The idea for writing this book crystallized from an interest in methods of short-wave asymptotics and symplectic geometry. Later followed a course about theoretical optics, which gave
me great pleasure. This pleasure turned out to be lasting, and so the present book arose from
several revisions and extensions of the original manuscript.
Indeed, there are many reasons to present the venerable and traditional field of optics in a
new form. The discovery of lasers, the steady progress of powerful data-processing systems,
and the development of new materials with unusual optical properties have all revolutionized
the field of optics.
Lasers are light sources of unprecedented intensity and coherence, without which such
new branches as nonlinear optics and holography would have been impossible. Computer
technology allows the processing of optical signals and the construction of diffractive optical
devices, which have already taken their place next to common lenses and mirrors. Glass-fiber
cables, compact disks, and simple holograms are proof that the products of the new kind of
optics have already entered our daily life.
However, not only have experimental physics and technology experienced rapid progress,
but also we have seen the development and application of new theoretical methods in optics:
The modern theory of nonlinear dynamical systems has found many applications in nonlinear optics. Here we meet bifurcation and chaotic behavior as well as dispersion-free solutions
of nonlinear integrable systems.
The adoption of the concepts and methods from the theory of stochastic processes for the
description of fluctuating light wave fields turned out to be extremely fruitful. In this way,
stochastic optics became a new branch of theoretical optics; the notion of coherence found
a more profound formulation, and today applications for image processing and correlation
spectroscopy have become standard routines.
Progress in the theory of short-wave asymptotics within the framework of symplectic geometry not only led to an improvement of the WKB method and to a better understanding of
the quasi-classical limit of quantum mechanics, but “symplectic optics” also allows a deeper
insight into the geometrical structures of the realm between wave optics and ray optics, into
the nature of caustics, and into the theory of diffraction.
These overwhelming developments in the applications and the theory of optics have led
to a considerable number of publications in recent years. However, these presentations, often written in the form of an experimental textbook, either provide a summary of methods,
phenomena, and applications of modern optics, or they describe, in the form of a monograph,
special parts of experimental, applied, or theoretical optics.