A metamaterial for converging electromagnetic waves propagating in a z direction, the metamaterial comprising a plurality of metamaterial sheet layers stacked integrally in an x direction, perpendicular to the z direction, each of the metamaterial sheet layers comprising a plurality of metamaterial units, each of the metamaterial units having an identical substrate unit and a man-made microstructure attached on the substrate unit, the metamaterial units being arranged into a first array which takes a y direction perpendicular to both the z direction and the x direction as a first column direction and the z direction as a first row direction, wherein the man-made microstructure of each metamaterial unit is designed to be anisotropic and a non-90° rotationally symmetrical structure, the metamaterial units of each column comprise a first metamaterial section having have refractive indices of a1, a2, a3,......, as, and a second metamaterial section having refractive indices of b1, b2, b3,......, bq, and a third metamaterial section having refractive indices of bq+1, bq+2, bq+3,......, bm, and a fourth metamaterial section having refractive indices of c1, c2, c3,......, cp in sequence, the refractive indices of the metamaterial sections are distributed non-uniformly, the third metamaterial section and the fourth material section are symmetrical in structure with the second metamaterial section and the first metamaterial section, respectively; wherein sites corresponding to the refractive indices of a1 to bq and cp to bq are gradual toward a center of the metamaterial units of each column, and the refractive indices satisfy: a1≤a2≤a3......≤as, b1≤b2≤b3......≤bq, bq≥bq+1≥bq+2≥bq+3......≥bm, c1≥c2≥c3... ≥cp; where b1<as, bm<c1, s and p are both equal natural numbers no less than 2, and m is a natural number no less than 1, q is a natural number less than m and more than s; characterized in that the extraordinary light optical axis of each microstructure's refractive index ellipsoid thereof is neither perpendicular nor parallel to the y direction; wherein the number of the metamaterial sheet layers is such that the dimension in the x direction is much larger than the dimension in the z direction, and the metamaterial in its entirety constitutes a sheet and the dimension in the z direction is the thickness of the sheet; wherein the man-made microstructures in each column in the y direction are incrementally rotated clockwise or counterclockwise in sequence respectively from a middle metamaterial unit towards two ends of the column, and the man-made microstructures of the metamaterial units located at the two ends are rotated by no more than 90° with respect to the man-made microstructure of the middle metamaterial unit. the man-made microstructure of each metamaterial unit is designed to be anisotropic and a non-90° rotationally symmetrical structure, the metamaterial units of each column comprise a first metamaterial section having have refractive indices of a1, a2, a3,......, as, and a second metamaterial section having refractive indices of b1, b2, b3,......, bq, and a third metamaterial section having refractive indices of bq+1, bq+2, bq+3,......, bm, and a fourth metamaterial section having refractive indices of c1, c2, c3,......, cp in sequence, the refractive indices of the metamaterial sections are distributed non-uniformly, the third metamaterial section and the fourth material section are symmetrical in structure with the second metamaterial section and the first metamaterial section, respectively; wherein sites corresponding to the refractive indices of a1 to bq and cp to bq are gradual toward a center of the metamaterial units of each column, and the refractive indices satisfy: a1≤a2≤a3......≤as, b1≤b2≤b3......≤bq, bq≥bq+1≥bq+2≥bq+3......≥bm, c1≥c2≥c3... ≥cp; where b1<as, bm<c1, s and p are both equal natural numbers no less than 2, and m is a natural number no less than 1, q is a natural number less than m and more than s; characterized in that the extraordinary light optical axis of each microstructure's refractive index ellipsoid thereof is neither perpendicular nor parallel to the y direction; wherein the number of the metamaterial sheet layers is such that the dimension in the x direction is much larger than the dimension in the z direction, and the metamaterial in its entirety constitutes a sheet and the dimension in the z direction is the thickness of the sheet; wherein the man-made microstructures in each column in the y direction are incrementally rotated clockwise or counterclockwise in sequence respectively from a middle metamaterial unit towards two ends of the column, and the man-made microstructures of the metamaterial units located at the two ends are rotated by no more than 90° with respect to the man-made microstructure of the middle metamaterial unit.