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arXiv:2204.10280 · The European Physical Journal Plus

Stochastic and corpuscular theory of (polarized) light

J Procházka

Published Aug 7, 2023• 1 citation
arXivHTMLPDF

Abstract

Abstract Both the corpuscular theory of light and the theory of stochastic processes are well known in the literature. However, they are not systematically used together for description of optical phenomena. There are optical phenomena, such as the well-known three-polarizer 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-polarizer experiment is performed and numerical result of the probability (density) functions are determined. These original results were missing in the 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.

DOI
10.1140/epjp/s13360-023-04210-y

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Abstract Both the corpuscular theory of light and the theory of stochastic processes are well known in the literature. However, they are not systematically used together for description of optical phenomena. There are optical phenomena, such as the well-known three-polarizer 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-polarizer experiment is performed and numerical result of the probability (density) functions are determined. These original results were missing in the 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.
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We discuss an event-based corpuscular model of optical phenomena that does not require the knowledge of the solution of a wave equation of the whole system and reproduces the results of Maxwell's theory through a series of cause-and-effect processes, starting with the emission and ending with the detection of a particle. Event-based models of a single-photon detector and of light propagation through an interface of two dielectrics are used as modular building blocks to give a unified, corpuscular description of many optical phenomena. The approach is illustrated by applications to Wheeler's delayed choice, Einstein-Podolsky-Rosen-Bohm and Hanbury Brown-Twiss experiments.
We develop a theory that describes the interaction of radiation and multilevel particles on the basis of the classical description of the orientation of angular momentum. For examples of application of this theory we take the problems of stimulated Raman scattering and of parametric generation of light in four-wave mixing. We find that the efficiency of the radiation processes largely depends on the polarization of the pump waves and on the types of optical transitions (Δ J ) and to a much lesser extent on the value of the angular momentum J . We also explain some polarization phenomena observed in experiments on four-wave mixing.
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