Fundamentals of Nonlinear Optics

Description

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.

Features

• 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

Reviews

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

Table of Contents

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

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

• Introduction to the Nonlinear Susceptibility
• Introduction
• 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
• Tolerances
• Fabricating Quasi-Phase-Matched Structures

• Three-Wave Mixing beyond the Small-Signal Limit
• Introduction
• 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
• Introduction
• Optimizing Device Performance: Focusing
• Resonator Devices

• χ(3) Processes
• Introduction
• 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
• Introduction
• Spontaneous Raman Scattering
• Stimulated Raman Scattering
• Anti-Stokes Generation
• Raman Amplifiers
• Photoacoustic Effects: Raman–Nath Diffraction
• Brillouin Scattering

• Nonlinear Optics Including Diffraction and Dispersion
• Introduction
• 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

Author

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.