farfield

Farfield, or the Fraunhofer region, is the region of a radiated wave field where wavefronts are effectively planar and the angular distribution of radiation is essentially distance‑independent. In the far field the field amplitude decreases roughly as 1/r and the phase varies linearly with distance. The concept applies across electromagnetism, acoustics, and optics for sources such as antennas, loudspeakers, and optical apertures.

Boundaries between near and far field depend on wavelength λ and the source size D (largest dimension). A common electromagnetic criterion is r > 2D^2/λ, with r also assumed large compared with λ. The near field includes the reactive region (r < 0.62 sqrt(D^2+λ^2)) and the radiating near-field or Fresnel region (0.62 sqrt(D^2+λ^2) < r < 2D^2/λ).

In the far field, the electric and magnetic fields are transverse to the propagation direction and related by a constant polarization. Fields behave as E,H ∝ e^{-ikr}/r, with a distance‑independent angular pattern set by the aperture or antenna geometry. The time‑averaged power flux falls as 1/r^2. In optics, far-field behavior leads to Fraunhofer diffraction, where the angular intensity is the Fourier transform of the aperture function.

Applications include antenna and radar design, wireless and optical communications, and acoustic testing. The far-field approximation enables straightforward measurement and modeling of directivity, gain, and beam shape, by focusing on the angular distribution of radiation at large distances.