A universal expression of near-filed/far-field boundary in stratified structures

TL;DR

This paper derives a universal empirical expression for the near-field/far-field boundary in stratified structures, considering the influence of lateral waves and refractive index variations, aiding electromagnetic applications.

Contribution

It introduces a universal empirical formula for the NFFF boundary in stratified media, accounting for lateral wave effects and refractive index differences, with validation through asymptotic and reciprocal theorem methods.

Findings

NFFF boundary is larger than two wavelengths in high refractive index media.

In air, the NFFF boundary is approximately ten wavelengths.

The derived boundary expression is validated through numerical comparisons.

Abstract

The division of the near-field and far-field zones for electromagnetic waves is important for simplifying theoretical calculations and applying far-field results. In this paper, we have studied the far-field asymptotic behaviors of dipole radiations in stratified backgrounds and obtained a universal empirical expression of near-field/far-field (NFFF) boundary. The boundary is mainly affected by lateral waves, which corresponds to branch point contributions in Sommerfeld integrals. In a semispace with a higher refractive index, the NFFF boundary is determined by a dimensional parameter and usually larger than the operating wavelength by at least two orders of magnitude. In a semispace with the lowest refractive index in the structure (usually air), the NFFF boundary is about ten wavelengths. Moreover, different treatments in the asymptotic method are discussed and numerically compared. An equivalence between the field expressions obtained from the asymptotic method and those from reciprocal theorem is demonstrated. Our determination of the NFFF boundary will be useful in the fields such as antenna design, remote sensing, and underwater communication.