Types of Polarization
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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. -
Static and Dynamic Effects of Chirality in Dielectric Media
Static and dynamic effects of chirality in dielectric media R. S. Lakes Department of Engineering Physics, Department of Materials Science, University of Wisconsin, 1500 Engineering Drive, Madison, WI 53706-1687 [email protected] January 31, 2017 adapted from R. S. Lakes, Modern Physics Letters B, 30 (24) 1650319 (9 pages) (2016). Abstract Chiral dielectrics are considered from the perspective of continuum representations of spatial heterogeneity. Static effects in isotropic chiral dielectrics are predicted, provided the electric field has nonzero third spatial derivatives. The effects are compared with static chiral phenomena in Cosserat elastic materials which obey generalized continuum constitutive equations. Dynamic monopole - like magnetic induction is predicted in chiral dielectric media. keywords: chirality, dielectric, Cosserat 1 Introduction Chirality is well known in electromagnetics 1; it gives rise to optical activity in which left or right handed cir- cularly polarized waves propagate at different velocities. Known effects are dynamic only; there is considered to be no static effect 2. The constitutive equations for a directionally isotropic chiral material are 3, 4. @H D = kE − g (1) @t @E B = µH + g (2) @t in which E is electric field, D is electric displacement, B is magnetic field, H is magnetic induction, k is the dielectric permittivity, µ is magnetic permeability and g is a measure of the chirality. Optical rotation of polarized light of wavelength λ by an angle Φ (in radians per meter) is given by Φ = (2π/λ)2cg with c as the speed of light. The quantity g embodies the length scale of the chiral structure because cg has dimensions of length. -
Principles of Retarders
Polarizers PRINCIPLES OF RETARDERS etarders are used in applications where control or Ranalysis of polarization states is required. Our retarder products include innovative polymer and liquid crystal materials. Crystalline materials such as quartz and Retarders magnesium fluoride are also available upon request. Please call for a custom quote. A retarder (or waveplate) is an optical device that resolves a light wave into two orthogonal linear polarization components and produces a phase shift between them. The resulting light wave is generally of a different polarization form. Ideally, retarders do not polarize, nor do they induce an intensity change in the Crystals Liquid light beam, they simply change its polarization form. state. The transmitted light leaves the retarder elliptically All standard catalog Meadowlark Optics’ retarders are polarized. made from birefringent, uniaxial materials having two Retardance (in waves) is given by: different refractive indices – the extraordinary index ne = tր and the ordinary index no. Light traveling through a retarder has a velocity v where: dependent upon its polarization direction given by  = birefringence (ne - no) Spatial Light Modulators v = c/n = wavelength of incident light (in nanometers) t = thickness of birefringent element where c is the speed of light in a vacuum and n is the (in nanometers) refractive index parallel to that polarization direction. Retardance can also be expressed in units of length, the By definition, ne > no for a positive uniaxial material. distance that one polarization component is delayed For a positive uniaxial material, the extraordinary axis relative to the other. Retardance is then represented by: is referred to as the slow axis, while the ordinary axis is ␦Ј ␦  referred to as the fast axis. -
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. -
Circular Polarization and Nonreciprocal Propagation in Magnetic Media Circular Polarization and Nonreciprocal Propagation in Magnetic Media Gerald F
• DIONNE, ALLEN, Haddad, ROSS, AND LaX Circular Polarization and Nonreciprocal Propagation in Magnetic Media Circular Polarization and Nonreciprocal Propagation in Magnetic Media Gerald F. Dionne, Gary A. Allen, Pamela R. Haddad, Caroline A. Ross, and Benjamin Lax n The polarization of electromagnetic signals is an important feature in the design of modern radar and telecommunications. Standard electromagnetic theory readily shows that a linearly polarized plane wave propagating in free space consists of two equal but counter-rotating components of circular polarization. In magnetized media, these circular modes can be arranged to produce the nonreciprocal propagation effects that are the basic properties of isolator and circulator devices. Independent phase control of right-hand (+) and left-hand (–) circular waves is accomplished by splitting their propagation velocities through differences in the e±m± parameter. A phenomenological analysis of the permeability m and permittivity e in dispersive media serves to introduce the corresponding magnetic- and electric-dipole mechanisms of interaction length with the propagating signal. As an example of permeability dispersion, a Lincoln Laboratory quasi-optical Faraday- rotation isolator circulator at 35 GHz (l ~ 1 cm) with a garnet-ferrite rotator element is described. At infrared wavelengths (l = 1.55 mm), where fiber-optic laser sources also require protection by passive isolation of the Faraday-rotation principle, e rather than m provides the dispersion, and the frequency is limited to the quantum energies of the electric-dipole atomic transitions peculiar to the molecular structure of the magnetic garnet. For optimum performance, bismuth additions to the garnet chemical formula are usually necessary. Spectroscopic and molecular theory models developed at Lincoln Laboratory to explain the bismuth effects are reviewed. -
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. -
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. -
Lecture Notes - Optics 4: Retardation, Interference Colors
Lecture Notes - Optics 4: Retardation, Interference Colors • In anisotropic crystals, the two rays of light produced by double refraction travel at different velocities through the crystal. It takes the slow ray longer to traverse the crystal than it takes the fast ray. The fast ray will have passed through the crystal and traveled some distance ∆ beyond the crystal before the slow ray reaches the surface of the crystal. This distance ∆ is called the retardation. n < n ∆ (+) n < n ∆ O E EO (-) h O E O E ∆ • The retardation may be calculated as follows. If tS is the time in seconds that it takes the slow ray to traverse the crystal and tF is the time it takes the fast ray to traverse the crystal, then the distance ∆ that the fast ray travels beyond the crystal before the slow ray emerges is ∆ = c (tS - tF) {units: m = (m/s)(s)}, where c is the velocity of light in a vacuum, which is very close to the velocity of light in air. For a crystal of thickness h with velocities vF and vS, tF and tS may be replaced by h/vF and h/vS {units: (m)/(m/s) = s}, respectively, to give h h c c ∆ = c - = h - v S v F v S v F Recalling the definition of the refractive index n, the equation for ∆ becomes ∆ = h (nS - nF). Because refractive indices are dimensionless, ∆ will be in the same units as h, normally nanome- ters (nm). Note that the difference in path length for the O and E rays has been neglected in this calculation. -
Diamond 2008 Element Six Paper Friel Et Al
Control of surface and bulk crystalline quality in single crystal diamond grown by chemical vapour deposition I. Friel †, S. L. Clewes, H. K. Dhillon, N. Perkins, D. J. Twitchen, G. A. Scarsbrook Element Six Ltd, King’s Ride Park, Ascot, SL5 8BP, United Kingdom Abstract : In order to improve the performance of existing technologies based on single crystal diamond grown by chemical vapour deposition (CVD), and to open up new technologies in fields such as quantum computing or solid state and semiconductor disc lasers, control over surface and bulk crystalline quality is of great importance. Inductively coupled plasma (ICP) etching using an Ar/Cl gas mixture is demonstrated to remove sub-surface damage of mechanically processed surfaces, whilst maintaining macroscopic planarity and low roughness on a microscopic scale. Dislocations in high quality single crystal CVD diamond are shown to be reduced by using substrates with a combination of low surface damage and low densities of extended defects. Substrates engineered such that only a minority of defects intersect the epitaxial surface are also shown to lead to a reduction in dislocation density. Anisotropy in the birefringence of single crystal CVD diamond due to the preferential direction of dislocation propagation is reported. Ultra low birefringence plates (< 10 -5) are now available for intra-cavity heat spreaders in solid state disc lasers, and the application is no longer limited by depolarisation losses. Birefringence of less than 5×10 -7 along a direction perpendicular to the CVD growth direction has been demonstrated in exceptionally high quality samples. †Corresponding author 1 of 25 1. Introduction Chemical vapour deposition (CVD) growth of single crystal diamond has progressed rapidly in recent years, stimulating much research work and leading to the emergence of commercial technology based on this material.