1st Edition

Waves in Focal Regions Propagation, Diffraction and Focusing of Light, Sound and Water Waves

By J.J Stamnes Copyright 1986

    Using numerous mathematical and numerical techniques of diffraction theory, Waves in Focal Regions: Propagation, Diffraction and Focusing of Light, Sound and Water Waves provides a full and richly illustrated description of waves in focal regions. Unlike most books, the author treats electromagnetic, acoustic, and water waves in one comprehensive volume.

    After an introductory section, the book describes approximate diffraction theories and efficient numerical methods to study the focusing of various kinds of waves. It then covers the physical interpretation of the theories, their accuracy, and the computational savings obtained, emphasizing uniform asymptotic results that remain valid in the vicinity of shadow boundaries and caustics. The next part deals with the focusing of scalar waves, including thorough theoretical analyses and detailed contour maps of diffraction patterns in focal regions for a variety of different system parameters, such as f-number, Frensel number, aperture shape, amplitude distribution, and wavefront aberration. The author proceeds to explore the diffraction and focusing of electromagnetic waves. First solutions are derived for fields radiated by sources, reflected and refracted at plane interfaces, or diffracted by apertures in plane screens, and then these solutions are applied to study the focusing in homogeneous media and through a plane dielectric interface. In both cases, the author includes many computed results of the electromagnetic field distribution near focus. Presenting both theoretical and experimental results, the following part examines the focusing of sound and water waves by means of zone-plate lenses. The book concludes with a detailed study of the diffraction and focusing of water waves and a comparison of the results of both linear and nonlinear theories with those of experiments.

    INTRODUCTION TO IMAGE FORMATION AND FOCUSING
    Brief history
    Applications
    Combined method of ray tracing and diffraction

    DIFFRACTION OF SCALAR WAVES
    Diffraction of three-dimensional waves
    Diffraction of two-dimensional waves
    Ray connection of Huygens principle
    Numerical methods for evaluating diffraction integrals

    ASYMPTOTIC THEORIES OF DIFFRACTION
    Method of stationary phase for single integrals
    Method of stationary phase for double integrals
    Asymptotic theory of diffraction for two-dimensional waves
    Asymptotic theory of diffraction for three-dimensional waves

    FOCUSING OF SCALAR WAVES
    Three-dimensional waves
    Two-dimensional waves
    Computation of focused fields

    DIFFRACTION AND FOCUSING OF ELECTROMAGNETIC WAVES
    Diffraction theory
    Focusing problems

    ZONE-PLATE LENSES OF SOUND
    Zone-plate lenses for sound waves in water
    Zone-plate lens for focusing of ocean swells

    FOCUSING OF WATER WAVES
    Linear waves
    Nonlinear waves

    REFERENCES
    INDEX

    Biography

    Stamnes, J.J