Fig. 1. (a) Square CS with a period $a$. (b) Rectangular CS with a period $a$ along the $x$ direction and $\mathrm{a}$ period $b$ along the $y$ direction. The permittivity of the yellow region and white region is ${ϵ}_1$ and ${ϵ}_2$, respectively.

Fig. 2. The field patterns $H_z$ when incident with (a) a plane wave and (c) a point source on a square CS, with $50\times 50$ unit cells in the middle (only the sketch is shown here). The period $a$ is set as 200 nm, with ${ϵ}_1=4$ and ${ϵ}_2=1$. (b), (d) Field patterns when using the isotropic and uniform medium in the middle region.

Fig. 3. The field patterns $H_z$ when incident with (a) a plane wave and (c) a point source to the middle bulk material composed with rectangular CS. The middle region of the effective medium has $50\times 100$ unit cells (only the sketch is shown here), with $a=200\mathrm{nm}$, $b=100\mathrm{nm}$, ${ϵ}_1=4$, and ${ϵ}_2=1$. (b), (d) Field patterns when using the anisotropic and uniform medium.

Fig. 4. Field patterns $H_z$ when (a) a plane wave and (c) a cylindrical wave pass through a gradient circular ring. The circular grids (only the sketch is shown here) are formed by many sector units in the CS, including $10(r)\times 24(\theta )$ unit cells. Inner and outer radii of this ring are 1 μm and 4 μm, and we keep the permittivity of ${ϵ}_1=4$ and ${ϵ}_2=1$ unchanged in each unit cell. (b), (d) Field patterns when using a gradient and anisotropic medium incident by (b) a plane wave or (d) a point source, where the same layers along the radial direction are set.

Table 1. Effective Permittivity ${ϵ}_x$ and ${ϵ}_y$ Obtained from the Slopes along $\mathit{\Gamma }X$ and $\mathit{\Gamma }Y$ Directions in the Band Structure, While Keeping ${ϵ}_1/{ϵ}_2$ Unchanged for Each Row and Tuning the Ratios of $a/b$ from 0.5 to 4

Table 2. Fitted Anisotropic Permittivity ${ϵ}_x$ and ${ϵ}_y$ of the Circular Ring Material Based on Eq. (3), Where the Permittivity ${ϵ}_1=4$ and ${ϵ}_2=1$ Are Kept Unchanged in Each Unit Cell