Substrate effects onto complex modes and optical properties of 2D arrays of linear trimers of plasmonic nanospheres

Abstract

-We first introduce the formulation of 2D periodic dyadic Green's function to account for all the field contributions required to thoroughly describe the physics of a 2D array of nanospheres on top of a multilayered substrate. Then, we analyze substrate effects onto complex modes and optical properties of 2D arrays of linear trimers of plasmonic nanospheres and show that Fano resonant features appear for oblique TM-polarized plane wave incidence illumination. These features are attributed to the forced excitation of free modes supported by the array, here computed via modal analysis. We observe strengthened Fano features due to the presence of the multilayered substrate.

Enhanced Magnetic and Electric Fields via Fano Resonances in Metasurfaces of Circular Clusters of Plasmonic Nanoparticles

“…The total electric field at a general position r = x x̂ + y ŷ + z ẑ is given by boldE ( r , k B ) = boldE inc ( r ) + boldE ref ( r ) + prefix∑ i = 1 N G̲ ml ∞ false( boldr , boldr i , boldk normalB false) · p i where E inc is the incident electric field, E ref is the portion of incident electric field reflected by the multilayered substrate, ∑ i = 1 N G ml ∞ ( r , r i , k B )· p i is the field scattered by the metasurface including the effect of the multilayered substrate, and G ml ∞ represents the multilayered electric dyadic GF for the periodic phased array of electric dipoles that relates the induced electric dipole moment to the electric field. The term G ml ∞ is here computed by summing two terms as in ref to guarantee fast convergence when evaluating fields at the array plane: (i) the periodic dyadic GF of an array of electric dipoles in homogeneous host medium computed through the Ewald method and (ii) the periodic dyadic scattering GF computed through a spectral approach that takes into account the effect of the multilayered substrate. It is apparent that once the Green’s function of a dipole in the multilayered environment is known, the dipole moments p i are evaluated by solving the system for i = 1, 2, ..., N , ∑ j = 1 N A̲ i j · boldp j = α ee [ E inc …”

“…35,36 ■ FORMULATION EMPLOYING 2D PERIODIC DYADIC GREEN'S FUNCTIONS We briefly summarize the formulation based on two-dimensional periodic dyadic Green's functions that accounts for all the field contributions required to thoroughly describe the physics of a metasurface of nanoparticle clusters on top of a multilayered substrate. 37 The monochromatic time harmonic convention exp(−iωt) is implicitly assumed.…”