How to Generate Polarized Light?
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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. -
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. -
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. -
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 -
Lecture 11: Introduction to Nonlinear Optics I
Lecture 11: Introduction to nonlinear optics I. Petr Kužel Formulation of the nonlinear optics: nonlinear polarization Classification of the nonlinear phenomena • Propagation of weak optic signals in strong quasi-static fields (description using renormalized linear parameters) ! Linear electro-optic (Pockels) effect ! Quadratic electro-optic (Kerr) effect ! Linear magneto-optic (Faraday) effect ! Quadratic magneto-optic (Cotton-Mouton) effect • Propagation of strong optic signals (proper nonlinear effects) — next lecture Nonlinear optics Experimental effects like • Wavelength transformation • Induced birefringence in strong fields • Dependence of the refractive index on the field intensity etc. lead to the concept of the nonlinear optics The principle of superposition is no more valid The spectral components of the electromagnetic field interact with each other through the nonlinear interaction with the matter Nonlinear polarization Taylor expansion of the polarization in strong fields: = ε χ + χ(2) + χ(3) + Pi 0 ij E j ijk E j Ek ijkl E j Ek El ! ()= ε χ~ (− ′ ) (′ ) ′ + Pi t 0 ∫ ij t t E j t dt + χ(2) ()()()− ′ − ′′ ′ ′′ ′ ′′ + ∫∫ ijk t t ,t t E j t Ek t dt dt + χ(3) ()()()()− ′ − ′′ − ′′′ ′ ′′ ′′′ ′ ′′ + ∫∫∫ ijkl t t ,t t ,t t E j t Ek t El t dt dt + ! ()ω = ε χ ()ω ()ω + ω χ(2) (ω ω ω ) (ω ) (ω )+ Pi 0 ij E j ∫ d 1 ijk ; 1, 2 E j 1 Ek 2 %"$"""ω"=ω +"#ω """" 1 2 + ω ω χ(3) ()()()()ω ω ω ω ω ω ω + ∫∫d 1d 2 ijkl ; 1, 2 , 3 E j 1 Ek 2 El 3 ! %"$""""ω"="ω +ω"#+ω"""""" 1 2 3 Linear electro-optic effect (Pockels effect) Strong low-frequency -
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. -
Polarization Phenomena of Certain Fluorites
142 TIIE AMERICAN MINERALOGIST Pleochroic,e :colorless, ,:pale blue-green, It thus differs from the average vesuvianite only in slightly higher birefringence. The writer wishes to acknowledge his indebtedness to Col. Roebling, Mr. Gage, and Ward's Natural ScienceEstablishment for the privilege of examining specimensand to Dr. Larsen for the opticaldeterminations. POLARIZATION PHENOMENA OF CERTAIN FLUORITES A. L. PansoNs, Uniaersity oJ Toronto While determining the refractive index of fluorite by the method of minimum deviation the writer introduced a nicol prism before the telescopeof the goniometer to determine the plane of polarization of the refracted ray. On rotating the nicol no difference in the intensity of light could be observed,but on examining the reflected ray nearly complete polarization was obtained so that it was thought that the prism was not cut at the angle that should give polarization if Brewster's law applies to isometric crystals. A new prism was then cut from a crystal of fluorite from Madoc, Ontario, so that the angle between the reflected ray and the refracted ray should be ninety degrees. With this new prism the same phenomena were observed. A second nicol was now intro- duced between the collimator and the crystal so that the signal was extinguished. On rotating the two nicols simultaneously extinction was obtained throughout a complete rotation so that it would appear as though we may accept without question the state- ment that a ray of light passing through fluorite vibrates with equal facility in all directions at right angles to the direction of propagation and is not polarized. -
GEOL 221 Mineralogy and Mineral Optics Course Syllabus
SAN DIEGO STATE UNIVERSITY GEOL 221 Mineralogy and Mineral Optics Course Syllabus Instructor: Professor David L. Kimbrough Email: [email protected], Phone: 594-1385 Lecture: MW 1000-1050 CSL 422, Lab: W 1400-1640, Lab study: M 1400-1640 CSL 425 Office: GMCS-229A; Office hours: MW 1100-1200; T 1115-1215; by appointment TA: Mark Nahabidian GMCS-133 TBA Course Prerequisite: Chem 200 or concurrent registration. Credit or concurrent registration in OCEAN 100 or GEOL 100 and 101 or GEOL 104 and 101; Geol 200; Required Texts: Introduction to Mineralogy, William D. Nesse, Oxford University Press. Minerals in Thin Section, Perkins & Henke, Prentice Hall Recommended Text: Dictionary of Geological Terms, AGI Bates & Jackson eds. or similar, The Complete Guide to Rocks & Minerals by John Farndon or similar Other required materials: Hand lens; calculator Classroom management: Attendance is crucial. Please let me know if you’re going to be absent for any reason. Be on time for class, don’t participate in excessive side-chatter or cause disruptions during class. Always respond to the instructor, the Teaching Assistant, and your fellow students in a respectful and civil manner. Cheating or plagiarism is not tolerated. It’s easy to spot and constitutes serious academic misconduct. Helpful hints to make Mineralogy easier and more fun! Attend class: Studies show that the most valuable time commitment by students in a course is the time actually spent in the classroom. Class time is the most important determinant of student success and yields the greatest improvement in student learning outcomes. Information is covered in class that is not in the textbook, and parts of the book are hard to understand. -
Huygen's Explanation of Double Refraction
06/08/2018 Before this lecture there were two lectures: 1. Introduction about this course. 2. Qualitative description about the various polarizations. Retarders • In retarders, one polarization gets ‘retarded’, or delayed, with respect to the other one. There is a final phase difference between the 2 components of the polarization. Therefore, the polarization is changed. • Most retarders are based on birefringent materials (quartz, mica, polymers) that have different indices of refraction depending on the polarization of the incoming light. 3 Phase shift of half wavelength Quarter Wave plate Circular polarization (IV) 7 How to generate Polarized Light? 1.Dichroic materials 2.Polarizer 3.Birefringent materials 4.Reflection 5.Scattering Wire grid polarizer Polaroid How to generate Polarized Light? 1.Dichroic materials 2.Polarizer 3.Birefringent materials 4.Reflection 5.Scattering Birefringence How to generate Polarized Light? 1.Dichroic materials 2.Polarizer 3.Birefringent materials 4.Reflection 5.Scattering Polarized Reflecting Light • When an unpolarized light wave reflects off a non-metallic surface, it can be completely polarized, partially polarized or unpolarized depending on the angle of incidence. A completely polarized wave occurs for an angle called Brewster’s angle (named after Sir David Brewster) Snell's law Incident Reflected ray ray p n 90o 1 n2 r n1sin P = n2sin r n1sin P = n2sin r = n2sin (90-P) = n2cos P tan P = n2/n1 P = Brewster’s angel Reflection • When an unpolarized wave reflects off a nonmetallic surface, the reflected wave is partially plane polarized parallel to the surface. The amount of polarization depends upon the angle (more later). The reflected ray contains more vibrations parallel to the reflecting surface while the transmitted beam contains more vibrations at right angles to these. -
Polarized Light 1
EE485 Introduction to Photonics Polarized Light 1. Matrix treatment of polarization 2. Reflection and refraction at dielectric interfaces (Fresnel equations) 3. Polarization phenomena and devices Reading: Pedrotti3, Chapter 14, Sec. 15.1-15.2, 15.4-15.6, 17.5, 23.1-23.5 Polarization of Light Polarization: Time trajectory of the end point of the electric field direction. Assume the light ray travels in +z-direction. At a particular instance, Ex ˆˆEExy y ikz() t x EEexx 0 ikz() ty EEeyy 0 iixxikz() t Ex[]ˆˆEe00xy y Ee e ikz() t E0e Lih Y. Lin 2 One Application: Creating 3-D Images Code left- and right-eye paths with orthogonal polarizations. K. Iizuka, “Welcome to the wonderful world of 3D,” OSA Optics and Photonics News, p. 41-47, Oct. 2006. Lih Y. Lin 3 Matrix Representation ― Jones Vectors Eeix E0x 0x E0 E iy 0 y Ee0 y Linearly polarized light y y 0 1 x E0 x E0 1 0 Ẽ and Ẽ must be in phase. y 0x 0y x cos E0 sin (Note: Jones vectors are normalized.) Lih Y. Lin 4 Jones Vector ― Circular Polarization Left circular polarization y x EEe it EA cos t At z = 0, compare xx0 with x it() EAsin tA ( cos( t / 2)) EEeyy 0 y 1 1 yxxy /2, 0, E00 EA Jones vector = 2 i y Right circular polarization 1 1 x Jones vector = 2 i Lih Y. Lin 5 Jones Vector ― Elliptical Polarization Special cases: Counter-clockwise rotation 1 A Jones vector = AB22 iB Clockwise rotation 1 A Jones vector = AB22 iB General case: Eeix A 0x A B22C E0 i y bei B iC Ee0 y Jones vector = 1 A A ABC222 B iC 2cosEE00xy tan 2 22 EE00xy Lih Y. -
Mounting Media - an Untouched Aspect
REVIEW ARTICLE Mounting Media - An Untouched Aspect Fatema Saify1, Nidhi Tiwari2 ABSTRACT Introduction: Mounting a tissue specimen is essential for preserving the specimen during storage as well as for enhancing imaging quality during microscopy. Samples are mounted in a wide variety of media, with a corresponding range of properties, for examination under microscope in the biomedical sciences. The mounting medium holds the specimens in place between the cover slip and the slide. Objective: This review is an attempt to summarize on various types of mounting media and their uses in histopathology as less is discussed about mounting media in the literature. Material and methods: Data was obtained and analyzed from previously published literature and electronic database search- es from PubMed and Google Scholar. Results: Mounting media for permanent slides can be categorized into water-based and organic solvent based mounting me- dia. Different mounting media are used for electron microscopy, immunofluorescence slides and ground sections. Conclusion: There are many commercial and home-made mounting media available. Refractive index plays an important role in choosing a mountant. A mounting media should be chosen which suits the preser- vation of the required sections for future research. Key words: Coverslip, Canada balsam, mounting media Oral and Maxillofacial Pathology Journal (2020): http://www.ompj.org/archives. INTRODUCTION 1-2Department of Oral Pathology and Microbiology, Government Mounting is the last step in the series of histological preparation Dental College, Raipur, India. of a slide. This protects the cell film from damage, air drying and Corresponding Author: Fatema Saify, Department of Oral stain fading. For proper visualization of cellular characteristics, Pathology and Microbiology, Room No -6, Government Dental the refractive index (RI) of the glass, cellular material, coverslip, College, Raipur (C.G), India. -
B.Sc.( Srmester-3) Subject: Physics Course: US03CPHY01 Title: Optics
B.Sc.( Srmester-3) Subject: Physics Course: US03CPHY01 Title: Optics UNIT – III Polarization Introduction:- • Interference and diffraction phenomena proved that light is a wave motion. These phenomena are used to find wavelength of light. However, they do not give any indication regarding the character of waves. • Maxwell developed electromagnetic theory and suggested that light-waves are electromagnetic waves. Electromagnetic waves are transverse waves, so it is obvious that light waves are also transverse waves. • Longitudinal waves are waves in which particles of medium oscillate along the direction of propagation of wave (e.g. sound wave). • Transverse waves are waves in which particles of medium oscillate perpendicular to the direction of propagation of wave. (e.g. Electromagnetic waves.) • Polarization is possible in transverse wave. • Unpolarized Light is the light is which the planes of vibration are symmetrically distributed about the propagation direction of the wave. • Plane Polarized light is a wave in which the electric vector is everywhere confined to a single plane. • A linearly polarized light wave is a wave in which the electric vector oscillates in a given constant orientation. Production of Linearly Polarized Light: Linearly polarized light may be produced from unpolarized light using following optical phenomena. (i) Reflection (ii) Refraction (iii) Scattering (iv) Selective absorption (v) Double reflection. Polarized light has many important applications in industry and engineering. One of the most important applications is in liquid crystal displays (LCDs) which are widely used in wristwatches, calculators, T.V. Screens etc. An understanding of polarization is essential for understanding the propagation of electromagnetic waves guided through wave-guides and optical fibers.