Random errors for a nonlocal Epsilon Negative medium

A medium embedded with finite length perfectly conducting needles can be taken as a nonlocal Epsilon Negative medium. The medium is nonlocal due to the presence of spatial dispersion. A theoretical analysis for effects of random errors in positioning and orientation of finite length needles upon the ensemble averaged nonlocal effective permittivity is presented. It is studied that an increase in positioning and orientation errors of needles can reduce and even eliminate the negative bandwidth. The word negative bandwidth is used to represent the range of frequency for which the real part of the effective permittivity is negative. Also these errors widen the bandwidth of an absorption peak associated with an imaginary part of the effective permittivity.