Electromagnetic chirality-induced negative refraction with the same amplitude and anti-phase of the two chirality coefficients

We suggest a scheme of electromagnetic chirality-induced negative refraction utilizing magneto-electric cross coupling in a four-level atomic system. The negative refraction can be achieved with the two chirality coefficients having the same amplitude but the opposite phase,and without requiring the simultaneous presence of an electric-dipole and a magnetic-dipole transition near the same transition frequency. The simultaneously negative electric permittivity and magnetic permeability does not require, either.