I ?rst heard of k·p in a course on semiconductor physics taught by my thesis adviser William Paul at Harvard in the fall of 1956. He presented the k·p Hamiltonian as a semiempirical theoretical tool which had become rather useful for the interpre- tion of the cyclotron resonance experiments, as reported by Dresselhaus, Kip and Kittel. This perturbation technique had already been succinctly discussed by Sho- ley in a now almost forgotten 1950 Physical Review publication. In 1958 Harvey Brooks, who had returned to Harvard as Dean of the Division of Engineering and Applied Physics in which I was enrolled, gave a lecture on the capabilities of the k·p technique to predict and ?t non-parabolicities of band extrema in semiconductors. He had just visited the General Electric Labs in Schenectady and had discussed with Evan Kane the latter’s recent work on the non-parabolicity of band extrema in semiconductors, in particular InSb. I was very impressed by Dean Brooks’s talk as an application of quantum mechanics to current real world problems. During my thesis work I had performed a number of optical measurements which were asking for theoretical interpretation, among them the dependence of effective masses of semiconductors on temperature and carrier concentration. Although my theoretical ability was rather limited, with the help of Paul and Brooks I was able to realize the capabilities of the k·p method for interpreting my data in a simple way.

Reducing the size of a coherently grown semiconductor cluster in all three directions of space to a value below the de Broglie wavelength of a charge carrier leads to complete quantization of the energy levels, density of states, etc. Such “quantum dots” are more similar to giant atoms in a dielectric cage than to classical solids or semiconductors showing a dispersion of energy as a function of wavevector. Their electronic and optical properties depend strongly on their size and shape, i.e. on their geometry. By designing the geometry by controlling the growth of QDs, absolutely novel possibilities for material design leading to novel devices are opened. This multiauthor book written by world-wide recognized leaders of their particular fields and edited by the recipient of the Max-Born Award and Medal 2006 Professor Dieter Bimberg reports on the state of the art of the growing of quantum dots, the theory of self-organised growth, the theory of electronic and excitonic states, optical properties and transport in a variety of materials. It covers the subject from the early work beginning of the 1990s up to 2006. The topics addressed in the book are the focus of research in all leading semiconductor and optoelectronic device laboratories of the world.

Linear current-voltage pattern, has been and continues to be the basis for characterizing, evaluating performance, and designing integrated circuits, but is shown not to hold its supremacy as channel lengths are being scaled down. In a nanoscale circuit with reduced dimensionality in one or more of the three Cartesian directions, quantum effects transform the carrier statistics. In the high electric field, the collision free ballistic transform is predicted, while in low electric field the transport remains predominantly scattering-limited. In a micro/nano-circuit, even a low logic voltage of 1 V is above the critical voltage triggering nonohmic behavior that results in ballistic current saturation. A quantum emission may lower this ballistic velocity.

The soliton represents one ofthe most important ofnonlinear phenomena in modern physics. It constitutes an essentially localizedentity with a set ofremarkable properties. Solitons are found in various areas of physics from gravitation and field theory, plasma physics, and nonlinear optics to solid state physics and hydrodynamics. Nonlinear equations which describe soliton phenomena are ubiquitous. Solitons and the equations which commonly describe them are also of great mathematical interest. Thus, the dis covery in 1967and subsequent development ofthe inversescattering transform method that provides the mathematical structure underlying soliton theory constitutes one of the most important developments in modern theoretical physics. The inversescattering transform method is now established as a very powerful tool in the investigation of nonlinear partial differential equations. The inverse scattering transform method, since its discoverysome two decades ago, has been applied to a great variety of nonlinear equations which arise in diverse fields of physics. These include ordinary differential equations, partial differential equations, integrodifferential, and differential-difference equations. The inverse scattering trans form method has allowed the investigation of these equations in a manner comparable to that of the Fourier method for linear equations.

This is the first book to treat combinatorial and geometric aspects of two-dimensional solitons. Based on recent research by the author and his collaborators, the book presents new developments focused on an interplay between the theory of solitons and the combinatorics of finite-dimensional Grassmannians, in particular, the totally nonnegative (TNN) parts of the Grassmannians. The book begins with a brief introduction to the theory of the Kadomtsev–Petviashvili (KP) equation and its soliton solutions, called the KP solitons. Owing to the nonlinearity in the KP equation, the KP solitons form very complex but interesting web-like patterns in two dimensions. These patterns are referred to as soliton graphs. The main aim of the book is to investigate the detailed structure of the soliton graphs and to classify these graphs. It turns out that the problem has an intimate connection with the study of the TNN part of the Grassmannians. The book also provides an elementary introduction to the recent development of the combinatorial aspect of the TNN Grassmannians and their parameterizations, which will be useful for solving the classification problem. This work appeals to readers interested in real algebraic geometry, combinatorics, and soliton theory of integrable systems. It can serve as a valuable reference for an expert, a textbook for a special topics graduate course, or a source for independent study projects for advanced upper-level undergraduates specializing in physics and mathematics.

Integrated optoelectronics is becoming ever more important to communications, computer, and consumer industries. It is the enabling technology in a variety of systems, ranging from low-cost, robust optical componentsin consumer electronics to high-performance broadband information networks capable of supporting video and multimedia conferencing. The requirements for producing low-cost, highly reliable components for deployment in these new systems have created a technology challenge. Integrated optoelectronics promises to meet the performance and cost objectives of these applications by integrating both optical and electronic components in a highly functional chip. This book provides an overview of this exciting newtechnology.Integrated Optoelectronics brings together a group of acknowledged experts from both universities and industry around the world to focus on a common theme of integration. These experts have reported not only on the state-of-the-art, but also on the physics and design experience that goes into implementing integrated chips and modules. This book is a cohesive series of articles that includes a discussion of the intimate trade-offs between materials, processes, devices, functional blocks, packaging,and systems requirements in a truly integrated technology. This integration encompasses electrical, optoelectronic, and optical devices onto monolithic or hybrid chips, and into multichip modules.This volume surveys state-of-the-art research activities in integrated optoelectronics and gathers most of the important references into a single place. It outlines the major issues involved in integrating both optical and electronic components, provides an overview of design and fabrication concepts, and discusses the issues involved in bringing these new chips to the marketplace.This exciting new book:Provides a broad overview of the optoelectronic field, including materials processing, devices, and systems applicationsFeatures authors who are acknowledged research experts in this field, from both industry and universities around the worldIncludes new information on device fabrication, including the latest epitaxial growth and lift-off techniques to permit the mixing of dissimilar materials onto single chipsCovers planar processed laser fabrication leading to wafer level automated testingDiscusses optimization of devices for integration, including a detailed treatment of the vertical emitting laser and theoretical and experimental coverage of optimization of photodetectors for integration into receiver chipsDescribes design approaches for multifunctional chips, including photonic circuits for all-optical networks and the design of integrated optoelectronic chips with lasers, photodiodes, and electronic ICsCovers the infrastructure needed to support an integrated technology, including automated design systems which treat both optical and electrical circuits, and multichip packaging approaches for both optical and IC chips