1st Edition

Mathematical Optics Classical, Quantum, and Computational Methods

    630 Pages 188 B/W Illustrations
    by CRC Press

    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.

    Special Problems in Ray Optics
    Orbital Angular Momentum: A Ray Optical Interpretation, M. Padgett
    Wigner Distributions Moments for Beam Characterization, T. Alieva, A. Camara, and M.J. Bastiaans
    Dynamic Programming Applications in Optics, M.L. Calvo, J. Perez-Rios, and V. Lakshminarayanan

    Mathematical Formalism in Wave Optics
    Basis Expansions for Monochromatic Field Propagation in Free Space, M.A. Alonso and N.J. Moore
    Solutions of Paraxial Equations and Families of Gaussian Beams, E. Abramochkin, T. Alieva, and J.A. Rodrigo
    The Decomposition Method to Solve Differential Equations: Optical Applications, V. Lakshminarayanan and S. Nandy

    An Introduction to Mathematics of Transformational Plasmonics, M. Kadic, S. Guenneau, and S. Enoch
    Plasmonics: Computational Approach, M. Sukharev

    Applications of Group Theory in Optics
    Lorentz Group in Ray and Polarization Optics, S. Baskal and Y.S. Kim
    Paraxial Wave Equation: Lie Algebra-Based Approach, A. Torre
    Dihedral Polynomials, M. Viana
    Lie Algebra and Liouville Space Methods in Quantum Optics, M. Ban

    Quantum Optics Methods
    From Classical to Quantum Light and Vice Versa: Quantum Phase-Space Methods, A. Luis
    Coherence Functions in Classical and Quantum Optics, I. Ashraf Zahid and V. Lakshmianrayanan
    Quantum Memory Channels in Quantum Optics, T. Rybar, M. Zyman, and V. Buzek

    Computational Optics/Image Processing
    An Introduction to Super-Resolution Imaging, J.D. Simpkins and R.L. Stevenson
    The Differential Structure of Images, B.M. ter Haar Romeny



    Vasudevan Lakshminarayanan, María L. Calvo, Tatiana Alieva