Speaker: Junshan Lin (Auburn University)

Title: Embedded eigenvalues and Fano resonance for metallic structures with small holes

 

Abstract: Fano resonance, which was initially discovered in quantum mechanics by Ugo Fano, has been extensively explored in photonics since the past decade due to its unique resonant feature of a sharp transition from total transmission to total reflection. Mathematically, Fano resonance is related to certain eigenvalues embedded in the continuum spectrum of the underlying differential operator.  For photonic structures, the quantitative studies of embedded eigenvalues mostly rely on numerical approaches. In this talk, based on layer potential technique and asymptotic analysis, I will present quantitative analysis of embedded eigenvalues and their perturbation as resonances for a periodic array of subwavelength metallic structure. From a quantitative analysis of the wave field for the scattering problem, a rigorous proof of Fano resonance will be given.  In addition, the field enhancement at Fano resonance frequencies will be discussed.