Determination of the effective constitutive parameters of bianisotropic metamaterials from reflection and transmission coefficients

We propose a method to retrieve the effective constitutive parameters of a slab of bianisotropic metamaterial from reflection and transmission coefficients (or scattering parameters). In our retrieval method, only the scattering parameters in one propagation direction are used. Analytical inversion equations are derived in order to retrieve the effective parameters of the permittivity, permeability, and magnetoelectric coupling coefficient of the bianisotropic metamaterial. To demonstrate the validity of the method, we used it to retrieve the parameters of four different metamaterials, among which two were normal media without bianisotropy and the other two were bianisotropic media. In using our retrieval method, including bianisotropy, the intrinsic differences between a normal medium and a bianisotropic medium were illustrated clearly. Our simulation and retrieval results also corroborate the conclusions of the previously published literature.

Figure 1

(Color online) Schematic of a split-ring resonator used to construct metamaterials. When a plane wave polarized along the $z$ axis is incident in the $x$ direction, the metamaterial will show bianisotropy.

Figure 2

(Color online) Schematics of a homogeneous bianisotropic slab placed in open space for the calculation of $S$ parameters. (a) and (b) are for plane waves incident in the $+x$ and $-x$ directions, respectively.

Figure 3

(Color online) (a)–(d) are the schematics of four single cells of metamaterials of SRR-I, SRR-II, CMM-I, and CMM-II, respectively. (e) shows the detailed structure of the SRR included in the metamaterials. The geometric parameters of the SRR are $d=t=0.2\mathrm{mm}$, $w=0.9\mathrm{mm}$, and $r=1.6\mathrm{mm}$.

Figure 4

(Color online) Transmission spectra of the metamaterials SRR-I, SRR-II, CMM-I, CMM-II, and CCMM.

Figure 5

(Color online) (a) Magnitude and (b) phase of the calculated $S$ parameters for the unit cell of SRR-I in Fig. 3a. (c) Magnitude and (d) phase of the calculated $S$ parameters for the unit cell of SRR-II in Fig. 3b.

Figure 6

(Color online) Retrieved indices (a), impedances (b), permittivity (c), permeability (d), and magnetoelectric coupling coefficient (e) for the unit cells of SRR-I and SRR-II, respectively.

Figure 7

(Color online) (a) Magnitude and (b) phase of the calculated $S$ parameters for the unit cell of SRR-I in Fig. 3c. (c) Magnitude and (d) phase of the calculated $S$ parameters for the unit cell of SRR-II in Fig. 3d.

Figure 8

(Color online) Retrieved indices (a), impedances (b), permittivity (c), permeability (d), and magnetoelectric coupling coefficient (e) for the unit cells of CMM-I and CMM-II, respectively.