Chapter 4 - Interference

Abstract

The term interference refers to phenomena that can be explained in terms of the superposition of two or more wave solutions of Maxwell’s equations, where such an explanation is in the nature of an approximation. We address the problem of interference in a double-slit setup and also in a variant of the Michelson interferometer setup, taking into account the vector nature of electromagnetic waves, and then explain how and to what extent one can obtain an equivalent description of the interference patterns in terms of scalar waves. A fact of central importance is that an interference pattern can be explained primarily in terms of the phase difference of the interfering waves (whether of scalar or vector nature) at various points in space. The vector nature of the waves relates to their states of polarization, which, however, can be accounted for in terms of two sets of scalar waves. The concepts of temporal and spatial coherence are elaborated, and their relevance in explaining interference patterns is underlined. The interference pattern in a double-slit setup with a linearly extended source is considered as an instance of interference by division of the wave front, where an extended fringe system is formed. This is followed by an examination of interference by division of amplitude in a thin film, where, once again, temporal and spatial coherence are of crucial relevance. The use of an extended source leads to loss of spatial coherence, whereby one gets a localized fringe system. For a film of uniform thickness the fringes are localized at infinity, while for a wedge-shaped film, the localization is on the surface of the film. Examples of the two types are found in the Michelson interferometer (fringes of equal inclination) and in Newton’s rings (fringes of equal thickness). The working principle of the Mach-Zehnder interferometer is explained, along with its different modes of operational use. The principle of the stellar interferometer is explained with reference to the aspects of temporal and spatial coherence. The working principles of the Fabry-Pérot and Lummer-Gehrcke interferometers are outlined as instances of multiple beam interferometry. A few applications of interferometers are described. Finally, we briefly look at interference as a quantum phenomenon.