DOCSLIB.ORG

Optic Axis of a Crystal: the Direction of Linear Polarization Along Which the Resonance Is Different from the Other Two Axes (Assuming Them Equal) Calcite (Caco3)

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Optic Axis of a Crystal: the Direction of Linear Polarization Along Which the Resonance Is Different from the Other Two Axes (Assuming Them Equal) Calcite (Caco3) Phys 322 Chapter 8 Lecture 22 Polarization Dichroism = selective absorption of light of certain polarization Linear dichroism - selective absorption of one of the two P-state (linear) orthogonal polarizations Circular dichroism - selective absorption of L-state or R-state circular polarizations Using dichroic materials one can build a polarizer Dichroic crystals Anisotropic crystal structure: one polarization is absorbed more than the other Example: tourmaline Elastic constants for electrons may be different along two axes Polaroid 1928: dichroic sheet polarizer, J-sheet long tiny crystals of herapathite aligned in the plastic sheet Edwin Land 1938: H-sheet 1909-1991 Attach Iodine molecules to polymer molecules - molecular size iodine wires Presently produced: HN-38, HN-32, HN-22 Birefringence Elastic constants for electrons may be different along axes Resonance frequencies will be different for light polarized Refraction index depends on along different axes polarization: birefringence Dichroic crystal - absorbs one of the orthogonal P-states, transmits the other Optic axis of a crystal: the direction of linear polarization along which the resonance is different from the other two axes (assuming them equal) Calcite (CaCO3) Ca C O Image doubles Ordinary rays (o-rays) - unbent Extraordinary rays (e-rays) - bend Calcite (CaCO3) emerging rays are orthogonaly polarized Principal plane - any plane that contains optical axis Principal section - principal plane that is normal to one of the cleavage surfaces Birefringence and Huygens’ principle Crystal structure and birefringence NaCl - cubic crystal Four 3-fold symmetry axes - optically isotropic Anisotropic, uniaxial birefringent crystals: hexagonal, tetragonal, trigonal Uniaxial crystal: atoms are arranged symmetrically around optic axis O-wave - E everywhere is perpendicular to the optic axis, no c/v When E is parallel to optic axis: ne c/v|| Birefringence ne - no principal indices of refraction Calcite: (ne - no) = -0.172 (negative uniaxial crystal) Crystal structure and birefringence Negative uniaxial crystal Positive uniaxial crystal Biaxial crystals Two optic axes and three principal indices of refraction Orthorhombic, monoclinic, triclinic Example: mica, KH2Al3(SiO4)3 Birefringent polarizers Nicol prism Glan-Thompson Wollaston prism polarizer 1828, William Nicol Polarization by scattering Scattering can polarize light Scattering can depolarize light Polarization by reflection Reminder: Fresnel equations show r||=0 at B - Brewster angle 1 B tan n2 n1 At Brewster angle reflected and transmitted rays form right angle B Reflected light will be fully polarized at B Fresnel equations 2 2 tan i t R r R|| 2 Fresnel equations tan i t 2 sin sin i t i t R r 2 sin i t sini t tan r i t || tan … i t Reflectance of unpolaized light: R R R || 2 Fresnel equations Multiple plate polarizer Degree of polarization: V I p Itot analyzing polarizer I I V max min Imax Imin detector Glare is horizontally polarized Puddle reflection viewed Puddle reflection viewed through polarizer that through polarizer that transmits only horizontally transmits only vertically polarized light polarized light Light reflected into our eyes from the puddle reflects at about Brewster's Angle. So parallel (i.e., vertical) polarization sees zero reflection. Polarizer sunglasses transmit only vertically polarized light. Polarizers are very useful in photography. Without a polarizer With a polarizer The effect of a polarizer is probably the one “filter” effect that you can’t reproduce later using Photoshop! Retarders The two orthogonal P-states develop mutual phase shift as they pass through a retarder After propagating through: E E|| E polarized light phase shift: E E|| E birefringence extraordinary 2 in-phase ordinary dne no 0 in vacuum direction of polarization: E|| E0|| coskx t fast axis - the one that propagates faster slow axis - the one that propagates slower E E0 coskx t Full-wave plate 2 dn n e o = m.2, m=…,-1,0,+1,… 0 E|| E0|| coskx t Alternatively: dne no m0 E E0 coskx t full wave - no observable effect Note: n=n(), and it is generally true only for one wavelength Half-wave plate = +m.2, m=…,-1,0,+1,… 2 dne no 0 dne no 0 / 2 m0 E|| E0|| coskx t E E0 coskx t Polarization is rotated around the optic axis Special case: =45o Polarization is rotated by 90o Quarter-wave plate . 2 = /2 +m 2, m=…,-1,0,+1,… dne no 0 dne no 0 / 4 m0 E|| E0|| coskx t E E coskx t Linear polarization is converted into 0 circular/elliptical and vice versa Reflective retarders Total internal reflection: phase shift between the two components. Glass - n=1.51, and 45o shift occurs at incidence angle 54.6o. Fresnel rhomb Unlike devices that use birefringent materials this is achromatic Circular polarizer Can you make a polarizer that transmits right circularly polarized light but not the left circularly polarized light?.
Load more

Recommended publications
  • Polarization Optics Polarized Light Propagation Partially Polarized Light
    The physics of polarization optics Polarized light propagation Partially polarized light Polarization Optics N. Fressengeas Laboratoire Mat´eriaux Optiques, Photonique et Syst`emes Unit´ede Recherche commune `al’Universit´ede Lorraine et `aSup´elec Download this document from http://arche.univ-lorraine.fr/ N. Fressengeas Polarization Optics, version 2.0, frame 1 The physics of polarization optics Polarized light propagation Partially polarized light Further reading [Hua94, GB94] A. Gerrard and J.M. Burch. Introduction to matrix methods in optics. Dover, 1994. S. Huard. Polarisation de la lumi`ere. Masson, 1994. N. Fressengeas Polarization Optics, version 2.0, frame 2 The physics of polarization optics Polarized light propagation Partially polarized light Course Outline 1 The physics of polarization optics Polarization states Jones Calculus Stokes parameters and the Poincare Sphere 2 Polarized light propagation Jones Matrices Examples Matrix, basis & eigen polarizations Jones Matrices Composition 3 Partially polarized light Formalisms used Propagation through optical devices N. Fressengeas Polarization Optics, version 2.0, frame 3 The physics of polarization optics Polarization states Polarized light propagation Jones Calculus Partially polarized light Stokes parameters and the Poincare Sphere The vector nature of light Optical wave can be polarized, sound waves cannot The scalar monochromatic plane wave The electric field reads: A cos (ωt kz ϕ) − − A vector monochromatic plane wave Electric field is orthogonal to wave and Poynting vectors
    [Show full text]
  • James Clerk Maxwell
    James Clerk Maxwell JAMES CLERK MAXWELL Perspectives on his Life and Work Edited by raymond flood mark mccartney and andrew whitaker 3 3 Great Clarendon Street, Oxford, OX2 6DP, United Kingdom Oxford University Press is a department of the University of Oxford. It furthers the University’s objective of excellence in research, scholarship, and education by publishing worldwide. Oxford is a registered trade mark of Oxford University Press in the UK and in certain other countries c Oxford University Press 2014 The moral rights of the authors have been asserted First Edition published in 2014 Impression: 1 All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, without the prior permission in writing of Oxford University Press, or as expressly permitted by law, by licence or under terms agreed with the appropriate reprographics rights organization. Enquiries concerning reproduction outside the scope of the above should be sent to the Rights Department, Oxford University Press, at the address above You must not circulate this work in any other form and you must impose this same condition on any acquirer Published in the United States of America by Oxford University Press 198 Madison Avenue, New York, NY 10016, United States of America British Library Cataloguing in Publication Data Data available Library of Congress Control Number: 2013942195 ISBN 978–0–19–966437–5 Printed and bound by CPI Group (UK) Ltd, Croydon, CR0 4YY Links to third party websites are provided by Oxford in good faith and for information only.
    [Show full text]
  • Polarizer QWP Mirror Index Card
    PH 481 Physical Optics Winter 2014 Laboratory #8 Week of March 3 Read: pp. 336-344, 352-356, and 360-365 of "Optics" by Hecht Do: 1. Experiment VIII.1: Birefringence and Optical Isolation 2. Experiment VIII.2: Birefringent crystals: double refraction 3. Experiment VIII.3: Optical activity: rotary power of sugar Experiment VIII.1: Birefringence and Optical Isolation In this experiment the birefringence of a material will be used to change the polarization of the laser beam. You will use a quarter-wave plate and a polarizer to build an optical isolator. This is a useful device that ensures that light is not reflected back into the laser. This has practical importance since light reflected back into a laser can perturb the laser operation. A quarter-wave plate is a specific example of a retarder, a device that introduces a phase difference between waves with orthogonal polarizations. A birefringent material has two different indices of refraction for orthogonal polarizations and so is well suited for this task. We will refer to these two directions as the fast and slow axes. A wave polarized along the fast axis will move through the material faster than a wave polarized along the slow axis. A wave that is linearly polarized along some arbitrary direction can be decomposed into its components along the slow and fast axes, resulting in part of the wave traveling faster than the other part. The wave that leaves the material will then have a more general elliptical polarization. A quarter-wave plate is designed so that the fast and slow Laser components of a wave will experience a relative phase shift of Index Card π/2 (1/4 of 2π) upon traversing the plate.
    [Show full 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.
    [Show full text]
  • Fresnel Rhombs As Achromatic Phase Shifters for Infrared Nulling Interferometry: First Experimental Results
    Fresnel Rhombs as Achromatic Phase Shifters for Infrared Nulling Interferometry: First experimental results Hanot c.a, Mawet D.a, Loicq J.b, Vandormael D.b, Plesseria J.Y.b, Surdej J.a, Habraken s.a,b alnstitut d'Astrophysique et de Geophysique, University of Liege, 17 allee du 6 Aout, B-4000, Sart Tilman, Belgium; bCentre Spatial de Liege, Avenue du Pre-Aily, B-4031, Liege-Angleur, Belgium ABSTRACT One of the most critical units of nulling interferometers is the Achromatic Phase Shifter. The concept we propose here is based on optimized Fresnel rhombs, using the total internal reflection phenomenon, modulated or not. The total internal reflection induces a phase shift between the polarization components of the incident light. We present the principles, the current status of the prototype manufacturing and testing operations, as well as preliminary experiments on a ZnSe Fresnel rhomb in the visible that have led to a first error source assessment study. Thanks to these first experimental results using a simple polarimeter arrangement, we have identified the bulk scattering as being the main error source. Fortunately, we have experimentally verified that the scattering can be mitigated using spatial filters and does not decrease the phase shifting capabilities of the ZnSe Fresnel rhomb. Keywords: Fresnel Rhomb, Achromatic Phase Shifters, nulling interferometry, subwavelength gratings, Zinc Selenide, bulk scattering 1. INTRODUCTION The detection of extrasolar planets and later on the presence of life on them is one of the most interesting and ambitious astrophysical projects for the next decades. Up to now, despite our technological progresses, most exoplanets have been detected using indirect methods.
    [Show full text]
  • Dual Beam Detection Technique to Study Magneto-Optical Kerr
    DUAL BEAM DETECTION TECHNIQUE TO STUDY MAGNETO-OPTICAL KERR EFFECT By Shankar Chandra Acharya, Msc A thesis submitted to the Graduate Council of Texas State University in partial fulfillment of the requirements for the degree of Master of Science with a Major in Physics May 2019 Committee Members: Wilhelmus J Geerts, Chair Nikoleta Theodoropoulou Alexander Zakhidov COPYRIGHT By Shankar Chandra Acharya 2019 FAIR USE AND AUTHOR’S PERMISSION STATEMENT Fair Use This work is protected by the Copyright Laws of the United States (Public Law 94-553, section 107). Consistent with fair use as defined in the Copyright Laws, brief quotations from this material are allowed with proper acknowledgement. Use of this material for financial gain without the author’s express written permission is not allowed. Duplication Permission As the copyright holder of this work I, Shankar Chandra Acharya, authorize duplication of this work, in whole or in part, for educational or scholarly purposes only. ACKNOWLEDGEMENTS First of all, I would like to than my supervisor Dr. Wilhelmus J Geerts for his constant support and guidance. I feel grateful to have worked under such an inspiring researcher who has given me this opportunity to learn and explore scientific knowledge. I would also like to thank my committee members Dr. Nikoleta Theodoropoulou and Dr. Alexander Zakhidov for their constructive feedback which have contributed to my thesis project. I am grateful for my family and friends for their motivation and encouragement all these years of my studies. My mother and father have supported me during the difficult times and inspired me throughout my research.
    [Show full text]
  • Polarization of EM Waves
    Light in different media A short review • Reflection of light: Angle of incidence = Angle of reflection • Refraction of light: Snell’s law Refraction of light • Total internal reflection For some critical angle light beam will be reflected: 1 n2 c sin n1 For some critical angle light beam will be reflected: Optical fibers Optical elements Mirrors i = p flat concave convex 1 1 1 p i f Summary • Real image can be projected on a screen • Virtual image exists only for observer • Plane mirror is a flat reflecting surface Plane Mirror: ip • Convex mirrors make objects smaller • Concave mirrors make objects larger 1 Spherical Mirror: fr 2 Geometrical Optics • “Geometrical” optics (rough approximation): light rays (“particles”) that travel in straight lines. • “Physical” Classical optics (good approximation): electromagnetic waves which have amplitude and phase that can change. • Quantum Optics (exact): Light is BOTH a particle (photon) and a wave: wave-particle duality. Refraction For y = 0 the same for all x, t Refraction Polarization Polarization By Reflection Different polarization of light get reflected and refracted with different amplitudes (“birefringence”). At one particular angle, the parallel polarization is NOT reflected at all! o This is the “Brewster angle” B, and B + r = 90 . (Absorption) o n1 sin n2 sin(90 ) n2 cos n2 tan Polarizing Sunglasses n1 Polarized Sunglasses B Linear polarization Ey Asin(2x / t) Vertically (y axis) polarized wave having an amplitude A, a wavelength of and an angular velocity (frequency * 2) of , propagating along the x axis. Linear polarization Vertical Ey Asin(2x / t) Horizontal Ez Asin(2x / t) Linear polarization • superposition of two waves that have the same amplitude and wavelength, • are polarized in two perpendicular planes and oscillate in the same phase.
    [Show full text]
  • (EM) Waves Are Forms of Energy That Have Magnetic and Electric Components
    Physics 202-Section 2G Worksheet 9-Electromagnetic Radiation and Polarizers Formulas and Concepts Electromagnetic (EM) waves are forms of energy that have magnetic and electric components. EM waves carry energy, not matter. EM waves all travel at the speed of light, which is about 3*108 m/s. The speed of light is often represented by the letter c. Only small part of the EM spectrum is visible to us (colors). Waves are defined by their frequency (measured in hertz) and wavelength (measured in meters). These quantities are related to velocity of waves according to the formula: 풗 = 흀풇 and for EM waves: 풄 = 흀풇 Intensity is a property of EM waves. Intensity is defined as power per area. 푷 푺 = , where P is average power 푨 o Intensity is related the magnetic and electric fields associated with an EM wave. It can be calculated using the magnitude of the magnetic field or the electric field. o Additionally, both the average magnetic and average electric fields can be calculated from the intensity. ퟐ ퟐ 푩 푺 = 풄휺ퟎ푬 = 풄 흁ퟎ Polarizability is a property of EM waves. o Unpolarized waves can oscillate in more than one orientation. Polarizing the wave (often light) decreases the intensity of the wave/light. o When unpolarized light goes through a polarizer, the intensity decreases by 50%. ퟏ 푺 = 푺 ퟏ ퟐ ퟎ o When light that is polarized in one direction travels through another polarizer, the intensity decreases again, according to the angle between the orientations of the two polarizers. ퟐ 푺ퟐ = 푺ퟏ풄풐풔 휽 this is called Malus’ Law.
    [Show full text]
  • Second Harmonic Generation in Nonlinear Optical Crystal
    Second Harmonic Generation in Nonlinear Optical Crystal Diana Jeong 1. Introduction In traditional electromagnetism textbooks, polarization in the dielectric material is linearly proportional to the applied electric field. However since in 1960, when the coherent high intensity light source became available, people realized that the linearity is only an approximation. Instead, the polarization can be expanded in terms of applied electric field. (Component - wise expansion) (1) (1) (2) (3) Pk = ε 0 (χ ik Ei + χ ijk Ei E j + χ ijkl Ei E j Ek +L) Other quantities like refractive index (n) can be expanded in terms of electric field as well. And the non linear terms like second (E^2) or third (E^3) order terms become important. In this project, the optical nonlinearity is present in both the source of the laser-mode-locked laser- and the sample. Second Harmonic Generation (SHG) is a coherent optical process of radiation of dipoles in the material, dependent on the second term of the expansion of polarization. The dipoles are oscillated with the applied electric field of frequency w, and it radiates electric field of 2w as well as 1w. So the near infrared input light comes out as near UV light. In centrosymmetric materials, SHG cannot be demonstrated, because of the inversion symmetries in polarization and electric field. The only odd terms survive, thus the second order harmonics are not present. SHG can be useful in imaging biological materials. For example, the collagen fibers and peripheral nerves are good SHG generating materials. Since the SHG is a coherent process it, the molecules, or the dipoles are not excited in terms of the energy levels.
    [Show full text]
  • De Sénarmont Bias Retardation in DIC Microscopy Stanley Schwartz1, Douglas B
    de Sénarmont Bias Retardation in DIC Microscopy Stanley Schwartz1, Douglas B. Murphy2, Kenneth R. Spring3, and Michael W. Davidson4 1Bioscience Department, Nikon Instruments, Inc., 1300 Walt Whitman Road, Melville, New York 11747. 2Department of Cell Biology and Anatomy and Microscope Facility, Johns Hopkins University School of Medicine, 725 N. Wolfe Street, 107 WBSB, Baltimore, Maryland 21205. 3National Heart, Lung, and Blood Institute, National Institutes of Health, Building 10, Room 6N260, Bethesda, Maryland 20892 4National High Magnetic Field Laboratory, Florida State University, Tallahassee, Florida 3231 Keywords: microscopy, de Senarmont, Henri Hureau de Sénarmont, Francis Smith, Georges Nomarski, William Hyde Wollaston, Michel- Levy color chart, contrast-enhancement techniques, depth of field, bias, retardation, compensating, plates, DIC, differential interference, contrast, prisms, compensators, shadow-cast, relief, pseudo, three-dimensional, birefringence, optical staining, sectioning, spherical aberrations, wavefronts, shear, fast, slow, axes, axis, linear, circularly, elliptically, polarized light, polarizers, analyzers, orthogonal, path, differences, OPD, gradients, phase, ordinary, extraordinary, maximum extinction, quarter-wavelength, full-wave plates, first-order red, halo, artifacts, interference plane, VEC, video enhanced, VE-DIC, Newtonian, interference colors, Nikon, Eclipse E600, microscopes, buccal, mucosa, epithelial, cheek cells, ctenoid, fish scales, Obelia, hydroids, polyps, coelenterates, murine, rodents, rats,
    [Show full text]
  • Lecture 14: Polarization
    Matthew Schwartz Lecture 14: Polarization 1 Polarization vectors In the last lecture, we showed that Maxwell’s equations admit plane wave solutions ~ · − ~ · − E~ = E~ ei k x~ ωt , B~ = B~ ei k x~ ωt (1) 0 0 ~ ~ Here, E0 and B0 are called the polarization vectors for the electric and magnetic fields. These are complex 3 dimensional vectors. The wavevector ~k and angular frequency ω are real and in the vacuum are related by ω = c ~k . This relation implies that electromagnetic waves are disper- sionless with velocity c: the speed of light. In materials, like a prism, light can have dispersion. We will come to this later. In addition, we found that for plane waves 1 B~ = ~k × E~ (2) 0 ω 0 This equation implies that the magnetic field in a plane wave is completely determined by the electric field. In particular, it implies that their magnitudes are related by ~ ~ E0 = c B0 (3) and that ~ ~ ~ ~ ~ ~ k · E0 =0, k · B0 =0, E0 · B0 =0 (4) In other words, the polarization vector of the electric field, the polarization vector of the mag- netic field, and the direction ~k that the plane wave is propagating are all orthogonal. To see how much freedom there is left in the plane wave, it’s helpful to choose coordinates. We can always define the zˆ direction as where ~k points. When we put a hat on a vector, it means the unit vector pointing in that direction, that is zˆ=(0, 0, 1). Thus the electric field has the form iω z −t E~ E~ e c = 0 (5) ~ ~ which moves in the z direction at the speed of light.
    [Show full text]
  • Lecture 26 – Propagation of Light Spring 2013 Semester Matthew Jones Midterm Exam
    Physics 42200 Waves & Oscillations Lecture 26 – Propagation of Light Spring 2013 Semester Matthew Jones Midterm Exam Almost all grades have been uploaded to http://chip.physics.purdue.edu/public/422/spring2013/ These grades have not been adjusted Exam questions and solutions are available on the Physics 42200 web page . Outline for the rest of the course • Polarization • Geometric Optics • Interference • Diffraction • Review Polarization by Partial Reflection • Continuity conditions for Maxwell’s Equations at the boundary between two materials • Different conditions for the components of or parallel or perpendicular to the surface. Polarization by Partial Reflection • Continuity of electric and magnetic fields were different depending on their orientation: – Perpendicular to surface = = – Parallel to surface = = perpendicular to − cos + cos − cos = cos + cos cos = • Solve for /: − = !" + !" • Solve for /: !" = !" + !" perpendicular to cos − cos cos = cos + cos cos = • Solve for /: − = !" + !" • Solve for /: !" = !" + !" Fresnel’s Equations • In most dielectric media, = and therefore # sin = = = = # sin • After some trigonometry… sin − tan − = − = sin + tan + ) , /, /01 2 ) 45/ 2 /01 2 * = - . + * = + * )+ /01 2+32* )+ /01 2+32* 45/ 2+62* For perpendicular and parallel to plane of incidence. Application of Fresnel’s Equations • Unpolarized light in air ( # = 1) is incident
    [Show full text]