Critical conductivity-length product for electromagnetic instability in negative-differential-conductivity media

For a slab of uniform negative-differential-conductivity medium, such as nGaAs, it is shown that unstable plane electromagnetic waves may exist when the thickness exceeds a critical value determined by the product of differential conductivity and length. When the slab is terminated on both sides by vacuum, the critical |¿|L is found to be 2/377S. This instability explains the error in a paradoxical result recently published, namely that a thick slab of negative-conductance material should attenuate rather than amplify incident waves.