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arXiv:2409.16520 · Sitientibus Série Ciências Físicas

Classical and Quantum Analysis of Light Polarization in Filter Systems

Davi Antonio Assunção, Samuel Bueno Soltau

Published Dec 6, 2024• 0 citations
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Abstract

We analyze the behavior of light as it passes through systems composed of polarizing filters at different angular orientations. The analysis is initially conducted in the context of classical optics, using Malus's Law to calculate the transmitted intensity for the cases of two perpendicular filters (0° and 90°) and three filters (0°, 45°, and 90°). We then apply quantum mechanics to describe the phenomenon using state notation and the probabilistic interpretation of the projection of the polarization states of photons.

DOI
10.13102/sscf.v20i.11330

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We analyze the behavior of light as it passes through systems composed of polarizing filters at different angular orientations. The analysis is initially conducted in the context of classical optics, using Malus's Law to calculate the transmitted intensity for the cases of two perpendicular filters (0° and 90°) and three filters (0°, 45°, and 90°). We then apply quantum mechanics to describe the phenomenon using state notation and the probabilistic interpretation of the projection of the polarization states of photons.
A polarized beam of energy is usually interpreted as a set of particles, all having the same polarization state. Difference in behavior between the one and the other particle is then explained by a number of counter-intuitive quantum mechanical concepts like probability distribution, superposition, entanglement and quantized spin. Alternatively, I propose that a polarized beam is composed of a set of particles with a cosine distribution of polarization angles within a polarization area. I show that Malus’ law for the intensity of a beam of polarized light can be derived in a straightforward manner from this distribution. I then show that none of the above-mentioned counter-intuitive concepts are necessary to explain particle behavior and that the ontology of particles, passing through a polarizer, can be easily and intuitively understood. I conclude by formulating some questions for follow-up research.
Maxwell showed that light consists of electric and magnetic fields that oscillate in directions perpendicular to the direction of propagation. Associated with this picture of light as an electromagnetic wave is an important property—the polarization of light. The polarization of light is related to the direction of oscillation of the electric field in an electromagnetic wave. In this chapter, the basic principles of quantum mechanics are discussed by studying the polarization property of a single photon. First the properties of a polarizer are presented and Malus’ law for polarized light is derived. Next it is shown that the basic features of quantum mechanics can be understood via an analysis of a single photon passing through a polarizer. This simple system allows an introduction of Dirac’s ket and bra notations for a quantum state. Finally the transformation properties of the quantum beam splitter and the polarization beam splitters are discussed.
Traditional polarizer provides a way to convert an unknown polarization into a specified polarization. According to Malus, the intensity of the transmission is directly proportional to the square of the cosine of angle between the transmission axes of the polarizer and the incident polarization. There, the intensity refers to the collective behavior of many photons. Here we propose a novel approach to realizing polarization-filtering at single-photon level. We discuss how a single planepolarized photon transports through a polarized analyzer generated by a single atom (the so-called "single-atom polarizer"), and provide a single quantum version of Malus's law. We investigate the quantum scattering of a single photon by a controllable four-level atom inside a one-dimensional waveguide. By using real-space theoretical approach, we obtain analytic expressions of the transmission spectrum of the photon. Then, our numerical experiments show that the transmitted probability of the incident photon can be controlled by selecting the polarized-dependent transition configuration of the driven atom. The application of such a single-atom polarizer to linear optical quantum information processing is also discussed.
The light propagation through system a polarizer-analyzer is investigated on the basis of quantum conceptions about the nature of light. It is shown, that Malus law based on principles of classical electrodynamics not completely takes into account all effects which can occur at the light propagation through system a polarizer-analyzer. The phenomenon of possible change of frequency of light in particular drops out, for example in the region of X-ray radiation. The deduction of Malus law based on quantum principles is given. For comparison the differential effective section of interaction of a photon and electron with take into account of rotation of a plane of polarization of a photon in Compton’s effect is found.
It is shown that the Malus law based on the principles of classical electrodynamics not completely takes into account all effects which can occur at passage of a linearly polarized light through the analyzer. On the basis of the quantum representations about the nature of light the form of Malus law which is taking into account transfer of a part of a photon impulse to particle on which occurs reradiation of light forward is found. Calculations are carried out within the framework of the perturbations theory with use of the Feynman diagram technics.