The Mathematics of Geometrical and Physical Optics
The k-function and its Ramifications
1. Auflage Mai 2006
XIV, 226 Seiten, Hardcover
38 Abbildungen
Monographie
Kurzbeschreibung
Mathematische Grundlagen der Strahlen- und Wellenoptik diskutiert dieser übersichtlich in drei Teile gegliederte Band. Der erste Teil ist den im Buch angewendeten mathematischen Formalismen gewidmet. Im zweiten Teil wird die k-Funktion eingeführt, Eikonal und maxwellsche Gleichungen werden gelöst und diskutiert. Schlussfolgerungen und Anwendungen stellt der dritte Teil vor, zu dessen Themen unter anderem das kartesische Oval, das huygenssche Prinzip sowie das maxwellsche Modell der idealen gaußschen Linse gehören.
In this sequel to his book, "The Optics of Rays, Wavefronts, and Caustics," Stavroudis not only covers his own research results, but also includes more recent developments. The book is divided into three parts, starting with basic mathematical concepts that are further applied in the book. Surface geometry is treated with classical mathematics, while the second part covers the k-function, discussing and solving the eikonal equation as well as Maxwell equations in this context. A final part on applications consists of conclusions drawn or developed in the first two parts of the book, discussing such topics as the Cartesian oval, the modern Schiefspiegler, Huygen's principle, and Maxwell's model of Gauss' perfect lens.
1. Calculus of Variations
2. Calculus of Variations: Differential Geometry of Space Curves (Helix and Ellipse)
3. Fermat's Principle and the Ray Equation for Inhomogeneous Isotropic Media
4. Hilber Integral, the Derivation of the Hamilton-Jacobi Theory, and the Eikonal Equation
5. First-order Partial Differential Equations
Part II: The k-Function
6. Calculation of Surface Differential Geometry Parameters
7. Ray Tracing
8. Refraction of Wavefronts at Surfaces
9. Solution of the Maxwell Equation in the Context of the k-function
Part III: Applications
10. Pseudo Maxwell Equations
11. Derivation and Discussion of the Cartesian Oval
12. The Modern Schiefspiegler
13. Huygen's Principle
14. Maxwell's Model of Gauss' Perfect Lens