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Caustic Light in Nonlinear Photonic Media
Caustics are natural phenomena, forming light patterns in rainbows or through drinking glasses, and creating light networks at the bottom of swimming pools. Only in recent years have scientists started to artificially create simple caustics with laser light. However, these realizations have already contributed to progress in advanced imaging, lithography, and micro-manipulation. In this book, Alessandro Zannotti pioneers caustics in many ways, establishing the field of artificial caustic optics. He employs caustic design to customize high-intensity laser light. This is of great relevance for laser-based machining, sensing, microscopy, and secure communication. The author also solves a long standing problem concerning the origin of rogue waves which appear naturally in the sea and can have disastrous consequences. By means of a far-reaching optical analogy, he identifies scattering of caustics in random media as the origin of rogue waves, and shows how nonlinear light-matter interaction increases their probability.
The Optics of Rays, Wavefronts, and Caustics
The Optics of Rays, Wavefronts, and Caustics presents the fundamental principles of geometrical optics and its unique role in modern technology. It also discusses the procedures used in optical design, which are based on geometrical optics. Organized into 16 chapters, this volume begins with an overview of the underlying general mathematical facts, which constitute the substance of geometrical optics. It then presents the various techniques used to solve the ray and wavefront problems in general inhomogeneous medium. Other chapters consider the concept of ray tracing as a tool for calculating the principal curvatures of a wavefront as it propagates through a lens. In addition, the book tackles several topics, including the aspects of lens design, as well as a system of equations that are similar to the Maxwell equations. The last chapter deals with orthotomic systems of rays. Optical designers, optical physicists, theoretical physicists, and mathematicians will find the information and methods in this book extremely useful.
Caustics, Catastrophes and Wave Fields
Caustics, Catastrophes and Wave Fields in a sense continues the treatment of the earlier volume 6 "Geometrical Optics of Inhomogeneous Media" in the present book series, by analysing caustics and their fields on the basis of modern catastrophe theory. This volume covers the key generalisations of geometrical optics related to caustic asymptotic expansions: The Lewis-Kravtsov method of standard functions, Maslov's method of caonical operators, Orlov's method of interference integrals, as well as their modifications for penumbra, space-time, random and other types of caustics. All the methods are amply illustrated by worked problems concerning relevant wave-field applications.
Natural Focusing and Fine Structure of Light
A new kind of optics has grown up during the last 25 years. Geometrical optics has been studied for centuries (the law of reflection was known to the ancient Greeks) and wave optics (heralded by Huygens' Treatise on Light) has been studied for more than 300 years. But in the mid 1970s it began to be understood that when natural processes focus light, as when sunlight is reflected from the sea at sunset, the light caustics that are produced have a systematic behavior previously unrecognized. Natural Focusing and Fine Structure of Light: Caustics and Wave Dislocations provides a definitive account of how classical optics has been reconstructed in a modern way by emphasizing the hierarchy of singularities that exists in light fields. The book discusses the singularities of geometrical optics and their systematization by catastrophe theory. It explores the diffraction patterns associated with caustics that are dominated by wave dislocations, line singularities of the phase, and analogous to crystal dislocations. The book is a perfect blend of mathematics and physics, combining theory, computer simulation, and beautiful experimental photographs of the phenomena studied.
Caustics, Catastrophes and Wave Fields
The second edition of Histological Typing of Salivary Gland Tumours is more extensive and detailed than the previous edition. New technical methods haveincreased our understanding of many tumours. The various types of carcinomas are categorized separately and the inclusion of the TNM Classification of salivary gland tumours and the more detailed description of the lesions will contribute to a better understanding.
Caustics, Catastrophes and Wave Fields
Caustics, Catastrophes and Wave Fields in a sense continues the treatment of the earlier volume 6 "Geometrical Optics of Inhomogeneous Media" by analysing caustics and their fields on the basis of modern catastrophe theory. The present volume covers local and uniform caustic asymptotic expansions: The Lewis-Kravtsov method of standard functions, Maslov's method of canonical operators , Orlov's method of interference integrals, as well as their modifications for penumbra, space-time, random and other types of caustics. All the methods are amply illustrated by worked problems concerning relevant wave-field applications.
Singularities of Caustics and Wave Fronts
One service mathematics has rendered the 'Et moi ...) si j'avait su comment en revenir, human race. It has put common sense back je n'y serais point aile.' Jules Verne where it belongs, on the topmost shelf next to the dusty canister labelled 'discarded non The series is divergent; therefore we may be sense'. ErieT. Bell able to do something with it. O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series.
