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The condition for a negative index of refraction with respect to the vacuumindex is established in terms of permittivity and permeabilitysusceptibilities. It is found that the imposition of analyticity to satisfy theKramers-Kronig relations is a sufficiently general criterion for a physicalnegative index. The satisfaction of the Kramers-Kronig relations is amanifestation of the principle of causality and the predicted frequency regionof negative index agrees with the Depine-Lakhtakia condition for the phasevelocity being anti-directed to the Poynting vector, although the conditionspresented here do not assume {\it a priori} a negative solution branch for n.

Relationship between the Kramers-Kronig relations and negative index of refraction