Determining the Effective Constitutive Parameters of Finite Periodic Structures: Photonic Crystals and Metamaterials

Abstract

A novel approach to find the effective electric and magnetic parameters of finite periodic structures is proposed. The method uses the reflection coefficients at the interface between a homogenous half-space and the periodic structure of different thicknesses. The reflection data are then approximated by complex exponentials, from which one can deduce the wavenumber, and the effective electric and magnetic properties of the equivalent structure by a simple comparison to the geometrical series representation of the generalized reflection from a homogenous slab. Since the effective parameters are for the homogenous equivalent of the periodic structure, the results obtained are expected to be independent of the number of unit cells used in the longitudinal direction. Although the proposed method is quite versatile and applicable to any finite periodic structure, photonic crystals and metamaterials with metallic inclusions have been used to demonstrate the application of the method in this paper.

The effect of media parameters on wave propagation in a chiral metamaterials slab using FDTD

“…The constitutive relation for frequency dispersive CMMs or chiral media can be expressed as where ε , μ , and κ are permittivity, permeability, and chirality parameters, respectively. D and B represent electric displacement and magnetic induction, respectively.…”

Effect of left-handed materials in surface plasmon excitation and propagationlength

“…In order to determine the component of the wavevector at the metal surface ( k x ) , we used the GPOF method (see Supporting Information text for details), where we can approximate field functions as sum of complex exponentials [19][20][21]. Here, we first multiplied the field data by √ x in order to have only a sum of exponentials, i.e.…”

Topology optimization of patch-typed left-handed metamaterial configurations for transmission performance within the radio frequency band based on the genetic algorithm

“…In the flow chart described in section 2.2, equivalent electromagnetic parameters of left-handed metamaterials are obtained by an inversion of electromagnetic field information. Currently the transmission/reflection method [24][25][26], the homogenization theory [27,28] and the undetermined coefficient method of dispersion models [29,30] are the three main inversion methods. As an important branch of the transmission/reflection method, the S-parameter retrieval method [31][32][33][34] has been widely supported by researchers due to its computing simplicity and general applicability.…”