Intersubband Transitions in Quantum Wells

This book contains the lectures delivered at the NATO Advanced Research Workshop on the "Intersubband Transistions in Quantum Wells" held in Cargese, France, between the t 9 h and the 14th of September 1991. The urge for this Workshop was justified by the impressive growth of work dealing with this subject during the last two or three years. Indeed, thanks to recent progresses of epitaxial growth techniques, such as Molecular Beam Epitaxy, it is now possible to realize semiconductor layers ( e.g. GaAs) with thicknesses controlled within one atomic layer, sandwiched between insulating layers (e.g. AlGaAs). When the semiconducting layer is very thin, i.e. less than 15 nm, the energy of the carriers corresponding to their motion perpendicular to these layers is quantized, forming subbands of allowed energies. Because of the low effective masses in these semiconducting materials, the oscillator strengths corresponding to intersubband transitions are extremely large and quantum optical effects become giant in the 5 - 20 ~ range: photoionization, optical nonlinearities, ... Moreover, a great theoretical surprise is that - thanks to the robustness of the effective mass theory - these quantum wells are a real life materialization of our old text book one-dimensional quantum well ideal. Complex physical phenomena may then be investigated on a simple model system.

Dedication. Preface. Acknowledgments. Clifford Geometric Algebras in Multilinear Algebra and Non-Euclidean Geometries.- Geometric algebra Projective Geometries; Affine and other geometries; Affine Geometry of pseudo-euclidean space; Conformal Geometry and the Horosphere; References. Content-Based Information Retrieval by Group Theoretical Methods.- Introduction; Motivating Examples; General Concept; Fault Tolerance.- Applications, Prototypes, and Test Results; Related Work and Future Research; References.- Four Problems in Radar.-Introduction; Radar Fundamentals; Radar Waveforms; Signal Processing; Space-Time Adaptive Processing; Four Problems in Radar; Conclusions. Introduction to Generalized Classical and Quantum Signal and System Theories on Groups and Hypergroups.-Generalized classical signal/system theory on hypergroups; Generalized quantum signal/system theory on hypergroups; Conclusion; References. Lie Groups and Lie Algebras in Robotics.- Introduction -- Rigid Body Motions; Lie Groups; Finite Screw Motions; Mechanical Joints; Invisible Motion and Gripping; Forward Kinematics; Lie Algebra; The Adjoint Representation; The Exponential Map Derivatives of Exponentials; Jacobians; Concluding Remarks; References. Quantum/Classical Interface: a Geometric Approach from the Classical Side.- Introduction Paravector Space as Spacetime; Eigenspinors; Spin; Dirac Equation; Bell's Theorem; Qubits and Entanglement; Conclusions; References. PONS, Reed-Muller Codes, and Group Algebras.- Introduction; Analytic Theory of One-Dimensional PONS (Welti); Shapiro Sequences, Reed-Muller Codes, and Functional Equations; Group Algebras; Reformulation of Classical PONS; Group Algebra of Classical PONS; GroupAlgebra Convolution; Splitting Sequences; Historical Appendix on PONS; References. Clifford Algebras as a Unified Language.- Introduction; Clifford algebras as models of physical spaces; Clifford Algebras as Models of Perceptual Multicolor Spaces; Hypercomplex-Valued invariants of nD multicolor images; Conclusions; Acknowledgments; References. Recent Progress and Applications in Group FFTs.-Introduction; Finite group FFTs; FFTs for compact groups; Noncompact groups; References. Group Filters and Image Processing.- Introduction: Classical Digital Signal Processing; Abelian Group DSP; Nonabelian Groups; Examples; Group Transforms; Group Filters; Line-like Images; Acknowledgments; References. A Geometric Algebra Approach to Some Problems of Robot Vision.- Introduction; Local Analysis of Multi-dimensional Signals; Knowledge Based Neural Computing; Acknowledgments; References. Group Theory in Radar and Signal Processing.- Introduction; How a Radar Works; Representations; Representations and Radar; Ambiguity Functions; The Wide Band Case; References. Geometry of Paravector Space with Applications to Relativistic Physics.- Clifford Algebras in Physics; Paravector Space as Spacetime; Interpretation; Eigenspinors; Maxwell's Equation; Conclusions; References. A Unified Approach to Fourier-Clifford-Prometheus Transforms- Introduction; New construction of classical and multiparametric Prometheus transforms; PONS associated with Abelian groups; Fast Fourier-Prometheus Transforms; Conclusions; Acknowledgments; References. Fast Color Wavelet Transforms.- Introduction; Color images; Color Wavelet-Haar-Prometheus transforms; Edge detection and compression of color images; Conclusion; Acknowledgments; References. Selected Problems; Various Authors.- Transformations of Euclidean Space and Clifford Geometric; Algebra; References; On the Distribution of Kloosterman Sums on Polynomials over Quaternions; References; Harmonic Sliding Analysis Problems; References; Spectral Analysis under Conditions of Uncertainty; A Canonical Basis for Maximal Tori of the Reductive Centrizer of a Nilpotent Element; References; 6 The Quantum Chaos Conjecture References; Four Problems in Radar; Topic Index; Author Index

Emmanuel Rosencher is a highly regarded scientist in the field of optoelectronics. Formerly head of the physics laboratory at the Central Research Laboratory of Thomson-CSF, he is now Research Director at the Physics Branch of ONERA (the French National Aerospace Research Agency) and an Associate Professor at the Ecole Polytechnique, Palaiseau, France. Rosencher is a Fellow of the Institute of Physics and a Senior Member of the IEEE.

Borge Vinter is also a highly regarded scientist in the field of optoelectonics. He is a Senior Scientist at the Corporate Research Laboratory of the THALES Group (formerly Thomson-CSF). He teaches semiconductor physics for graduate students at the Versailles-Saint-Quentin-en-Yvelines University. Vinter is a Member of the Societe Francaise de Physique and of the American Physical Society.