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Two waves: interference

Charles S. Adams, Ifan G. Hughes

Published Dec 13, 2018• 0 citations
Publisher

Abstract

Abstract 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.

DOI
10.1093/oso/9780198786788.003.0003

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Abstract 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.
The superposition principle states that the sum of solutions of the wave equation is also a solution. Linearity forbids scattering of one photon by another and waves with orthogonal polarization will not interfer and if no interference is observed the light is said to be incoherent. There is no record carried by any of the waves to indicate outside of the overlap region that the waves ever commingled. Interference involve dielectric layers can produce antireflection coatings. Michelson interferometer, temporal coherence and its use in spectroscopy. The interferometer coupled with a light source with well defined coherence properties are currently used in optical coherence imaging. With multiple reflections a Fabry Perot interferometer can be created to provide optical feedback in a laser. Young’s two slits interferometer can be used to measure the size of distant stars.
Interference is a classic property of waves. It can be seen most clearly when a coherent wave is split into two partial waves that are then recombined to produce periodic variations in the measured intensity. These variations can be observed directly as a pattern of bright and dark interference fringes on a screen. The classic interferometer set-up is the Young's double-slit experiment: a small light source emitting in a narrow frequency band is placed on one side of the slits, and an interference pattern is observed at the screen on the other side (figure a). The fringes are bright where the partial waves interfere constructively, and dark where the interference is destructive.
The two-slit interference experiment is usually adopted to discuss the superposition principle applied to radiation and to show the peculiar wave behaviour of material particles. Diffraction and interference of electrons have been demonstrated using, as interferometry devices, a hole, a slit, double hole, two-slits, an electrostatic biprism etc. A number of books, short movies and lectures on the web try to popularize the mysterious behaviour of electrons on the basis of Feynman thought experiment which consists of a Young two-hole interferometer equipped with a detector to reveal single electrons. A short review is reported regarding, i) the pioneering attempts carried out to demonstrate that interference patterns could be obtained with single electrons through an interferometer and, ii) recent experiments, which can be considered as the realization of the thought electron interference experiments adopted by Einstein-Bohr and subsequently by Feynman to discuss key features of quantum physics.
Interference by division of wavefront. The two-slit experiment Preliminary remarks In this chapter we shall be concerned with various types of interference effects exhibited by matter waves. It might be argued that all quantum mechanical phenomena are ultimately a consequence of interference, being governed as they are by a linear wave equation. Of particular interest here is the analogue for material waves of Young's double-slit experiment in optics, a classic problem in the history of quantum theory. Feynman, Leighton & Sands (1965) state that it ‘ … has in it the heart of quantum mechanics. In reality, it contains the only mystery’. We shall also treat the process of tunnelling into classically forbidden regions, a phenomenon which also involves interference in an essential way. To observe the interference of waves issuing from a common source we must split the emerging beam into two spatially separated coherent parts and subsequently recombine them (the superposition of waves from physically independent sources is a many-body problem – see §§8.8 and 12.7). As in optics there are two methods of achieving this: by division of wavefront where, for example, a wave falls on a screen containing two apertures, and by division of amplitude in which a wave is incident on a semi-transparent barrier. Interference effects achieved by the first method, discussed in this section, have been observed for electrons (Jönsson, 1961; Lichte, 1986; Tonomura et al ., 1989), neutrons (Zeilinger et al ., 1988) and (helium) atoms (Carnal & Mlynek, 1991).
When two waves overlap, the resultant wave function is the sum ( superposition ) of the two individual wave functions. This overlap is also called interference , which is not necessarily a negative term as might be anticipated from its everyday use. Constructive interference occurs when the resultant wave has an amplitude larger than the individual waves, and destructive interference occurs when the resultant wave amplitude is smaller. The term diffraction refers to the interference of “many” waves originating from many sources, but where the term “many” is ill-defined.