This chapter is devoted to the study of dispersive effects that affect short pulses inside a graded-index fiber. An equation governing the evolution of optical pulses inside a GRIN medium is found in Section 4.1. The dispersion parameters appearing in this equation change, depending on which mode is being considered. Section 4.2 focuses on the distortion of optical pulses resulting from differential group delay and group velocity dispersion. Section 4.3 deals with the effects of linear coupling among the modes, occurring because of random variations in the core’s shape and size along a fiber’s length. A non-modal approach is developed in Section 4.4 for the propagation of short optical pulses inside a GRIN medium. The focus of Section 4.5 is on the applications where optical pulses are sent through a GRIN rod or fiber

This chapter focuses on photonic analog of the spin-orbit coupling of electrons occurring inside a graded index medium. Section 9.1 describes two physical mechanisms that can produce changes in the state of polarization of an optical beam. The vectorial form of the wave equation is solved in Section 9.2 to introduce a path-dependent geometrical phase. The photonic analog of the spin-orbit coupling and its implications are also discussed in this section. Section 9.3 considers how the scalar LPlm modes change when the coupling term is taken into account. We treat this term first as a perturbation and then obtain the exact vector modes of a GRIN medium. A quantum approach is used in Section 9.4 to discuss various polarization-dependent effects.

The focus of this chapter is on focusing and self-imaging of optical beams occurring in a graded-index rod. Section 3.1 provides a geometrical-optics perspective and shows why optical rays follow a curved path inside a GRIN medium. The modes of such a medium are used in Section 3.2 to find a propagation kernel and use it discuss the phenomenon of self-imaging. Section 3.3 is devoted to studying how a GRIN rod can be used as a flat lens to focus an incoming optical beam. Imaging characteristics of such a lens are also considered in this section. Several important applications of GRIN devices are discussed in Section 3.4.