Optical interactions can generally be categorized into parametric processes and nonparametric processes. A parametric process does not cause any change in the quantum-mechanical state of the material, whereas a nonparametric process causes some changes in the quantum-mechanical state of the material. Phase matching among interacting optical fields is not automatically satisfied in a parametric process but is always automatically satisfied in a nonparametric process. All second-order nonlinear optical processes are parametric in nature. The nonlinear polarization and phase-matching condition of each second-order process are discussed in the second section. Some third-order nonlinear optical processes are parametric, and others are nonparametric. The nonlinear polarization and phase-matching condition of each third-order process are discussed in the third section.

There are basically two types of nonlinear optical frequency converters. The majority are based on parametric processes, which require phase matching. Devices that use the nonparametric third-order processes of stimulated Raman or Brillouin scattering to shift the optical frequency are the other type. In this chapter, only those based on parametric processes are considered. The first six sections cover practical optical frequency converters that are based on second-order parametric processes, including second-harmonic generation, sum-frequency generation, difference-frequency generation, optical parametric up-conversion, optical parametric down-conversion, optical parametric amplification, optical parametric generation, and optical parametric oscillation. Frequency conversion based on the third-order parametric four-wave mixing of small frequency shifts is discussed in Section 10.7. The generation of high-order harmonics is discussed in Section 10.8.