Fundamentals Of Nonlinear Optics

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.

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.

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

Index

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