Stochastic and corpuscular theory of (polarized) light

TL;DR

This paper introduces a stochastic process framework to enhance the corpuscular theory of light, enabling quantitative analysis of polarization phenomena and the three-polarizers experiment, bridging a gap in existing explanations.

Contribution

It systematically combines corpuscular and stochastic process theories, deriving new formulae and providing the first quantitative analysis of polarization experiments using this approach.

Findings

Derived probability density functions for photon interactions with optical elements.

Successfully analyzed the three-polarizers experiment numerically.

Extended the corpuscular theory of light with stochastic process methods.

Abstract

Both the corpuscular theory of light and the theory of stochastic processes are well known in literature. However, they are not systematically used together for description of optical phenomena. There are optical phenomena, such as the well known three-polarizers experiment or other phenomena related to polarization of light, which have never been quantitatively and qualitatively explained using the concept of quantum of light (photon). The situation changed in 2022 when stochastic memoryless and independent (IM) process formulated within the framework of the theory of stochastic processes was introduced. It is suitable for determination of probability (density) functions characterizing interaction (transmission or reflection) of individual photons with optical elements on the basis of experimental data. The process has memoryless (Markov) property and it is assumed that the interactions of individual photons with an optical system are independent. Formulae needed for analysis of data in the context of polarization of light are derived. An example analysis of the three-polarizers experiment is performed and numerical result of the probability (density) functions are determined. These original results were missing in literature. The results imply that the possibilities of the corpuscular theory of light to describe optical phenomena can be significantly extended with the help of stochastic IM process and the theory of stochastic processes in general.