This chapter provides an introduction to the subject known as gradient-index optics. In Section 1.1, we present a historical perspective on this subject before introducing the essential concepts needed in later chapters. Section 1.2 is devoted to various types of refractive-index profiles employed for making gradient index devices, with particular emphasis to the parabolic index profile because of its practical importance. In Section 1.3, we discuss the relevant properties of such devices such as optical losses, chromatic dispersion, and intensity dependence of the refractive index occurring at high power levels. The focus of Section 1.4 is on the materials and the techniques used for fabricating gradient-index devices in the form of a rod or a thin fiber

This chapter focuses on the effects of loss or gain in a graded-index (GRIN) medium. In Section 6.1, we discuss the impact of losses on the modes of such a medium. Section 6.2 considers the mechanisms used for providing optical gain inside a GRIN medium. Section 6.3 is devoted to Raman amplifiers and Raman lasers, built with GRIN fibers and pumped suitably to provide optical gain. Parametric amplifiers are discussed in Section 6.4, together with the phase matching required for four-wave mixing to occur. The focus of Section 6.5 is on amplifiers and lasers made by doping a GRIN fiber with rare-earth ions. Section 6.6 includes the nonlinear effects and describes the formation of spatial solitons and similaritons inside an active GRIN medium.