Nonlinear optics

Abstract

In most dielectrics, the linear relation between electric polarization and applied electric field is accurately obeyed even for fairly large fields of 107 V/m. The reason is that the atomic displacements are extremely small, in the range of nuclear sizes—millions of times smaller than the size of atoms. Though nonlinear effects such as electrostriction have been known for some time, it was not until the invention of the laser that sufficiently large optical fields became available to produce sizeable nonlinear optical effects. The induced polarization P can be written as a power series in an electric field, . . . P = χE + dE2 +· · · , . . . where χ is the linear electric susceptibility, and the higher-order terms lead to nonlinear effects such as second harmonic generation. The electric field associated with the incident light is sinusoidal, E = E0 sin ωt, and when E is substituted in the expression for P, a power series in sin ωt results. The second term is dE20 sin2 ωt = 1/2dE20 (1 − cos 2ωt), which includes a component of polarization with twice the frequency of the impressed field E. This rapidly oscillating induced dipole moment is the source of second harmonic light. The intensity of the light depends on the size of d, the second order coefficient. Crystal symmetry is a major factor in the second-order effect. The one-dimensional polar chain in Fig. 29.2 illustrates the origin of the quadratic term. When the applied field is directed to the left, the ions and bonding electrons are in very close contact and the displacements will be small because of short range repulsive forces. These forces do not oppose motion in the opposite direction, so that fields directed to the right give larger motions and larger polarizations. A centric chain does not show this effect. Such a chain can give rise to odd-order terms producing saturation but not to even power terms in the P(E) relation. This means that centric crystals are useless as second harmonic generators.