# Intrinsic left-handed electromagnetic properties in anisotropic superconductors

## TL;DR

This paper demonstrates that certain anisotropic superconductors inherently exhibit left-handed electromagnetic properties within specific frequency ranges, enabling negative refraction and backward wave phenomena useful for terahertz applications.

## Contribution

It reveals that some anisotropic superconductors are intrinsic left-handed materials under specific conditions, expanding the understanding beyond artificial metamaterials.

## Key findings

- Demonstration of negative refraction in anisotropic superconductors
- Identification of frequency conditions for left-handed behavior
- Potential for terahertz electromagnetic device applications

## Abstract

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.