Analysis of Waterman’s Method in the Case of Layered Scatterers
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...
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Series: | Advances in Mathematical Physics |
Online Access: | http://dx.doi.org/10.1155/2017/7862462 |
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doaj-66e74c23f42c47aca69d318c743b38ad2021-07-02T08:44:03ZengHindawi LimitedAdvances in Mathematical Physics1687-91201687-91392017-01-01201710.1155/2017/78624627862462Analysis of Waterman’s Method in the Case of Layered ScatterersVictor Farafonov0Vladimir Il’in1Vladimir Ustimov2Evgeny Volkov3St. Petersburg State University of Aerospace Instrumentation, Bol. Morskaya 67, St. Petersburg 190000, RussiaSt. Petersburg State University of Aerospace Instrumentation, Bol. Morskaya 67, St. Petersburg 190000, RussiaSt. Petersburg State University of Aerospace Instrumentation, Bol. Morskaya 67, St. Petersburg 190000, RussiaSt. Petersburg University, Universitetsky Pr. 28, St. Petersburg 198504, RussiaThe 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.http://dx.doi.org/10.1155/2017/7862462 |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Victor Farafonov Vladimir Il’in Vladimir Ustimov Evgeny Volkov |
spellingShingle |
Victor Farafonov Vladimir Il’in Vladimir Ustimov Evgeny Volkov Analysis of Waterman’s Method in the Case of Layered Scatterers Advances in Mathematical Physics |
author_facet |
Victor Farafonov Vladimir Il’in Vladimir Ustimov Evgeny Volkov |
author_sort |
Victor Farafonov |
title |
Analysis of Waterman’s Method in the Case of Layered Scatterers |
title_short |
Analysis of Waterman’s Method in the Case of Layered Scatterers |
title_full |
Analysis of Waterman’s Method in the Case of Layered Scatterers |
title_fullStr |
Analysis of Waterman’s Method in the Case of Layered Scatterers |
title_full_unstemmed |
Analysis of Waterman’s Method in the Case of Layered Scatterers |
title_sort |
analysis of waterman’s method in the case of layered scatterers |
publisher |
Hindawi Limited |
series |
Advances in Mathematical Physics |
issn |
1687-9120 1687-9139 |
publishDate |
2017-01-01 |
description |
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. |
url |
http://dx.doi.org/10.1155/2017/7862462 |
work_keys_str_mv |
AT victorfarafonov analysisofwatermansmethodinthecaseoflayeredscatterers AT vladimirilin analysisofwatermansmethodinthecaseoflayeredscatterers AT vladimirustimov analysisofwatermansmethodinthecaseoflayeredscatterers AT evgenyvolkov analysisofwatermansmethodinthecaseoflayeredscatterers |
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1721334277954600960 |