In modern optical processing and display applications, there are increased needs of a real-time device and such a device is called a spatial light modulator (SLM). Typical examples of SLMs are acousto-optics modulators (AOMs), electro-optic modulators (EOMs) and liquid crystal displays. In this chapter, we will concentrate on these types of modulators and discuss their uses, such as phase modulation and intensity modulation, in information processing.

We have introduced Gaussian optics and used a matrix formalism to describe light rays through optical systems in Chapter 1. Light rays are based on the particle nature of light. Since light has a dual nature, light is waves as well. In 1924, de Broglie formulated the de Broglie hypothesis, which relates wavelength and momentum. In this chapter, we explore the wave nature of light, which accounts for wave effects such as interference and diffraction.

The purpose of this chapter is twofold. We will first discuss basic aspect of signals and linear systems in the first part. As we will see in subsequent chapters that diffraction as well as optical imaging systems can be modelled as linear systems. In the second part, we introduce the basic properties of Fourier series, Fourier transform as well as the concept of convolution and correlation. Indeed, many modern optical imaging and processing systems can be modelled with the Fourier methods, and Fourier analysis is the main tool to analyze such optical systems. We shall study time signals in one dimension and signals in two dimensions will then be covered. Many of the concepts developed for one-dimensional (1-D) signals and systems apply to two-dimensional (2-D) systems. This chapter also serves to provide important and basic mathematical tools to be used in subsequent chapters.

This chapter contains Gaussian optics and employs a matrix formalism to describe optical image formation through light rays. In optics, a ray is an idealized model of light. However, in a subsequent chapter, we will also see a matrix formalism can also be used to describe, for example, a Gaussian laser beam under diffraction through the wave optics approach. The advantage of the matrix formalism is that any ray can be tracked during its propagation though the optical system by successive matrix multiplications, which can be easily programmed on a computer. This is a powerful technique and is widely used in the design of optical element. In this chapter, some of the important concepts in resolution, depth of focus, and depth of field are also considered based on the ray approach.

Two selected Exercises are solved in full: a question relevant to the twin paradox and a method using special relativity for deriving the Biot–Savart equation.

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.