Criterion for negative refraction with low optical losses from a fundamental principle of causality

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 designing new left-handed materials: testing the expected polarizabilities of a medium against this criterion would check the compliance with the causality and verify the design feasibility.