Fundamental causality and a criterion of negative refraction with low optical losses

From the fundamental requirement of causality, we derive a rigorous criterion of negative refraction (left-handedness). This criterion imposes the lower limits on the electric and magnetic losses in the region of the negative refraction. If these losses are eliminated or significantly reduced by any means, including the compensation by active (gain) media, then the negative refraction will disappear. This theory can be particularly useful in testing the feasibility of the left-handed materials design.