Standard patterns of radiation distribution about their source. The term radiation applies primarily to the transport of energy by acoustic, elastic, electromagnetic, or gravitational waves, and extends to the transport of atomic or subatomic particles (as represented by quantum-mechanical wave functions). See Electromagnetic radiation, Quantum mechanics, Sound, Wave motion

Each multipole pattern reflects the source's geometrical shape (or the shape of a source component). These geometrical features stand out clearly for the static electric potentials generated by fixed charges as shown by the small set of monopole, dipole, and quadrupole charges (see illustration), elements of all multipoles being named (in terms of powers of 2) 2l-poles, with l equal to any nonnegative integer. A monopole (l = 0) acoustic wave radiates from a perfectly spherical bubble with oscillating radius; higher multipoles would arise from bubble distortions. So-called transverse waves, elastic or electromagnetic (including light), have only l ≥ 1 components, gravitational waves only l ≥ 2. The angular distributions, in azimuth (&phiv;) and colatitude (Θ), of 2l-pole waves have amplitudes distributed in directions (Θ, &phiv;) in proportion to the spherical harmonic functions Ylm (Θ, &phiv;). The index m is a positive or negative integer whose absolute value is equal to less than l. See Dipole

The multipolarity index l also represents the number of angular momentum quanta &planck; (Planck's constant divided by 2&pgr;) radiated together with each energy quantum h&ngr; (phonon, photon, graviton, and so forth). Detection and measurement of received energy quanta, together with measurement of their detection rate and mapping of their directional distribution, generally serve to diagnose the mechanics of the radiation source. Energy and momentum conservation underlie this analysis; so does the conservation of angular momentum which states that the initial angular momentum of the source equals the vector sum of the final angular momentum of the source and the angular momentum of the radiation. The quantitative implications of this vector relation are studied by the branch of quantum theory called angular momentum algebra. The balancing of parity, that is, of each variable's sign reversal (or persistence) under reflection through the source's center, also contributes to the analysis of experimental data. Further, more complex angular-momentum considerations play a role in the analysis of the behavior of spin-carrying particles. See Angular momentum, Conservation laws (physics), Graviton, Phonon, Selection rules (physics), Spin (quantum mechanics)