Geometrical Optics of Inhomogeneous Media

Geometrical Optics of Inhomogeneous Media presents a systematic treatment of geometrical optics, the most effective and widely used method of wave theory. The treatment includes the major developments of recent decades, among them the space-time geometrical optics of dispersive media, the quasi-isotropic approximation, new perturbation techniques for rays, and universally valid limits of applicability.

This monograph is concerned with the fundamentals of up-to-date geo metrical optics treated as an approximate method of wave theory. Geometrical optics has changed dramatically over the last two decades. Primarily, it has acquired a number of novel disciplines: space-time geo metrical optics, the quasi-isotropic approximation, the modern theory of caustics related to catastrophe theory, and perturbation techniques for rays, to name only a few. Another acquisition is the reliable boundaries of appli cability for geometrical optics, based upon the concept of the Fresnel volume for a ray. These recent additions to the field are the focus of dis cussion in the book. We did not attempt to separate study-oriented and illustrative material from that intended for professionals, but rather we spread it throughout the text to facilitate for the reader the mastering of this attractive, intuitively appealing and efficient ray method. In preparing the manuscript we used a set of lecture notes devised for All-Union Schools on Diffraction and Wave Propagation, published in Rus sian. Sections 2.1-4,6 and 10 result from joint efforts of both authors. The other material of the book we wrote separately. I contributed Sects. 2.5,9 and 3.17 and Chap.4; Yu.l. Orlov prepared the rest. Unfortunately, he could not take part in the preparation of the English edition, as he died in 1982 at the age of 41, on the verge of what would have been great achieve ments considering his strong and original talent.

Geometrical Optics of Inhomogeneous Media presents a systematic treatment of geometrical optics, the most effective and widely used method of wave theory. The treatment includes the major developments of recent decades, among them the space-time geometrical optics of dispersive media, the quasi-isotropic approximation, new perturbation techniques for rays, and universally valid limits of applicability.

1. Introduction.- 2. The Scalar Wave Field.- 2.1 Equations of Geometrical Optics.- 2.2 Rays and the Eikonal.- 2.3 Wave Amplitude.- 2.4 Caustics.- 2.5 Reflection and Refraction of Waves at Interfaces.- 2.6 Reciprocity of Rays and Caustics.- 2.7 Space-Time Geometrical Optics.- 2.8 Separation of Variables in the Eikonal Equation.- 2.9 Perturbation Techniques for Geometrical-Optics Equations.- 2.10 Applicability of Geometrical Optics.- 3. Applications of the Ray Methods.- 3.1 Waves in Homogeneous Media.- 3.2 Reflection and Refraction at an Interface Between Homogeneous Media.- 3.3 Rays and Caustics in Plane-Stratified Media.- 3.4 Wave Fields in Plane-Stratified Media.- 3.5 Waves in Radially Inhomogeneous Media.- 3.6 Tapered and Other Inhomogeneous Media.- 3.7 Geometrical Optics of Waveguides and Resonators.- 3.8 Wave Scattering at Localized Inhomogeneities.- 3.9 Pulse Propagation.- 3.10 Numerical Methods in the Geometrical Optics of Inhomogeneous Media.- 3.11 Inverse Problems of Geometrical Optics.- 4. Vector Wave Fields.- 4.1 Transverse Electromagnetic Waves in Isotropic Media.- 4.2 Independent Normal Waves in an Anisotropic Medium.- 4.3 Interaction of Normal Modes in Inhomogeneous Anisotropic Media.- 4.4 Equations of Geometrical Optics for Nonharmonic Electromagnetic Waves in the General Case of Inhomogeneous and Nonstationary Dispersive Media.- 4.5 Constitutive Equations for Nonstationary and Inhomogeneous Dispersive Media. Existence of Adiabatic Invariance.- 4.6 Wave Processes in Nonstationary Media.- 5. Conclusion.- References.