Fundamentals of Nonlinear Optics

Fundamentals of Nonlinear Optics

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  • Illustrates how the theory and concepts of nonlinear optics are used in the laboratory
  • Explores important technological phenomena encountered in laboratories and commercial systems, including second harmonic generation, difference frequency generation, sum-frequency generation, and optical parametric oscillation
  • Offers in-depth coverage of phase matching and corresponding tolerances
  • Makes material accessible to readers without a background in quantum mechanics
  • Includes extensive end-of-chapter exercises

Solutions manual available with qualifying course adoption


Fundamentals of Nonlinear Optics encompasses a broad spectrum of nonlinear phenomena from second-harmonic generation to soliton formation. The wide use of nonlinear optical phenomena in laboratories and commercial devices requires familiarity with the underlying physics as well as practical device considerations. This text adopts a combined approach to analyze the complimentary aspects of nonlinear optics, enabling a fundamental understanding of both a given effect and practical device applications.

After a review chapter on linear phenomena important to nonlinear optics, the book tackles nonlinear phenomena with a look at the technologically important processes of second-harmonic generation, sum-frequency and difference-frequency generation, and the electro-optic effect. The author covers these processes in considerable detail at both theoretical and practical levels as the formalisms developed for these effects carry to subsequent topics, such as four-wave mixing, self-phase modulation, Raman scattering, Brillouin scattering, and soliton formation.

Consistently connecting theory, process, effects, and applications, this introductory text encourages students to master key concepts and to solve nonlinear optics problems—preparing them for more advanced study. Along with extensive problems at the end of each chapter, it presents general algorithms accessible to any scientific graphical and programming package.

Watch the author speak about the book.

Table of Contents

Historical Background
Unifying Themes
Overview of Nonlinear Effects Covered in this Book
Labeling Conventions and Terminology

Linear Optics
Tensor Properties of Materials
Wave Equation
Determining e-Waves and o-Waves in Crystals
Index Ellipsoid

Introduction to the Nonlinear Susceptibility
Classical Origin of the Nonlinearity
Details of the Nonlinear Susceptibility, χ(2)
Connection between Crystal Symmetry and the d-Matrix
Electro-Optic Effect

Three-Wave Processes in the Small-Signal Regime
Introduction to the Wave Equation for Three Fields
Birefringent Phase Matching
Tuning Curves and Phase-Matching Tolerances
Taylor Series Expansion Techniques for Determining Bandwidth
Noncollinear Phase Matching

Quasi-Phase Matching
Introduction to Quasi-Phase Matching
Linear and Nonlinear Material Considerations
QPM with Periodic Structures
QPM Calculation: An Example
Fourier Transform Treatment of QPM
Fabricating Quasi-Phase-Matched Structures

Three-Wave Mixing beyond the Small-Signal Limit
DFG with a Single Strong Pump
DFG with Strong Pump and Loss
Solutions for All Three Coupled Amplitude Equations
Spontaneous Parametric Scattering (Optical Parametric Generation)

χ(2) Devices
Optimizing Device Performance: Focusing
Resonator Devices

χ(3) Processes
Nonlinear Polarization for χ(3) Processes
Wave Equation for χ(3) Interactions
Self-Induced Effects
Parametric Amplifiers
Noncollinear Processes
Degenerate Four-Wave Mixing
Z -Scan

Raman and Brillouin Scattering
Spontaneous Raman Scattering
Stimulated Raman Scattering
Anti-Stokes Generation
Raman Amplifiers
Photoacoustic Effects: Raman–Nath Diffraction
Brillouin Scattering

Nonlinear Optics Including Diffraction and Dispersion
Spatial Effects
Temporal Effects
Solutions to the Nonlinear Envelope Equation

Appendix A: Complex Notation
Appendix B: Sellmeier Equations
Appendix C: Programming Techniques
Appendix D: Exact Solutions to the Coupled Amplitude Equations


Problems, References, and Further Reading appear at the end of most chapters.

Author Bio(s)

Peter E. Powers is a professor of physics and electro-optics and the Brother Leonard A. Mann Chair in the Sciences at the University of Dayton. Dr. Powers previously worked at Sandia National laboratories as a post-doctoral research associate. He earned a Ph.D. in applied and engineering physics from Cornell University. His research interests include nonlinear optics and its application to other branches of physics and applied physics.

Editorial Reviews

Peter Powers’s rigorous but simple description of a difficult field keeps the reader’s attention throughout. … All chapters contain a list of references and large numbers of practice examples to be worked through. … By carefully working through the proposed problems, students will develop a sound understanding of the fundamental principles and applications. … the book serves perfectly for an introductory-level course for second- and third-order nonlinear optical phenomena. The author’s writing style is refreshing and original. I expect that Fundamentals of Nonlinear Optics will fast become popular among students, professors, and professionals interested in basic and applied research in the field.
—Aristides Marcano, Physics Today, Vol. 65, October 2012

Fundamentals of Nonlinear Optics is well written and up to date. … The problem sets at the end of each chapter reinforce and enhance the material presented, and may give students confidence in handling real-world problems.
—Reva Garg, Optics & Photonics News, September 2012

This book fills a longstanding need for a nonlinear optics textbook at an advanced college/introductory graduate level. One of its best features is inclusion of many of the subtleties that are often glossed over in other books on the subject. … Another excellent feature is the provision of a large number of problems at the end of each chapter.
—Mark Cronin-Golomb, Tufts University, Medford, Massachusetts, USA

The book is very well written. I like very much his writing style. His choice of topics is excellent and the book is well organized. The problem sets are also well formulated to give the students confidence in handling real-world problems … . Professor Powers has mastered the subject matter.
—C.L. Tang, Cornell University, Ithaca, New York, USA

The author introduces key concepts in simplified terms, and then generalizes to realistic treatments that emphasize how the various equations are actually used in everyday practice. The diversity of specific topics, worked problems, and homework problems should make the book of interest to a wide audience.
—Jeff F. Young, University of British Columbia, Canada

This book is of great interest both to students and researchers wishing to develop or expand their knowledge of nonlinear optics. It contains details of derivations and practical implementation that are often missing from other texts. It also has extensive problems at the end of each chapter that reinforce and enhance the material presented.
—Marc Dignam, Queen’s University, Ontario, Canada

The author provides a sound, logically presented introduction to the subject with good coverage.
—Malcolm Dunn, University of St. Andrews, Scotland

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