Intrinsic left-handed electromagnetic properties in anisotropic superconductors

Left-handed materials usually are realized in artificial subwavelength structures. Here we show that some anisotropic superconductors, such as $\mathrm{Bi_2Sr_2CaCu_2O_{8+\delta}}$, $\mathrm{YBa_2Cu_xO_y}$ and $\mathrm{La_{2-x}Sr_xCuO_4}$, are intrinsic left-handed materials. The condition is that the plasma frequency in the $c$ axis, $\omega_c$, and in the $ab$ plane, $\omega_{ab}$, and the operating frequency, $\omega$, satisfy $\omega_c<\omega<\omega_{ab}$. In addition $\omega$ should be smaller than the superconducting energy gap to sustain superconductivity. We study the reflection and transmission of electromagnetic waves, and reveal negative refraction and backward wave with phase velocity opposite to the direction of energy flux propagation. We also discuss possible approaches of improvement, making these properties feasible for experimental validation. Being intrinsic left-hand materials, the anisotropic superconductors are promising for applications in novel electromagnetic devices in the terahertz frequency band.