DOCSLIB.ORG

Thin Film Polarizers and Polarizing Beam Splitters

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Thin Film Polarizers and Polarizing Beam Splitters Thin Film Polarizers and Polarizing Beam Splitters Angus Macleod Thin Film Center, Inc, Tucson, AZ Contributed Original Article Introduction normal to the plane of incidence, known as s-polarization. The proper- Optical coatings are stratified media. Thus, although individual films ties of the layers appear different to each eigenmode of polarization, may be isotropic, an optical coating as a whole is anisotropic, and this and so the properties of the coating also vary. This implies a different appears in the performance at oblique incidence as a sensitivity to performance for each eigenmode, which is called polarization splitting. polarization. This sensitivity can be a problem when insensitivity is a For a high-performance polarizer or analyzer it is desirable that one requirement, but, of great benefit, when the objective is the manipula- eigenmode should be completely reflected, while the other is completely tion of polarized light. Typical components are polarizers and polariz- transmitted. This is possible under certain circumstances, leading to a ing beam splitters. Most polarizers and analyzers are based on anisotro- coating that can perform the function of a polarizer or analyzer, and, pic materials, the traditional ones being birefringent crystals. A limita- because the two modes are physically separated, a polarizing beam tion common to most of them is size. Also many of the high-perfor- splitter. mance devices are not useful as polarizing beam splitters. At first sight, There are enormous advantages in thin-film devices. Their charac- the usual thin-film calculations tend to show that polarizers and polar- teristics can be placed at virtually any wavelength in the wide region of izing beam splitters can have performance almost without limit, the transparency of their materials simply by altering the thicknesses of their only restriction being the total number of layers in the coating. layers, and, once a design has been established, the time to production is However, there are important limitations that should be understood if exceptionally short. the devices are to be correctly deployed. The range of different types and designs of polarization-sensitive The Thin-Film Polarizer coatings is enormous and well beyond the capacity of this article. We There are two effects of oblique incidence on thin film coatings. The limit ourselves to one or two well-known types. first effect is that the layers appear thinner to the light. This is a strange effect, but completely understandable in terms of the change in phase Polarizers, Analyzers and Polarizing Beam Splitters induced in the light by the traversal of the film. It is explained in an Polarizers and analyzers are identical devices but used in slightly differ- earlier Bulletin [1]. It causes the characteristic of the coating to shift ent ways. They both pass linearly polarized light of a definite orienta- towards shorter wavelengths when tilted to oblique incidence. The sec- tion and block orthogonally polarized light. We call the device a polar- ond effect is a shift in the optical admittances of the layers. The admit- izer when it is used to produce polarized light from unpolarized, and tances for s-polarization fall, and those for p-polarization rise. However, an analyzer when it is used to detect the orientation of polarized light. the high-index layers are less affected than low-index, and this implies A polarizing beam splitter divides incident unpolarized light into two that the ratio of the admittance of a high-index layer to that of a low- orthogonally polarized beams. index layer in a coating becomes smaller for p-polarization but larger for Most high-performance polarizers are based on birefringent crys- s-polarization. This, in turn, implies a weakening of the characteristic for tals. Unpolarized light is incident internally on a tilted surface. The p-polarization and a strengthening of that for s-polarization. In crystal presents a refractive index that depends on the orientation of fact, under certain conditions the high and low-index admittances for the polarization, and the surface tilt is arranged so that, for the greater p-polarization can actually coincide, so that the reflectance characteris- of the two refractive indices, the surface is slightly beyond critical tic of the coating collapses completely. The name Brewster, after David angle, and, for the lower index, slightly below critical. Then that por- Brewster the original discoverer, is given to this condition. If the two tion of the incident light with appropriate orientation of polarization indices of refraction of the materials on either side of the interface are is totally internally reflected, while the other portion is largely trans- n1 and n2, then the angle of propagation, , in material n1 that corre- mitted. The total internal reflection removes its component essentially sponds to the Brewster condition is given by: completely and, although there may be a residual loss in transmission (1) through the surface, the transmitted light is polarized to a very high The common thin-film reflecting coating is based on a series of degree. Usually a second component that is the reverse of the first is quarterwave optical thicknesses of dielectric materials of alternate high added beyond the surface to return the orientation of the transmitted and low refractive index. This structure is known as a quarterwave beam to that of the input. The reflected beam contains also the residu- stack. The characteristic performance of a quarterwave stack is a band ally reflected orthogonally polarized light and the device is, therefore, of high reflectance, the width of which depends on the ratio of the high unsuitable as a polarizing beam splitter. The rejected light is usually to low admittances of the layers. Outside this band, the reflectance falls trapped by a blackened surface so that it does not emerge. rapidly to a low value with a superimposed ripple that can be reduced by The thin-film polarizer, or beam splitter, makes use of the phe- suitable outer matching layers. When tilted, the high-reflectance band nomenon known as polarization splitting [1]. The plane of incidence is moves towards shorter wavelengths and its width changes because the defined as that plane containing the normal to the coated surface and ratios of the admittances have changed. The weakening and strength- the incident ray direction. The reflected and transmitted ray directions ening effects just mentioned imply that for p-polarization, the width are also in this plane. In general, the polarization of the incident ray is reduced, but for s-polarization it is increased. There is, therefore, a is altered by either a reflection or transmission, except in the cases of band of wavelengths at the edge of the high-reflectance zone where two special modes of polarization, called the eigenmodes, that are not the system reflects strongly for s-polarization but transmits strongly perturbed. These eigenmodes are linearly polarized with electric vector for p-polarization. In transmission in that region the light is, therefore, oriented either in the plane of incidence, known as p-polarization, or 24 2009 Summer Bulletin strongly p-polarized. The result in Figure 1 is typical. The angle of tilt is chosen to be the Brewster angle for a glass-air interface. This implies no reflection loss at the uncoated rear surface of the component, avoiding an antireflection coating. (2) so that (3) Typical values of n1 and n2 require values of n0 rather greater than ϑ unity to yield real values of 0. This implies that a polarizer based on this principle must be immersed in a medium of elevated index. In the most usual arrangement the device is made up of two isosceles right- angle prisms, at least one having a coated hypotenuse, cemented into a cube. An early polarizer of this type was patented by MacNeille [3] and is Figure 1. The transmittance of the plate polarizer including the rear surface of usually known by his name. Its construction was described by Banning the substrate. The coating is deposited on glass and the angle of incidence is [4]. Banning used zinc sulfide (n = 2.30) and cryolite (n = 1.25) as the 56.43° so that the rear glass surface is at the Brewster angle in the useful materials, and to obtain an angle of incidence of 45° and, hence, a cube zone. prism, used glass of index 1.55. Banning correctly pointed out that the dispersion of the film materials would imply a variation in the value of n0 The Extinction Ratio is sometimes quoted as a guide to performance from equation (3). In order to preserve the angle of incidence, and hence of a polarizer. It is the ratio of the irradiance of the undesired mode the optimum polarization, the glass of the prism should have the correct of polarization to that of the desired. The polarizer in Figure 1 has an dispersion. The Abbe Number (or sometimes the V-Number) is defined extinction ratio of 6.6×10-5 at 1.06μm. This can be improved simply by as: adding more layers. Extinction ratio takes no account of the level of (4) throughput of the device. It has virtually the same value in the center of the high-reflectance zone (because of the difference between p- and where the symbols D, F and C indicate that the indices are measured at s-performance) and so we must supplement it by some measure of effi- the corresponding Fraunhofer lines at 589.2 nm, 486.1 nm and ciency, usually the transmittance, or the reflectance if appropriate. 656.3 nm respectively. Note that the Abbe Number is inversely pro- There is virtually no absorption in the device of Figure 1, and so the portional to the degree of dispersion.
Load more

Recommended publications
  • Introduction ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ Li
    This guide is designed to show someone with a basic undergraduate background in physics how to perform a presentation on the topic Introduction ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ Page 1 of holography and how to demonstrate the making of a hologram. Although holography can be a very complex area of study, the material has been explained mostly qualitatively, so as to match the target audience’s background in mathematics and physics. The List of Equipment ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ Page 2 target audience high school students in grades 9‐ 11 and so limited to no previous knowledge on optics, lasers or holograms is assumed. The presentation and demonstrations will teach the students about basic optics such as reflection, refraction, and interference. The Preparation for presentation ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ Page 2‐3 students will learn the basic physics of lasers, with a focus on the apparatus set up of a laser and the necessity of a coherent light source for the creation of interference patterns. The last part of the presentation covers the two most popular types of holographic Presentation guideline ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ Page 3‐7 production apparatuses which are reflection and transmission holograms respectively. Some historical background and fun facts are also included throughout the presentation. The module ends Demonstration guideline ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ Page 7 with a live demonstration on how to make a hologram to give the students some exposure to the care that must be taken in experiments and to give them a taste of what higher level physics laboratories can include. The following flow chart summarizes the References ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ Page 8 basics of how the presentation will flow. 1 First and foremost, you should find out the location you’ll Laptop be presenting at and when the presentation will take place.
    [Show full text]
  • The Paradox of Recombined Beams Frank Rioux Emeritus Professor of Chemistry CSB|SJU
    The Paradox of Recombined Beams Frank Rioux Emeritus Professor of Chemistry CSB|SJU French and Taylor illustrate the paradox of the recombined beams with a series of experiments using polarized photons in section 7-3 in An Introduction to Quantum Physics. It is my opinion that it is easier to demonstrate this so-called paradox using photons, beam splitters and mirrors. Of course, the paradox is only apparent, being created by thinking classically about a quantum phenomenon. Single photons illuminate a 50-50 beam splitter and mirrors direct the photons to detectors D1 and D2. For a statistically meaningful number of observations, it is found that 50% of the photons are detected at D1 and 50% at D2. One might, therefore, conclude that each photon is either transmitted or reflected at the beam splitter. Recombining the paths with a second beam splitter creates a Mach-Zehnder interferometer (MZI). On the basis of the previous reasoning one might expect again that each detector would fire 50% of the time. Half of the photons are in the T branch of the interferometer and they have a 50% chance of being transmitted to D2 and a 50% chance of being reflected to D1 at the second beam splitter. The same reasoning applies to the photons in the R branch. However what is observed in an equal arm MZI is that all the photons arrive at D1. The reasoning used to explain the first result is plausible, but we see that the attempt to extend it to the MZI shown below leads to a contradiction with actual experimental results.
    [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]
  • The Paradoxes of the Interaction-Free Measurements
    The Paradoxes of the Interaction-free Measurements L. Vaidman Centre for Quantum Computation, Department of Physics, University of Oxford, Clarendon Laboratory, Parks Road, Oxford 0X1 3PU, England; School of Physics and Astronomy, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel-Aviv University, Tel-Aviv 69978, Israel Reprint requests to Prof. L. V.; E-mail: [email protected] Z. Naturforsch. 56 a, 100-107 (2001); received January 12, 2001 Presented at the 3rd Workshop on Mysteries, Puzzles and Paradoxes in Quantum Mechanics, Gargnano, Italy, September 17-23, 2000. Interaction-free measurements introduced by Elitzur and Vaidman [Found. Phys. 23,987 (1993)] allow finding infinitely fragile objects without destroying them. Paradoxical features of these and related measurements are discussed. The resolution of the paradoxes in the framework of the Many-Worlds Interpretation is proposed. Key words: Interaction-free Measurements; Quantum Paradoxes. I. Introduction experiment” proposed by Wheeler [22] which helps to define the context in which the above claims, that The interaction-free measurements proposed by the measurements are interaction-free, are legitimate. Elitzur and Vaidman [1,2] (EVIFM) led to numerousSection V is devoted to the variation of the EV IFM investigations and several experiments have been per­ proposed by Penrose [23] which, instead of testing for formed [3- 17]. Interaction-free measurements are the presence of an object in a particular place, tests very paradoxical. Usually it is claimed that quantum a certain property of the object in an interaction-free measurements, in contrast to classical measurements, way. Section VI introduces the EV IFM procedure for invariably cause a disturbance of the system.
    [Show full text]
  • The Fresnel Equations and Brewster's Law
    The Fresnel Equations and Brewster's Law Equipment Optical bench pivot, two 1 meter optical benches, green laser at 543.5 nm, 2 10cm diameter polarizers, rectangular polarizer, LX-02 photo-detector in optical mount, thick acrylic block, thick glass block, Phillips multimeter, laser mount, sunglasses. Purpose To investigate polarization by reflection. To understand and verify the Fresnel equations. To explore Brewster’s Law and find Brewster’s angle experimentally. To use Brewster’s law to find Brewster’s angle. To gain experience working with optical equipment. Theory Light is an electromagnetic wave, of which fundamental characteristics can be described in terms of the electric field intensity. For light traveling along the z-axis, this can be written as r r i(kz−ωt) E = E0e (1) r where E0 is a constant complex vector, and k and ω are the wave number and frequency respectively, with k = 2π / λ , (2) λ being the wavelength. The purpose of this lab is to explore the properties the electric field in (1) at the interface between two media with indices of refraction ni and nt . In general, there will be an incident, reflected and transmitted wave (figure 1), which in certain cases reduce to incident and reflected or incident and transmitted only. Recall that the angles of the transmitted and reflected beams are described by the law of reflection and Snell’s law. This however tells us nothing about the amplitudes of the reflected and transmitted Figure 1 electric fields. These latter properties are defined by the Fresnel equations, which we review below.
    [Show full text]
  • Chapter 6 Light at Interfaces – Law of Reflection and Refraction
    Chapter 6 Light at Interfaces – Law of Reflection and Refraction Part I Introduction Law of Reflection and Refraction Law of Reflection and Refraction normal Law of reflection: i r i r n1 n2 Law of refraction “Snell’s Law”: sin n t i 2 sint n1 Incident, reflected, refracted, and surface normal in same plane Huygens’ Principle Every point on a wavefront may be regarded as a secondary source of wavelets Huygens’ Principle Law of refraction Fermat’s Principle The path a beam of light takes between two points is the one which is traversed in the least time Law of reflection Fermat’s Principle Law of refraction SO OP t vi vt h2 x2 b2 (a x)2 t vi vt To minimize t(x) with respect to x, dt x (a x) dx 2 2 2 2 vi h x vt b (a x) 0. sin sin Thus, i t , vi vt so, ni sini nt sint Fermat’s Principle For a ray passing through a multilayer (m layers) material s s s t 1 2 m v1 v2 vm Then 1 m t ni si , c i1 The summation is known as the optical path length (OPL) traversed by the ray. P (OPL) S n(s)ds. The route light travels having the smallest optical path length EM Wave Point of View Light is an electromagnetic wave, obeys the Maxwell’s equations Plane of incidence: formed by k and the normal of the interface plane normal EB k EM Wave Point of View i(tkr) E E0e i(tkr) B B0e E cB 1.
    [Show full text]
  • Highly Angular Resolving Beam Separator Based on Total Internal Reflection
    Highly angular resolving beam separator based on total internal reflection MORITZ MIHM,1,* ORTWIN HELLMIG,2 ANDRÉ WENZLAWSKI,1 KLAUS SENGSTOCK,2 AND PATRICK WINDPASSINGER1 1Johannes Gutenberg-Universität Mainz, Staudingerweg 7, 55128 Mainz, Germany 2Institut für Laserphysik/Zentrum für optische Quantentechnologien, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany *[email protected] Abstract: We present an optical element for the separation of superimposed beams which only differ in angle. The beams are angularly resolved and separated by total internal reflection at an air gap between two prisms. As a showcase application, we demonstrate the separation of superimposed beams of different diffraction orders directly behind acousto-optic modulators for an operating wavelength of 800nm. The wavelength as well as the component size can easily be adapted to meet the requirements of a wide variety of applications. The presented optical element allows to reduce the lengths of beam paths and thus to decrease laser system size and complexity. © 2019 Optical Society of America. One print or electronic copy may be made for personal use only. Sys- tematic reproduction and distribution, duplication of any material in this paper for a fee or for commercial purposes, or modifications of the content of this paper are prohibited. 1. Introduction Obtaining high angular resolution, i.e. separating light beams, which stem from the same source but propagate under slightly different angles, is a common challenge when designing optical systems. Typically, for a given design concept, one can improve the angular resolution by adapting the beam waist or its wavelength and extended propagation distances. However, if waist and wavelength are fixed and system compactness and simplicity are a design goal, alternative approaches need to be considered.
    [Show full text]
  • Wiregrid Polarizing Beam Splitter – ICE Cube
    POLARIZERS Wiregrid Polarizing Beam Splitter – ICE Cube Meadowlark Optics is now the exclusive provider of the ICE Cube™ formerly • offered by Moxtek. This polarizing beam splitter (PBS) cube is optimized for LIGHT MODULATORS SPATIAL use over a wide range of acceptance angles while maintaining color uniformity and image contrast in the visible wavelength ranges. The ICE Cube allows compact optical designs with reduced optical paths. Engineers are now able to design smaller systems while maintaining excellent optical performance. The Key Features ICE Cube polarizer performance exceeds that for the commonly used thin film • • • MacNeille cubes in both acceptable wavelength range and angle of incidence range while providing more than twice the contrast ratio in the transmitted Wide angle of incidence range beam for most wavelengths. Uniformity over wide range of angles High contrast and transmission over The ICE Cube is assembled by embedding our polarizing beam splitter plate between two AR coated glass prisms. These cubes are designed with wide range of angles • • Nanowire® grid structures centered on the hypotenuse of the ICE Cube. Polarization Suite WAVEPLATES The ICE Cube PBS separates natural light into two main orthogonal, linearly polarized components; the p-polarized light which is transmitted while the • • • s-polarized light is reflected at a 90˚ angle. In principle, half of the incident light Linear Polarizers is reflected, and the other half is transmitted. Precision Linear Polarizer High Contrast Linear Polarizer 1.00” (25.4
    [Show full text]
  • Quantum Interferometry with Multiports: Entangled Photons in Optical Fibers
    Quantum Interferometry with Multiports: Entangled Photons in Optical Fibers Dissertation zur Erlangung des akademischen Grades eines Doktors der Naturwissenschaften eingereicht von Mag. phil. Mag. rer. nat. Michael Hunter Alexander Reck im Juli 1996 durchgef¨uhrt am Institut f¨ur Experimentalphysik, Naturwissenschaftliche Fakult¨at der Leopold-Franzens Universit¨at Innsbruck unter der Leitung von o. Univ. Prof. Dr. Anton Zeilinger Diese Arbeit wurde vom FWF im Rahmen des Schwerpunkts Quantenoptik (S06502) unterst¨utzt. Contents Abstract 5 1 Entanglement and Bell’s inequalities 7 1.1 Introduction .............................. 7 1.2 Derivation of Bell’s inequality for dichotomic variables ...... 10 1.3 Tests of Bell’s inequality ....................... 14 1.3.1 First experiments ....................... 14 1.3.2 Entanglement and the parametric downconversion source .16 1.3.3 New experiments with entangled photons .......... 17 1.4 Bell inequalities for three-valued observables ............ 18 2 Theory of linear multiports 23 2.1 The beam splitter ........................... 24 2.2 Multiports ............................... 25 2.2.1 From experiment to matrix ................. 26 2.2.2 From matrix to experiment ................. 27 2.3 Symmetric multiports ......................... 32 2.3.1 Single-photon eigenstates of a symmetric multiport .... 33 2.3.2 Two-photon eigenstates of a symmetric multiport ..... 33 2.4 Multiports and quantum computation ................ 35 3 Optical fibers 39 3.1 Single mode fibers ........................... 39 3.1.1 Optical parameters of fused silica .............. 40 3.1.2 Material dispersion and interferometry ........... 43 3.2 Components of fiber-optical systems ................. 46 3.3 Coupled waveguides as multiports ................. 47 4 Experimental characterization of fiber multiports 49 4.1 A three-path Mach-Zehnder interferometer using all-fiber tritters .49 4.1.1 Experimental setup .....................
    [Show full text]
  • Electromagnetic Waves
    Electromagnetic Waves Lecture34: Electromagnetic Theory Professor D. K. Ghosh, Physics Department, I.I.T., Bombay Electromagnetic wave at the interface between two dielectric media We have so far discussed the propagation of electromagnetic wave in an isotropic, homogeneous, dielectric medium, such as in air or vacuum. In this lecture, we woulddiscuss what happens when a plane electromagnetic wave is incident at the interface between two dielectric media. For being specific, we will take one of the medium to be air or vacuum and the other to be a dielectric such as glass. We have come across this in school in connection with the reflection and transmission of light waves at such an interface. In this lecture, we would investigate this problem from the point of view of electromagnetic theory. Let us choose the interface to be the xy plane (z=0). The angles of incidence, reflection and refraction are the angles made by the respective propagation vectors with the common normal at the interface. 1 We have indicated the propation vectors in the apprpriate medium by capital letters I, R and T so as not to confuse with the notation for the position vector and time t. The principle that we use to establish the laws of reflection⃗ and refraction is the continuity of the tangential components of the electric field at the interface, as discussed extensively during the course of these lectures. Let us represent the component of the electric field parallel to the interface by the superscript . We then have, ∥ 0 exp + 0 exp = 0 exp ∥ ∥ This equation� ���⃗ ⋅ must⃗ − remain� valid at� all����⃗ points⋅ ⃗ − in the� interface � and ����⃗ at⋅ ⃗all− times.� That is obviously possible if the exponential factors is the same for all the three terms or if they differe at best by a constant phase factor.
    [Show full text]
  • Experiments for B. Tech. 1St Year Physics Laboratory Department Of
    Experiments for B. Tech. 1st Year Physics Laboratory Experiment No. 12 Brewster’s Angle Aim : To determine the of Brewster’s angle for glass using a polarized monochromatic light source. Apparatus Required: He laser, dial fitted polarizer, photo detector, micro ammeter, rotational mount, glass plate, constant power supply . Formula Used : Brewsters angle for a given pair of medium is 푛 θB = 휃 = 푡푎푛 ( ) 푛 Where n1 and n2 are refractive index of medium 1 and 2 respectively Principle: When light moves between two media of differing refractive index (n), some of the light is reflected from the surface of the denser material. This reflected ray’s intensity changes with change in the incident angle (휃) at the interface of two mediums. At one specific angle of incidence of light only perpendicular vibrations of electric field vectors are reflected whereas parallel vibrations are restricted or polarized. This loss in light intensity is due to polarization by reflection and the angle of incidence for which reflected ray is polarized is called the Brewster's angle θ (also known as the Polarization angle). B This phenomenon of polarization by reflection is illustrated in the figure below. Figure1. Polarization by reflection and Brewster's angle (θ ) B Department of Physics, IIT Roorkee © 1 Experiments for B. Tech. 1st Year Physics Laboratory The fraction of the incident light that is reflected depends on both the angle of incidence and the polarization direction of the incident light. The functions that describe the reflection of light polarized parallel and perpendicular to the plane of incidence are called the Fresnel Equations.
    [Show full text]
  • A Study of Reflection and Transmission of Birefringent Retarders
    JUST, Vol. IV, No. 1, 2016 Trent University A study of reflection and transmission of birefringent retarders James Godfrey Keywords Optics — Computational Physics — Theoretical Physics Champlain College 1. Interference in Rotating Waveplates The transmitted intensity of along each axis must be con- sidered separately, since equation (1-1) dictates that the re- 1.1 Research Goal flectance of the fast- and slow-axis components of the incident The objective of this project was to obtain a realistic theoreti- light will be different. The reflectance along the fast axis (Ro) cal prediction of the transmission curve for linearly-polarized and slow axis (Rs) are may be expressed: light incident normal on a [birefringent] retarder that behaves 2 as a Fabry-Perot etalon. The birefringent retarder considered n f − ni is a slab of birefringent crystal cut with the optic axis in the Ro = n f + ni face of the slab, and with parallel faces, and the waveplate has 2 no coating of any kind. ns − ni Rs = (1-2) Results of this project hoped to possibly explain the results ns + ni of work done by a previous student, Nolan Woodley, for his Physics project course in the 2013/14 academic year. In his Assuming the sides of the etalon are essentially paral- project, Woodley took many polarimeter scans which had a lel, the retarder may now be treated as a low-finesse (low- roughly sinusoidal shape [as they should], but adjacent peaks reflectance, R << 1) Fabry-Perot etalon. Their coefficients of of different heights. These differing heights were completely finesse (Fo and Fs, respectively) will also be different: unexplained, and not predicted by theory.
    [Show full text]