Revisiting Toroidal Dipolar Moment in Planar Metamaterial

This article revisits the electric, magnetic, and toroidal dipolar moments in the metamaterial structure and presents the flatland design for generating a toroidal dipolar response for the electromagnetic plane wave at normal incidence. Based on the numerical analysis of the surface current, the electric field, the magnetic field, and the quantitative analysis of scattered power supported by the electromagnetic multipole theory, it is shown that the earlier design involving symmetric unit cells is not able to produce toroidal dipolar moment. This study resulted in a new design of a planar metasurface, which provides a toroidal response as the dominant mode when excited by the transverse magnetic (TM)-polarized electromagnetic wave. The scattered power calculated for the proposed toroidal flatland metamaterial is found to be $1.7\times 10^{5}$ times larger than the earlier design under investigation. The scattered power due to the toroidal dipole in the proposed design is found to be at least 70 times and $8\times 10^{8}$ times larger than the electric dipole and the magnetic dipole, respectively, in the $z$ -direction.