Asymptotic Spatial Expansion Method of Radiated Field for Single-Cut Antenna Pattern Based on Near-Field Measurement

This communication proposes a kind of asymptotic spatial expansion method for fast determination of a single-cut antenna radiation pattern from near-field measurements. When the radiated field is generally given by cylindrical Hankel harmonics, the steepest descent method in the complex plane is adopted to study the Hankel function that can be rewritten as an asymptotic series expansion expression. Furthermore, the single-cut radiated field can be rewritten as a series of spherical waves with different expansion orders, where the first-order coefficient exactly corresponds to the far-field radiation pattern. More importantly, far-field pattern and its derivative function completely determine the high-order expansion coefficients, yielding another mathematical relationship between the near field and far-field. Finally, based on the different forms of the derivative function, the far-field can be directly solved from the near-field sampling data, which is obviously different from the existing transformation methods relying on intermediate variables like Fourier coefficients. Besides, the presented method not only outperforms the conventional Fourier method in the presence of spatial truncation, but also provides another mathematical derivation for the existing Wilcox expansion which is then applied to the near-field measurement. Thus, the study indicates an intrinsic mathematical structure of the radiated field, showing great theoretical significance and application prospects.