The Theory of Light and Wave Mechanics

Oliver Reiser

Richard M. Sillitto

Biswas, Sayanho, Kolahal Bhattacharya

An exact analogy between wave mechanics in quantum theory and the scalar wave treatment of optics emerges from the marriage of Newtonian formulation of geometrical optics [1] and the ``formal quantum theory of light rays'' [2]. Here the incidence of a ray of light on the interface between two media is treated as the incidence of a wavefunction on a potential barrier. This leads to the coefficient of reflection identical to Fresnel's formula for s-polarised light [3], although there is no concept of the polarisation of light in this model. In the present work, we apply this model to the total internal reflection of light and evanescent waves. We also deduce a one-to-one correspondence between the transmission coefficient in wave mechanics and frustrated total internal reflection for all angles of incidence. Further, we demonstrate that this model can also be used to derive the Goos-Hänchen shift for s-polarised light. This work augments the discussion on these topics found in the standard texts in optics [4].

J. Richard Christman, David Halliday, Robert J. Resnick

Soumik Biswas, Kolahal Bhattacharya

Abstract In this article, we work with an optical-mechanical analogy model that exploits the analogy between wave mechanics in quantum theory and the scalar wave treatment of optics. We discuss the application of this model to the evanescent waves and the frustrated total internal reflection of light. Further, we demonstrate that this model can also be used to derive the Goos–Hänchen shift for s -polarised light. This work provides the advanced undergraduate students and instructors of optics and quantum mechanics courses with a platform, where they can apply the methods of the quantum theory to optics, which is not discussed in depth in the standard texts.

L. V. Matos

In this theory, we attempt to predict the behavior of light and explain the optical duality caused by traditional physics, connecting Newtonian mechanics, wave mechanics, and, subsequently, quantum physics.