Effective medium theory for two-dimensional non-magnetic metamaterial lattices up to quadrupole expansions

Abstract

We present a formulation for deriving effective medium properties of infinitely periodic two-dimensional metamaterial lattice structures beyond the conventional static and quasi-static limits. We utilize the multipole expansions, where the polarization currents associated with the supported Bloch modes are expressed via the electric dipole, magnetic dipole, and electric quadrupole moments per unit length. We then propose a method to calculate the Bloch modes based on the lattice geometry and individual unit element structure. The results revert to well-known formulas in the traditional quasistatic limit and are useful for the homogenization of nanorod-type metamaterials which are frequently used in optical applications.

Printable all-dielectric water-based absorber

“…1 , we replace the induced polarisation currents J excited inside the cylindrical volume with electric and magnetic multipoles that act as equivalent point sources for the scattered field in free space. From multipole theory 37 , 38 , the per-unit-length electric dipole p , magnetic dipole m , electric quadrupole Q e and magnetic quadrupole Q m moments for the two-dimensional case can be obtained via integrating the induced current over the cross-section surface (S) where r is the observation vector in the cylindrical coordinates and the indices specify the vector component along a particular spatial direction. It should be noted, that depending on the excitation, the behaviour of the system is significantly different.…”

Physics-informed neural networks for inverse problems in nano-optics and metamaterials

“…Photonic metamaterials are artificial structures composed of designed subwavelength building blocks that can achieve unusual optical properties [12]. The current underpinning of metamaterials design relies on the effective medium theory (EMT) [13][14][15], which is actively investigated in electromagnetic research from different perspectives such as the methods of coherent potential approximation (CPA) [16,17], the multipole expansion method [18], or the field averaging procedure [19] are used to homogenize metamaterials properties. Here we propose to use PINNs for the homogenization of dielectric metamaterials formulated as an inverse medium problem for finite-size systems.…”

Photonic crystals for optimal color conversion in light-emitting diodes: a semi-analytical approach

“…Note also that the formulas (2) and (3) are derived for an isotropic background (namely, for the case ε t ε l ) but are still physically sound in our consideration because ε t ≅ ε l , as mentioned previously. Furthermore, for the transversal permeabilities μ x , μ y we use a finer approximation [32] than the one derived in the work from which Eqs. (2) and (3) are reproduced [23].…”