Semiconductor quantum wells. Electronic states in quantum wells in the conduction and valence bands; envelope function approximation. Density of states: electron and hole density. Transition selection rules: interband and intraband transitions. Absorption and gain in a quantum well. Intersubband absorption. Strained quantum wells. Transparency density and differential gain. Exciton in bulk and quantum well semiconductors.

The Lorentz transformation between frames of reference is determined and presented in a matrix form. The transformation of velocities is derived with an example presented in the form of the relativistic rocket equation. The Doppler effect is discussed. Relativistic momentum and energy are presented. The quantum nature of particles and light is discussed. The four-vector and tensor notation are introduced.

The Fizeau effect in a flowing refractive medium is treated and extended to when light propagates at an angle to the medium velocity. The reflection optics with relativistically moving mirrors is examined. Using Stokes parameters, it is shown that polarization is preserved in Lorentz transformation between frames of reference.

The chapter commences with an introduction to the ideas of special relativity. A brief discussion of the life and work of Albert Einstein is presented. The propagation of light, relativistic time dilation, and length contraction followed by a simple explanation of the production of light by accelerating charges are presented.

Bulk semiconductors. Stimulated transitions: selection rules. Joint density of states. Absorption coefficient and gain in bulk semiconductors; Bernard-Duraffourg condition; transparency condition and differential gain. Spontaneous emission; bimolecular recombination: low and strong injection. Nonradiative recombination. Shockley-Read-Hall model. Auger recombination. Surface recombination. Radiative efficiency.

The motion of single electrons in electromagnetic waves is determined. The propagation of light in plasma with many electrons is treated leading to ,for example, an expression for the refractive index of a plasma. Cherenkov radiation and incoherent and coherent Thomson scatter and Compton scatter of light are examined.

Basic concepts of quantum mechanics: Schroedinger equation; Dirac notation; the energy representation; expectation value; Hermite operators; coherent superposition of states and motion in the quantum world; perturbation Hamiltonian. Time-dependent perturbation theory: harmonic perturbation. Transition rate: Fermi’s golden rule. The density matrix; pure and mixed states. Temporal dependence of the density operator: von Neuman equation. Randomizing Hamiltonian. Longitudinal and transverse relaxation times. Density matrix and entropy.

Basic concepts of electromagnetic theory; Coulomb gauge; intensity of electromagnetic field. Electrons in an electromagnetic field: from the Lagrangian to the Hamiltonian; canonical momentum. Interaction Hamiltonian. Semiclassical approximation; weak-field limit. Electric dipole approximation. Calculation of the optical susceptibility by using the density matrix approach. From optical susceptibility to absorption coefficient. Momentum of an electron in a periodic crystal.

Equilibrium distribution functions are determined for fermions (e.g. electrons) and bosons (e.g. photons). The Saha–Boltzmann equation, the Maxwellian distribution, and relativistic Maxwell–Juttner distribution are derived. The relativistic equation of state for a distribution where particle velocities approach the speed of light is examined.

General structure of quantum cascade lasers: resonant tunnelling, minigap and miniband. Gain coefficient. Rate equations and threshold conditions. Output power, slope efficiency and wall-plug efficiency. Applications of quantum cascade lasers.

Semiconductor lasers: rate equations and threshold conditions for laser action. Confinement factor. Temperature dependence of the threshold current: characteristic temperature. Output power: external quantum efficiency and slope efficiency. Quantum well lasers. General structures of semiconductor lasers. Spectral and spatial characteristics of diode laser emission.

Radiative transfer, the Einstein A and B coefficients, emission and absorption coefficients, and Doppler line broadening are discussed. Continuum radiation emission coefficients are derived using the idea of virtual photon scattering. Inverse Compton scattering is treated in some detail. The radiation reaction force is examined.

Crystal, lattices and cells; Bravais lattice; the reciprocal lattice; electrons in a periodic crystal: Bloch’s theorem; momentum of an electron in a periodic crystal; effective mass; electrons and holes in a semiconductor; calculation of the band structure: tight-binding method and k·p method; bandstructure of Si, GaAs and GaN.

A table of Lorentz invariant parameters and grouping of parameters is presented.