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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Light Scattering Through the Eyes of the Singulari
ty Expansion Method - Nicolas Bonod (Institut Fres
nel)
DTSTART;TZID=Europe/London:20230209T133000
DTEND;TZID=Europe/London:20230209T141500
UID:TALK194806AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/194806
DESCRIPTION:Isam Ben Soltane\, Ré\;mi Colom\, Brian Stou
t\, Nicolas Bonod\nLight can be reflected\, transm
itted\, scattered\, or diffracted by optical compo
nents. Knowledge of such optical responses is fund
amental for optical component design and the tailo
ring of light-matter interactions. Optical respons
e is typically studied in either the time or harmo
nic domains. In the time domain\, the scattered fi
eld can be described through transient and steady
states\, while in the harmonic domain\, the spectr
al response features resonances that are of crucia
l interest for enhancing the light matter interact
ions. When monitoring the optical response as a fu
nction of the frequency\, resonances typically app
ear in the form of sharp maxima. When extending th
e optical response to the complex frequency plane\
, one finds singularities\, for which the optical
response becomes infinite. A fundamental question
that has attracted attention for several decades i
s to establish how these singularities in the comp
lex plane influence the response of optical system
s at real frequencies and the extent to which this
response\, is fully predicted by these singularit
ies\, for both time and harmonic domains. This met
hod is called Singularity Expansion Method (SEM) [
1\,2].\n \;\nIn this talk\, we first present t
he fundamentals of this method and then show how a
simplified expression of the expansion\, the Appr
oximate Singularity Expansion (ASE)\, is convenien
t and accurate for studying optical responses in b
oth harmonic and time domains. We also show how th
e ASE method can predict the optical response of p
lasmonic metasurfaces and resonant light scatterin
g of sub-wavelength sized particles [3-5]. The con
vergence of this method is verified for these diff
erent configurations in terms of the number of sin
gularities considered. In a second step\, we will
consider a Fabry-Perot 1D optical cavity to apply
this expansion to the Fresnel coefficients [6]. Th
is allows a derivation of the singularity expansio
n of the Impulse Response Function (IRF)\, by whic
h the response in the time domain can be retrieved
by a convolution with the excitation field. We po
int out the importance of causality that prevents
divergence of the expansion [5-7]. We then analyse
the steady and transient states expansions and th
eir link with the singularities. In a third and fi
nal step\, we show how the SEM can be generalized
to the case of singularities of arbitrary order [8
] and will discuss the perspectives of this method
.\nReferences\n[1] C. E. Baum\, &ldquo\;On the sin
gularity expansion method for the solution of elec
tromagnetic interaction problems\,&rdquo\; Tech. r
ep. AIR FORCE WEAPONS LAB KIRTLAND AFB NM (1971)\n
[2] P. Vincent\, &ldquo\;Singularity expansions fo
r cylinders of finite conductivity\,&rdquo\; Appli
ed Physics 17\, 239&ndash\;248 (1978)\n[3] V. Grig
oriev\, A. Tahri\, S. Varault\, B. Rolly\, B. Stou
t\, J. Wenger\, N. Bonod\, &ldquo\;Optimization of
resonant effects in nanostructures via Weierstras
s factorization\,&rdquo\; Phys. Rev. A 88\, 011803
(R) (2013)\n[4] V. Grigoriev\, S. Varault\, G. Bou
darham\, B. Stout\, J. Wenger\, N. Bonod\, &ldquo\
;Singular analysis of Fano resonances in plasmonic
nanostructures\,&rdquo\; Phys. Rev. A 88\, 063805
(2013)\n[5] R. Colom\, R. C. McPhedran\, B. Stout
\, N. Bonod\, &ldquo\;Modal Expansion of the scatt
ered field \;: Causality\, Non-Divergence and
Non-Resonant Contribution\,&rdquo\; Phys. Rev. B 9
8\, 085418 (2018)\n[6] I. Ben Soltane\, R. Colom\,
B. Stout\, N. Bonod\, &ldquo\;Derivation of the T
ransient and Steady Optical States from the Poles
of the S-Matrix\,&rdquo\; Lasers Photonic Rev.\, 2
200141 (2022)\n[7] I. Ben Soltane\, R. Colom\, F.
Dierick\, B. Stout\, N. Bonod\, &ldquo\; Multiple-
Order Singularity Expansion Method\,&rdquo\; arXiv
(2023)
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:
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