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 generalisat...
| Main Authors: | , |
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| Format: | eBook |
| Language: | English |
| Published: |
Berlin, Heidelberg
Springer Berlin Heidelberg
1993, 1993
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| Edition: | 2nd ed. 1993 |
| Series: | Springer Series on Wave Phenomena
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| Subjects: | |
| Online Access: | |
| Collection: | Springer Book Archives -2004 - Collection details see MPG.ReNa |
Table of Contents:
- 1 Introduction
- 1.1 Caustic Fields in Physical Problems
- 1.2 The Geometrical Aspect of the Caustic Problem
- 1.3 The Wave Aspect of the Caustic Problem
- 2 Rays and Caustics
- 2.1 Equations of Geometrical Optics
- 2.2 The Role of Rays in the Method of Geometrical Optics
- 2.4 Complex Rays
- 3 Caustics as Catastrophes
- 3.1 Mappings Induced by Rays
- 3.2 Classification of Typical Caustics
- 4 Typical Integrals of Catastrophe Theory
- 4.1 Standard Caustic Integrals
- 4.2 The Airy Integral
- 4.3. The Pearcey Integral
- 4.4 Other Typical Integrals
- 5 Uniform Caustic Asymptotics Derived with Standard Integrals
- 5.1 Uniform Airy Asymptotic of a Scalar Field
- 5.2 Uniform Caustic Asymptotics Based on General Standard Integrals
- 5.3 Illustrative Examples
- 6 Maslov’s Method of the Canonical Operator
- 6.1 Principal Relationships
- 6.2 Specific Problems
- 6.3. Generalization by Using Fractional Transformations
- 7 Method of Interference Integrals
- 7.1 Ray Type Integrals
- 7.2 Caustic Integrals
- 7.3 Additional Topics and Generalizations
- 8 Penumbra Caustics
- 8.1 Broken Penumbra Caustics
- 8.2 Penumbra Caustics of Diffraction Rays
- 8.3 Penumbra Caustics and Edge Catastrophes
- 9 Modifications and Generalizations of Standard Integrals and Functions
- 9.1 Nonpolynomial Phase Standard Integrals
- 9.2 Structurally Unstable Caustics
- 9.3 Standard Integrals with Amplitude Correction
- 9.4 Reflection from a Barrier and Oscillations in a Potential Well
- 9.5 Standard Functions Induced by Ordinary Differential Equations
- 10 Caustics Revisited
- 10.1 Caustics in Dispersive Media
- 10.3 Complex Caustics
- 10.4 Random Caustics
- 10.5 Caustics in Quantum Mechanical Problems
- 10.6 Concluding Remarks
- References
- List of Symbols