCS max_Chi_X = -5 dB B. RCS max_Diel = 15.5 dB B. RCS max_Chi_Co = 0 dB B. RCS max_Chi_X = -10 dB RCS Radiation Pattern in dB for a TE z Plane Wave  c =  c =  c =  c =  c =  c =

40 The University of Mississippi Department of Electrical Engineering Center of Applied Electromagnetic Systems Research (CAESR) Conclusions  Techniques are developed for time and frequency domain analysis of chiral material.  Application of chiral material is demonstrated for:  designing anti-reflection composite structures  controlling or altering the RCS of scatterers.

41 The University of Mississippi Department of Electrical Engineering Center of Applied Electromagnetic Systems Research (CAESR) End of Presentation

42 The University of Mississippi Department of Electrical Engineering Center of Applied Electromagnetic Systems Research (CAESR) Intrinsic Impedance and Wave Number Versus Chiral Admittance Parameters 1

43 The University of Mississippi Department of Electrical Engineering Center of Applied Electromagnetic Systems Research (CAESR) Parametric Study for a vertical Inhomogeneous Strip Back-ward Scattered field for different Radius values For-ward Scattered field for different Radius values

44 The University of Mississippi Department of Electrical Engineering Center of Applied Electromagnetic Systems Research (CAESR) Bistatic Echo Width of a Circular Chiral Cylinder Illuminated by a TM z Plane Wave * Majeed A. Al-Kanhal and Ercument Arvas, “Electromagnetic Scattering from a Chiral Cylinder of Arbitrary Cross Section,” IEEE Trans. Antennas Propagate., vol. 44, pp , July CO-POLARIZED ( E z ) CROSS POLARIZED ( E  ) x y

45 The University of Mississippi Department of Electrical Engineering Center of Applied Electromagnetic Systems Research (CAESR) Internal H-field along y = 0 of a Circular Chiral Cylinder Excited by a TE z Wave x y * Majeed A. Al-Kanhal and Ercument Arvas, “Electromagnetic Scattering from a Chiral Cylinder of Arbitrary Cross Section,” IEEE Trans. Antennas Propagate., vol. 44, pp , July 1996.

46 The University of Mississippi Department of Electrical Engineering Center of Applied Electromagnetic Systems Research (CAESR) |E z | of a TM z Plane Wave within a Homogeneous Dielectric Cylinder x y A cylinder of circumference 1.0 and  r = 3 * Andrew F. Peterson, Scott L. Ray and Raj Mittra, “Computational Methods for Electromagnetics,” IEEE Antennas Propagate.,© 1998 by the Institute of Electrical and Electronics Engineers, Inc.

47 The University of Mississippi Department of Electrical Engineering Center of Applied Electromagnetic Systems Research (CAESR) |H z /H inc | of a TE z Plane Wave within a Circular, Homogeneous Dielectric Cylinder y x A cylinder of circumference 1.0 and  r =2.56 * Andrew F. Peterson, Scott L. Ray and Raj Mittra, “Computational Methods for Electromagnetics,” IEEE Antennas Propagate.,© 1998 by the Institute of Electrical and Electronics Engineers, Inc.