Electromagnetic wave propagation and scattering by the left-and right-handed material cylinder is investigated by incident wave. The schematic geometry of double-layered cylinders alternatively constitutive of left-and right-handed materials is also proposed. Furthermore, the distribution of the electric fields inside and outside the cylinder is calculated by numerical methods. Bizarre EM scattering characteristics of fields affected by introducing the Left-handed material are analyzed on the basis of simulation results. Consequently, the unique property of this medium is further elucidated by...