Composition law for polarizers
TL;DR: In this paper, the trajectories of the wave light polarization during the polarization process were determined using the Stokes vector representation, and it was shown that such trajectories are not always geodesics of the Poincare sphere as is usually thought.
Abstract: The polarization process when polarizers act on an optical field is studied. We give examples for two kinds of polarizers. The first kind presents an anisotropic absorption—as in a Polaroid film—and the second one is based on total reflection at the interface with a birefringent medium. Using the Stokes vector representation, we determine explicitly the trajectories of the wave light polarization during the polarization process. We find that such trajectories are not always geodesics of the Poincare sphere as is usually thought. Using the analogy between light polarization and special relativity, we find that the action of successive polarizers on the light wave polarization is equivalent to the action of a single resulting polarizer followed by a rotation achieved, for example, by a device with optical activity. We find a composition law for polarizers similar to the composition law for noncollinear velocities in special relativity. We define an angle equivalent to the relativistic Wigner angle which can be used to quantify the quality of two composed polarizers.
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TL;DR: In this article, a generalization in the complex plane of the addition law of parallel velocities is presented, which directly provides phase factors such as the Wigner angle in special relativity and is related to the composition of 2×2 S-matrices.
Abstract: Many results that are difficult can be found more easily by using a generalization in the complex plane of Einstein’s addition law of parallel velocities. Such a generalization is a natural way to add quantities that are limited to bounded values. We show how this generalization directly provides phase factors such as the Wigner angle in special relativity and how this generalization is related in the simplest case to the composition of 2×2 S-matrices.
21 citations
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TL;DR: In this paper, a generalization in the complex plane of the addition law of parallel velocities is presented. But this generalization does not directly provide phase factors such as the Wigner angle in special relativity.
Abstract: Many results that are difficult can be found more easily by using a generalization in the complex plane of Einstein's addition law of parallel velocities. Such a generalization is a natural way to add quantities that are limited to bounded values. We show how this generalization directly provides phase factors such as the Wigner angle in special relativity and how this generalization is connected in the simplest case with the composition of 2x2 S matrices.
18 citations
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TL;DR: In the frame of a generic language extended from the polarization theory, a geometric approach to Lorentz transformations alternative to the Minkowskian one is given, which operates in the three-dimensional space of Poincare vectors.
Abstract: In the frame of a generic language extended from the polarization theory—comprising the notions of Poincare vectors, Poincare sphere, and P-spheres—a geometric approach to Lorentz transformations alternative to the Minkowskian one is given. Unlike the four-dimensional Minkowskian approach, this new approach operates in the three-dimensional space of Poincare vectors.
11 citations
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TL;DR: In a pure operatorial (nonmatrix) Pauli algebraic approach, this Letter shows that the Poincaré vector of the light transmitted by a dichroic device can be expressed as function of the PoINCaré vectors of the incoming light and of the device by a composition law of the same kind as the composition law as the noncolinear relativistic velocities.
Abstract: In a pure operatorial (nonmatrix) Pauli algebraic approach, this Letter shows that the Poincare vector of the light transmitted by a dichroic device can be expressed as function of the Poincare vectors of the incoming light and of the device by a composition law of the same kind as the composition law of the noncolinear relativistic velocities. This is, in fact, a general law of composition for three-dimensional (3D) vectors remaining in the Poincare ball (where they have a group-like structure). The differences between this problem and that of the composition law of two dichroic devices are pointed out and justified.
11 citations
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TL;DR: In this article, the authors used the quantum kinematic approach to revisit geometric phases associated with polarizing processes of a monochromatic light wave and gave the expressions of geometric phases for any, unitary or non-unitary, cyclic or noncyclic transformations of the light wave state.
Abstract: We use the quantum kinematic approach to revisit geometric phases associated with polarizing processes of a monochromatic light wave. We give the expressions of geometric phases for any, unitary or non-unitary, cyclic or non-cyclic transformations of the light wave state. Contrarily to the usually considered case of absorbing polarizers, we found that a light wave passing through a polarizer may acquire in general a nonzero geometric phase. This geometric phase exists despite the fact that initial and final polarization states are in phase according to the Pancharatnam criterion and cannot be measured using interferometric superposition. Consequently, there is a difference between the Pancharatnam phase and the complete geometric phase acquired by a light wave passing through a polarizer. We illustrate our work with the particular example of total reflection based polarizers.
9 citations
References
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01 Jan 1959
TL;DR: In this paper, the authors discuss various topics about optics, such as geometrical theories, image forming instruments, and optics of metals and crystals, including interference, interferometers, and diffraction.
Abstract: The book is comprised of 15 chapters that discuss various topics about optics, such as geometrical theories, image forming instruments, and optics of metals and crystals. The text covers the elements of the theories of interference, interferometers, and diffraction. The book tackles several behaviors of light, including its diffraction when exposed to ultrasonic waves.
19,815 citations
[...]
01 Oct 1999
TL;DR: In this article, the authors discuss various topics about optics, such as geometrical theories, image forming instruments, and optics of metals and crystals, including interference, interferometers, and diffraction.
Abstract: The book is comprised of 15 chapters that discuss various topics about optics, such as geometrical theories, image forming instruments, and optics of metals and crystals. The text covers the elements of the theories of interference, interferometers, and diffraction. The book tackles several behaviors of light, including its diffraction when exposed to ultrasonic waves.
19,503 citations
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TL;DR: In this article, the existence of the phase is attributed to the non-transitivity of Pancharatnam's connection between different states of polarization, and the precise relation is established using the algebra of spinors and 2 × 2 Hermitian matrices.
Abstract: In 1955 Pancharatnam showed that a cyclic change in the state of polarization of light is accompanied by a phase shift determined by the geometry of the cycle as represented on the Poincare sphere. The phase owes its existence to the non-transitivity of Pancharatnam's connection between different states of polarization. Using the algebra of spinors and 2 × 2 Hermitian matrices, the precise relation is established between Pancharatnam's phase and the recently discovered phase change for slowly cycled quantum systems. The polarization phase is an optical analogue of the Aharonov-Bohm effect. For slow changes of polarization, the connection leading to the phase is derived from Maxwell's equations for a twisted dielectric. Pancharatnam's phase is contrasted with the phase change of circularly polarized light whose direction is cycled (e.g. when guided in a coiled optical fibre).
874 citations
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TL;DR: In science we like to emphasize the novelty and originality of our ideas, but this is harmless enough, provided it does not blind us to the fact that concepts rarely arise out of nowhere as discussed by the authors.
Abstract: In science we like to emphasize the novelty and originality of our ideas. This is harmless enough, provided it does not blind us to the fact that concepts rarely arise out of nowhere. There is always a historical context, in which isolated precursors of the idea have already appeared. What we call “discovery” sometimes looks, in retrospect, more like emergence into the air from subterranean intellectual currents.
170 citations
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TL;DR: In this paper, it was shown that the Thomas precession of special relativity theory is the mechanism that stores the mathematical regularity in the set of all relativistically admissible three-dimensional velocities.
Abstract: Mathematics phenomena and discovers the secret analogies which unite them. Joseph Fourier. Where there is physical significance, there is pattern and mathematical regularity. The aim of this article is to expose a hitherto unsuspected grouplike structure underlying the set of all relativistically admissible velocities, which shares remarkable analogies with the ordinary group structure. The physical phenomenon that stores the mathematical regularity in the set of all relativistically admissible three‐velocities turns out to be the Thomas precession of special relativity theory. The set of all three‐velocities forms a group under velocity addition. In contrast, the set of all relativistically admissible three‐velocities does not form a group under relativistic velocity addition. Since groups measure symmetry and exhibit mathematical regularity it seems that the progress from velocities to relativistically admissible ones involves a loss of symmetry and mathematical regularity. This article reveals that the...
96 citations