Numerical investigation of the Rayleigh hypothesis for electromagnetic scattering by a particle

Auguie, Baptiste; Somerville, Walter R C; Roache, Stanley; Le Ru, Eric C.

Abstract

The validity of the Rayleigh hypothesis has been a long-standing issue in the applicability of the T-matrix method to near-field calculations, and despite numerous theoretical works, the practical consequences for numerical simulations have remained unclear. Such calculations are increasingly important in the field of nanooptics, for which accurate and efficient modeling tools are in high demand. We here tackle this challenge by investigating numerically the convergence behavior of series expansions of the electric field around spheroidal particles, which provides us with unambiguous examples to clarify the conditions of convergence. This study is made possible by the combination of alternative methods to compute near-fields accurately, and crucially, the recent improvements in the calculation of T-matrix elements free from numerical instabilities, as such errors would otherwise obfuscate the intrinsic convergence properties of the field series. The resulting numerical confirmation for the range of validity of the Rayleigh hypothesis, complemented by a better understanding of the convergence behavior of the field expansions, is a crucial step toward future developments.

Citation

Auguie, B., Somerville, W. R. C., Roache, S., & Le Ru, E. C. (2016). Numerical investigation of the Rayleigh hypothesis for electromagnetic scattering by a particle. Journal of Optics, 18(7), Article 075007. https://doi.org/10.1088/2040-8978/18/7/075007

• Journal Article Type: Article
• Acceptance Date: Apr 11, 2016
• Online Publication Date: May 26, 2016
• Publication Date: May 26, 2016
• Deposit Date: May 12, 2016
• Publicly Available Date: May 26, 2016
• Journal: Journal of optics
• Print ISSN: 2040-8978
• Electronic ISSN: 2040-8986
• Publisher: IOP Publishing
• Peer Reviewed: Peer Reviewed
• Volume: 18
• Issue: 7
• Article Number: 075007
• DOI: https://doi.org/10.1088/2040-8978/18/7/075007
• Keywords: Rayleigh hypothesis
• Public URL: https://hull-repository.worktribe.com/output/437866
• Publisher URL: http://iopscience.iop.org/article/10.1088/2040-8978/18/7/075007
• Additional Information: This is an author-created, un-copyedited version of an article accepted for publication in Journal of optics. The publisher is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at http://dx.doi.org/10.1088/2040-8978/18/7/075007