Near and Far Field - Classical EM Modelling

Classical EM Modelling

Solving Maxwell's equations for the electric and magnetic fields for a localized oscillating source, such as an antenna, surrounded by a homogeneous material (typically vacuum or air), yields fields that, far away, decay in proportion to 1/r where r is the distance from the source. These are the radiating fields, and the region where r is large enough for these fields to dominate is the far field.

In general, the fields of a source in a homogeneous isotropic medium can be written as a multipole expansion. The terms in this expansion are spherical harmonics (which give the angular dependence) multiplied by spherical Bessel functions (which give the radial dependence). For large r, the spherical Bessel functions decay as 1/r, giving the radiated field above. As one gets closer and closer to the source (smaller r), approaching the near-field, other powers of r become significant.

The next term that becomes significant is proportional to 1/r2 and is sometimes called the induction term. It can be thought of as the primarily magnetic energy stored in the field, and returned to the antenna in every half-cycle, through self-induction. For even smaller r, terms proportional to 1/r3 become significant; this is sometimes called the electrostatic field term and can be thought of as stemming from the electrical charge in the antenna element.

Very close to the source, the multipole expansion is less useful (too many terms are required for an accurate description of the fields). Rather, in the near-field, it is sometimes useful to express the contributions as a sum of radiating fields combined with evanescent fields, where the latter are exponentially decaying with r. And in the source itself, or as soon as one enters a region of inhomogeneous materials, the multipole expansion is no longer valid and the full solution of Maxwell's equations is generally required.