TY - JOUR

T1 - Analysis of Waterman's method in the case of layered scatterers

AU - Farafonov, Victor

AU - Il'in, Vladimir

AU - Ustimov, Vladimir

AU - Volkov, Evgeny

PY - 2017

Y1 - 2017

N2 - The method suggested by Waterman has been widely used in the last years to solve various light scattering problems. We analyze the mathematical foundations of this method when it is applied to layered nonspherical (axisymmetric) particles in the electrostatic case. We formulate the conditions under which Waterman's method is applicable, that is, when it gives an infinite system of linear algebraic equations relative to the unknown coefficients of the field expansions which is solvable (i.e., the inverse matrix exists) and solutions of the truncated systems used in calculations converge to the solution of the infinite system. The conditions obtained are shown to agree with results of numerical computations. Keeping in mind the strong similarity of the electrostatic and light scattering cases and the agreement of our conclusions with the numerical calculations available for homogeneous and layered scatterers, we suggest that our results are valid for light scattering as well.

AB - The method suggested by Waterman has been widely used in the last years to solve various light scattering problems. We analyze the mathematical foundations of this method when it is applied to layered nonspherical (axisymmetric) particles in the electrostatic case. We formulate the conditions under which Waterman's method is applicable, that is, when it gives an infinite system of linear algebraic equations relative to the unknown coefficients of the field expansions which is solvable (i.e., the inverse matrix exists) and solutions of the truncated systems used in calculations converge to the solution of the infinite system. The conditions obtained are shown to agree with results of numerical computations. Keeping in mind the strong similarity of the electrostatic and light scattering cases and the agreement of our conclusions with the numerical calculations available for homogeneous and layered scatterers, we suggest that our results are valid for light scattering as well.

UR - http://www.scopus.com/inward/record.url?scp=85014498993&partnerID=8YFLogxK

U2 - 10.1155/2017/7862462

DO - 10.1155/2017/7862462

M3 - Article

AN - SCOPUS:85014498993

VL - 2017

JO - Advances in Mathematical Physics

JF - Advances in Mathematical Physics

SN - 1687-9120

M1 - 7862462

ER -