TY - JOUR

T1 - Light Scattering by Small Multilayer Nonconfocal Spheroids Using Suitable Spheroidal Basis Sets

AU - Farafonov, V. G.

AU - Ustimov, V. I.

AU - Il'in, V. B.

PY - 2018/12

Y1 - 2018/12

N2 - We construct a Rayleigh approximation for multilayer particles the layer boundaries of which are nonconfocal spheroids. The geometry of the problem is taken into account to the maximum extent by representing the field potentials inside nonconfocal shells as expansions in terms of spheroidal harmonics in different coordinate systems in which the surfaces of the layers are coordinate. To sew two expansions inside each layer, we use relations between spheroidal harmonics of the Laplace equation in systems with different focal lengths that we obtained. The extended boundary conditions method (?BCM) and the separation of variables method (SVM) prove to be equivalent, because they yield the same results. The polarizability of the particle and, therefore, the characteristics of the scattered radiation are written in terms of infinite-dimensional matrices, the elements of which are determined either explicitly or in the form of finite sums. In particular cases of confocal spheroids, this solution is completely consistent with the known results.

AB - We construct a Rayleigh approximation for multilayer particles the layer boundaries of which are nonconfocal spheroids. The geometry of the problem is taken into account to the maximum extent by representing the field potentials inside nonconfocal shells as expansions in terms of spheroidal harmonics in different coordinate systems in which the surfaces of the layers are coordinate. To sew two expansions inside each layer, we use relations between spheroidal harmonics of the Laplace equation in systems with different focal lengths that we obtained. The extended boundary conditions method (?BCM) and the separation of variables method (SVM) prove to be equivalent, because they yield the same results. The polarizability of the particle and, therefore, the characteristics of the scattered radiation are written in terms of infinite-dimensional matrices, the elements of which are determined either explicitly or in the form of finite sums. In particular cases of confocal spheroids, this solution is completely consistent with the known results.

U2 - 10.1134/S0030400X18120068

DO - 10.1134/S0030400X18120068

M3 - статья

VL - 125

SP - 957

EP - 965

JO - OPTICS AND SPECTROSCOPY

JF - OPTICS AND SPECTROSCOPY

SN - 0030-400X

IS - 6

ER -