Indirect mode-matching solution to scattering from a dielectric sphere with an eccentric inclusion

Scattering of a pulsed wave by a sphere with an eccentric spherical inclusion

“…Similar expansions can be written for the spectrum of the electric-field intensity in the host sphere and in the inclusion: [18]. The continuity of the fields across the spherical interfaces S 1 , S 2 can be imposed indirectly by use of IMM equations [2], derived by application of Green's second vector theorem [20]:…”

“…(B1)-(B8) represent a set of 6n max n max 2 linear equations for 6n max n max 2 unknowns, which can be solved by matrix-inversion. Following [2], we define n max as the smallest integer that ensures fourdigit convergence of the backscattering cross section. Subsequently, we assume that the wave amplitudes of the scattered wave are available, albeit through use of computer code.…”

“…Following a numerical example of [2] as far as possible, we start this numerical investigation with a cavity of size α 1 α 2 ∕3 at the north pole of the acrylic sphere (Θ 1 0°). However, this is where similarity to the numerical example of [2] ends because excitation comes in the form of a band of frequencies around a carrier frequency. The latter must be chosen so that the frequency spectrum of the incident wave will change as much as possible after its encounter with the scatterer.…”

“…This paper combines the Fourier transform with the indirectmode-matching (IMM) method [2][3][4][5][6] to formulate a set of linear equations for the wave amplitudes of the electric-field intensity, scattered by, and refracted within, a dielectric sphere with an eccentric spherical dielectric inclusion. The analytical formulation is carried out entirely in the frequency domain; the time-domain electric-field intensity can be determined numerically by application of the fast Fourier transform (FFT).…”

“…The problem dealt with in this paper has been studied before in the asymptotic case of excitation by cw plane em wave [2,[8][9][10]. The electric-field intensity has, in all those previous research efforts, been expanded into a series of vector spherical harmonics and the proper boundary conditions have been enforced to obtain the wave amplitudes, i.e., the coefficients of vector spherical harmonics in those expansions.…”