Electromagnetic wave transmission through a subwavelength nano-hole in a two-dimensional plasmonic layer

Abstract

An integral equation is formulated to describe electromagnetic wave transmission through a subwavelength nano-hole in a thin plasmonic sheet in terms of the dyadic Green's function for the associated Helmholtz problem. Taking the subwavelength radius of the nano-hole to be the smallest length of the system, we have obtained an exact solution of the integral equation for the dyadic Green's function analytically and in closed form. This dyadic Green's function is then employed in the numerical analysis of electromagnetic wave transmission through the nano-hole for normal incidence of the incoming wave train. The electromagnetic transmission involves two distinct contributions, one emanating from the nano-hole and the other is directly transmitted through the thin plasmonic layer itself (which would not occur in the case of a perfect metal screen). The transmitted radiation exhibits interference fringes in the vicinity of the nano-hole, and they tend to flatten as a function of increasing lateral separation from the hole, reaching the uniform value of transmission through the sheet alone at large separations.

Dyadic Helmholtz Green’s Function for Electromagnetic Wave Transmission/Diffraction through a Subwavelength Nano-Hole in a 2D Quantum Plasmonic Layer: An Exact Solution Using “Contact Potential”-like Dirac Delta Functions

“…Such exactness is elusive in earlier work and in classic approaches to the analysis of electromagnetic transmission problems involving diffraction. Our results for the Green's function have been applied to a number of calculations of electromagnetic wave transmission/diffraction through a perforated plasmonic layer with a subwavelength nano-hole for both normal and non-normal incidence, including both nano-hole transmission/diffraction effects jointly with transmission through the entire plasma layer [1][2][3].…”

“…The requisite matrix inversions and integrations are carried out in detail in Ref. [2], and in the next section, we present a full graphical exposition of G hole ( r , 0; z, 0; ω) as a function of position, based on our numerical evaluation of the exact analytical solutions for the matrix elements of G hole ( r , 0; z, 0; ω) set forth in References [1][2][3].…”

“…The transmission/diffraction properties of an electromagnetic dyadic Green's function for wave propagation through a nano-hole in a two-dimensional (2D) quantum plasmonic layer are analyzed here using a succession of two coupled integral equations jointly with "contact interaction"-like Dirac delta functions representing positional localization of the layer and the nano-hole [1][2][3]. The nano-hole is taken to lie on a 2D plasmonic sheet (located on the plane z = 0 embedded in a three-dimensional (3D) bulk host medium with background dielectric constant ε detail the analytic determination of the electromagnetic dyadic Helmholtz Green's function G f s in the presence of the layer in which a uniform two-dimensional quantum plasma is embedded.…”

“…(Color online). Schematic illustration of a two-dimensional plasmonic layer S 1 of thickness d embedded at z = 0 in a three-dimensional bulk medium with dielectric constant ε (3D) b .The solution of Equation (1) for G f s ( k ; z, z ; ω) in k representation may be determined algebraically in terms of G 3D by using Equation (4) in the indicated integrations of Equation (1), with the result[1][2][3]…”

Light scattering by plasmonic disks and holes arrays: different or the same?

“…with the same diameter) PEC disks [33][34][35] and implementing the Babinet's principle, one can interchange transmittance and reflectance of disks and holes arrays: T d ↔ R h and R d ↔ T h . For realistic materials with losses, one inevitably (except for the case of a single NH [36]) has to invoke timeconsuming full-field methods and brute-force simulations to get optical properties of NHs perforated in metal films, which does not provide almost any insights into the underlying physics. Nonetheless, the Babinet principle has inspired a number of works [4,[37][38][39][40][41] where complementary structures of various configurations (holes/disks and far beyond) have been designed with almost perfectly complementary electromagnetic properties.…”