Über die Greenschen Funktionen des Zylinders und der Kugel

Abstract

Die Kugelfunktions-Reihen für die Greenschen Funktionen werden der Watson-Transformation unterworfen, dabei jedoch ein der geometrisch-optischen Welle entsprechendes Integral abgespalten. Auf diese Weise erhält man, abgesehen von einer nunmehr genaueren Bestimmung der Koeffizienten, gerade die früher von Deppermann und dem Verf. (für den Spezialfall einer ebenen Primärwelle) angegebene Aufspaltung in einen geometrisch-optischen und einen Kriechwellen-Anteil, und damit eine bis zu ziemlich kleinen Objekten bequem zu handhabende semi-asymptotische Lösung des Beugungsproblems. Die Kriechwellen erweisen sich identisch mit den in der Theorie der drahtlosen Telegraphie wichtigen Residuenwellen nach Watson und Van der Pol-Bremmer. — Die mittels der Watson-Transformation bestimmten Erregungsstärken der Kriechwellen lassen sich auf beliebig gekrümmte Flächen übertragen; dies gestattet eine semi-asymptotische Behandlung der Beugung am beliebigen (kantenfreien)Objekt mittels der Integralgleichungsmethode.

Relation between the ringing of resonances and surface waves in radar scattering

“…These would be located in the first quadrant of the X-plane, along lines inclined 60" with respect to the Re X axis. Their locations along these lines are somewhat similar to those found before [4], [SI, for cylindrical targets (see ( I l a ) and (14a)). Later on in this paper we will use the SEM roots of (1 1 b) with respect to the argument x of these functions, as we will display them in Figs. 3(a) and 3(b).…”

“…The present paper has studied the relation between the SEM approximation [SI and the Watson-transformation approach [4], [5] for the case of radar scattering from a perfectly conducting sphere. We noted that on the basis of the customary SEM procedure [9], when applied to the exact Mie series, the ensuing SEM pole series can be used in a judicious fashion (by forming residue sums over one pole layer at a time) in order to synthesize the creeping waves; but that in the SEM series extracted straightforwardly from the Mie series, the specularly reflected amplitude is not contained.…”

“…Use of the Watson transformation [4] - [ 7 ] provides such an interpretation by splitting the scattered field into a component corresponding to a geometrically reflected wave. and into a series of creeping waves that circumnavigate the sphere.…”

“…Later on in this paper we will use the SEM roots of (1 1 b) with respect to the argument x of these functions, as we will display them in Figs. 3(a) and 3(b). Qr) = dQi(+)(cos 0 ) , Ql;t)l= QA(+)(cos 8) I ( 1 Ob) [4]. This leads: using (13): to a These multiple poles are located at h = p; where dispersion for the TE phase velocity to this order: plotted for u = 1 using (14b).…”

Electromagnetic resonances of immersed dielectric spheres

“…These poles are related to surface propagating waves (creeping waves) [3]. The same wave mechanisms are also called "Franz waves" for acoustic scattering from a "rigid sphere" in fluids [4], [5].…”