The design of negative electric permittivity with level set method

This paper reports a new procedure for the design of metamaterial structures to attain negative electrical permittivity. The level-set method is adopted to trace the evolution process of topology. The sensitivity of permittivity is derived to achieve a electromagnetic resonance at an appointed frequency, thereby generating a permittivity peak. Since such a peak immediately turn to a drop on its right-hand side of spectra while the permittivity is rather sensitive at this critical point, a small shape change in subsequent evolution steps can make the permittivity negative. The examples presented demonstrate the attainability of negative permittivity. By presenting different objective functions, this approach is applicable to other desired electromagnetic properties of metamaterials.