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Linear Polarization, Graphical Representation

Kamal L Rajpal

Published Mar 1, 2013• 0 citations
OpenAlex

Abstract

No light passes through two crossed polarizers. However, if a third polarizer is inserted, at let’s say 45 degrees, in between the two crossed polarizers then, light does go through the three polarizers in series. This behavior can be explained with the help of a mathematical analysis. This paper explains it using a simple graphical approach. A graphical derivation of Malus Law is given and the EPR paradox has been made clear in a graphical manner.

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Oxford University Press eBooks•May 7, 2020•0 citations
No light passes through two crossed polarizers. However, if a third polarizer is inserted, at let’s say 45 degrees, in between the two crossed polarizers then, light does go through the three polarizers in series. This behavior can be explained with the help of a mathematical analysis. This paper explains it using a simple graphical approach. A graphical derivation of Malus Law is given and the EPR paradox has been made clear in a graphical manner.
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.
A system of two polarized photons in singlet state appears as being in one of two product states independent of any measurement. These states depend on the selected polarization angles. With the polarizers on either side perpendicular to each other, both photons pass the polarizers without any disturbance. Action at a distance is therefore not needed to explain the results of the measurements. In general, the elements of physical reality demanded by EPR are the polarization states of the two photons of the entangled pair. As these are local elements in the regions of space of the polarizers the EPR paradox for the case of entangled photons can be regarded as resolved.
This note reconstructs Malus’ law as the minimal optical expression of interface-mediated admission. A prepared photon polarization is treated not as a fully pre-existing physical record, but as a pre-record admissibility structure QBγ(φ). A polarizer at angle θ acts as a finite admissibility interface Iθ. The detector outcome is an irreversible binary distinction IBD, recovered as a physical detector record PD. The standard projection calculation is retained: a prepared linear polarization is represented by u(φ) = (cos φ, sin φ), the polarizer admits the component along e(θ) = (cos θ, sin θ), and the admitted amplitude is a(φ,θ) = e(θ) · u(φ) = cos(φ − θ). Squaring the admitted amplitude gives Malus’ law: P(D = 1 | φ, θ) = cos²(φ − θ). The note then treats the three-polarizer experiment as a direct consequence: while direct 0° → 90° transmission is zero in the ideal case, insertion of an intermediate 45° interface gives total transmission 1/4 relative to light already prepared at 0°. The intermediate polarizer is therefore interpreted as establishing a new admissible polarization condition rather than merely acting as a passive obstruction. The result is not presented as a new optical law. It is a primitive reconstruction of a known law: Malus’ law appears as the simplest quantitative signature of finite interface-mediated admission, linking the foundational chain τ0 → QB → IB to a laboratory optical law.
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.