By Anderson D.R., Munkholm H.J.
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Additional resources for Boundedly Controlled Topology: Foundations of Algebraic Topology and Simple Homotopy Theory
3. 128). The latter is known as the TE, or the Hpolarization, case. 4. Pattern factors with an angular dependence, of course, can be added to the fields from such line sources, and these will remain y /\ 4 Equlphaae Surface REDUCTION OF RESULTS TO TWO-DIMENSIONAL RAY TUBES For two-dimensional ray tubes, the fields are independent of one of the three Cartesian coordinates (assumed here without loss of generality to be the z-coordinate), and assume a "cylindrical" character. We will refer to such G O fields as 2D with respect to the z-axis.
This is a carry-over from the field of acoustics, which also uses many of the results demonstrated for electromagnetics problems in this text. 38) is In this matrix format, the dyadic relation: Er(Qr) = Ei(Qr) . R The dyadic reflection coefficient R in general would be a 3 x 3 matrix. The reduction to a 2 x 2 matrix results from the selection of the local ray-fixed coordinate system. The adoption of an edge-fixed coordinate system in later chapters on edge diffraction similarly will reduce the dyadic diffraction coefficient to a 2 x 2 matrix.
Thus, we are able to identify different wave processes such as reflection, edge diffraction, or curved surface diffraction. The next chapter considers the reflection of geometrical optics fields by smooth conducting surfaces. The additional scattering phenomena mentioned form the subject of later chapters of this text. That the reader be aware of the manner in which terms such as incident field and scattered field are defined in electromagnetic theory is essential. In rigorous scattering formulations there is no consideration of rays, and the meaning of such terms is generally not the same as that used in the geometrical theory of diffraction.
Boundedly Controlled Topology: Foundations of Algebraic Topology and Simple Homotopy Theory by Anderson D.R., Munkholm H.J.