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SUMMARY:Light Scattering Through the Eyes of the Singularity Expansion Met
 hod - Nicolas Bonod (Institut Fresnel)
DTSTART:20230209T133000Z
DTEND:20230209T141500Z
UID:TALK194806@talks.cam.ac.uk
DESCRIPTION:Isam Ben Soltane\, R&eacute\;mi Colom\, Brian Stout\, Nicolas 
 Bonod\nLight can be reflected\, transmitted\, scattered\, or diffracted by
  optical components. Knowledge of such optical responses is fundamental fo
 r optical component design and the tailoring of light-matter interactions.
  Optical response is typically studied in either the time or harmonic doma
 ins. In the time domain\, the scattered field can be described through tra
 nsient and steady states\, while in the harmonic domain\, the spectral res
 ponse features resonances that are of crucial interest for enhancing the l
 ight matter interactions. When monitoring the optical response as a functi
 on of the frequency\, resonances typically appear in the form of sharp max
 ima. When extending the 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 complex plane influence the 
 response of optical systems at real frequencies and the extent to which th
 is response\, is fully predicted by these singularities\, for both time an
 d harmonic domains. This method is called Singularity Expansion Method (SE
 M) [1\,2].\n&nbsp\;\nIn this talk\, we first present the fundamentals of t
 his method and then show how a simplified expression of the expansion\, th
 e Approximate Singularity Expansion (ASE)\, is convenient and accurate for
  studying optical responses in both harmonic and time domains. We also sho
 w how the ASE method can predict the optical response of plasmonic metasur
 faces and resonant light scattering of sub-wavelength sized particles [3-5
 ]. The convergence of this method is verified for these different configur
 ations in terms of the number of singularities considered. In a second ste
 p\, we will consider a Fabry-Perot 1D optical cavity to apply this expansi
 on to the Fresnel coefficients [6]. This allows a derivation of the singul
 arity expansion of the Impulse Response Function (IRF)\, by which the resp
 onse in the time domain can be retrieved by a convolution with the excitat
 ion field. We point out the importance of causality that prevents divergen
 ce of the expansion [5-7]. We then analyse the steady and transient states
  expansions and their link with the singularities. In a third and final st
 ep\, we show how the SEM can be generalized to the case of singularities o
 f arbitrary order [8] and will discuss the perspectives of this method.\nR
 eferences\n[1] C. E. Baum\, &ldquo\;On the singularity expansion method fo
 r the solution of electromagnetic interaction problems\,&rdquo\; Tech. rep
 . AIR FORCE WEAPONS LAB KIRTLAND AFB NM (1971)\n[2] P. Vincent\, &ldquo\;S
 ingularity expansions for cylinders of finite conductivity\,&rdquo\; Appli
 ed Physics 17\, 239&ndash\;248 (1978)\n[3] V. Grigoriev\, A. Tahri\, S. Va
 rault\, B. Rolly\, B. Stout\, J. Wenger\, N. Bonod\, &ldquo\;Optimization 
 of resonant effects in nanostructures via Weierstrass factorization\,&rdqu
 o\; Phys. Rev. A 88\, 011803(R) (2013)\n[4] V. Grigoriev\, S. Varault\, G.
  Boudarham\, B. Stout\, J. Wenger\, N. Bonod\, &ldquo\;Singular analysis o
 f Fano resonances in plasmonic nanostructures\,&rdquo\; Phys. Rev. A 88\, 
 063805 (2013)\n[5] R. Colom\, R. C. McPhedran\, B. Stout\, N. Bonod\, &ldq
 uo\;Modal Expansion of the scattered field&nbsp\;: Causality\, Non-Diverge
 nce and Non-Resonant Contribution\,&rdquo\; Phys. Rev. B 98\, 085418 (2018
 )\n[6] I. Ben Soltane\, R. Colom\, B. Stout\, N. Bonod\, &ldquo\;Derivatio
 n of the Transient and Steady Optical States from the Poles of the S-Matri
 x\,&rdquo\; Lasers Photonic Rev.\, 2200141 (2022)\n[7] I. Ben Soltane\, R.
  Colom\, F. Dierick\, B. Stout\, N. Bonod\, &ldquo\; Multiple-Order Singul
 arity Expansion Method\,&rdquo\; arXiv (2023)
LOCATION:Seminar Room 1\, Newton Institute
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