Optical waveguides are the basic elements for confinement and transmission of light over various distances, ranging from tens or hundreds of micrometers in integrated photonics to hundreds or thousands of kilometers in long-distance fiber-optic transmission. They are used to connect various photonic devices. In many devices, they form important parts or key structures, such as thewaveguides providing optical confinement in semiconductor lasers. Furthermore, they form important active or passive photonic devices by themselves, such as waveguide couplers and modulators. In this chapter, we consider the basic characteristics of linear, lossless dielectric waveguides. Optical fibers are discussed in Chapter 3. Other waveguide devices are discussed in later chapters.

Waveguide modes

The basic structure of a dielectric optical waveguide consists of a longitudinally extended high-index optical medium, called the core, which is transversely surrounded by low-index media, called the cladding. A guided optical wave propagates in the waveguide along its longitudinal direction. We consider a straight waveguide whose longitudinal direction is taken to be the z direction, as shown in Fig. 2.1(a). The characteristics of a waveguide are determined by the transverse profile of its dielectric constant ∈(x, y)/∈0, which is independent of the z coordinate. For a waveguide made of optically isotropic media, we can simply characterize the waveguide with a single spatially dependent transverse profile of the index of refraction, n(x, y).

In a nonplanar waveguide of two-dimensional transverse optical confinement, the core is surrounded by cladding in all transverse directions, and n(x, y) is a function of both x and y coordinates. The channel waveguides, discussed in Section 2.8, and the circular optical fibers, discussed in Chapter 3, are such waveguides.