Matrix Description of Wave Propagation and Polarization
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Polarization of Electron and Photon Beams
Revista Brasileira de Física, Vol. 11, NP 4, 1981 Polarization of Electron and Photon Beams ?. R. S. GOMES Instituto de Física, Universidade Federal Fluminense, Niterdi, RJ. Recebido eni 17 de Fevereiro de 1981 In this work the concepts of polarization of photons and re- lativistic electrons are introduced in a simplified form. Although there are important differences in the concepts of photon and electron polarization, it is shown that the saine formal ism may be used to des- cribe them, which is very useful in the study oF interactions concer- ned with polarizations of both photons and electrons, as in the yho- toelectric and Compton effects. Photons are considered, in this work, as a special case of relativistic spin 1 particles, with zero rest mass. Neste trabalho são apresentados, de uma forma simplificada, os conceitos de polarização de fotons e eletrons. Embora existam im- portantes diferenças nos conceitos de polarizaçao de fot0ns.e eletrons, mostra-se que o mesmo formalismo pode ser usado para descreve-los, o que é muito útil no estudo de interações envolvendo polarizações de ambos, fotons e eletrons, como em efeitos fotoelétrico e Compton. Nes- te trabalho os fotons são considerados como um caso especial de partí- culas relativísticas de spin 1, com massa de repouso nula. 1. INTRODUCTION Dur ing a research progi-am concerned xi th correlat ions between polarizãtions of photons and electror~sin relativistic photoelectric effect, i t was noticed the lack of a text which brings together thecon- cepts and simplified descriptions of polarization of electron and pho- ton beams . That was the reason for trying to write such a text. -
Lab 8: Polarization of Light
Lab 8: Polarization of Light 1 Introduction Refer to Appendix D for photos of the appara- tus Polarization is a fundamental property of light and a very important concept of physical optics. Not all sources of light are polarized; for instance, light from an ordinary light bulb is not polarized. In addition to unpolarized light, there is partially polarized light and totally polarized light. Light from a rainbow, reflected sunlight, and coherent laser light are examples of po- larized light. There are three di®erent types of po- larization states: linear, circular and elliptical. Each of these commonly encountered states is characterized Figure 1: (a)Oscillation of E vector, (b)An electromagnetic by a di®ering motion of the electric ¯eld vector with ¯eld. respect to the direction of propagation of the light wave. It is useful to be able to di®erentiate between 2 Background the di®erent types of polarization. Some common de- vices for measuring polarization are linear polarizers and retarders. Polaroid sunglasses are examples of po- Light is a transverse electromagnetic wave. Its prop- larizers. They block certain radiations such as glare agation can therefore be explained by recalling the from reflected sunlight. Polarizers are useful in ob- properties of transverse waves. Picture a transverse taining and analyzing linear polarization. Retarders wave as traced by a point that oscillates sinusoidally (also called wave plates) can alter the type of polar- in a plane, such that the direction of oscillation is ization and/or rotate its direction. They are used in perpendicular to the direction of propagation of the controlling and analyzing polarization states. -
Observation of Elliptically Polarized Light from Total Internal Reflection in Bubbles
Observation of elliptically polarized light from total internal reflection in bubbles Item Type Article Authors Miller, Sawyer; Ding, Yitian; Jiang, Linan; Tu, Xingzhou; Pau, Stanley Citation Miller, S., Ding, Y., Jiang, L. et al. Observation of elliptically polarized light from total internal reflection in bubbles. Sci Rep 10, 8725 (2020). https://doi.org/10.1038/s41598-020-65410-5 DOI 10.1038/s41598-020-65410-5 Publisher NATURE PUBLISHING GROUP Journal SCIENTIFIC REPORTS Rights Copyright © The Author(s) 2020. Open Access This article is licensed under a Creative Commons Attribution 4.0 International License. Download date 29/09/2021 02:08:57 Item License https://creativecommons.org/licenses/by/4.0/ Version Final published version Link to Item http://hdl.handle.net/10150/641865 www.nature.com/scientificreports OPEN Observation of elliptically polarized light from total internal refection in bubbles Sawyer Miller1,2 ✉ , Yitian Ding1,2, Linan Jiang1, Xingzhou Tu1 & Stanley Pau1 ✉ Bubbles are ubiquitous in the natural environment, where diferent substances and phases of the same substance forms globules due to diferences in pressure and surface tension. Total internal refection occurs at the interface of a bubble, where light travels from the higher refractive index material outside a bubble to the lower index material inside a bubble at appropriate angles of incidence, which can lead to a phase shift in the refected light. Linearly polarized skylight can be converted to elliptically polarized light with efciency up to 53% by single scattering from the water-air interface. Total internal refection from air bubble in water is one of the few sources of elliptical polarization in the natural world. -
Ellipsometry
AALBORG UNIVERSITY Institute of Physics and Nanotechnology Pontoppidanstræde 103 - 9220 Aalborg Øst - Telephone 96 35 92 15 TITLE: Ellipsometry SYNOPSIS: This project concerns measurement of the re- fractive index of various materials and mea- PROJECT PERIOD: surement of the thickness of thin films on sili- September 1st - December 21st 2004 con substrates by use of ellipsometry. The el- lipsometer used in the experiments is the SE 850 photometric rotating analyzer ellipsome- ter from Sentech. THEME: After an introduction to ellipsometry and a Detection of Nanostructures problem description, the subjects of polar- ization and essential ellipsometry theory are covered. PROJECT GROUP: The index of refraction for silicon, alu- 116 minum, copper and silver are modelled us- ing the Drude-Lorentz harmonic oscillator model and afterwards measured by ellipsom- etry. The results based on the measurements GROUP MEMBERS: show a tendency towards, but are not ade- Jesper Jung quately close to, the table values. The mate- Jakob Bork rials are therefore modelled with a thin layer of oxide, and the refractive indexes are com- Tobias Holmgaard puted. This model yields good results for the Niels Anker Kortbek refractive index of silicon and copper. For aluminum the result is improved whereas the result for silver is not. SUPERVISOR: The thickness of a thin film of SiO2 on a sub- strate of silicon is measured by use of ellip- Kjeld Pedersen sometry. The result is 22.9 nm which deviates from the provided information by 6.5 %. The thickness of two thick (multiple wave- NUMBERS PRINTED: 7 lengths) thin polymer films are measured. The polymer films have been spin coated on REPORT PAGE NUMBER: 70 substrates of silicon and the uniformities of the surfaces are investigated. -
Understanding Polarization
Semrock Technical Note Series: Understanding Polarization The Standard in Optical Filters for Biotech & Analytical Instrumentation Understanding Polarization 1. Introduction Polarization is a fundamental property of light. While many optical applications are based on systems that are “blind” to polarization, a very large number are not. Some applications rely directly on polarization as a key measurement variable, such as those based on how much an object depolarizes or rotates a polarized probe beam. For other applications, variations due to polarization are a source of noise, and thus throughout the system light must maintain a fixed state of polarization – or remain completely depolarized – to eliminate these variations. And for applications based on interference of non-parallel light beams, polarization greatly impacts contrast. As a result, for a large number of applications control of polarization is just as critical as control of ray propagation, diffraction, or the spectrum of the light. Yet despite its importance, polarization is often considered a more esoteric property of light that is not so well understood. In this article our aim is to answer some basic questions about the polarization of light, including: what polarization is and how it is described, how it is controlled by optical components, and when it matters in optical systems. 2. A description of the polarization of light To understand the polarization of light, we must first recognize that light can be described as a classical wave. The most basic parameters that describe any wave are the amplitude and the wavelength. For example, the amplitude of a wave represents the longitudinal displacement of air molecules for a sound wave traveling through the air, or the transverse displacement of a string or water molecules for a wave on a guitar string or on the surface of a pond, respectively. -
Results from the QUIET Q-Band Observing Season COLUMBIA
Results from the QUIET Q-Band Observing Season Robert Nicolas Dumoulin Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the Graduate School of Arts and Science COLUMBIA UNIVERSITY 2011 ©2011 Robert Nicolas Dumoulin All Rights Reserved Abstract Results from the QUIET Q-Band Observing Season Robert Nicolas Dumoulin The Q/U Imaging ExperimenT (QUIET) is a ground-based telescope located in the high Atacama Desert in Chile, and is designed to measure the polarization of the Cosmic Mi- crowave Background (CMB) in the Q and W frequency bands (43 and 95 GHz respec- tively) using coherent polarimeters. From 2008 October to 2010 December, data from more than 10,000 observing hours were collected, first with the Q-band receiver (2008 October to 2009 June) and then with the W-band receiver (until the end of the 2010 ob- serving season). The QUIET data analysis effort uses two independent pipelines, one consisting of a max- imum likelihood framework and the other consisting of a pseudo-C` framework. Both pipelines employ blind analysis methods, and each provides analysis of the data using large suites of null tests specific to the pipeline. Analysis of the Q-band receiver data was completed in November of 2010, confirming the only previous detection of the first acoustic peak of the EE power spectrum and setting competitive limits on the scalar-to- tensor ratio, r. In this dissertation, the results from the Q-band observing season using the maximum likelihood pipeline will be presented. Contents 1 The Cosmic Microwave Background 1 1.1 The Origins and Features of the CMB . -
Elliptical Polarization
Lecture 5: Polarization and Related Antenna Parameters (Polarization of EM fields – revision. Polarization vector. Antenna polarization. Polarization loss factor and polarization efficiency.) 1. Polarization of EM fields. The polarization of the EM field describes the time variations of the field vectors at a given point. In other words, it describes the way the direction and magnitude the field vectors (usually E ) change in time. The polarization is the figure traced by the extremity of the time- varying field vector at a given point. According to the shape of the trace, three types of polarization exist for harmonic fields: linear, circular and elliptical: y y y E E E ω z x z x z x (a) linear polarization (b) circular polarization (c) elliptical polarization Any type of polarization can be represented by two orthogonal linear polarizations, ( EExy, )or(EEHV, ), whose fields are out of phase by an angle δ of L . • δ = π IfL 0 or n , then a linear polarization results. • δπ= = If L /2 (90) and EExy, then a circular polarization results. • In the most general case, elliptical polarization is defined. 1 It is also true that any type of polarization can be represented by a right-hand circular and a left-hand circular polarizations (EELR , ). We shall revise the above statements and definitions, while introducing the new concept of polarization vector. 2. Field polarization in terms of two orthogonal linearly polarized components. The polarization of any field can be represented by a suitable set of two orthogonal linearly polarized fields. Assume that locally a far field propagates along the z-axis, and the field vectors have only transverse components. -
Polarized Light, It Is Important That the Azimuthal Angle of a Polarization Optic (I.E
An Economical Means for Accurate Azimuthal Alignment of Polarization Optics © 2005 Meadowlark Optics, Inc. Joel R. Blum* Meadowlark Optics, 5964 Iris Parkway, PO Box 1000, Frederick, CO, USA 80530 ABSTRACT For many applications involving polarized light, it is important that the azimuthal angle of a polarization optic (i.e. polarizer, retarder, etc…) be accurately aligned to a physical datum or to an eigenaxis of another polarization optic. A simple opto-mechanical tool for azimuthal alignment can be used to perform accurate alignments and consists of two “rotatable” mounts. One mount holds a polarizer, while the other holds a half-wave retarder. The method of swings is used to aid in the azimuthal alignment of the polarization optic and is illustrated using the Poincaré Sphere. Additionally, imperfections in polarization optics are discussed. Keywords: alignment, polarization, optic, polarizer, azimuthal, kinematic, swings, waveplate 1. INTRODUCTION 1.1.Polarized Light Basics Polarized light can be divided into three different states: linear, elliptical, and circular. For monochromatic light, these three states can be represented using their electric field amplitudes and a phase lag term. The electric field amplitudes are broken down into their x and y components, which are aligned to a convenient reference frame. The phase lag term describes the phase relationship between the x and y components. A phase lag of ±90˚ describes circularly polarized light, while a phase lag of 0˚ describes linearly polarized light. Other phase lags between -180˚ and +180˚ describe elliptically polarized light. The ellipticity, ε, is defined as the ratio of the minor axis, b, over the major axis, a, and α is the angle of the major axis from the horizontal, as shown in Figure 1. -
Electron-Spin Dynamics in Elliptically Polarized Light Waves
Electron-spin dynamics in elliptically polarized light waves 1, 1, 2 1, 2 Heiko Bauke, ∗ Sven Ahrens, and Rainer Grobe 1Max-Planck-Institut für Kernphysik, Saupfercheckweg 1, 69117 Heidelberg, Germany 2Intense Laser Physics Theory Unit and Department of Physics, Illinois State University, Normal, Illinois 61790-4560 USA (Dated: November 4, 2014) We investigate the coupling of the spin angular momentum of light beams with elliptical polarization to the spin degree of freedom of free electrons. It is shown that this coupling, which is of similar origin as the well-known spin-orbit coupling, can lead to spin precession. The spin-precession frequency is proportional to the product of the laser-field’s intensity and its spin density. The electron-spin dynamics is analyzed by employing exact numerical methods as well as time-dependent perturbation theory based on the fully relativistic Dirac equation and on the nonrelativistic Pauli equation that is amended by a relativistic correction that accounts for the light’s spin density. PACS numbers: 03.65.Pm, 31.15.aj, 31.30.J– 1. Introduction quantum mechanical equations of motion, relativistic and non- relativistic. Subsequently, we solve these equations via time- dependent perturbation theory in Sec. 3 and by numerical meth- Novel light sources such as the ELI-Ultra High Field Facility, ods in Sec. 4. In Sec. 5 we estimate under which experimental for example, envisage to provide field intensities in excess of 20 2 conditions the predicted spin precession may be realized before 10 W/cm and field frequencies in the x-ray domain [1–6]. we summarize our results in Sec. -
Modeling and Measuring the Polarization of Light: from Jones Matrices to Ellipsometry
MODELING AND MEASURING THE POLARIZATION OF LIGHT: FROM JONES MATRICES TO ELLIPSOMETRY OVERALL GOALS The Polarization of Light lab strongly emphasizes connecting mathematical formalism with measurable results. It is not your job to understand every aspect of the theory, but rather to understand it well enough to make predictions in a variety of experimental situations. The model developed in this lab will have parameters that are easily experimentally adjustable. Additionally, you will refine your predictive models by accounting for systematic error sources that occur in the apparatus. The overarching goals for the lab are to: Model the vector nature of light. (Week 1) Model optical components that manipulate polarization (e.g., polarizing filters and quarter-wave plates). (Week 1) Measure a general polarization state of light. (Week 1) Model and measure the reflection and transmission of light at a dielectric interface. (Week 2) Perform an ellipsometry measurement on a Lucite surface. WEEK 1 PRELIMINARY OBSERVATIONS Question 1 Set up the optical arrangement shown in Figure 1. It consists of (1) a laser, (2) Polarizing filters, (3) A quarter-wave plate (4) A photodetector. Observe the variation in the photodetector voltage as you rotate the polarizing filters and/or quarter-wave plate. This is as complicated as the apparatus gets. The challenge of week 1 is to build accurate models of these components and model their combined effect in an optical system. An understanding of polarized light and polarizing optical elements forms the foundation of many optical applications including AMO experiments such as magneto-optical traps, LCD displays, and 3D projectors. -
A Simple Method for Changing the State of Polarization from Elliptical Into Circular
INVESTIGACION´ REVISTA MEXICANA DE FISICA´ 51 (5) 510–515 OCTUBRE 2005 A simple method for changing the state of polarization from elliptical into circular M. Montoya, G. Paez, D. Malacara-Hernandez,´ and J. Garc´ıa-Marquez´ Centro de Investigaciones en Optica,´ A.C., Loma del Bosque 115, Col. Lomas del Campestre, Leon,´ Gto., 37150 Mexico,´ e-mail: [email protected], [email protected], [email protected], [email protected] Recibido el 25 de mayo de 2005; aceptado el 7 de julio de 2005 Changes of polarization occur as a consequence of the interaction of light and the various optical elements through which it passes. A circularly polarized light beam may change its state to slightly elliptically polarized for many reasons. To correct this is not always easy but we show a very simple method for correcting circular polarization that has changed slightly into elliptic polarization. In this paper we propose to restore the circular state of polarization of an elliptically polarized light beam back to circular by means of a glass plate properly oriented while polarization is being measured. The basic idea is to modulate the transmittances of the electric field in both the major and minor axes of the ellipse of polarization. It is done by means of glass plates at non-normal incidence. Experimental results are consistent with theory. Keywords: Interference; polarization; polarizers; interferometers; interferometry. Al pasar la luz a traves´ de diferentes elementos opticos,´ ocurren cambios de polarizacion.´ Un haz circularmente polarizado puede cambiar ligeramente a el´ıpticamente polarizado por muchas razones. Corregir esto puede ser complicado. -
Arxiv:1309.5454V1 [Astro-Ph.SR] 21 Sep 2013 E-Mail: Stenfl[email protected] 2 J.O
The Astronomy and Astrophysics Review manuscript No. (will be inserted by the editor) Solar magnetic fields as revealed by Stokes polarimetry J.O. Stenflo Received: 10 July 2013 / Accepted: 4 September 2013 Abstract Observational astrophysics started when spectroscopy could be applied to astronomy. Similarly, observational work on stellar magnetic fields became possible with the application of spectro-polarimetry. In recent decades there have been dramatic advances in the observational tools for spectro- polarimetry. The four Stokes parameters that provide a complete represen- tation of partially polarized light can now be simultaneously imaged with megapixel array detectors with high polarimetric precision (10−5 in the degree of polarization). This has led to new insights about the nature and properties of the magnetic field, and has helped pave the way for the use of the Hanle effect as a diagnostic tool beside the Zeeman effect. The magnetic structuring continues on scales orders of magnitudes smaller than the resolved ones, but various types of spectro-polarimetric signatures can be identified, which let us determine the field strengths and angular distributions of the field vectors in the spatially unresolved domain. Here we review the observational properties of the magnetic field, from the global patterns to the smallest scales at the magnetic diffusion limit, and relate them to the global and local dynamos. Keywords Sun: atmosphere · magnetic fields · polarization · dynamo · magnetohydrodynamics (MHD) 1 Historical background The discovery and classification by Joseph Fraunhofer of the absorption lines in the Sun's spectrum and the demonstration by Bunsen and Kirchhoff that such lines represent “fingerprints" of chemical elements marked the birth of modern astrophysics.