TIE-29: Refractive Index and Dispersion
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The Walman Optical Perspective on High Index Lenses
Optical Perspective of Polycarbonate Material JP Wei, Ph. D. November 2011 Introduction Among the materials developed for eyeglasses, polycarbonate is one that has a number of very unique properties and provides real benefits to eyeglass wearers. Polycarbonate lenses are not only cosmetically thinner, lighter, and provide superior impact-resistance, but also produce sharp optical clarity for both central and peripheral vision. It is well-known that as the index of refraction increases dispersion also increases. In other words, the higher the refractive index, the low the ABBE value. An increase in dispersion will cause an increase in chromatic aberration. Therefore, one of the concerns in the use of lens materials such as polycarbonate is: will chromatic aberration negatively affect patient adaption? MID 1.70 LENS MATERIAL CR39 TRIVEX INDEX POLYCARBONATE 1.67 INDEX INDEX REFRACTIVE INDEX 1.499 1.529 1.558 1.586 1.661 1.700 ABBE VALUES 58 45 37 30 32 36 The refractive index of a material is often abbreviated “n.” Except for air, which has a refractive index of approximately 1, the refractive index of most substances is greater than 1 (n > 1). Water, for instance, has a refractive index of 1.333. The higher the refractive index of a lens material, the slower the light will travel through it. While it is commonly recognized that high index materials will have greater chromatic aberration than CR-39 or low refractive index lenses, there has been no quantification of the amount of visual acuity loss that results from chromatic aberration. The purpose of this paper is to review the optical properties of polycarbonate material, its advantages over other lens materials, and the impact of chromatic aberration caused by the relative low ABBE value of the material on vision and clinical significance. -
Negative Refractive Index in Artificial Metamaterials
1 Negative Refractive Index in Artificial Metamaterials A. N. Grigorenko Department of Physics and Astronomy, University of Manchester, Manchester, M13 9PL, UK We discuss optical constants in artificial metamaterials showing negative magnetic permeability and electric permittivity and suggest a simple formula for the refractive index of a general optical medium. Using effective field theory, we calculate effective permeability and the refractive index of nanofabricated media composed of pairs of identical gold nano-pillars with magnetic response in the visible spectrum. PACS: 73.20.Mf, 41.20.Jb, 42.70.Qs 2 The refractive index of an optical medium, n, can be found from the relation n2 = εμ , where ε is medium’s electric permittivity and μ is magnetic permeability.1 There are two branches of the square root producing n of different signs, but only one of these branches is actually permitted by causality.2 It was conventionally assumed that this branch coincides with the principal square root n = εμ .1,3 However, in 1968 Veselago4 suggested that there are materials in which the causal refractive index may be given by another branch of the root n =− εμ . These materials, referred to as left- handed (LHM) or negative index materials, possess unique electromagnetic properties and promise novel optical devices, including a perfect lens.4-6 The interest in LHM moved from theory to practice and attracted a great deal of attention after the first experimental realization of LHM by Smith et al.7, which was based on artificial metallic structures -
Correlation of the Abbe Number, the Refractive Index, and Glass Transition Temperature to the Degree of Polymerization of Norbornane in Polycarbonate Polymers
polymers Article Correlation of the Abbe Number, the Refractive Index, and Glass Transition Temperature to the Degree of Polymerization of Norbornane in Polycarbonate Polymers Noriyuki Kato 1,2,*, Shinya Ikeda 1, Manabu Hirakawa 1 and Hiroshi Ito 2,3 1 Mitsubishi Gas Chemical Company, 2-5-2 Marunouchi, Chiyoda-ku, Tokyo 100-8324, Japan; [email protected] (S.I.); [email protected] (M.H.) 2 Graduate School of Science and Engineering, Yamagata University, 4-3-16 Jonan, Yonezawa, Yamagata 992-8510, Japan; [email protected] 3 Graduate School of Organic Materials Science, Yamagata University, 4-3-16 Jonan, Yonezawa, Yamagata 992-8510, Japan * Correspondence: [email protected] Received: 1 September 2020; Accepted: 16 October 2020; Published: 26 October 2020 Abstract: The influences of the average degree of polymerization (Dp), which is derived from Mn and terminal end group, on optical and thermal properties of various refractive indexed transparent polymers were investigated. In this study, we selected the alicyclic compound, Dinorbornane dimethanol (DNDM) homo polymer, because it has been used as a representative monomer in low refractive index polymers for its unique properties. DNDM monomer has a stable amorphous phase and reacts like a polymer. Its unique reaction allows continuous investigation from monomer to polymer. For hydroxy end group and phenolic end group polymers, the refractive index (nd) decreased with increasing Dp, and both converged to same value in the high Dp region. However, the Abbe number (νd) of a hydroxy end group polymer is not dependent on Dp, and the νd of a phenolic end group polymer is greatly dependent on Dp. -
Development of Highly Transparent Zirconia Ceramics
11 Development of highly transparent zirconia ceramics Isao Yamashita *1 Masayuki Kudo *1 Koji Tsukuma *1 Highly transparent zirconia ceramics were developed and their optical and mechanical properties were comprehensively studied. A low optical haze value (H<1.0 %), defined as the diffuse transmission divided by the total forward transmission, was achieved by using high-purity powder and a novel sintering process. Theoretical in-line transmission (74 %) was observed from the ultraviolet–visible region up to the infra-red region; an absorption edge was found at 350 nm and 8 µm for the ultraviolet and infrared region, respectively. A colorless sintered body having a high refractive index (n d = 2.23) and a high Abbe’s number (νd = 27.8) was obtained. A remarkably large dielectric constant (ε = 32.7) with low dielectric loss (tanδ = 0.006) was found. Transparent zirconia ceramics are candidates for high-refractive index lenses, optoelectric devices and infrared windows. Transparent zirconia ceramics also possess excellent mechanical properties. Various colored transparent zirconia can be used as exterior components and for complex-shaped gemstones. fabricating transparent cubic zirconia ceramics.9,13-19 1.Introduction Transparent zirconia ceramics using titanium oxide as Transparent and translucent ceramics have been a sintering additive were firstly reported by Tsukuma.15 studied extensively ever since the seminal work on However, the sintered body had poor transparency translucent alumina polycrystal by Coble in the 1960s.1 and low mechanical strength. In this study, highly Subsequently, researchers have conducted many transparent zirconia ceramics of high strength were studies to develop transparent ceramics such as MgO,2 developed. -
Chapter 19/ Optical Properties
Chapter 19 /Optical Properties The four notched and transpar- ent rods shown in this photograph demonstrate the phenomenon of photoelasticity. When elastically deformed, the optical properties (e.g., index of refraction) of a photoelastic specimen become anisotropic. Using a special optical system and polarized light, the stress distribution within the speci- men may be deduced from inter- ference fringes that are produced. These fringes within the four photoelastic specimens shown in the photograph indicate how the stress concentration and distribu- tion change with notch geometry for an axial tensile stress. (Photo- graph courtesy of Measurements Group, Inc., Raleigh, North Carolina.) Why Study the Optical Properties of Materials? When materials are exposed to electromagnetic radia- materials, we note that the performance of optical tion, it is sometimes important to be able to predict fibers is increased by introducing a gradual variation and alter their responses. This is possible when we are of the index of refraction (i.e., a graded index) at the familiar with their optical properties, and understand outer surface of the fiber. This is accomplished by the mechanisms responsible for their optical behaviors. the addition of specific impurities in controlled For example, in Section 19.14 on optical fiber concentrations. 766 Learning Objectives After careful study of this chapter you should be able to do the following: 1. Compute the energy of a photon given its fre- 5. Describe the mechanism of photon absorption quency and the value of Planck’s constant. for (a) high-purity insulators and semiconduc- 2. Briefly describe electronic polarization that re- tors, and (b) insulators and semiconductors that sults from electromagnetic radiation-atomic in- contain electrically active defects. -
Super-Resolution Imaging by Dielectric Superlenses: Tio2 Metamaterial Superlens Versus Batio3 Superlens
hv photonics Article Super-Resolution Imaging by Dielectric Superlenses: TiO2 Metamaterial Superlens versus BaTiO3 Superlens Rakesh Dhama, Bing Yan, Cristiano Palego and Zengbo Wang * School of Computer Science and Electronic Engineering, Bangor University, Bangor LL57 1UT, UK; [email protected] (R.D.); [email protected] (B.Y.); [email protected] (C.P.) * Correspondence: [email protected] Abstract: All-dielectric superlens made from micro and nano particles has emerged as a simple yet effective solution to label-free, super-resolution imaging. High-index BaTiO3 Glass (BTG) mi- crospheres are among the most widely used dielectric superlenses today but could potentially be replaced by a new class of TiO2 metamaterial (meta-TiO2) superlens made of TiO2 nanoparticles. In this work, we designed and fabricated TiO2 metamaterial superlens in full-sphere shape for the first time, which resembles BTG microsphere in terms of the physical shape, size, and effective refractive index. Super-resolution imaging performances were compared using the same sample, lighting, and imaging settings. The results show that TiO2 meta-superlens performs consistently better over BTG superlens in terms of imaging contrast, clarity, field of view, and resolution, which was further supported by theoretical simulation. This opens new possibilities in developing more powerful, robust, and reliable super-resolution lens and imaging systems. Keywords: super-resolution imaging; dielectric superlens; label-free imaging; titanium dioxide Citation: Dhama, R.; Yan, B.; Palego, 1. Introduction C.; Wang, Z. Super-Resolution The optical microscope is the most common imaging tool known for its simple de- Imaging by Dielectric Superlenses: sign, low cost, and great flexibility. -
Trivex & Polycarbonate Lenses
Trivex Trivex was originally developed for the military, as visual armor. PPG Industries took the technology and adapted it for the optical industry. Trivex is a urethane-based pre-polymer. PPG named the material Trivex because of its three main performance properties. The three main properties are superior optics, ultra- lightweight, and extreme strength. Trivex has a high abbe value. Abbe value is a measure of the dispersion or color distortion of light through a lens into its color elements. Abbe number can also be referred to as v-value. The higher the abbe number, the less dispersion, the lower the number, the more dispersion. Trivex has an abbe number of 43-45. This is significantly higher than polycarbonate. Polycarbonate's abbe number is 30. Trivex has a very high level of light transmittance. The level is 91.4%. This is one of the highest levels of all lens materials. The high percentage is a factor that directly affects the brightness, clarity, and crispness of Trivex. Trivex has a specific gravity of 1.11. Specific gravity is the weight in grams of one cubic centimeter of the material. Specific gravity is also referred to as density. The higher the number, the more dense, or heavy, a lens material is. Trivex has the lowest specific gravity of any commonly used lens material. This makes Trivex the lightest lens material. Trivex is 16% lighter than CR-39, 25% lighter than 1.66, and 8% lighter than polycarbonate! Trivex has a refractive index of 1.53. This allows for a thinner lens than a CR-39 lens. -
Realization of an All-Dielectric Zero-Index Optical Metamaterial
Realization of an all-dielectric zero-index optical metamaterial Parikshit Moitra1†, Yuanmu Yang1†, Zachary Anderson2, Ivan I. Kravchenko3, Dayrl P. Briggs3, Jason Valentine4* 1Interdisciplinary Materials Science Program, Vanderbilt University, Nashville, Tennessee 37212, USA 2School for Science and Math at Vanderbilt, Nashville, TN 37232, USA 3Center for Nanophase Materials Sciences, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA 4Department of Mechanical Engineering, Vanderbilt University, Nashville, Tennessee 37212, USA †these authors contributed equally to this work *email: [email protected] Metamaterials offer unprecedented flexibility for manipulating the optical properties of matter, including the ability to access negative index1–4, ultra-high index5 and chiral optical properties6–8. Recently, metamaterials with near-zero refractive index have drawn much attention9–13. Light inside such materials experiences no spatial phase change and extremely large phase velocity, properties that can be applied for realizing directional emission14–16, tunneling waveguides17, large area single mode devices18, and electromagnetic cloaks19. However, at optical frequencies previously demonstrated zero- or negative- refractive index metamaterials require the use of metallic inclusions, leading to large ohmic loss, a serious impediment to device applications20,21. Here, we experimentally demonstrate an impedance matched zero-index metamaterial at optical frequencies based on purely dielectric constituents. Formed from stacked silicon rod unit cells, the metamaterial possesses a nearly isotropic low-index response leading to angular selectivity of transmission and directive emission from quantum dots placed within the material. Over the past several years, most work aimed at achieving zero-index has been focused on epsilon-near-zero metamaterials (ENZs) which can be realized using diluted metals or metal waveguides operating below cut-off. -
Refractive Index and Dispersion of Liquid Hydrogen
&1 Bureau of Standards .ifcrary, M.W. Bldg OCT 11 B65 ^ecknlcciL ^iote 9?©. 323 REFRACTIVE INDEX AND DISPERSION OF LIQUID HYDROGEN R. J. CORRUCCINI U. S. DEPARTMENT OF COMMERCE NATIONAL BUREAU OF STANDARDS THE NATIONAL BUREAU OF STANDARDS The National Bureau of Standards is a principal focal point in the Federal Government for assuring maximum application of the physical and engineering sciences to the advancement of technology in industry and commerce. Its responsibilities include development and maintenance of the national stand- ards of measurement, and the provisions of means for making measurements consistent with those standards; determination of physical constants and properties of materials; development of methods for testing materials, mechanisms, and structures, and making such tests as may be necessary, particu- larly for government agencies; cooperation in the establishment of standard practices for incorpora- tion in codes and specifications; advisory service to government agencies on scientific and technical problems; invention and development of devices to serve special needs of the Government; assistance to industry, business, and consumers in the development and acceptance of commercial standards and simplified trade practice recommendations; administration of programs in cooperation with United States business groups and standards organizations for the development of international standards of practice; and maintenance of a clearinghouse for the collection and dissemination of scientific, tech- nical, and engineering information. The scope of the Bureau's activities is suggested in the following listing of its four Institutes and their organizational units. Institute for Basic Standards. Applied Mathematics. Electricity. Metrology. Mechanics. Heat. Atomic Physics. Physical Chemistry. Laboratory Astrophysics.* Radiation Physics. Radio Standards Laboratory:* Radio Standards Physics; Radio Standards Engineering. -
4.4 Total Internal Reflection
n 1:33 sin θ = water sin θ = sin 35◦ ; air n water 1:00 air i.e. ◦ θair = 49:7 : Thus, the height above the horizon is ◦ ◦ θ = 90 θair = 40:3 : (4.7) − Because the sun is far away from the fisherman and the diver, the fisherman will see the sun at the same angle above the horizon. 4.4 Total Internal Reflection Suppose that a light ray moves from a medium of refractive index n1 to one in which n1 > n2, e.g. glass-to-air, where n1 = 1:50 and n2 = 1:0003. ◦ If the angle of incidence θ1 = 10 , then by Snell's law, • n 1:50 θ = sin−1 1 sin θ = sin−1 sin 10◦ 2 n 1 1:0003 2 = sin−1 (0:2604) = 15:1◦ : ◦ If the angle of incidence is θ1 = 50 , then by Snell's law, • n 1:50 θ = sin−1 1 sin θ = sin−1 sin 50◦ 2 n 1 1:0003 2 = sin−1 (1:1487) =??? : ◦ So when θ1 = 50 , we have a problem: Mathematically: the angle θ2 cannot be computed since sin θ2 > 1. • 142 Physically: the ray is unable to refract through the boundary. Instead, • 100% of the light reflects from the boundary back into the prism. This process is known as total internal reflection (TIR). Figure 8672 shows several rays leaving a point source in a medium with re- fractive index n1. Figure 86: The refraction and reflection of light rays with increasing angle of incidence. The medium on the other side of the boundary has n2 < n1. -
Electromagnetism - Lecture 13
Electromagnetism - Lecture 13 Waves in Insulators Refractive Index & Wave Impedance • Dispersion • Absorption • Models of Dispersion & Absorption • The Ionosphere • Example of Water • 1 Maxwell's Equations in Insulators Maxwell's equations are modified by r and µr - Either put r in front of 0 and µr in front of µ0 - Or remember D = r0E and B = µrµ0H Solutions are wave equations: @2E µ @2E 2E = µ µ = r r r r 0 r 0 @t2 c2 @t2 The effect of r and µr is to change the wave velocity: 1 c v = = pr0µrµ0 prµr 2 Refractive Index & Wave Impedance For non-magnetic materials with µr = 1: c c v = = n = pr pr n The refractive index n is usually slightly larger than 1 Electromagnetic waves travel slower in dielectrics The wave impedance is the ratio of the field amplitudes: Z = E=H in units of Ω = V=A In vacuo the impedance is a constant: Z0 = µ0c = 377Ω In an insulator the impedance is: µrµ0c µr Z = µrµ0v = = Z0 prµr r r For non-magnetic materials with µr = 1: Z = Z0=n 3 Notes: Diagrams: 4 Energy Propagation in Insulators The Poynting vector N = E H measures the energy flux × Energy flux is energy flow per unit time through surface normal to direction of propagation of wave: @U −2 @t = A N:dS Units of N are Wm In vacuo the amplitudeR of the Poynting vector is: 1 1 E2 N = E2 0 = 0 0 2 0 µ 2 Z r 0 0 In an insulator this becomes: 1 E2 N = N r = 0 0 µ 2 Z r r The energy flux is proportional to the square of the amplitude, and inversely proportional to the wave impedance 5 Dispersion Dispersion occurs because the dielectric constant r and refractive index -
Monte-Carlo Path Tracing Transparency/Translucency
Monte-Carlo Path Tracing Transparency/Translucency Max Ismailov, Ryan Lingg Light Does a Lot of Reflecting ● Our raytracer only supported direct lighting ● Objects that are not light sources emit light! ➔ We need more attention to realism than direct light sources can offer Global Illumination: Shrek Tools to Solve this Problem 1. Appropriate model of reflectance for objects 2. A way to aggregate incoming light sources Formally: We’re Solving the Rendering Equation! Reflectance Models - BRDF’s ● To properly globally illuminate, we need accurate models of light reflectance ○ “Bidirectional Reflectance Distribution Function” ● We already have a few of these! ○ Lambertian ○ Blinn-Phong ○ Many more exist Basic Ingredients of a BRDF Microfaceted Surfaces Subsurface Scattering Aggregating Light Sources ● Ideally, we want to integrate over the light functions contributing to a point. ○ Integrals require an integrand, a function that we can integrate! ■ ...we don’t have this ○ We need something we can do in practice numerically Approximating an Integral ● Recall: an integral is the area under the curve of a function along interval [a,b] ● Rough Area Under a Curve: evaluate the function at a point that looks good, multiply it by the difference in the interval ○ You get a very crude approximation of the integral! Approximating an Integral ● Like most things in calculus: do it a lot, and you get closer to the truth! ● Sample random variable, X ∈ [a,b], from a uniform distribution ● Keep evaluating f(X), average the results, you get a better approximation of the integral ○ This is a “Basic Monte-Carlo Estimator” Approximating an Integral: Non-Uniform Distributions ● In practice, we often sample our random variable from a non-uniform distribution.