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CRC Press eBooks

Interference, Diffraction, Refraction, and Reflection via Dirac's Notation

F.J. Duarte

Published Jan 15, 2024• 0 citations
Publisher

Abstract

The generalized N -slit quantum interference probability equation is applied to describe the field of optics in a descending hierarchical order: interference → diffraction → refraction → reflection. Optics in this manner is presented in a succinct rational and cohesive manner. The discussion also includes positive and negative refractions. This approach to optics highlights the power of the application of quantum physics principles in the macroscopic domain.

DOI
10.1201/9781003398707-5

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The generalized N -slit quantum interference probability equation is applied to describe the field of optics in a descending hierarchical order: interference → diffraction → refraction → reflection. Optics in this manner is presented in a succinct rational and cohesive manner. The discussion also includes positive and negative refractions. This approach to optics highlights the power of the application of quantum physics principles in the macroscopic domain.
The interaction of coherent light with a set of slits, in the near field, gives rise to an interference pattern. Refraction is the change in the geometrical path, of a beam of light, due to transmission from the original medium of propagation to a second medium with a different refractive index. One of the beauties of the Dirac description of optics is the ability to continuously describe the evolution of the interferometric distribution, as it moves from the near to the far field, with a single mathematical equation. The interferometric distribution, in the near field, is mainly part of a single order. At the boundaries there is an incipient indication that of emerging orders. Explicitly, if a mirror is placed at an infinitesimal distance immediately behind the N-slit array then the transmission interferometer becomes a reflection interferometer.
Quantum interference, which is a physical phenomenon, and probability amplitudes à la Dirac are miraculously like synonyms. Indeed, the way probability amplitudes are written down on paper is very much as a single photon, or an ensemble of indistinguishable photons, propagates from one plane to the next. And then, if at one of the planes an N -slit array alternative is offered then the probability amplitude notation à la Dirac cleverly describes the N -path alternative via a mathematical summation. Here we should emphasize that since the photon is a nonlocal quantum entity, all the microscopic slits in the N -slit array, or transmission diffraction grating, are illuminated simultaneously.