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.

There are basically two types of nonlinear optical frequency converters. The majority are based on parametric processes, which require phase matching. Devices that use the nonparametric third-order processes of stimulated Raman or Brillouin scattering to shift the optical frequency are the other type. In this chapter, only those based on parametric processes are considered. The first six sections cover practical optical frequency converters that are based on second-order parametric processes, including second-harmonic generation, sum-frequency generation, difference-frequency generation, optical parametric up-conversion, optical parametric down-conversion, optical parametric amplification, optical parametric generation, and optical parametric oscillation. Frequency conversion based on the third-order parametric four-wave mixing of small frequency shifts is discussed in Section 10.7. The generation of high-order harmonics is discussed in Section 10.8.