Three and Four Wave Mixing

Abstract

One characteristic of nonlinear processes in quantum optics is the occurrence of products of interaction energies with complex conjugates of these energies, e.g., in the third-order product VV*V. This is built into the concept of the rotating-wave approximation, whether taken classically or quantum mechanically. Because of the V*, it is possible to conjugate a wave front. Section 2-4 discusses the conjugation of a plane wave front in a classical χ⁽³⁾ medium using four-wave mixing. More generally, imagine a point source emitting spherical waves that pass through a distorting medium. Impinging on an ordinary mirror, which obeys the rule angle of reflection equals angle of incidence, the diverging rays continue to diverge upon reflection (Fig. 9-1). However if all the exp(i K·r) plane waves comprising the wave front could be complex conjugated, i.e., turned into the corresponding exp(−i K·r) waves, the wave front would be inverted and sent back through the distorting medium to converge on the original point source. Such a phenomenon has been demonstrated using nonlinear optics and is of substantial interest in applications in laser fusion, weapons, and compensation for bad optics in general. In addition, it is an extension of the two and three-wave interactions discussed in Chap. 8 on saturation spectroscopy, and offers useful alternative configurations to study the characteristics of matter.