ABSTRACT
This chapter examines some cases that the nonlinearity, which exists to some extent in all physical systems, modifies the properties of the linear excitations. The development of a theoretical framework for nonlinear optics dates from the invention of the laser in the early 1960s, and there are many excellent textbooks on the subject, for example, by Y. R. Shen, A. Yariv and D. L. Mills. It was stated that the formulation of nonlinear optics by means of a Taylor expansion for the polarization involves an assumption of weak nonlinearity and that this assumption is usually well satisfied. On a historical basis nonlinear spin–wave processes first attracted attention in ferromagnetic resonance experiments at high power levels for the microwave-frequency exciting magnetic field. The chapter provides a Hamiltonian approach, including both the Heisenberg exchange and magnetic dipole–dipole coupling, in order to identify the leading-order nonlinear terms that give rise to interactions and scattering processes between spin waves.
