The principles of many photonic devices are based on the coupling between optical fields of different frequencies or different spatial modes. In general, the coupling mechanism can be described by a polarization ΔP on top of a background polarization representing the property of the medium in the absence of the coupling mechanism. In this chapter, we present the general coupled-wave and coupled-mode formalisms, which provide the foundation for understanding the functions of many devices in the following chapters. The coupled-wave formalism deals with the coupling of optical waves of different frequencies, whereas coupled-mode theory applies to the coupling of optical fields of different spatial modes.

Coupled-wave theory

In this section, the general formulation of the coupled-wave formalism for coupling of optical waves of different frequencies is presented. For simplicity, we consider only coupling among plane optical waves, but the formulation can be easily extended for nonplane waves, such as optical waves of Gaussian beam profiles.

As discussed in Section 1.3, coupling among opticalwaves of different frequencies is possible only if the optical property of the medium in which the optical waves propagate is either time varying or optically nonlinear. Time-varying optical properties can be induced by time-varying electric, magnetic, or acoustic fields through electro-optic, magneto-optic, or acousto-optic effects, which are discussed in Chapters 6, 7, and 8, respectively. In particular, an acoustic wave always induces time-varying changes in the optical property of a medium, whereas changes induced by electro-optic or magnetooptic effects can be static when they are caused by static electric or magnetic fields. Nonlinear optical properties are discussed in Chapter 9.