This book offers the first comprehensive introduction to the optical properties of the catenary function, and includes more than 200 figures. Related topics addressed here include the photonic spin Hall effect in inhomogeneous anisotropic materials, coupling of evanescent waves in complex structures, etc. After familiarizing readers with these new physical phenomena, the book highlights their applications in plasmonic nanolithography, flat optical elements, perfect electromagnetic absorbers and polarization converters. The book will appeal to a wide range of readers: while researchers will find new inspirations for historical studies combining mechanics, mathematics, and optics, students will gain a wealth of multidisciplinary knowledge required in many related areas. In fact, the catenary function was deemed to be a "true mathematical and mechanical form" in architecture by Robert Hooke in the 1670s. The discovery of the mathematical form of catenaries is attributed to Gottfried Leibniz, Christiaan Huygens and Johann Bernoulli in 1691. As the founders of wave optics, however, Hooke and Huygens did not recognize the importance of catenaries in optics. It is only in recent decades that the link between catenaries and optics has been established.