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The normal and the lateral Casimir interactions between corrugated idealmetallic plates in the presence of an amplifying or an absorptive dielectricslab has been studied by the path-integral quantization technique. The effectof the amplifying slab, which is located between corrugated conductors, is toincrease the normal and lateral Casimir interactions, while the presence of theabsorptive slab diminishes the interactions. These effects are more pronouncedif the thickness of the slab increases, and also if the slab comes closer toone of the bounding conductors. When both bounding ideal conductors are flat,the normal Casimir force is non-monotonic in the presence of the amplifyingslab and the system has a stable mechanical equilibrium state, while the forceis attractive and is weakened by intervening the absorptive dielectric slab inthe cavity. By replacing one of the flat conductors by a flat ideal permeableplate the force becomes non-monotonic and the system has an unstable mechanicalequilibrium state in the presence of either an amplifying or an absorptiveslab. When the left side plate is conductor and the right one is permeable, theforce is non-monotonic in the presence of a double-layer DA(dissipative-amplifying) dielectric slab with a stable mechanical equilibriumstate, while it is purely repulsive in the presence of a double-layer AD(amplifying-dissipative) dielectric slab.

Non-monotonic Casimir interaction: The role of amplifying dielectrics