Light propagation: beams and guides

This chapter considers the propagation of laser beams in free space and laser cavities, and light propagating in waveguides such as optical fibres.

Polarization

This chapter discusses the polarization of light, including the transverse nature of the plane-wave solution; the linear and circular bases are introduced, and the propagation of polarized light in media is analysed.

One wave: plane or curved

This chapter reviews simple wave solutions, in particular plane waves and spherical waves. The behaviour of plane waves inside a medium and at an interface is considered. The chapter concludes with a discussion of how lenses change the wave-front curvature.

Vector light fields

This chapter considers how all light fields contain non-transverse components. Situations where it is possible to make the longitudinal component larger than the transverse component are highlighted.

Many waves II: Fourier

This chapter considers the sum of many plane waves propagating at different angles. It is shown that the sum of many plane waves (Fourier optics) is mathematically equivalent to a sum of many curved waves (the Huygens–Fresnel principle). The Fourier approach is exploited to solve a range of common diffraction problems, including diffraction by a regular array.

Light as a wave

This chapter introduces the basic concepts, such as light as a wave, a brief overview of Maxwell’s equations, the harmonic wave solution, spatial frequency, phasors, intensity, complex representation, the scalar approximation, and light quanta.

Light and matter

This chapter considers the interaction between light and electrons in matter. The microscopic origins of refraction and dispersion are highlighted, as are the optical properties of metals and plasmas, and the effects of a non-linear optical response.

Spatial filtering

This chapter exploits the Fourier relationship between the fields at different positions for modifying images. Firstly, apodization is considered, where a filter is added in the plane of the lens to modify the spatial distribution in the focal plane. Secondly, spatial filtering is analysed, where a two-lens system is used to allow the manipulation of an image by modifying its Fourier transform.

Optical imaging

This chapter considers the ability of a lens to produce an image, in particular the effect of the finite size of the lens and the Fourier relationship between the field in the lens plane and the field in the focal plane.

Two waves: interference

This chapter considers the sum of two waves, including standing waves. The examples considered are Young’s two-hole experiment, the Fabry–Perot etalon, and Michelson’s interferometer. In most cases interference can be treated as a sum of two or more phasors, which may either add or cancel, producing constructive and destructive interference, respectively.