High Frequency Techniques in Electromagnetics

1. High Frequency Techniques in Electromagnetics Ayhan Altıntaş Bilkent University, Dept. of Electrical Engineering, Ankara, Turkey E-mail: altintas@ee.bilkent.edu.tr

2. Outline • Ray-basedTechniques • Geometrical Optics (GO) • Geometrical Theory of Diffraction (GTD-UTD) • Integral-based Techniques • Physical Optics (PO) • Physical Theory of Diffraction (PTD) • Equivalent Edge Currents (EEC)

3. Radiated by J Total Field E = Einc() +Escat() Scattering Problem PEC Scatterer J J: induced surface current Einc() Escat() Determine E or Escat !

4. Astigmatic Ray Tube s Line Caustics s 0 Geometrical Optics • PROPERTIES • Abides power conservation in the ray tubes • Phase factor is introduced along rays (local plane waves) • Polarization is preserved in ray-fixed coordinates • Can be derived from Maxwell’s Equations • DIFFICULTY • Not valid in caustics are two caustic distances

5. Geometrical Optics Disadvantages: • Requires finding of reflection point on the surface • Predicts null field in shadow regions • Predicts discontinuous field along shadow boundaries • Properties: • Conceptually simple • Localized scattering • Requires only tracing of incident and reflected rays • Pinpoints flash points Shadow boundary Incident rays Scatterer Shadow Region Shadow boundary Reflected rays

6. Geometrical Optics Geometrical Optics for reflection Caustic distance for reflected rays Source Radius of curvature of the surface at Qr S’ Wavefront Image Qr s Note that in 2-D there is only one caustic distance

7. Geometrical Optics Example – A strip

8. Half Plane Fields

9. Diffracted rays Incident ray s Q1 Q2 Incident ray Edge diffraction Diffracted rays Surface diffraction Observation direction Geometrical Theory of Diffraction (GTD) Shadow boundary Shadow boundary • Ray Theory • Solves some of GO difficulties

10. GTD Calculation GTD Formulation: Properties: • Conceptionally simple • Local phenomena • Tracing of diffracted rays • Pinpoints flash points • Predicts non-zero field in shadow regions • A higher order approximation than GO in terms of frequency • Uniform versions yield smooth and continuous fields at and around shadow boundaries (transition regions) Disadvantages: • Requires searching for diffraction points on the edge • Requires finding of attachment and launching points and geodesics on the surface • Fails at caustics where many diffracted rays merge

11. e Diffracted ray s Keller cone Ed o Edo Plane of Diffraction Eio´ o´ s´ Ei´ Incident ray Edge 3-D Edge Diffraction Keller Cone becomes a disk in 2-D problems

12. Edge Diffraction Coefficients Note there is only one caustic distance Where is the other one?

13. Keller’s Diffraction Coefficients (GTD) Keller´s edge diffraction coefficients Non-uniform Not valid when

14. Numerical Result – GTD

15. Numerical Result - UTD • In the UniformGeometrical Theory of Diffraction (UTD) Ds,h contain Fresnel integrals to make them valid in transition regions. (Invented at Ohio State University by Kouyoumjian and Pathak • Uniform Asypmtotic Theory(UAT) is similar to UTD but uses Keller diffraction and modifies reflected field, not very suitable for numerical work.(Invented at U.of Illinois)

16. GTD-UTD Example – A Disk

17. Backscattering from a square plate a z Diffracted Ray Caustics y a Diffracted Ray Caustics  einc x hinc

18. Flat Plate Modeling • Scattered field for RCS has many Caustics • Ray based techniques fail at caustics

19. Physical Optics approximation • Properties: • Simple • No need to search for flash points • Stationary phase evaluation of • the radiation integral yields • reflected field, so PO • asymptotically reduces to GO • Stays bounded in the caustics • Suited well for the RCS of targets build up with flat polygonal plates • Disadvantages: • Surface integral required • Reciprocity is not satisfied • Not accurate away from specular reflection is the GO based surface current.

20. Physical Theory of Diffraction Incident Plane Wave Half plane We do not know J fw ! How do we calculate the second integral? Use High frequency asymptotic approximation to E !

21. Note that singularities of and cancel so is valid in transition regions Physical Theory of Diffraction

22. PTD Equivalent Edge Currents (EEC) PTD - EEC Derived from the integration of fringe wave currents on a half plane. Then use asymptotic methods to convert the 2-D surface integral into a 1-D line integral. Surface Integral: Line Integral:

23. PTD Coefficients coefficients depending on angles of the geometry Various approaches exist to determine these coefficients, most useful ones are by Mitzner (ILDC) and Ando.

24. einc hinc RCS of a Flat Plate z y a x

25. Disk Example – Revisited

26. Disk - Cross Polar Radiation

27. HF work of A. Altintas

28. HF Work of A. Altintas

29. HF Work of A.Altintas

30. HF Work of A.Altintas

31. HF Work of A.Altintas

32. End of the Show

33. End

34. GTD Equivalent Edge Currents (EEC) GTD - EEC Replaces the edge with non-uniform electric and magnetic line sources. • Advantages: • Finite fields at or around caustics. • Field prediction even when there is no GO/GTD ray reaching the observation (corner diffraction). • Spatial variations of the incident field are inherently included. Problems: • Not valid in the transition regions of shadow boundaries. • Derived heuristically.