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Optical materials with varying refractive indices are called graded-index (GRIN) media and they are widely used within many industries, including telecommunications and medical imaging. Another recent application is space division multiplexing, an enormously improved technique for optical data transmission. This book synthesises recent research developments in this growing field, presenting both the underlying physical principles behind optical propagation in GRIN media, and the most important engineering applications. The principles of wave optics are employed for solving Maxwell's equations inside a GRIN medium, ensuring that diffractive effects are fully included. The mathematical development builds gradually and a variety of exact and approximate techniques for solving practical problems are included, in addition to coverage of modern topics such as optical vortices, photonic spin-orbit coupling, photonic crystals, and metamaterials. This text will be useful for graduate students and researchers working in optics, photonics and optical communications.