The term "waveguide" commonly refers to a structure, i.e., a dielectric medium that is able to confine and guide electromagnetic waves. In the simplest case, the waveguide is a material having a refractive index sufficiently high compared to the ambient medium, and appropriate dimensions, to guide light at distinctive wavelengths by total internal reflections. This principle applies to both planar
waveguides and optical fibers, which are known from telecommunications applications. Figure 1 shows the basic setup of planar and fiber optic waveguides. Sensor systems for chemical and biosensing applications implement both types of waveguides, depending on the setup and application.
Based on their dimensions and light-guiding properties, both planar and fiber optical waveguides can be subdivided into two classes, namely, single-mode (small waveguide thickness) and multimode (comparably large thickness). A light wave reproducing itself after two reflections in the waveguide is called an eigenmode, or simply, mode of a waveguide [4]. In single-mode waveguides, only one light mode can be guided, whereas thicker waveguides allow several modes. For multimode waveguides, a description based on the ray-optics approach is adequate. Yet, it does not suffice to describe thin-film (thin core) waveguides, where the electromagnetic approach is more suitable. These two approaches, which are presented in this chapter, basically follow the description of the optical waveguide theory in Snyder and Love [5]. We exclude a description of laterally structured waveguides, which can be found, for example, in the publications by Kogelnik [6].