Following the birth of the laser in 1960, the field of "nonlinear optics" rapidly emerged. Today, laser intensities and pulse durations are readily available, for which the concepts and approximations of traditional nonlinear optics no longer apply. In this regime of "extreme nonlinear optics," a large variety of novel and unusual effects arise, for example frequency doubling in inversion symmetric materials or high-harmonic generation in gases, which can lead to attosecond electromagnetic pulses or pulse trains. Other examples of "extreme nonlinear optics" cover diverse areas such as solid-state physics, atomic physics, relativistic free electrons in a vacuum and even the vacuum itself. This book starts with an introduction to the field based primarily on extensions of two famous textbook examples, namely the Lorentz oscillator model and the Drude model. Here the level of sophistication should be accessible to any undergraduate physics student. Many graphical illustrations and examples are given. The following chapters gradually guide the student towards the current "state of the art" and provide a comprehensive overview of the field. Every chapter is accompanied by exercises to deepen the reader's understanding of important topics, with detailed solutions at the end of the book.

Over the last few years, there has been a convergence between the fields of ultrafast science, nonlinear optics, optical frequency metrology, and precision laser spectroscopy. These fields have been developing largely independently since the birth of the laser, reaching remarkable levels of performance. On the ultrafast frontier, pulses of only a few cycles long have been produced, while in optical spectroscopy, the precision and resolution have reached one part in Although these two achievements appear to be completely disconnected, advances in nonlinear optics provided the essential link between them. The resulting convergence has enabled unprecedented advances in the control of the electric field of the pulses produced by femtosecond mode-locked lasers. The corresponding spectrum consists of a comb of sharp spectral lines with well-defined frequencies. These new techniques and capabilities are generally known as “femtosecond comb technology. ” They have had dramatic impact on the diverse fields of precision measurement and extreme nonlinear optical physics. The historical background for these developments is provided in the Foreword by two of the pioneers of laser spectroscopy, John Hall and Theodor Hänsch. Indeed the developments described in this book were foreshadowed by Hänsch’s early work in the 1970s when he used picosecond pulses to demonstrate the connection between the time and frequency domains in laser spectroscopy. This work complemented the advances in precision laser stabilization developed by Hall.

In the major part of this Thesis, we discuss the linear THz response of semiconductor nanostructures based on a microscopic theory. Here, two different problems are investigated: intersubband transitions in optically excited quantum wells and the THz plasma response of two-dimensional systems. In the latter case, we analyze the response of correlated electron and electron-hole plasmas. Extracting the plasma frequency from the linear response, we find significant deviations from the commonly accepted two-dimensional plasma frequency. Besides analyzing the pure plasma response, we also consider an intermediate regime where the response of the electron-hole plasma consists of a mixture of plasma contributions and excitonic transitions. A quantitative experiment-theory comparison provides novel insights into the behavior of the system at the transition from one regime to the other. The discussion of the intersubband transitions mainly focuses on the coherent superposition of the responses from true THz transitions and the ponderomotively accelerated carriers. We present a simple method to directly identify ponderomotive effects in the linear THz response. Apart from that, the excitonic contributions to intersubband transitions are investigated. The last part of the present Thesis deals with a completely different regime. Here, the extreme nonlinear optical response of low-dimensional semiconductor structures is discussed. Formally, extreme nonlinear optics describes the regime of light-matter interaction where the exciting field is strong enough such that the Rabi frequency is comparable to or larger than the characteristic transition frequency of the investigated system. Here, the Rabi frequency is given by the product of the electrical field strength and the dipole-matrix element of the respective transition. Theoretical investigations have predicted a large number of novel nonlinear effects arising for such strong excitations. Some of them have been observed in exper.

Enhancement cavities are passive optical resonators in which continuous-wave laser radiation or pulses of a frequency comb are coherently overlapped, allowing for a power and intensity scaling of up to several orders of magnitude. A prominent application is the table-top generation of bright, laser-like radiation in spectral regions where direct laser action is inefficient or not available at all, via intracavity nonlinear optical processes. However, to exploit the full capacity of this technique further progress is needed. This thesis covers central problems of enhancement cavities, such as finding limitations in scaling the circulating power, measuring cavity parameters with high accuracy, tailoring transverse modes and coupling out radiation generated in the cavity. Unprecedented intracavity laser powers were demonstrated, surpassing previous results by an order of magnitude. As an application, harmonics of the fundamental 1040-nm radiation up to the 21st order are generated. Besides reporting these fine experimental results, the thesis provides an excellent introduction into the physics of enhancement cavities, supported by more than 140 references.