Mathematical Theory Of Optics

This title is part of UC Press's Voices Revived program, which commemorates University of California Press’s mission to seek out and cultivate the brightest minds and give them voice, reach, and impact. Drawing on a backlist dating to 1893, Voices Revived makes high-quality, peer-reviewed scholarship accessible once again using print-on-demand technology. This title was originally published in 1964.

This title is part of UC Press's Voices Revived program, which commemorates University of California Press’s mission to seek out and cultivate the brightest minds and give them voice, reach, and impact. Drawing on a backlist dating to 1893, Voices Revived makes high-quality, peer-reviewed scholarship accessible once again using print-on-demand technology. This title was originally published in 1964.

In 1690, Christiaan Huygens (1629-1695) published Traité de la Lumière, containing his renowned wave theory of light. It is considered a landmark in seventeenth-century science, for the way Huygens mathematized the corpuscular nature of light and his probabilistic conception of natural knowledge. This book discusses the development of Huygens' wave theory, reconstructing the winding road that eventually led to Traité de la Lumière. For the first time, the full range of manuscript sources is taken into account. In addition, the development of Huygens' thinking on the nature of light is put in the context of his optics as a whole, which was dominated by his lifelong pursuit of theoretical and practical dioptrics. In so doing, this book offers the first account of the development of Huygens' mathematical analysis of lenses and telescopes and its significance for the origin of the wave theory of light. As Huygens applied his mathematical proficiency to practical issues pertaining to telescopes – including trying to design a perfect telescope by means of mathematical theory – his dioptrics is significant for our understanding of seventeenth-century relations between theory and practice. With this full account of Huygens' optics, this book sheds new light on the history of seventeenth-century optics and the rise of the new mathematical sciences, as well as Huygens' oeuvre as a whole. Students of the history of optics, of early mathematical physics, and the Scientific Revolution, will find this book enlightening.

A. Sommerfeld's "Mathematische Theorie der Diffraction" marks a milestone in optical theory, full of insights that are still relevant today. In a stunning tour de force, Sommerfeld derives the first mathematically rigorous solution of an optical diffraction problem. Indeed, his diffraction analysis is a surprisingly rich and complex mix of pure and applied mathematics, and his often-cited diffraction solution is presented only as an application of a much more general set of mathematical results. This complete translation, reflecting substantial scholarship, is the first publication in English of Sommerfeld's original work. The extensive notes by the translators are rich in historical background and provide many technical details for the reader.

This book is about the mathematical theory of light propagation in media on general-relativistic spacetimes. The first part discusses the transition from Maxwell's equations to ray optics. The second part establishes a general mathematical framework for treating ray optics as a theory in its own right, making extensive use of the Hamiltonian formalism. This part also includes a detailed discussion of variational principles (i.e., various versions of Fermat's principle) for light rays in general-relativistic media. Some applications, e.g. to gravitational lensing, are worked out. The reader is assumed to have some basic knowledge of general relativity and some familiarity with differential geometry. Some of the results are published here for the first time, e.g. a general-relativistic version of Fermat's principle for light rays in a medium that has to satisfy some regularity condition only.

"Mathematical Theory of Dispersion-Managed Optical Solitons" discusses recent advances covering optical solitons, soliton perturbation, optical cross-talk, Gabitov-Turitsyn Equations, quasi-linear pulses, and higher order Gabitov-Turitsyn Equations. Focusing on a mathematical perspective, the book bridges the gap between concepts in engineering and mathematics, and gives an outlook to many new topics for further research. The book is intended for researchers and graduate students in applied mathematics, physics and engineering and also it will be of interest to those who are conducting research in nonlinear fiber optics. Dr. Anjan Biswas is an Associate Professor at the Department of Applied Mathematics & Theoretical Physics, Delaware State University, Dover, DE, USA; Dr. Daniela Milovic is an Associate Professor at the Department of Telecommunications, Faculty of Electronic Engineering, University of Nis, Serbia; Dr. Matthew Edwards is the Dean of the School of Arts and Sciences at Alabama A & M University in Huntsville, AL, USA.