Upper Bounds on Scattering Processes and Metamaterial-Inspired Structures That Reach Them

The physical limitations on time-harmonic scattering processes are investigated on the basis of the optical theorem. Previously derived least upper bounds on the total scattering and absorption cross sections are obtained from it in a straightforward manner. In addition, it reveals a practical upper bound for the bistatic cross-section when evaluated in any direction. It is proved further that the maximum upper bound of the bistatic cross section occurs in the forward-scattering direction and that the corresponding upper bound for the backscattering direction is four times smaller than this maximum value. Metamaterial-inspired electrically small antennas and scattering particles that approach these upper bounds are demonstrated. These examples numerically validate the derived upper bounds, as well as illustrate the important physical principles underlying them.