Definitions

# Near and far field

The near field and far field of an antenna or other isolated source of electromagnetic radiation are regions around the source where different parts of the field are relatively more or less important. The boundary between the two regions is only vaguely defined, and depends on the dominant wavelength ($lambda$) emitted by the source. Roughly speaking, the near field is the region within a radius $r ll lambda$, while the far field is the region for which $r gg lambda$. The two regions are defined simply for mathematical convenience, enabling certain simplifying approximations. These regions are sometimes also called the near zone and far zone. The latter is also frequently referred to as the radiation zone.

The radiation zone is important because fields generally fall off in amplitude by $1/r$. This means that the total energy per unit area at a distance $r$ is proportional to $1/r^2$. But the area of the sphere is proportional to $r^2$, so the total energy passing through the sphere is constant. This means that the energy actually escapes to infinite distance (it radiates).

## Overview

If sinusoidal currents are applied to a structure of some type, electric and magnetic fields will appear in space about that structure. If those fields extend some distance into space the structure is often termed an antenna. Such an antenna can be an assemblage of conductors in space typical of radio devices or it can be an aperture with a given current distribution radiating into space as is typical of microwave or optical devices. The actual values of the fields in space about the antenna are usually quite complex and can vary with distance from the antenna in various ways.

Since in many practical applications one is only interested in effects where the distance from the antenna to the observer is very much greater than the largest dimension of the transmitting antenna, the equations describing the fields created about the antenna can be simplified by assuming a large separation and dropping all terms which provide only minor contributions to the final field. These simplified distributions have been termed the far field and usually have the property that the angular distribution of energy does not change with distance, however the energy levels still vary with distance and time. Such an angular energy distribution is usually termed an antenna pattern.

Remarkably, by the principle of reciprocity the pattern observed when a particular antenna is transmitting is identical to the pattern measured when the same antenna is used for reception. Typically one finds relatively simple relations describing the antenna far field patterns, often involving trigonometric functions or at worst Fourier or Hankel transform relationships between the antenna current distributions and the observed far field patterns. While far field simplifications are very useful in engineering calculations, this does not mean the near field functions cannot be calculated, especially using modern computer techniques. An examination of how the near fields form about an antenna structure can give great insight into the operations of such devices.

The near-field is remarkable for reproducing classical electromagnetic induction and electric charge effects on the EM field, which effects "die-out" with increasing distance from the antenna (proportional to the cube of the distance), far more rapidly than do the classical radiated EM far-field (proportional to the distance). Typically near-field effects are not important farther away than a few wavelengths of the antenna. These near-field effects also involve energy transfer effects which couple directly to receivers near the antenna, affecting the power output of the transmitter if they do couple, but not otherwise (again, as in classical magnetic induction). In a sense, the near-field offers energy which is available to a receiver only if the energy is tapped, and this is sensed by the transmitter by means of answering electromagnetic near-fields emanating from the receiver. This is different with the far-field, which draws constantly energy from the transmitter, whether it is immediately received, or not.

## Analysis

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.

More generally, 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 energy stored in the field and returned to the antenna in every half-cycle. 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.

In quantum mechanical terms, the far-field is due simply to radiation of classical photons. These remove energy from the transmitter whether they are immediately absorbed or not. By comparison, the near-field, if it must be seen in quantum terms, may be thought of being composed of virtual photons, which have a more evanescent existence, and which do not remove energy from the transmitter, unless they are absorbed by a close charge which signals the loss back to the antenna (for magnetic components, for example, this is simple inductive coupling).

## Near field

The term near-field region (also known as the near field or near zone) has the following meanings with respect to different telecommunications technologies:

• The close-in region of an antenna where the angular field distribution is dependent upon the distance from the antenna.
• In the study of diffraction and antenna design, the near field is that part of the radiated field that is within a small number of wavelengths of the diffracting edge or antenna.
• In optical fiber communications, the region close to a source or aperture.

The diffraction pattern in the near field typically differs significantly from that observed at infinity and varies with distance from the source.

## Far field

The far-field region is the region outside the near-field region, where the angular field distribution is essentially independent of distance from the source. If the source has a maximum overall dimension D that is large compared to the wavelength, the far-field region is commonly taken to exist at distances greater than D²/λ from the source, λ being the wavelength.

For a beam focused at infinity, the far-field region is sometimes referred to as the Fraunhofer region. Other synonyms are far field, far zone, and radiation field..

Local effects

## Patents

• George F. Leydorf, , Antenna near field coupling system. 1966.
• Grossi et al., , Trapped Electromagnetic Radiation Communication System. 1969.
• , Reducing-Noise With Dual-Mode Antenna. 1969.
• Coffin et al., , Deternination of Far Field Antenna Patterns Using Fresnel Probe Measurements. 1972.
• Hansen et al., , Method and Apparatus for Determining Near-Field Antenna Patterns. 1975