Design of field concentrators using transformation optics

This paper presents a transformation-optics framework for comparing four-direction, twisted, radial, and circular-core field concentrators using a common finite-difference frequency-domain (FDFD) model. The mappings are evaluated in terms of field enhancement, concentration ratio, field uniformity, material complexity, and attainable compression. At a common compression of Γ_A,ref≈2.56, the four-direction mapping gives the highest η_H=1.6635 and C_H=5.3578% but requires the highest tensor magnitude. The radial mapping gives the lowest U_H=0.0213 and max|μ_ij|=2.2527 and is selected for its best overall balance. Robustness analysis shows that material loss mainly reduces concentration performance, coarse discretization degrades uniformity, and geometric variations affect both concentration and field distribution. This framework provides a consistent basis for selecting concentrator mappings for different design objectives.