Throughout this book we consider the optical response of materials in the electric-dipole approximation. As mentioned in §2.5, this is a perfectly satisfactory approximation for the majority of practical cases in nonlinear optics because other interactions, such as electric quadrupole and magnetic dipole, are almost always very weak in comparison. However, there are a few cases in which these electric-multipole and magnetic effects need to be considered. For example, second-harmonic generation via electric-dipole interaction is forbidden in centrosymmetric media from symmetry considerations (see §5.3). Yet a weak effect is sometimes observed in centrosymmetric solids-such as the crystal calcite (Terhune et al, 1962)-which can be ascribed to an electric-quadrupole interaction. This is one of the contributory mechanisms being considered currently in an attempt to explain the observation that glass optical fibres can, in certain circumstances, perform efficient second-harmonic generation (Terhune and Weinberger, 1987). Also it is found that certain atomic gases are good systems for the observation of multipole and magnetic nonlinear-optical effects (Hanna et al, 1979). It is possible to tune the optical frequencies in the vicinity of selected electronic transitions that are forbidden in the electric-dipole approximation, but which are allowed via electric-quadrupole and magnetic-dipole interactions; with resonance enhancement, these nonlinear effects can therefore be significant. It is sometimes necessary to take account of such effects in the analysis of very sensitive spectroscopic measurements. As a further example, the electric-dipole approximation may be invalid for highly-extended charge distributions, such as long conjugated-chain molecules.