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

Abstract

A dielectric sphere with an eccentric spherical dielectric inclusion and an incident amplitude-modulated plane electromagnetic wave constitute an exterior radiation problem, which is solved in this paper. A solution is obtained by combined use of the Fourier transform and the indirect-mode-matching method. The analysis yields a set of linear equations for the wave amplitudes of the frequency-domain expansion of the electric-field intensity within and outside the externally spherical inhomogeneous body; that set is solved by truncation and matrix inversion. The shape of the backscattered pulse in the time domain is determined by application of the inverse fast Fourier transform. Numerical results are shown for a pulse backscattered by an acrylic sphere that contains an eccentric spherical cavity. The effects of cavity position and size on pulse spreading and delay are discussed.

Chirp backscattering by pec sphere eccentrically placed in a dielectric sphere

“…The analytical formulation of this radiation problem is concise and somewhat Setting d 1 = 0 into (7), we arrive at the following formula [24]: By substitution into the right-hand side of (6), we obtain, because of (36), in this marginal case: δ se F (ι) α,mn,e (k 2 r 1 ) + δ so F (ι) α,mn,o (k 2 r 1 ) = F (ι) α,mn,s (k 2 r 1 ) , which is the left-hand side of (6). Hence, W α,mn,s α ′ ,m ′ n ′ ,s ′ ≡ δ αα ′ δ mm ′ δ nn ′ δ ss ′ , if d 1 = 0.…”

“…However, in order to apply the boundary condition on S 2 we must reformulate E 2 (r, ω) so that only spherical eigenvectors that are natural on S 2 are used. This is done by use of the translational addition theorem of spherical eigenvectors [31,32,33,34], as formulated for the aforesaid use [24]:…”

“…Numerical solutions are available [19], too, but they are beyond the interest of this paper. Amplitude modulation of the incident wave has been considered by a few researchers [20,21,22,23] and by the first author in a previous paper [24]. The latter dealt with a dielectric sphere containing an eccentric spherical cavity.…”

Latest achievements in generalized Lorenz‐Mie theories: A commented reference database

“… dealt with picosecond time scale modification of forward scattered light induced by absorption inside particles, using again a Monte‐Carlo simulation with temporal phase function and Debye modes. Vervelidou and Chrissoulidis dealt with the scattering of a pulsed wave by a sphere with an eccentric spherical inclusion. Idlahcen et al .…”