Diffusion Multiple des Ondes ÉlectromagnÉtiques Par des Ellipsoïdes de RÉvolution AllongÉs

Rotational-translational addition theorems for spheroidal vector wave functions

“…[5], Eqs. (15), (16), (17))); 4) the spheroidal vector wave functions of a given set (with a equal to any one of the r,x,y,z) are, unfortunately, neither orthogonal themselves, nor orthogonal to those of the other sets (Ref. [6], p. 70); 5) each spheroidal vector wave function Ma or Nfl is connected to the corresponding spherical vector wave function and conversely (see Eqs.…”

“…The integration of the vector wave equation in terms of vector wave functions has found a direct and extensive application in studies on electromagnetic scattering and radiation by canonical objects such as spheres [7,8] and cylinders [7] and by more complicated ones such as spheroids [9][10][11][12][13][14][15][16][17][18], 3. Theorems converting spheroidal vector wave functions into spherical ones and conversely.…”

“…Translational addition theorems for vector wave functions 'Mr and 'Mr have had a direct application in studies on multiple scattering of electromagnetic waves from spheres [24] and afterwards from prolate spheroids in parallel alignment [16,18].…”

“…[5,21] and [2], we get, in the case r' < d: OO OO ■Mjiftr, M) = E E {[i)A™WMyvr\r',d',<j>') + 0')} H=-oov=\n\ (24) and a similar expression for is deduced from Eq. (24) by substituting N for M. For calculations of the coefficients and ^B™" related to ^a™", the reader is referred to the works by Cruzan [5] and by Dalmas and Deleuil [16].…”

“…To realize this, it is sufficient to examine the calculations developed in the work by Cruzan [5], Translational addition theorems for spheroidal vector wave functions Ma and Na have previously been established with a = x,y,z by Sinha and MacPhie [23] and with a = r by Dalmas and Deleuil (Ref. [16], Sec. 2.2 and Ref.…”