Limits and validity of the impedance boundary condition on penetrable surfaces

It has been shown that application of the impedance boundary condition (IBC), also known as the Leontovich boundary condition, is effective in solving electromagnetic scattering problems involving electrically large, penetrable bodies. However, it is important to clarify the limits and range of validity of the IBC. For example, as our results show, the IBC is not valid on pure dielectric (lossless) surfaces. Two specific criteria are given to clearly define the range of the IBC validity on arbitrary smooth surfaces. These criteria are verified with numerical calculations and theoretical analyses for scattering by spheres and cylinders from both the exact boundary conditions and the IBC. The scattering calculations for prolate spheroids show that the criteria presented here also hold for nonspherical cases.