Mathematical Optics: Classical, Quantum, and Computational Methods

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ISBN 9781439869604
Cat# K13194



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  • Illustrates the power of mathematics to elucidate underlying physical ideas
  • Deals with various mathematical formalisms used in wave optics
  • Explores current research and technological advances in plasmonics
  • Describes the powerful methods of group theory and modern quantum optics
  • Covers super-resolution imaging and differential geometric methods in image processing
  • Includes many examples and exercises
  • Provides Mathematica® codes and color figures at


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

Table of Contents

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


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Resource OS Platform Updated Description Instructions Cross Platform August 07, 2012 Figures Cross Platform August 07, 2012 Additional Materials