TY - JOUR
T1 - Gaussian beam summation representation of beam diffraction by an impedance wedge
T2 - A 3D electromagnetic formulation within the physical optics approximation
AU - Katsav, Michael
AU - Heyman, Ehud
N1 - Funding Information:
Manuscript received February 18, 2012; revised June 02, 2012; accepted June 05, 2012. Date of publication July 10, 2012; date of current version nulldate. This work has been supported by the Israeli Science Foundation, Grants No. 674/07 and 263/11, and by NATO’s Public Diplomacy Division in the frame-work of “Science for Peace” program, under Grant No. SfP982376. M. Katsav is with the Rafael, Advanced Defense Systems, Ltd., Israel (e-mail: [email protected]). E. Heyman is with the School of Electrical Engineering, Tel Aviv University, Tel Aviv 69978, Israel (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TAP.2012.2207694 Fig. 1. Physical configuration. (a) A general EM-GB (a red heavy arrow), impinges on as impedance wedge with apex angle at direction . The beam intersects the plane at point , such that if the beam axis intercepts the wedge, while if it passes near it. (b) The edge-fixed set of EM-GB propagators used in (I.2) to describe the scattered field. The beams emerge from the points along the edge with polar angles , set, tagged by the 3-index , consists of phase-space distribution of beams that (a) Physical configuration (b) Edge-fixed expansion beams set.
PY - 2012
Y1 - 2012
N2 - We present a beam summation (BS) representation for the field scattered by an impedance wedge illuminated by a general 3D electromagnetic Gaussian beam (EM-GB). The emphasis here is not only on the solution of the beam diffraction problem, but mainly on the BS representation. In this representation, the field is expressed as a beam optics (BO) term plus an edge field, described as a sum of diffracted EM-GB's emerging from a discrete set of points and directions along the edge. We introduce an edge-fixed set of EM-GB's that provides a basis for the edge field. The expansion coefficients (the beam's excitation amplitudes) account in a dyadic format for the polarization of the incident beam and also for its direction, displacement from the edge, collimation, and astigmatism. We derive exact expressions for these coefficients as well as simpler approximations that are valid uniformly as a function of the incident beam distance from the edge. The results of this paper provide essential building blocks for a BS representation of EM fields in complex configurations, where the source excited field is described as a sum of beam propagators, and the diffracted fields generated by propagators that hit near edges are also described using beams.
AB - We present a beam summation (BS) representation for the field scattered by an impedance wedge illuminated by a general 3D electromagnetic Gaussian beam (EM-GB). The emphasis here is not only on the solution of the beam diffraction problem, but mainly on the BS representation. In this representation, the field is expressed as a beam optics (BO) term plus an edge field, described as a sum of diffracted EM-GB's emerging from a discrete set of points and directions along the edge. We introduce an edge-fixed set of EM-GB's that provides a basis for the edge field. The expansion coefficients (the beam's excitation amplitudes) account in a dyadic format for the polarization of the incident beam and also for its direction, displacement from the edge, collimation, and astigmatism. We derive exact expressions for these coefficients as well as simpler approximations that are valid uniformly as a function of the incident beam distance from the edge. The results of this paper provide essential building blocks for a BS representation of EM fields in complex configurations, where the source excited field is described as a sum of beam propagators, and the diffracted fields generated by propagators that hit near edges are also described using beams.
KW - Beam diffraction
KW - beam-to-beam scattering matrix
KW - beams summation method (BS)
KW - edge-diffraction
KW - electromagnetic Gaussian beams (EM-GB)
KW - uniform asymptotics
UR - http://www.scopus.com/inward/record.url?scp=84870868171&partnerID=8YFLogxK
U2 - 10.1109/TAP.2012.2207694
DO - 10.1109/TAP.2012.2207694
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AN - SCOPUS:84870868171
SN - 0018-926X
VL - 60
SP - 5843
EP - 5858
JO - IEEE Transactions on Antennas and Propagation
JF - IEEE Transactions on Antennas and Propagation
IS - 12
M1 - 6236052
ER -