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Topology is the study of properties of geometrical objects that remain invariant as the object is bent, twisted, or otherwise continuously deformed. It has been an indispensable tool in particle physics and solid state physics for decades, but in recent years it has become increasingly relevant in classical and quantum optics as well. It makes appearances through such diverse phenomena as Pancharatnam-Berry phases, optical vortices and solitons, and optical simulations of solid-state topological phenomena. This book concisely provides the necessary mathematical background needed to understand these developments and to give a rapid survey of some of the optical applications where topological issues arise.

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From science fiction death rays to supermarket scanners, lasers have become deeply embedded in our daily lives and our culture. But in recent decades the standard laser beam has evolved into an array of more specialized light beams with a variety of strange and counterintuitive properties. Some of them have the ability to reconstruct themselves after disruption by an obstacle, while others can bend in complicated shapes or rotate like a corkscrew. These unusual optical effects open new and exciting possibilities for science and technology. For example, they make possible microscopic tractor beams that pull objects toward the source of the light, and they allow the trapping and manipulation of individual molecules to construct specially-tailored nanostructures for engineering or medical use. It has even been found that beams of light can produce lines of darkness that can be tied in knots. This book is an introductory survey of these specialized light beams and their scientific applications, at a level suitable for undergraduates with a basic knowledge of optics and quantum mechanics. It provides a unified treatment of the subject, collecting together in textbook form for the first time many topics currently found only in the original research literature.

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