Magnetic topological transition in transmission line metamaterials

We study the magnetic topological transition of the isofrequency curves in the wave vector space from a closed ellipsoid to an open hyperboloid in a metamaterial based on artificial transmission lines. In the radio frequency band we directly measure the emission pattern of a point source placed in the center of the lattice and demonstrate the elliptical wave fronts below the topological transition frequency and hyperbolic wave fronts above the topological transition frequency.

Figure 1

(a) Topological transition between elliptic and hyperbolic isofrequency curves. (b) Permeabilities of a two-dimensional uniaxial metamaterial with magnetic topological transition.

Figure 2

(a)–(e) Isofrequency curves obtained by numerical solution of the dispersion relation (3) for the unit cell parameters: $C=3300\mathrm{pF},C_y=0.01\mu \mathrm{F}$, and $L_x=L_y=100$ $\mu \text{H}$. (f)–(j) The simulated spatial distribution of the absolute values of the Green function of the metamaterial composed of $31\times 31$ unit cells at frequencies 1–5, respectively.

Figure 3

Photograph of the two-dimensional metamaterial prototype fabricated using commercial chip components on a FR4 printed circuit board. The inset shows the unit cell design.

Figure 4

(a)–(e) Measured Green function patterns at frequencies 1–5 in comparison with simulated Green function patterns (f)–(j) in the metamaterial with losses and 10% tolerance of the chip components taken in to account.