The pseudo-null geometric phase along optical fiber

2021 ◽  
Author(s):  
Nevin Ertuğ Gürbüz
Keyword(s):  
Optical Fiber ◽  
Light Wave ◽  
Null Space ◽  
Parallel Transport ◽  
Polarized Light ◽  
Tangent Vector ◽  
Polarization Vector ◽  
Frenet Frame ◽  
Null Curve ◽  
Vector Formula

In this study, a pseudo-null space curve in Minkowski 3-space is used to describe an optical fiber that is injected into monochromatic linear polarized light. The direction of the electric field vector with respect to the Frenet frame of a pseudo-null curve determines the state polarization of a monochromatic linearly polarized light wave traveling along an optical fiber. For the Frenet frame of a pseudo-null curve in Minkowski 3-space, the polarization vector [Formula: see text] is assumed to be perpendicular to the tangent vector [Formula: see text] with respect to anholonomic coordinates. Anholonomic coordinates for the Frenet frame of a pseudo-null curve are used to describe pseudo-null electromagnetic curves in the normal and binormal directions along an optical fiber. For the Frenet frame of the pseudo-null curve, Lorentz force equations in the normal and binormal directions along the optical fiber are presented. Pseudo-normal and binormal Rytov parallel transport laws for electric fields in the normal and binormal directions along with the optical fiber for the Frenet frame of the pseudo-null curve via anholonomic coordinates are presented. For anholonomic coordinates in Minkowski 3-space, rotations of the polarization planes of a light wave traveling in the normal and binormal directions along with the optical fiber with respect to the Frenet frame of the pseudo-null curve are obtained. Finally, a pseudo-null curve’s Maxwellian evolution is determined.

scholarly journals A Note on Parametric Surfaces in Minkowski 3-Space

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Esra Betul Koc Ozturk
Keyword(s):  
Linear Combination ◽  
Sufficient Conditions ◽  
Ruled Surface ◽  
Necessary And Sufficient Conditions ◽  
Frenet Frame ◽  
Parametric Surface ◽  
Parametric Surfaces ◽  
Null Curve ◽  
Necessary And Sufficient

With the help of the Frenet frame of a given pseudo null curve, a family of parametric surfaces is expressed as a linear combination of this frame. The necessary and sufficient conditions are examined for that curve to be an isoparametric and asymptotic on the parametric surface. It is shown that there is not any cylindrical and developable ruled surface as a parametric surface. Also, some interesting examples are illustrated about these surfaces.

Automated Fiber-Optic System for Monitoring the Stability of the Pit Quarry Mass and Dumps

2021 ◽  
pp. 19-26
Author(s):  
А.D. Меkhtiyev ◽  
◽  
E.G. Neshina ◽  
P.Sh. Madi ◽  
D.A. Gorokhov ◽  
...  
Keyword(s):  
Rock Mass ◽  
Optical Fiber ◽  
Optical Fibers ◽  
Fiber Optic ◽  
Light Wave ◽  
Single Mode ◽  
Fiber Optic Sensors ◽  
Fiber Optic Sensor ◽  
Laboratory Sample ◽  
Single Mode Optical Fiber

This article ls with the issues related to the development of a system for monitoring the deformation and displacement of the rock mass leading to the collapse of the quarry sides. Monitoring system uses point-to-point fiber-optic sensors. Fiber-optic sensors and control cables of the communication line are made based on the single mode optical fibers, which allows to measure with high accuracy the deformations and displacements of the rock mass at a distance of 30-50 km. To create fiber-optic pressure sensors, an optical fiber of the ITU-T G. 652.D standard is used. Laboratory sample is developed concerning the point fiber-optic sensor made based on the two-arm Mach-Zender interferometer using a single mode optical fiber for monitoring strain (displacements) with a change in the sensitivity and a reduced influence of temperature interference leading to zero drift. The article presents a mathematical apparatus for calculating the intensity of radiation of a light wave passing through an optical fiber with and without mechanical stress. A laboratory sample of single mode optical fibers based on the Mach-Zender interferometer showed a fairly high linearity and accuracy in the measurement and can be used to control the strain of the mass after appropriate refinement of its design. Mathematical expressions are also given for determining the intensity of the light wave when the distance between the fixing points of a single mode optical fiber changes depending on the change in the external temperature. A diagram for measuring strain using a point fiber-optic strain sensor is developed. Hardware and software package is developed, which can be used to perform a number of settings of measuring channels. The work is aimed at solving the production problems of the Kenzhem quarry of AK Altynalmas JSC.

Optical activity and enantiomorphism

2004 ◽  
Author(s):  
Robert E. Newnham
Keyword(s):  
Optical Activity ◽  
Polarized Light ◽  
Polarization Vector ◽  
Optically Active ◽  
Crystal Thickness ◽  
Helical Structures ◽  
Active Materials ◽  
Circularly Polarized ◽  
Space Groups ◽  
Polarized Waves

When plane-polarized light enters a crystal it divides into right- and lefthanded circularly polarized waves. If the crystal possesses handedness, the two waves travel with different speeds, and are soon out of phase. On leaving the crystal, the circularly polarized waves recombine to form a plane polarized wave, but with the plane of polarization rotated through an angle αt. The crystal thickness t is in mm, and α is the optical activity coefficient expressed in degrees/mm. The polarization vector of the combined wave can be visualized as a helix, turning α ◦/mm path length in the optically-active medium. Because of the low symmetry of a helix, optical activity is not observed in many high symmetry crystals. Point groups possessing a center of symmetry are inactive. In relating α to crystal chemistry it is convenient to divide optically-active materials into two categories: Those which retain optical activity in liquid form, and those which do not. It has long been known that optically-active solutions crystallize to give optically-active solids. This follows from the fact that molecules lacking mirror or inversion symmetry can never crystallize in a pattern containing such symmetry elements. Thus one way of obtaining optically-active materials is to begin with optically-active molecules, as in Rochelle salt, tartaric acid and cane sugar. Few of these crystals are very stable, however, and the optical activity coefficients are usually small, typically 2◦/mm. The same is true of many inorganic solids, though they are seldom optically active in the liquid state. For NaClO3 and MgSO4·7H2O, α is about 3◦/mm. Quartz and selenium, however, have coefficients an order of magnitude larger, showing the importance of helical structures to optical activity. Both compounds crystallize as right- and left-handed forms in space groups P312 and P322, with helices spiraling around the trigonal screw axes. Quartz contains nearly regular SiO4 tetrahedra with Si–O distances of 1.61 Å. Levorotatory quartz belongs to space group P312 and contains right-handed helices; enantiomorphic dextrorotatory quartz crystallizes in P322. Trigonal selenium also contains helical chains.

scholarly journals A New Angular Measurement in Minkowski 3-Space

Mathematics ◽  
2020 ◽  
Vol 8 (1) ◽  
pp. 56 ◽  
Author(s):  
Jinhua Qian ◽  
Xueqian Tian ◽  
Jie Liu ◽  
Young Ho Kim
Keyword(s):  
Euclidean Space ◽  
Minkowski Space ◽  
Angular Measurement ◽  
Frenet Frame ◽  
Measuring Methods ◽  
Null Curve

In Lorentz–Minkowski space, the angles between any two non-null vectors have been defined in the sense of the angles in Euclidean space. In this work, the angles relating to lightlike vectors are characterized by the Frenet frame of a pseudo null curve and the angles between any two non-null vectors in Minkowski 3-space. Meanwhile, the explicit measuring methods are demonstrated through several examples.

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