TY - JOUR A1 - Henkel, Carsten A1 - Joulain, Karl T1 - Casimir force between designed materials : what is possible and what not N2 - We establish strict upper limits for the Casimir interaction between multilayered structures of arbitrary dielectric or diamagnetic materials. We discuss the appearance of different power laws due to frequency-dependent material constants. Simple analytical expressions are in good agreement with numerical calculations based on Lifshitz theory. We discuss the improvements required for current ( meta) materials to achieve a repulsive Casimir force Y1 - 2005 SN - 0295-5075 ER -