TABLE OF CONTENTS In the preceding two chapters, the transmission characteristics of independent planar optical waveguides and optical fibers have been investigated. For the construction of practical optical devices, it is very important to utilize the mutual lightwave interaction between the two copropagating light beams in the adjacent waveguides or interaction between the contrapropagating two beams in the corrugated optical waveguides. Coupled mode theory deals with the mutual lightwave interactions between the two propagation modes. In this chapter derivation of coupled mode equations based on perturbation theory is first presented and then concrete methods calculating the coupling coefficients for several practically important devices are explained in detail. Finally, several waveguide devices using directional couplers such as Mach Zehnder interferometers, ring resonators, and bistable devices are described.
In axially uniform optical waveguides, a number of propagation modes exist, as has been described in the previous chapters. These propagation modes are specific to each waveguide and satisfy the orthogonality conditions between the modes.
If two waveguides are brought close together as shown in Fig. 4.1, optical modes of each waveguide either couple or interfere with each other. When the electromagnetic field distributions after mode coupling do not differ substantially from those before coupling, the propagation characteristics of the coupled waveguides can be analyzed by the perturbation method [1].
When we denote the eigen modes in each optical waveguide before mode coupling as 
, 
( p = 1, 2)
