Linear Ray and Wave Optics in Phase Space, Second Edition, is a comprehensive introduction to Wigner optics. The book connects ray and wave optics, offering the optical phase space as the ambience and the Wigner function based technique as the mathematical machinery to accommodate between the two opposite extremes of light representation: the localized ray of geometrical optics and the unlocalized wave function of wave optics. Analogies with other branches of classical and quantum physics-such as classical and quantum mechanics, quantum optics, signal theory and magnetic optics-are evidenced by pertinent comments and/or rigorous mathematics.
Lie algebra and group methods are introduced and explained through the elementary optical systems within the ray and wave optics contexts, the former being related to the symplectic group and the latter to the metaplectic group. In a similar manner, the Wigner function is introduced by following the original issue to individualize a phase space representation of quantum mechanics, which is mirrored by the issue to individualize a local frequency spectrum within the signal theory context.
The basic analogy with the optics of charged particles inherently underlying the ray-optics picture in phase space is also evidenced within the wave-optics picture in the Wigner phase space. This second edition contains 150 pages of new material on Wigner distribution functions, ambiguity functions for partially coherent beams, and phase-space picture and fast optics. All chapters are fully revised and updated. All topics have been developed to a deeper level than in the previous edition and are now supported with Mathematica and Mathcad codes.
- Provides powerful tools to solve problems in quantum mechanics, quantum optics and signal theory
- Includes numerous examples supporting a gradual and comprehensive introduction to Wigner optics
- Treats both ray and wave optics, resorting to Lie-algebra based methods
- Connects the subject with other fields, such as quantum optics, quantum mechanics, signal theory and optics of charged particles
- Introduces abstract concepts through concrete examples
- Includes logical diagrams to introduce mathematics in an intuitive way
- Contains 150 pages of new material on Wigner distribution functions, ambiguity functions for partially coherent beams, and phase-space picture and fast optics
- Supported with Mathematica and Mathcad codes
2. 1D first-order optical systems: The ray transfer matrix
3. The group of the 1D first-order optical systems
4. Wave-optical picture of first-order optical systems
5. 1D first order optical systems: The Huygens-Fresnel integral
6. The Wigner distribution function: The analytical evaluation
7. The Wigner distribution function: Optical production
8. 1D first order optical systems: Transfer law for the Wigner distribution function
9. 1D first order optical systems: Moments of the Wigner distribution function
10. Wigner distribution function and Ambiguity function for partially coherent beams
11. Phase-space picture and fast optics
Amalia Torre received her degree in physics at the University of Naples. She is a member of the Theory Group of the Department of Applied Physics at the ENEA Research Center of Frascati, Rome. Her research interests include Free Electron Laser, optics and special functions. She is presently involved in two research projects concerning the Extreme Ultra-Violet Lithography (FIRB project) and the X-ray production via Free Electron Laser operation (SPARC project).