xiv PREFACE important laser-matter interactions may usually be viewed as instantaneous.Extreme nonlinear optics phenomena,arising from high-intensity laser-matter interactions for which the laser field reaches or exceeds the interatomic field,are not covered.One important ex- ample of extreme nonlinear optics is high harmonic generation,in which visible wavelength femtosecond pulses result in emission of photons in the vacuum ultraviolet(XUV)and soft x-ray bands.The use of high harmonic generation to realize attosecond pulses has become an active research topic within the last few years.Attosecond time scales and XUV and x-ray frequencies bring in entirely new physics that are beyond the scope of this book. Attosecond technology and science are in a stage of rapid evolution and will undoubtedly be the subject of future treatises. The structure of the book is as follows: Chapter 1 begins with a brief overview and motivation,discussing key attributes of ultrashort laser pulses and some application examples.Important background material, including simple electromagnetics and laser essentials,is reviewed.The chapter contin- ues with a phenomenological introduction to short pulse generation via mode-locking and concludes with a review of Fourier transforms,a mathematical tool essential to much of our treatment. Chapter 2 covers basic principles of laser mode-locking in some depth.The intent is not only to cover one of the most interesting topics at the outset,but to use the discussion on mode-locking as a physical context in which to introduce a variety of important ultrafast optical effects(e.g.,dispersion,filtering,self-phase modulation). many of which are themselves treated in detail in subsequent chapters. .Measurement of pulses on the femtosecond time scale is an important issue,since the speed required is considerably faster than that of existing photodetectors and oscillo- scopes.In Chapter 3 we discuss methods for characterizing ultrashort pulses.Included are historical techniques dating back to the early years of ultrafast optics (these offer only partial information but remain in widespread use)as well as more powerful tech- niques offering full waveform information.The field of ultrashort pulse characteri- zation has continued to grow,and new techniques continue to be introduced.I have not attempted to cover all the interesting measurement techniques that have been in- vented.My hope is that the discussion accompanying those methods that are included will prepare the reader to quickly grasp additional methods that may interest him or her. Dispersion is often a key limiting effect in ultrafast systems.Accordingly,in Chap- ter 4 we focus on dispersion and its compensation.After defining key concepts,the discussion covers material dispersion,then temporal dispersion arising from angular dispersion (including important grating and prism pair setups),and finally,dispersion effects in mirror structures.The effect of dispersion in the focusing of light by lenses is also discussed,as are methods for measurement of dispersion. Chapters 5 and 6 deal with ultrafast nonlinear optics.Chapter 5 emphasizes second- order nonlinear effects.After an introduction to nonlinear optics and a review of continuous-wave second-harmonic generation (SHG),new effects arising in ultra- short pulse SHG,sum and difference frequency generation,and optical parametric generation are discussed.Such effects are of primary interest in frequency conver- sion and pulse measurement applications.Chapter 6 focuses on refractive index(third- order)nonlinearities,which have seen very wide applications in ultrafast optics.Topicsxiv PREFACE important laser–matter interactions may usually be viewed as instantaneous. Extreme nonlinear optics phenomena, arising from high-intensity laser–matter interactions for which the laser field reaches or exceeds the interatomic field, are not covered. One important ex￾ample of extreme nonlinear optics is high harmonic generation, in which visible wavelength femtosecond pulses result in emission of photons in the vacuum ultraviolet (XUV) and soft x-ray bands. The use of high harmonic generation to realize attosecond pulses has become an active research topic within the last few years. Attosecond time scales and XUV and x-ray frequencies bring in entirely new physics that are beyond the scope of this book. Attosecond technology and science are in a stage of rapid evolution and will undoubtedly be the subject of future treatises. The structure of the book is as follows: Chapter 1 begins with a brief overview and motivation, discussing key attributes of ultrashort laser pulses and some application examples. Important background material, including simple electromagnetics and laser essentials, is reviewed. The chapter contin￾ues with a phenomenological introduction to short pulse generation via mode-locking and concludes with a review of Fourier transforms, a mathematical tool essential to much of our treatment. Chapter 2 covers basic principles of laser mode-locking in some depth. The intent is not only to cover one of the most interesting topics at the outset, but to use the discussion on mode-locking as a physical context in which to introduce a variety of important ultrafast optical effects (e.g., dispersion, filtering, self-phase modulation), many of which are themselves treated in detail in subsequent chapters. Measurement of pulses on the femtosecond time scale is an important issue, since the speed required is considerably faster than that of existing photodetectors and oscillo￾scopes. In Chapter 3 we discuss methods for characterizing ultrashort pulses. Included are historical techniques dating back to the early years of ultrafast optics (these offer only partial information but remain in widespread use) as well as more powerful tech￾niques offering full waveform information. The field of ultrashort pulse characteri￾zation has continued to grow, and new techniques continue to be introduced. I have not attempted to cover all the interesting measurement techniques that have been in￾vented. My hope is that the discussion accompanying those methods that are included will prepare the reader to quickly grasp additional methods that may interest him or her. Dispersion is often a key limiting effect in ultrafast systems. Accordingly, in Chap￾ter 4 we focus on dispersion and its compensation. After defining key concepts, the discussion covers material dispersion, then temporal dispersion arising from angular dispersion (including important grating and prism pair setups), and finally, dispersion effects in mirror structures. The effect of dispersion in the focusing of light by lenses is also discussed, as are methods for measurement of dispersion. Chapters 5 and 6 deal with ultrafast nonlinear optics. Chapter 5 emphasizes second￾order nonlinear effects. After an introduction to nonlinear optics and a review of continuous-wave second-harmonic generation (SHG), new effects arising in ultra￾short pulse SHG, sum and difference frequency generation, and optical parametric generation are discussed. Such effects are of primary interest in frequency conver￾sion and pulse measurement applications. Chapter 6 focuses on refractive index (third￾order) nonlinearities, which have seen very wide applications in ultrafast optics. Topics