Chapter 12 - Operator formalism in polarization-nonlinear optics and spectroscopy of polarization-inhomogeneous media

In the general framework, the description of the process of propagation of electromagnetic radiation in a medium is reduced to seeking the self-consistent solution of equations describing the action of radiation on a substance, and the influence of the latter on the radiation field. For complete correspondence of the theory and experiment, it is necessary to undertake a quantum description of the medium and of the electromagnetic field.

In some descriptions, only quantum effects can be exhibited, such as photon antigrouping and generation of squeezed states. However, for a wide range of phenomena, good consistency between theory and experiment is achieved with the use of a semiclassical description and of the radiation field by the classical Maxwell's equations.

Further simplifications can be made under special conditions on the properties of the medium and the radiation. The description of photoinduced anisotropy in initially isotropic media is quite complicated and not always possible analytically. The methods of classical crystal optics can be used when the equations describing the nonlinear interaction are linearized in an examined field..