Convergence analysis and oscillations in the method of fictitious sources applied to dielectric scattering problems

Valagiannopoulos, CA; Tsitsas, NL; Fikioris, G

dc.contributor.author	Valagiannopoulos, CA	en
dc.contributor.author	Tsitsas, NL	en
dc.contributor.author	Fikioris, G	en
dc.date.accessioned	2014-03-01T02:08:34Z
dc.date.available	2014-03-01T02:08:34Z
dc.date.issued	2012	en
dc.identifier.issn	10847529	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/29670
dc.relation.uri	http://www.scopus.com/inward/record.url?eid=2-s2.0-84855374712&partnerID=40&md5=f9846adaac3c5f382c3d8766d54238b1	en
dc.subject.other	Asymptotic expressions	en
dc.subject.other	Asymptotic formula	en
dc.subject.other	Convergence analysis	en
dc.subject.other	Current filaments	en
dc.subject.other	Dielectric cylinder	en
dc.subject.other	Dielectric scattering	en
dc.subject.other	Fictitious sources	en
dc.subject.other	Ill-conditioning	en
dc.subject.other	Large N	en
dc.subject.other	Scattering problems	en
dc.subject.other	Wave scattering	en
dc.subject.other	Dielectric devices	en
dc.subject.other	Scattering	en
dc.title	Convergence analysis and oscillations in the method of fictitious sources applied to dielectric scattering problems	en
heal.type	journalArticle	en
heal.publicationDate	2012	en
heal.abstract	Several wave scattering phenomena in optics are modeled by the method of fictitious sources (MFS). Despite its interesting features, the effectiveness of the MFS and its applicability are restricted by open issues, including the placement of the fictitious sources (FS) and the fields' convergence. Concerning these issues, we investigate here the MFS convergence and study oscillations in its solutions for a representative scattering problem of a dielectric cylinder illuminated by a current filament. It is shown analytically that, when the FS radii lie in the interior and exterior of two disks with certain critical radii, the MFS currents' series diverge while the respective fields converge, as the FS number N tends to infinity. Asymptotic formulas of the divergent currents are established, exhibiting that they increase exponentially with N and oscillate. Numerical simulations are included, demonstrating that (i) the divergent currents oscillate for sufficiently large N, (ii) the oscillating values are fairly approximated by the derived asymptotic expressions, and (iii) these oscillations are inherent in MFS and are not due to illconditioning; hence, they cannot be overcome by improving the hardware or software. The possibility of obtaining convergent and correct fields from divergent intermediary currents may lead to a potential significant advance of the applicability of the MFS. © 2011 Optical Society of America.	en
heal.journalName	Journal of the Optical Society of America A: Optics and Image Science, and Vision	en
dc.identifier.volume	29	en
dc.identifier.issue	1	en
dc.identifier.spage	1	en
dc.identifier.epage	10	en