Introduction

In this chapter, we will present the coupled-mode theory of an ideal single-mode optical coupler, according to work originally developed by Dietrich Marcuse [1]. Section 8.2 introduces and discusses some relevant concepts of the generic four-port linear system, with particular reference to the optical coupler.

The classical approach to the coupled-mode theory of the directional optical coupler is presented in Section 8.3. The transition from isolated-waveguide to compound-waveguide modes, and the growth of field interference owing to different propagation constants, are highlighted as fundamental principles of the optical field coupling mechanism. In order to provide quantitative examples, the Gaussian model of even and odd compound modes is presented in Section 8.4, to be used for simulations and examples of field patterns through this chapter. The Gaussian field approximation takes its strength from a heuristic approach and the simplicity of its mathematical description. The excitation of a compound waveguide by superposition of fields is analyzed in Section 8.5, leading to the formulation of the coupled-waveguide equations.