Nonlinear optics covers very broad research directions and has been a very
active area of research for about fifty years since the invention of the first
laser at the beginning of 1960s. There are several excellent text books devoted
to various aspects of nonlinear optics including Nonlinear Optics by R.
W. Boyd, Nonlinear Optics by Y. R. Shen, Quantum Electronics by A. Yariv,
Principles of Nonlinear Optical Spectroscopy by S. Mukamel, and Nonlinear
Fiber Optics by G. P. Agrawal. Multi-wave mixings in gases, liquids, and
solid materials are important parts of the nonlinear optical process. Typically,
lower-order nonlinear optical processes always dominate since they are
more efficient than higher-order ones. So normally only two-wave, three-wave,
and four-wave mixing (FWM) processes, depending on symmetries of nonlinear
materials, are studied, and their basic principles are covered in detail
in those textbooks. FWM comes from the third-order nonlinearity, which is
one of the most popular nonlinear phenomena, and can be easily observed in
materials with the inversion central symmetry (in which the third-order nonlinearity
is the lowest nonlinear one). In certain specially designed material
systems, or in certain phase conjugation configurations, the FWM efficiency
can be very high, reaching 100% or even with gain. With newly developed
short-pulse high-power lasers, and new materials designed and optimized for
certain nonlinearities, higher-order wave-mixing processes, such as the sixwave
mixing (SWM, corresponding to the fifth-order nonlinearity) and even
the eight-wave mixing (EWM, corresponding to the seventh-order nonlinearity),
have been experimentally investigated in recent years.