Orbital Angular Momentum of Light: A Ray Optical Interpretation. Wigner Distributions Moments for Beam Characterization. Dynamic Programming: Applications in Optics. Basis Expansions for Monochromatic Field Propagation in Free Space. Solutions of Paraxial Equations and Families of Gaussian Beams. The Decomposition Method to Solve Differential Equations: Optical Applications. An Introduction to Mathematics of Transformational Plasmonics. Plasmonics: Computational Techniques. Lorentz Group in Ray and Polarization Optics. Paraxial Wave Equation: Lie Algebra-Based Approach. Dihedral Polynomials. Lie Algebra and Liouville Space Methods in Quantum Optics. From Classical to Quantum Light and Vice Versa. Coherence Functions in Quantum Optics. Quantum Memory Channels in Quantum Optics. An Introduction to Super-Resolution Imaging. The Differential Structure of Images.

Vasudevan Lakshminarayanan, María L. Calvo, Tatiana Alieva

Going beyond standard introductory texts, Mathematical Optics: Classical, Quantum, and Computational Methods brings together many new mathematical techniques from optical science and engineering research. Profusely illustrated, the book makes the material accessible to students and newcomers to the field.
Divided into six parts, the text presents state-of-the-art mathematical methods and applications in classical optics, quantum optics, and image processing.
Part I describes the use of phase space concepts to characterize optical beams and the application of dynamic programming in optical waveguides.
Part II explores solutions to paraxial, linear, and nonlinear wave equations.
Part III discusses cutting-edge areas in transformation optics (such as invisibility cloaks) and computational plasmonics.
Part IV uses Lorentz groups, dihedral group symmetry, Lie algebras, and Liouville space to analyze problems in polarization, ray optics, visual optics, and quantum optics.
Part V examines the role of coherence functions in modern laser physics and explains how to apply quantum memory channel models in quantum computers.
Part VI introduces super-resolution imaging and differential geometric methods in image processing.
As numerical/symbolic computation is an important tool for solving numerous real-life problems in optical science, many chapters include Mathematica® code in their appendices. The software codes and notebooks as well as color versions of the book's figures are available at www.crcpress.com.