Published online by Cambridge University Press: 03 May 2011
An integral feature of any optical amplifier is the interaction of light with the material used to extract the energy supplied to it by an external pumping source. In nearly all cases, the medium in which such interaction takes place can be classified as a dielectric medium. Therefore, a clear understanding of how light interacts with active and passive dielectric media of finite dimensions is essential for analyzing the operation of optical amplifiers. When light enters such a finite medium, its behavior depends on the global properties of the entire medium because of a discontinuous change in the refractive index at its boundaries. For example, the transmissive and reflective properties of a dielectric slab depend on its thickness and vary remarkably for two slabs of different thicknesses even when their material properties are the same .
In this chapter we focus on propagation of light through a dispersive dielectric slab, exhibiting chromatic dispersion through its frequency-dependent refractive index. Even though this situation has been considered in several standard textbooks [2, 3], the results of this chapter are more general than found there. We begin by discussing the state of polarization of optical waves in Section 2.1, followed with the concept of impedance in Section 2.2. We then devote Section 2.3 to a thorough discussion of the transmission and reflection coefficients of a dispersive dielectric slab in the case of a CW plane wave. Propagation of optical pulses through a passive dispersive slab is considered in Section 2.4, where we also provide simple numerical algorithms.