On the problem of comparing graded metamaterials

We use a simple effective model, obtained through the application of high-frequency homogenisation, to tackle the fundamental question of how the choice of gradient function affects the performance of a graded metamaterial. This approach provides a unified framework for comparing gradient functions efficiently and in a way that allows us to draw conclusions that apply to a range of different wave regimes. We consider the specific problem of single-frequency localisation, for which the appropriate effective model is a one-dimensional Schrodinger equation. Our analytic results both corroborate those of existing studies (which use either expensive full-field wave simulations or black-box numerical optimisation algorithms) and extend them to other metamaterial regimes. Based on our analysis, we are able to propose a design strategy for optimising monotonically graded metamaterials and offer an explanation for the lack of a universal optimal gradient function

Metamaterial applications of T <scp>matsolver</scp> , an easy-to-use software for simulating multiple wave scattering in two dimensions

Peer reviewed: TruePublication status: Published Multiple scattering of waves is eminent in a wide range of applications and extensive research is being undertaken into multiple scattering by ever more complicated structures, with emphasis on the design of metamaterial structures that manipulate waves in a desired fashion. Ongoing research investigates the design of structures and new solution methods for the governing partial differential equations. There is a pressing need for easy-to-use software that empowers rapid prototyping of designs and for validating other solution methods. We develop a general formulation of the multiple scattering problem that facilitates efficient application of the multipole-based method. The shape and morphology of the scatterers is not restricted, provided their T-matrices are available. The multipole method is implemented in the T matsolver software package, which uses our general formulation and the T-matrix methodology to simulate accurately multiple scattering by complex configurations with a large number of identical or non-identical scatterers that can have complex shapes and/or morphologies. This article provides a mathematical description of the algorithm and demonstrates application of the software to four contemporary metamaterial problems. It concludes with a brief overview of the object-oriented structure of the T matsolver code. </jats:p

Metamaterial applications of T matsolver, an easy-to-use software for simulating multiple wave scattering in two dimensions

Peer reviewed: TruePublication status: PublishedMultiple scattering of waves is eminent in a wide range of applications and extensive research is being undertaken into multiple scattering by ever more complicated structures, with emphasis on the design of metamaterial structures that manipulate waves in a desired fashion. Ongoing research investigates the design of structures and new solution methods for the governing partial differential equations. There is a pressing need for easy-to-use software that empowers rapid prototyping of designs and for validating other solution methods. We develop a general formulation of the multiple scattering problem that facilitates efficient application of the multipole-based method. The shape and morphology of the scatterers is not restricted, provided their T-matrices are available. The multipole method is implemented in the Tmatsolver software package, which uses our general formulation and the T-matrix methodology to simulate accurately multiple scattering by complex configurations with a large number of identical or non-identical scatterers that can have complex shapes and/or morphologies. This article provides a mathematical description of the algorithm and demonstrates application of the software to four contemporary metamaterial problems. It concludes with a brief overview of the object-oriented structure of the Tmatsolver code