URSI AP-RASC 2019, New Delhi, India; 09 - 15 March 2019 Computation of Slope Diffraction by Modified Edge Representation (MER) Equivalent Edge Currents (EECs) Line Integration Maifuz Ali (1) , Makoto Ando (2) (1) Electronics and Communication Enggineering, IIIT Naya Raipur, India, E-mail: maifuzali@hotmail.com (2) National Instituteof Technology, Higashi Asakawa, Hachioji, Tokyo, Japan, E-mail: ando@kosen-k.go.jp Abstract Equivalent edge currents (EECs) line integration to com- pute the diffracted field has the advantage of less require- ment of computation time and resources. The methods of EECs present some ambiguity in the definition of currents at general edge points which do not satisfy the diffraction law. Modified edge representation (MER) is an unique con- cept for a complete definition of EEC. The line integration of MER EEC results uniform and accurate fields every- where including geometrical boundaries. Here, MER EECs has been used to compute the diffracted field from the slope of the incident field. The dipole wave scattering from flat circular disk is considered as the numerical examples. 1 Introduction Physical Optics (PO) is an asymptotic high frequency nu- merical method based on surface currents. In PO, the scat- tering fields are obtained by surface integration of surface electric current density, which are performed numerically in general. Since the reduction of the surface integral to line one provides the great saving of the numerical compu- tation time, it has been investigated for long time by many workers in both exact [1–4] and asymptotic manners [5, 6]. PO surface integration is reduced to PO MER equivalent edge currents (EECs) line integration in [7] where EECs for physical optics (PO) components at general points are obtained by utilizing the fictitious edges and PO diffraction coefficient. In PO, fringe wave is neglected, If the fringe wave diffraction coefficients added with the PO diffraction coefficients, the diffraction coefficient takes the form of GTD diffraction coefficient given by Keller in [8, eq. (2)] and this MER EECs technique with GTD diffraction co- efficient is known as GTD MER. As PO MER is derived directly from PO surface integration, PO MER and hence GTD MER gives the slope effects of the incident field with- out any extra computation unlike UTD [9, eq. (13-110)]. The slope wave diffraction is a higher order diffraction and it becomes more significant when the incident field at the point of diffraction vanishes. In this paper GTD MER is used to compute the slope wave diffraction and computation of diffracted field of dipole wave from circu- lar disk is considered as the numerical example. Method of moments based numerical electromagnetic code Wipl-D (Wipl-D [10]) is considered as the reference. 2 MODIFIED EDGE REPRESENTATION (MER) FOR THE DEFINITION OF EEC The method enabling the surface to line integral reduction is the key element in deriving the equivalent edge currents (EECs). A concept of modified edge representation(MER), which extends the definition of EEC for diffraction points to those for general edge points was introduced in [11–13]. Classical Keller’s diffraction coefficients were adopted for the computations of the diffracted field as follows. 2.1 Modified Edge Representation ( τ ) ^ r o τ ^ o β β i i β ^ e ^ r i Modified edge Actual edge Q Arbitrary point on the edge n ^ Figure 1. Defination of the modified edge A fictitious edge  τ is defined to satisfy the diffraction law for the given directions of incidence and observation shown in Fig. 1 and it is simply expressed as: (  r o −  r i ) ·  τ = 0 (β o = β i ) ,  n ·  τ = 0 (1a) For the observer on ISB/RSB,  τ =  e (1b) since the vector  τ in equation (1a) is indefinite on the fol- lowing geometrical boundaries  r o =  r i for ISB (2a)  r o =  r i − 2 n ( n ·  r i ) for RSB (2b) Equations (1a) and (1b) determine a unique vector  τ for a given combination of  r i and  r 0 .