Asymptotic Study of the Radiation Operator for the Strip Current in Near Zone

Abstract

In this paper, we address the problem of how to efficiently sample the radiated field in the framework of near-field measurement techniques. In particular, the aim of the article is to find a sampling strategy for which the discretized model exhibits the same singular values of the continuous problem. The study is done with reference to a strip current whose radiated electric field is observed in the near zone over a bounded line parallel to the source. Differently from far zone configurations, the kernel of the related eigenvalue problem is not of convolution type, and not band-limited. Hence, the sampling-theory approach cannot be directly applied to establish how to efficiently collect the data. In order to surmount this drawback, we first use an asymptotic approach to explicit the kernel of the eigenvalue problem. After, by exploiting a warping technique, we recast the original eigenvalue problem in a new one. The latter, if the observation domain is not too large, involves a convolution operator with a band-limited kernel. Hence, in this case the sampling-theory approach can be applied, and the optimal locations of the sampling points can be found. Differently, if the observation domain is very extended, the kernel of the new eigenvalue problem is still not convolution. In this last case, in order to establish how to discretize the continuous model, we perform a numerical analysis.