Chapter 10 - Four-Wave Mixing

Abstract

This chapter reviews the origin of the four-wave mixing (FWM), and develops a simple scalar theory of this process and the techniques used for phase-matching. The origin of FWM lies in the non-linear response of bound electrons. In the stimulated scattering processes, the optical fibers play an active role such that the process depends on the molecular vibrations or density variations of silica. The main difference between FWM and stimulated scattering processes is that the phase matching condition is automatically satisfied in the case of Raman or Brillouin scattering as a result of the active participation of the non-linear medium. In a separate class of non-linear phenomena, known as parametric processes, the optical fibers play a passive role except for mediating interaction among several optical waves. Such processes involve modulation of a medium parameter such as the refractive index, and require phase-matching before they can build up along the fiber. The third-order parametric processes involve non-linear interactions among the four optical waves and include the phenomena such as the FWM and the third-harmonic generation. FWM is polarization-dependent and a full vector theory is usually developed for it. The theory of FWM is explained under topics: coupled amplitude equations, effects of phase-matching, and ultrafast FWM. Phase-matching techniques discuss several different methods for realizing phase-matching in practice. The chapter focuses on parametric amplifications in which the single- and dual-pump configuration used for modern fiber-optic parametric amplifiers (FOPAs) are discussed. The chapter concludes by enlisting the various applications of FWM–for instance, quantum noise and correlation that has found number of applications including reduction of quantum noise through a phenomenon called squeezing.