Surfaces with holes in them: new plasmonic metamaterials


 Andrew Kelley
 2 years ago
 Views:
Transcription
1 INSTITUTE OF PHYSICS PUBLISHING JOURNAL OF OPTICS A: PURE AND APPLIED OPTICS J Opt A: Pure Appl Opt 7 5 S97 S oi:88/ /7//3 Surfaces with holes in them: new plasmonic metamaterials FJGarciaVial,LMartínMoreno an J B Penry 3 Departamento e Fisica Teorica e la Materia Conensaa, Universia Autonoma e Mari, E849 Mari, Spain Departamento e Fisica e la Materia Conensaa, ICMACSIC, Universia e Zaragoza, E59 Zaragoza, Spain 3 Imperial College Lonon, Department of Physics, The Blackett Laboratory, Lonon SW7 AZ, UK Receive June 4, accepte for publication 7 August 4 Publishe January 5 Online at stacksioporg/jopta/7/s97 Abstract In this paper weeplore the eistence of surface electromagnetic moes in corrugate surfaces of perfect conuctors We analyse two cases: oneimensional arrays of grooves an twoimensional arrays of holes In both cases we fin that these structures support surface boun states an that the ispersions of these moes have strong similarities with the ispersion of the surface plasmon polariton bans of real metals Importantly, the ispersion relation of these surface states is mainly ictate by the geometry of the grooves or holes an these results open the possibility of tailoring the properties of these moes by just tuning the geometrical parameters of the surface Keywors: surface plasmons, metamaterials, enhance transmission Some figures in this article are in colour only in the electronic version Introuction Since the appearance of the paper by Ebbesen et al [] reporting etraorinary optical transmission EOT in twoimensional D arrays of subwavelength holes in metallic films, the stuy of the optical properties of subwavelength apertures has become one of the most eciting areas in optics research In this seminal paper [], the relation between transmission resonances appearing in the spectra an the ecitation of the surface plasmon polaritons SPPs of the metallic surface was alreay pointe out The link between EOT an surface plasmons was corroborate theoretically three years after that [] Interestingly, in this last paper we also showe that similar anomalous transmission appears in arrays of subwavelength hole arrays perforate in a perfect conuctor It is well known that the surface of a perfect conuctor oes not support surface plasmons This seeme to suggest that the physical origins of EOT in real metals an in perfect conuctors were ifferent, leaing to iscussions asregars the true origin of the EOT phenomenon In this paper we solve this parao by showing that although a flat perfectly conucting surface supports no boun states, the presence of any perioic inentation of the flat surface for eample, D arrays of grooves or D hole arrays provokes the appearance of surface boun states that have strong similarities with the canonical SPPs of a flat metal surface [3, 4] Importantly, we also show that, as long as the size an spacing of the holes are much smaller than the wavelength, a perforate perfectly conucting surface behaves as an effective meium This meium is characterize by an effective ielectric function that has a plasmon form with a plasma frequency ictate by the geometry of the hole or the groove In other wors, the system behaves as a plasmonic metamaterial in which its electromagnetic response is governe by the surface moes that ecorate its surface It is worth commenting that this new class of metamaterials has some links with the metallic metamaterials invente in recent years in connection with the concept of negative refraction [5] D arrays of grooves First, we analyse the case of a D array of grooves rille in aperfect conuctor see figure a; a is the with of the grooves, h is the epth an the perio of the array We are intereste in looking at the surface EM moes supporte by /5/97+5$3 5 IOP Publishing Lt Printe in the UK S97
2 FJGarciaVial et al a b Figure a A oneimensional array of grooves of with a an epth h separate by a istance Weareintereste in ppolarize surface moes running in the irection with E lying in the z plane b In the effective meium approimation the structure isplaye in a behaves as an homogeneous but anisotropic layer of thickness h on top of a perfect conuctor this structure The proceure for calculating the ispersion relation of these surface moes, ωk,isthefollowing First, we calculate the reflectance of an incient ppolarize incient plane wave with parallel momentum k Asweareintereste in a truly surface moe, we will then analyse the epression for the reflectance for the particular case in which the incient plane wave is evanescent, k >ω/c a truly surface moe has tolive outsie the light cone The locations of the ivergences in the reflectance will give us the esire ispersion relation for the surface EM moes The electromagnetic EM fiels associate with the incient wave are E inc e ik e ikz z k /k z H inc e ik e ikz z k /k z where k is the wavenumber, ω/c,ank z k k The reflecte wave associate with the niffraction orer can be written as E ref,n e ikn H ref,n e ikn e ikn z z e ikn z z k n /k z n k /k z n where k n k +πn/ n,,,, an k z n k kn As we assume that the wavelength of light is much larger than the with of the grooves λ a, in the moal epansion of the EM fiels insie the grooves we only consier the funamental TE moe: E TE,± e ±ikz a H TE,± a e ±ik z Then, the EM fiels in region I vacuum can be epresse as a sum of the incient plane wave an the reflecte ones: E I E inc + H I H inc + n n ρ n E ref,n 3 ρ n H ref,n 4 where ρ n is the reflection coefficient associate with the iffraction orer n InregionIIinsiethe grooves, the EM fiels can be written as a linear combination of the forwar an backwar propagating TE moes: E II C + E TE,+ + C E TE, H II C + H TE,+ + C H TE, By applying the stanar matching bounary conitions at z continuity of E at every point of the unit cell an continuity of H y only at the groove s location an at z h; E must be zero, we can easily etract the reflection coefficients, ρ n : i tank hs S n k /k z ρ n δ n itank h n S n k /k z n 6 where S n is the overlap integral between the nthorer plane wave an the TE moe: S n a a/ e ikn a/ a sink n k n a/ 5 a/ 7 In principle, we coul calculate the surface bans of our system by just analysing the zeros of the enominator of equation 6 [6] The calculation is much simpler if we assume λ Then, all the iffraction orers can be safely neglecte ecept the specular one an ρ takes the form ρ +is tank hk /k z is tank 8 hk /k z For the case k > k k z i k k,wecan calculate the ispersion relation of the surface boun state by calculating the location of the ivergences of ρ : k k S k tank h 9 This is the ispersion relation of the surface EM moes supporte by a D array of grooves in the limit λ an λ a It is interesting to note here that the same ispersion relation coul be obtaine if we replace the array of grooves S98
3 Surfaces with holes in them: new plasmonic metamaterials y z Figure 3 Atwoimensional square array ofsquare holes sie aperforate on a semiinfinite perfect conuctor Figure The ispersion relation ωk ofthe surface boun states supporte by a D array of grooves with geometrical parameters a/ anh/ asobtaine with equation 4 by a single homogeneous but anisotropic layer of thickness h on top of the surface of a perfect conuctor see the schematic rawing in figure b The homogeneous layer woul have the following parameters: ɛ /a ɛ y ɛ z As light propagates in the grooves in the y or z irections with the velocity of light, ɛ µ y ɛ µ z an, hence, µ y µ z ɛ µ After some straightforwar algebra the specular reflection coefficient, R, for a ppolarize plane wave impinging at the surface of a homogeneous layer of thickness h with ɛ an µ given by equations an can be written as R ɛ k z k + k + ɛ k z e ikh 3 ɛ k z + k k ɛ k z eikh Again, by etening this formula to the case k > k an looking at the zeros of the enominator of R we can calculate the ispersion relation of the surface moes: k k a k tank h 4 Note that this epression coincies with equation 9 in the limit k a In figure we plot the ispersion relation equation 4 for the particular case a/ anh/ We have checke that this epression equation 4 gives accurate results for the range of wavelengths analyse in this case λ > 4h bycomparing them with the ispersion relation obtaine by calculating the zeros of the enominator of equation 6 in which the approimation λ is not applie It is worth commenting on the similarities between this ispersion an the one associate with the bans of SPPs supporte by the surfaces of real metals In a SPP ban, at large k, ω approaches ω p /, whereas in this case, ω approaches πc /h that is, the frequency location of a cavity waveguie moe insie the groove in the limit a/, the locations of the ifferent cavity waveguie moes correspon to the conition cos k h 3 D hole array Now we consier the caseofsquare holes of sie a arrange on a lattice perforate on a perfect conuctor semiinfinite structure see figure 3 [7] We assume that the holes are fille with a material whose ielectric constant is ɛ h Asinthe case of the array of grooves, we are intereste in looking at the possible surface states supporte by this system by looking at ivergences of the reflection coefficient of a ppolarize plane wave impinging at the perforate surface As we are intereste in the long wavelength limit λ, now we only take into account the specular reflecte wave The normalize EM fiels associate with the incient an specular reflecte waves are E inc eik e ikz z k /k z H inc eik e ikz z k /k z E ref e eik ikz z k /k z H ref e eik ikz z k /k z 5 6 Insie the holes, as we are intereste in the limit λ a, we assume that the funamental eigenmoe will ominate because it is the least strongly ecaying The EM fiels are zero insie the perfect metal but insie the holes they take the form E TE a eiqzz sin πy a where q z H TE ɛ h k π /a a eiqzz sin πy q z /k a iπ/ak 7 S99
4 FJGarciaVial et al Again, the EM fiels in region I can be epresse as a sum of the incient plane wave an the reflecte one: E I E inc + ρ E ref H I H inc + ρ H ref 8 where ρ is the specular reflection coefficient, an in region II insie the holes, as we are ealing with a semiinfinite structure, we only have to consier the ecaying moe: E II τ E TE H II τ H TE 9 where τ is the transmission coefficient In the matching proceure at z, E must be continuous over the entire unit cell an y ranging from an whereas H y has to be continuous only at the hole This woul yiel ρ k S q zk z k S + q zk z where S is the overlap integral of the incient plane wave an the funamental moe insie the hole: a a S e ik y sin πy a a y a sink a/ π k a/ By analysing the zeros of the enominator of ρ an etening the epression to k > k, we can etract the ispersion relation of the surface states supporte by the D hole array: k k k S k π /a ɛ h k As in the case of D arrays of grooves, we woul like to test whether the semiinfinite perfect conuctor perforate with holes coul be replace by a semiinfinite homogeneous system, characterize by an effective ielectric constant an an effective magnetic permeability Due to the symmetry of the structure, ɛ eff ɛ yeff ɛ eff an µ eff µ yeff µ eff Asthe ispersion of the waveguie moe insie the hole is unaffecte by parallel momentum, ɛ zeff µ zeff In a homogeneous structure, the reflection coefficient for a normally incient plane wave can be epresse as a function of the impeance of the meium, Z µ ɛ : R Z Z + 3 Then, the effective impeance of a D hole array perforate on a perfect conuctor can be easily calculate by analysing equation in the particular case of a normally incient plane wave k, k z k : µeff Z eff S k 4 ɛ eff q z where S S k a/π The other equation linking ɛ eff an µ eff can be obtaine from π q z k ɛeff µ eff i a ɛ hk 5 Figure 4 The ispersion relation ωk oftheppolarize surface boun states supporte by a D array of holes with a/ 6an fille with a ielectric material with ine of refraction n h 3, as obtaine with equation 9 Combining equations 4 an 5 we can write own the effective magnetic permeability an effective ielectric permittivity of our system: µ eff µ yeff S 6 ɛ eff ɛ yeff ɛ h π S a ɛ h k ɛ h π c 7 S a ɛ h ω which isthe canonical plasmon form with a plasma frequency, ω pl πc / ɛ h athisfrequency is just the cutoff frequency of a square waveguie of sie a fille with a material characterize by a ielectric constant ɛ h The net step is to calculate the ispersion relation of the surface moes supporte by this effective meium an compare it with equation For an interface between vacuum an a semiinfinite structure characterize by ɛ eff,thesurface moes have to fulfil the equation k z + q z ɛ eff 8 where k z k i k is the inverse of the ecaying length of the surface moe insie the vacuum, e k z z,anq z is the analogue magnitue in the effective meium By using ɛ eff from equation 7 we obtain k k k S k π /a ɛ h k 9 which coincies with equation in the long wavelength limit when the effective meium approimation makes sense, k a In figure 4 we plot the ispersion relation of these surface moes for the particular case a/ 6 anɛ h 9 3 D arrays of holes of finite epth imples It is quite interesting to analyse also the case of a D square array ofsquare holes sie a offiniteepth, h The proceure for calculating the ispersion relation of the surface S
5 Surfaces with holes in them: new plasmonic metamaterials moes supporte by this type of structure is quite similar to the one presente for the previous case The only ifference is that in equation 9 we have to consier not only the ecaying moe e qz z but also the growing one, e + qz z : E II C + E TE,+ + C E TE, H II C + H TE,+ + C H TE, 3 Apart from the continuity equations at z, we have to a the conition E atthebottom of the hole, z h By oing straightforwar algebra, we en up with a ispersion relation of the surface moes: k k k S k π /a ɛ h k e qz h 3 +e qz h Note that in the limit h, k k light line an for h we recover equation 9, as we shoul 4 Conclusions We have emonstrate that a semiinfinite perfect conuctor perforate with a oneimensional array of grooves or a twoimensional array of holes can be optically escribe in the long wavelength limit as an effective meium characterize by a ielectric function of plasmon form in which the plasma frequency only epens on the geometry of the inentation groove or hole The surface moes supporte by this system have close resemblances with the surface plasmon polaritons of a real metal In these new plasmonic metamaterials, their electromagnetic response coul be engineere by tuning the geometrical parameters efining the corrugate surface Then, these tailore surface plasmons coul be moifie at will at almost any frequency because metals are nearly perfect conuctors from zero frequency up to the threshol of the THz regime Surface electromagnetic moes ecite at a metal surface can also be analyse as propagating waves in two imensions [8, 9] Our results coul be use as an alternative way to control the flow of light in the surface of a metal by just playing with the geometry size an separation of the inentations ispose at the surface Acknowlegments Financial support by the Spanish MCyT uner grant BES an contracts MAT534 an MAT 39 an by EC project FP6NMP4CT Surface Plasmon Photonics is gratefully acknowlege References [] Ebbesen T W, Lezec H J, Ghaemi H F, Thio T an Wolff P A 998 Nature [] MartínMoreno L, GarciaVial F J, Lezec H J, Pellerin K M, Thio T, Penry J B an Ebbesen T W Phys RevLett 86 4 [3] Ritchie R H 957 Phys Rev [4] A very recent review of works relate to surface plasmons can be foun in: Barnes W L, Dereu A an Ebbesen T W 3 Nature [5] Penry J B, Holen A J, Robbins D J an Stewart W J 998 J Phys: Conens Matter 4785 Penry J B, Holen A J, Robbins D J an Stewart W J 999 IEEE Trans Microw Theory Tech [6] GarciaVial F J an MartínMoreno L Phys Rev B [7] A previous theoretical analysis of this case although using a slightly ifferent approach can be foun in: Penry J B, MartínMoreno L an GarciaVial F J 4 Science [8] Bozhevolnyi S I, Erlan J, Leosson K, Skovgaar P M an Hvam J M Phys RevLett [9] Ditlbacher H, Krenn J R, Schier G, Leitner A an Aussenegg F R Appl Phys Lett S
CHAPTER 5 : CALCULUS
Dr Roger Ni (Queen Mary, University of Lonon)  5. CHAPTER 5 : CALCULUS Differentiation Introuction to Differentiation Calculus is a branch of mathematics which concerns itself with change. Irrespective
More information9.3. Diffraction and Interference of Water Waves
Diffraction an Interference of Water Waves 9.3 Have you ever notice how people relaxing at the seashore spen so much of their time watching the ocean waves moving over the water, as they break repeately
More informationSOLUTIONS TO CONCEPTS CHAPTER 17
1. Given that, 400 m < < 700 nm. 1 1 1 700nm 400nm SOLUTIONS TO CONCETS CHATER 17 1 1 1 3 10 c 3 10 (Where, c = spee of light = 3 10 m/s) 7 7 7 7 7 10 4 10 7 10 4 10 4.3 10 14 < c/ < 7.5 10 14 4.3 10 14
More informationPHY101 Electricity and Magnetism I Course Summary
TOPIC 1 ELECTROSTTICS PHY11 Electricity an Magnetism I Course Summary Coulomb s Law The magnitue of the force between two point charges is irectly proportional to the prouct of the charges an inversely
More informationLecture L253D Rigid Body Kinematics
J. Peraire, S. Winall 16.07 Dynamics Fall 2008 Version 2.0 Lecture L253D Rigi Boy Kinematics In this lecture, we consier the motion of a 3D rigi boy. We shall see that in the general threeimensional
More informationLagrangian and Hamiltonian Mechanics
Lagrangian an Hamiltonian Mechanics D.G. Simpson, Ph.D. Department of Physical Sciences an Engineering Prince George s Community College December 5, 007 Introuction In this course we have been stuying
More informationDIFFRACTION AND INTERFERENCE
DIFFRACTION AND INTERFERENCE In this experiment you will emonstrate the wave nature of light by investigating how it bens aroun eges an how it interferes constructively an estructively. You will observe
More informationAnswers to the Practice Problems for Test 2
Answers to the Practice Problems for Test 2 Davi Murphy. Fin f (x) if it is known that x [f(2x)] = x2. By the chain rule, x [f(2x)] = f (2x) 2, so 2f (2x) = x 2. Hence f (2x) = x 2 /2, but the lefthan
More informationMeasures of distance between samples: Euclidean
4 Chapter 4 Measures of istance between samples: Eucliean We will be talking a lot about istances in this book. The concept of istance between two samples or between two variables is funamental in multivariate
More informationTerahertz transmission properties of an individual slit in a thin metallic plate
Terahertz transmission properties of an individual slit in a thin metallic plate J. W. Lee, 1 T. H. Park, 2 Peter Nordlander, 2 and Daniel M. Mittleman 1,* 1 Department of Electrical and Computer Engineering,
More informationarxiv:1309.1857v3 [grqc] 7 Mar 2014
Generalize holographic equipartition for FriemannRobertsonWalker universes WenYuan Ai, Hua Chen, XianRu Hu, an JianBo Deng Institute of Theoretical Physics, LanZhou University, Lanzhou 730000, P.
More informationInverse Trig Functions
Inverse Trig Functions c A Math Support Center Capsule February, 009 Introuction Just as trig functions arise in many applications, so o the inverse trig functions. What may be most surprising is that
More informationChalcopyrite CuGaJn, se2 semiconducting thin films produced by radio frequency sputtering
Chalcopyrite CuGaJn, se2 semiconucting thin films prouce by raio frequency sputtering J. L. HernAnezRojas, M. L. Lucfa, I. M&N, J. Santamaria, G. GonzAlezDfaaz, an F. SgnchezQuesaa Departamento e Electricia
More informationIntroduction to Integration Part 1: AntiDifferentiation
Mathematics Learning Centre Introuction to Integration Part : AntiDifferentiation Mary Barnes c 999 University of Syney Contents For Reference. Table of erivatives......2 New notation.... 2 Introuction
More informationReading: Ryden chs. 3 & 4, Shu chs. 15 & 16. For the enthusiasts, Shu chs. 13 & 14.
7 Shocks Reaing: Ryen chs 3 & 4, Shu chs 5 & 6 For the enthusiasts, Shu chs 3 & 4 A goo article for further reaing: Shull & Draine, The physics of interstellar shock waves, in Interstellar processes; Proceeings
More informationDefinition of the spin current: The angular spin current and its physical consequences
Definition of the spin current: The angular spin current an its physical consequences Qingfeng Sun 1, * an X. C. Xie 2,3 1 Beijing National Lab for Conense Matter Physics an Institute of Physics, Chinese
More information10.2 Systems of Linear Equations: Matrices
SECTION 0.2 Systems of Linear Equations: Matrices 7 0.2 Systems of Linear Equations: Matrices OBJECTIVES Write the Augmente Matrix of a System of Linear Equations 2 Write the System from the Augmente Matrix
More informationOn Adaboost and Optimal Betting Strategies
On Aaboost an Optimal Betting Strategies Pasquale Malacaria 1 an Fabrizio Smerali 1 1 School of Electronic Engineering an Computer Science, Queen Mary University of Lonon, Lonon, UK Abstract We explore
More informationUnsteady Flow Visualization by Animating EvenlySpaced Streamlines
EUROGRAPHICS 2000 / M. Gross an F.R.A. Hopgoo Volume 19, (2000), Number 3 (Guest Eitors) Unsteay Flow Visualization by Animating EvenlySpace Bruno Jobar an Wilfri Lefer Université u Littoral Côte Opale,
More informationFAST JOINING AND REPAIRING OF SANDWICH MATERIALS WITH DETACHABLE MECHANICAL CONNECTION TECHNOLOGY
FAST JOINING AND REPAIRING OF SANDWICH MATERIALS WITH DETACHABLE MECHANICAL CONNECTION TECHNOLOGY Jörg Felhusen an Sivakumara K. Krishnamoorthy RWTH Aachen University, Chair an Insitute for Engineering
More informationElectronically Controlled Surface Plasmon Dispersion and Optical Transmission through Metallic Hole Arrays Using Liquid Crystal
Electronically Controlled Surface Plasmon Dispersion and Optical Transmission through Metallic Hole Arrays Using Liquid Crystal NANO LETTERS 2008 Vol. 8, No. 1 281286 Wayne Dickson,* Gregory A. Wurtz,
More informationReflectance of a layered system with a gaussian distribution of the refractive index and inserted metamaterial
Reflectance of a layered system with a gaussian distribution of the refractive index and inserted metamaterial Xóchitl Saldaña Saldaña Instituto de Física de la Benemérita Universidad Autónoma de Puebla
More informationCalculating Viscous Flow: Velocity Profiles in Rivers and Pipes
previous inex next Calculating Viscous Flow: Velocity Profiles in Rivers an Pipes Michael Fowler, UVa 9/8/1 Introuction In this lecture, we ll erive the velocity istribution for two examples of laminar
More informationExponential Functions: Differentiation and Integration. The Natural Exponential Function
46_54.q //4 :59 PM Page 5 5 CHAPTER 5 Logarithmic, Eponential, an Other Transcenental Functions Section 5.4 f () = e f() = ln The inverse function of the natural logarithmic function is the natural eponential
More informationA Generalization of Sauer s Lemma to Classes of LargeMargin Functions
A Generalization of Sauer s Lemma to Classes of LargeMargin Functions Joel Ratsaby University College Lonon Gower Street, Lonon WC1E 6BT, Unite Kingom J.Ratsaby@cs.ucl.ac.uk, WWW home page: http://www.cs.ucl.ac.uk/staff/j.ratsaby/
More informationLecture 10: TEM, TE, and TM Modes for Waveguides. Rectangular Waveguide.
Whites, EE 481/581 Lecture 10 Page 1 of 10 Lecture 10: TEM, TE, and TM Modes for Waveguides. Rectangular Waveguide. We will now generalie our discussion of transmission lines by considering EM waveguides.
More informationJON HOLTAN. if P&C Insurance Ltd., Oslo, Norway ABSTRACT
OPTIMAL INSURANCE COVERAGE UNDER BONUSMALUS CONTRACTS BY JON HOLTAN if P&C Insurance Lt., Oslo, Norway ABSTRACT The paper analyses the questions: Shoul or shoul not an iniviual buy insurance? An if so,
More information11 CHAPTER 11: FOOTINGS
CHAPTER ELEVEN FOOTINGS 1 11 CHAPTER 11: FOOTINGS 11.1 Introuction Footings are structural elements that transmit column or wall loas to the unerlying soil below the structure. Footings are esigne to transmit
More informationUltrabroadband Microwave Metamaterial Absorber
Ultrabroadband Microwave Metamaterial Absorber Fei Ding 1, Yanxia Cui 1,3, Xiaochen Ge 1, Feng Zhang 1, Yi Jin 1*, and Sailing He 1,2 1 Centre for Optical and Electromagnetic Research, State Key Laboratory
More informationPurpose of the Experiments. Principles and Error Analysis. ε 0 is the dielectric constant,ε 0. ε r. = 8.854 10 12 F/m is the permittivity of
Experiments with Parallel Plate Capacitors to Evaluate the Capacitance Calculation an Gauss Law in Electricity, an to Measure the Dielectric Constants of a Few Soli an Liqui Samples Table of Contents Purpose
More informationExample Optimization Problems selected from Section 4.7
Example Optimization Problems selecte from Section 4.7 19) We are aske to fin the points ( X, Y ) on the ellipse 4x 2 + y 2 = 4 that are farthest away from the point ( 1, 0 ) ; as it happens, this point
More informationAchieving quality audio testing for mobile phones
Test & Measurement Achieving quality auio testing for mobile phones The auio capabilities of a cellular hanset provie the funamental interface between the user an the raio transceiver. Just as RF testing
More informationProducts no longer available
Technical ata sheet R6..R haracterize control valves, 2way, with flange PN 6 for open an close col an warm water systems for moulating control on the water sie of airhanling an heating systems air bubbletight
More informationAn intertemporal model of the real exchange rate, stock market, and international debt dynamics: policy simulations
This page may be remove to conceal the ientities of the authors An intertemporal moel of the real exchange rate, stock market, an international ebt ynamics: policy simulations Saziye Gazioglu an W. Davi
More informationi( t) L i( t) 56mH 1.1A t = τ ln 1 = ln 1 ln 1 6.67ms
Exam III PHY 49 Summer C July 16, 8 1. In the circuit shown, L = 56 mh, R = 4.6 Ω an V = 1. V. The switch S has been open for a long time then is suenly close at t =. At what value of t (in msec) will
More informationAlmost Everything You Always Wanted to Know About the Toda Equation
Jahresber. Deutsch. Math.Verein. 103, no. 4, 149162 (2001) Mathematics Subject Classification: 35Q51, 37K10; 37K15, 39A70 Keywors an Phrases: Toa equation, Kac van Moerbeke equation, Solitons, Lax pair
More informationThe oneyear nonlife insurance risk
The oneyear nonlife insurance risk Ohlsson, Esbjörn & Lauzeningks, Jan Abstract With few exceptions, the literature on nonlife insurance reserve risk has been evote to the ultimo risk, the risk in the
More informationAs customary, choice (a) is the correct answer in all the following problems.
PHY2049 Summer 2012 Instructor: Francisco Rojas Exam 1 As customary, choice (a) is the correct answer in all the following problems. Problem 1 A uniformly charge (thin) nonconucting ro is locate on the
More informationAnalysis of Electromagnetic Propulsion on a TwoElectricDipole System
Electronics and Communications in Japan, Part 2, Vol. 83, No. 4, 2000 Translated from Denshi Joho Tsushin Gakkai Ronbunshi, Vol. J82CI, No. 6, June 1999, pp. 310 317 Analysis of Electromagnetic Propulsion
More informationInductors and Capacitors Energy Storage Devices
Inuctors an Capacitors Energy Storage Devices Aims: To know: Basics of energy storage evices. Storage leas to time elays. Basic equations for inuctors an capacitors. To be able to o escribe: Energy storage
More informationELECTROMAGNETIC ANALYSIS AND COLD TEST OF A DISTRIBUTED WINDOW FOR A HIGH POWER GYROTRON
ELECTROMAGNETIC ANALYSIS AND COLD TEST OF A DISTRIBUTED WINDOW FOR A HIGH POWER GYROTRON M.A.Shapiro, C.P.Moeller, and R.J.Temkin Plasma Science and Fusion Ceer, Massachusetts Institute of Technology,
More informationFluid Pressure and Fluid Force
0_0707.q //0 : PM Page 07 SECTION 7.7 Section 7.7 Flui Pressure an Flui Force 07 Flui Pressure an Flui Force Fin flui pressure an flui force. Flui Pressure an Flui Force Swimmers know that the eeper an
More informationJitter effects on Analog to Digital and Digital to Analog Converters
Jitter effects on Analog to Digital an Digital to Analog Converters Jitter effects copyright 1999, 2000 Troisi Design Limite Jitter One of the significant problems in igital auio is clock jitter an its
More informationCrossOver Analysis Using TTests
Chapter 35 CrossOver Analysis Using ests Introuction his proceure analyzes ata from a twotreatment, twoperio (x) crossover esign. he response is assume to be a continuous ranom variable that follows
More informationWeb Appendices to Selling to Overcon dent Consumers
Web Appenices to Selling to Overcon ent Consumers Michael D. Grubb MIT Sloan School of Management Cambrige, MA 02142 mgrubbmit.eu www.mit.eu/~mgrubb May 2, 2008 B Option Pricing Intuition This appenix
More informationHomework 8. problems: 10.40, 10.73, 11.55, 12.43
Hoework 8 probles: 0.0, 0.7,.55,. Proble 0.0 A block of ass kg an a block of ass 6 kg are connecte by a assless strint over a pulley in the shape of a soli isk having raius R0.5 an ass M0 kg. These blocks
More informationMath 230.01, Fall 2012: HW 1 Solutions
Math 3., Fall : HW Solutions Problem (p.9 #). Suppose a wor is picke at ranom from this sentence. Fin: a) the chance the wor has at least letters; SOLUTION: All wors are equally likely to be chosen. The
More informationMASSACHUSETTS INSTITUTE OF TECHNOLOGY 6.436J/15.085J Fall 2008 Lecture 14 10/27/2008 MOMENT GENERATING FUNCTIONS
MASSACHUSETTS INSTITUTE OF TECHNOLOGY 6.436J/15.085J Fall 2008 Lecture 14 10/27/2008 MOMENT GENERATING FUNCTIONS Contents 1. Moment generating functions 2. Sum of a ranom number of ranom variables 3. Transforms
More information2 Metamaterials: Fundamental Revolution and Potential Future
3 2 Metamaterials: Fundamental Revolution and Potential Future Materials properties have troubled scientists since old ages [1]. From an electromagnetic outlook, researchers have had different concerns
More informationState of Louisiana Office of Information Technology. Change Management Plan
State of Louisiana Office of Information Technology Change Management Plan Table of Contents Change Management Overview Change Management Plan Key Consierations Organizational Transition Stages Change
More informationExperimental retrieval of the effective parameters of metamaterials based on a waveguide method
Experimental retrieval of the effective parameters of metamaterials based on a waveguide method Hongsheng Chen 1,3, Jingjing Zhang 1,, Yang Bai 4, Yu Luo 1,, Lixin Ran 1,, Qin Jiang 1, and Jin Au Kong
More information5. Scanning NearField Optical Microscopy 5.1. Resolution of conventional optical microscopy
5. Scanning NearField Optical Microscopy 5.1. Resolution of conventional optical microscopy Resolution of optical microscope is limited by diffraction. Light going through an aperture makes diffraction
More informationThe Classical Particle Coupled to External Electromagnetic Field Symmetries and Conserved Quantities. Resumo. Abstract
The Classical Particle Couple to External Electromagnetic Fiel Symmetries an Conserve Quantities G. D. Barbosa R. Thibes, Universiae Estaual o Suoeste a Bahia Departamento e Estuos Básicos e Instrumentais
More informationNear Field Imaging with Magnetic Wires
Near Field Imaging with Magnetic Wires M C K Wiltshire and J V Hajnal Imaging Sciences Department, Imperial College London, Hammersmith Hospital, Du Cane Road, London W12 HS, UK michael.wiltshire@imperial.ac.uk;
More informationProgress In Electromagnetics Research, Vol. 138, 647 660, 2013
Progress In Electromagnetics Research, Vol. 138, 647 660, 2013 FARFIELD TUNABLE NANOFOCUSING BASED ON METALLIC SLITS SURROUNDED WITH NONLINEAR VARIANT WIDTHS AND LINEARVARIANT DEPTHS OF CIRCULAR DIELECTRIC
More informationNotes on tangents to parabolas
Notes on tangents to parabolas (These are notes for a talk I gave on 2007 March 30.) The point of this talk is not to publicize new results. The most recent material in it is the concept of Bézier curves,
More informationHybrid Model Predictive Control Applied to ProductionInventory Systems
Preprint of paper to appear in the 18th IFAC Worl Congress, August 28  Sept. 2, 211, Milan, Italy Hybri Moel Preictive Control Applie to ProuctionInventory Systems Naresh N. Nanola Daniel E. Rivera Control
More informationSensitivity Analysis of Nonlinear Performance with Probability Distortion
Preprints of the 19th Worl Congress The International Feeration of Automatic Control Cape Town, South Africa. August 2429, 214 Sensitivity Analysis of Nonlinear Performance with Probability Distortion
More informationDetecting Possibly Fraudulent or ErrorProne Survey Data Using Benford s Law
Detecting Possibly Frauulent or ErrorProne Survey Data Using Benfor s Law Davi Swanson, Moon Jung Cho, John Eltinge U.S. Bureau of Labor Statistics 2 Massachusetts Ave., NE, Room 3650, Washington, DC
More informationMODELING OF PLANAR METAMATERIAL STRUCTURE AND ITS EFFECTIVE PARAMETER EXTRACTION
International Journal of Electronics and Communication Engineering & Technology (IJECET) Volume 7, Issue 1, JanFeb 2016, pp. 5562, Article ID: IJECET_07_01_006 Available online at http://www.iaeme.com/ijecetissues.asp?jtype=ijecet&vtype=7&itype=1
More informationModelling and Resolving Software Dependencies
June 15, 2005 Abstract Many Linux istributions an other moern operating systems feature the explicit eclaration of (often complex) epenency relationships between the pieces of software
More informationSAR REDUCTION IN HUMAN HEAD FROM MOBILE PHONE RADIATION USING SINGLE NEGATIVE META MATERIALS
J. of Electromagn. Waves and Appl., Vol. 23, 1385 1395, 2009 SAR REDUCTION IN HUMAN HEAD FROM MOBILE PHONE RADIATION USING SINGLE NEGATIVE META MATERIALS M. B. Manapati and R. S. Kshetrimayum Department
More informationA wave lab inside a coaxial cable
INSTITUTE OF PHYSICS PUBLISHING Eur. J. Phys. 25 (2004) 581 591 EUROPEAN JOURNAL OF PHYSICS PII: S01430807(04)76273X A wave lab inside a coaxial cable JoãoMSerra,MiguelCBrito,JMaiaAlves and A M Vallera
More informationFactoring Dickson polynomials over finite fields
Factoring Dickson polynomials over finite fiels Manjul Bhargava Department of Mathematics, Princeton University. Princeton NJ 08544 manjul@math.princeton.eu Michael Zieve Department of Mathematics, University
More informationMODELLING OF TWO STRATEGIES IN INVENTORY CONTROL SYSTEM WITH RANDOM LEAD TIME AND DEMAND
art I. robobabilystic Moels Computer Moelling an New echnologies 27 Vol. No. 23 ransport an elecommunication Institute omonosova iga V9 atvia MOEING OF WO AEGIE IN INVENOY CONO YEM WIH ANOM EA IME AN
More informationReducing the Synchrotron Radiation on RF Cavity Surfaces in the proposed Cornell EnergyRecovery Linac
Reucing the Synchrotron Raiation on RF Cavity Surfaces in the propose Cornell EnergyRecovery Linac G. H. Hoffstaetter, T. Tanabe February 8, 4 Report: Cornell ERL4 Abstract It has been suggeste to buil
More informationThe Quick Calculus Tutorial
The Quick Calculus Tutorial This text is a quick introuction into Calculus ieas an techniques. It is esigne to help you if you take the Calculus base course Physics 211 at the same time with Calculus I,
More informationCalculation of overvoltages and interference voltages
Calculation of overvoltages an interference voltages When installing telecom or computer systems close to heavy current equipment or traction power supplies, careful thought has to be given to the possibility
More informationKater Pendulum. Introduction. It is wellknown result that the period T of a simple pendulum is given by. T = 2π
Kater Penulum ntrouction t is wellknown result that the perio of a simple penulum is given by π L g where L is the length. n principle, then, a penulum coul be use to measure g, the acceleration of gravity.
More informationAn Alternative Approach of Operating a Passive RFID Device Embedded on Metallic Implants
An Alternative Approach of Operating a Passive RFID Device Embee on Metallic Implants Xiaoyu Liu, Ravi Yalamanchili, Ajay Ogirala an Marlin Mickle RFID Center of Excellence, Department of Electrical an
More informationLecture 17: Implicit differentiation
Lecture 7: Implicit ifferentiation Nathan Pflueger 8 October 203 Introuction Toay we iscuss a technique calle implicit ifferentiation, which provies a quicker an easier way to compute many erivatives we
More informationScalar : Vector : Equal vectors : Negative vectors : Proper vector : Null Vector (Zero Vector): Parallel vectors : Antiparallel vectors :
ELEMENTS OF VECTOS 1 Scalar : physical quantity having only magnitue but not associate with any irection is calle a scalar eg: time, mass, istance, spee, work, energy, power, pressure, temperature, electric
More informationThe waveguide adapter consists of a rectangular part smoothly transcending into an elliptical part as seen in Figure 1.
Waveguide Adapter Introduction This is a model of an adapter for microwave propagation in the transition between a rectangular and an elliptical waveguide. Such waveguide adapters are designed to keep
More informationCHARACTERIZATION OF ACETATE ESTERS BY CARBON NUCLEAR MAGNETIC RESONANCE (NMR) SPECTROSCOPY
EXPERIMENT 9 HARATERIZATIN F AETATE ESTERS BY ARBN NULEAR MAGNETI RESNANE (NMR) SPETRSPY Materials Neee approx 100 mg of an ester synthesize in Expt #5  (octyl acetate, propyl acetate, benzyl acetate,
More informationStock Market Value Prediction Using Neural Networks
Stock Market Value Preiction Using Neural Networks Mahi Pakaman Naeini IT & Computer Engineering Department Islamic Aza University Paran Branch email: m.pakaman@ece.ut.ac.ir Hamireza Taremian Engineering
More informationDEVELOPMENT OF A BRAKING MODEL FOR SPEED SUPERVISION SYSTEMS
DEVELOPMENT OF A BRAKING MODEL FOR SPEED SUPERVISION SYSTEMS Paolo Presciani*, Monica Malvezzi #, Giuseppe Luigi Bonacci +, Monica Balli + * FS Trenitalia Unità Tecnologie Materiale Rotabile Direzione
More informationRisk Management for Derivatives
Risk Management or Derivatives he Greeks are coming the Greeks are coming! Managing risk is important to a large number o iniviuals an institutions he most unamental aspect o business is a process where
More informationView Synthesis by Image Mapping and Interpolation
View Synthesis by Image Mapping an Interpolation Farris J. Halim Jesse S. Jin, School of Computer Science & Engineering, University of New South Wales Syney, NSW 05, Australia Basser epartment of Computer
More informationLagrange s equations of motion for oscillating centralforce field
Theoretical Mathematics & Applications, vol.3, no., 013, 99115 ISSN: 1799687 (print), 1799709 (online) Scienpress Lt, 013 Lagrange s equations of motion for oscillating centralforce fiel A.E. Eison
More information5 Isotope effects on vibrational relaxation and hydrogenbond dynamics in water
5 Isotope effects on vibrational relaxation an hyrogenbon ynamics in water Pump probe experiments HDO issolve in liqui H O show the spectral ynamics an the vibrational relaxation of the OD stretch vibration.
More informationGiven three vectors A, B, andc. We list three products with formula (A B) C = B(A C) A(B C); A (B C) =B(A C) C(A B);
1.1.4. Prouct of three vectors. Given three vectors A, B, anc. We list three proucts with formula (A B) C = B(A C) A(B C); A (B C) =B(A C) C(A B); a 1 a 2 a 3 (A B) C = b 1 b 2 b 3 c 1 c 2 c 3 where the
More informationTheoretical Considerations on Compensation of the Accommodation Vergence Mismatch by Refractive Power of FocusAdjustable 3D Glasses
Theoretical Consierations on Compensation of the Accommoation Vergence Mismatch by Refractive Power of FocusAjustable 3D Glasses DalYoung Kim* Department of Optometry, Seoul National University of Science
More information(We assume that x 2 IR n with n > m f g are twice continuously ierentiable functions with Lipschitz secon erivatives. The Lagrangian function `(x y) i
An Analysis of Newton's Metho for Equivalent Karush{Kuhn{Tucker Systems Lus N. Vicente January 25, 999 Abstract In this paper we analyze the application of Newton's metho to the solution of systems of
More informationParameterized Algorithms for dhitting Set: the Weighted Case Henning Fernau. Univ. Trier, FB 4 Abteilung Informatik 54286 Trier, Germany
Parameterize Algorithms for Hitting Set: the Weighte Case Henning Fernau Trierer Forschungsberichte; Trier: Technical Reports Informatik / Mathematik No. 086, July 2008 Univ. Trier, FB 4 Abteilung Informatik
More informationHere the units used are radians and sin x = sin(x radians). Recall that sin x and cos x are defined and continuous everywhere and
Lecture 9 : Derivatives of Trigonometric Functions (Please review Trigonometry uner Algebra/Precalculus Review on the class webpage.) In this section we will look at the erivatives of the trigonometric
More informationNew Trade Models, New Welfare Implications
New Trae Moels, New Welfare Implications Marc J. Melitz Harvar University, NBER an CEPR Stephen J. Reing Princeton University, NBER an CEPR August 13, 2014 Abstract We show that enogenous firm selection
More informationAPPLICATION OF CALCULUS IN COMMERCE AND ECONOMICS
Application of Calculus in Commerce an Economics 41 APPLICATION OF CALCULUS IN COMMERCE AND ECONOMICS æ We have learnt in calculus that when 'y' is a function of '', the erivative of y w.r.to i.e. y ö
More informationBACKWARD WAVES AND NEGATIVE REFRACTION IN UNIAXIAL DIELECTRICS WITH NEGATIVE DIELECTRIC PERMITTIVITY ALONG THE ANISOTROPY AXIS
2003 Wiley Periodicals, Inc. Reprinted, with permission, from P.A. Belov, Microwave and Optical Technology Letters, Vol. 37, No. 4, pp. 259263, 2003. mere prototype; the same method can be extended to
More informationOptimizing Multiple Stock Trading Rules using Genetic Algorithms
Optimizing Multiple Stock Traing Rules using Genetic Algorithms Ariano Simões, Rui Neves, Nuno Horta Instituto as Telecomunicações, Instituto Superior Técnico Av. Rovisco Pais, 04000 Lisboa, Portugal.
More informationHeatAndMass Transfer Relationship to Determine Shear Stress in Tubular Membrane Systems Ratkovich, Nicolas Rios; Nopens, Ingmar
Aalborg Universitet HeatAnMass Transfer Relationship to Determine Shear Stress in Tubular Membrane Systems Ratkovich, Nicolas Rios; Nopens, Ingmar Publishe in: International Journal of Heat an Mass Transfer
More informationMetamaterials and Transformation Optics
AFRLAFOSRUKTR20110021 Metamaterials and Transformation Optics John Pendry Imperial College London Physics Department South Kensington Campus Exhibition Road London, United Kingdom SW7 2AZ EOARD GRANT
More informationHull, Chapter 11 + Sections 17.1 and 17.2 Additional reference: John Cox and Mark Rubinstein, Options Markets, Chapter 5
Binomial Moel Hull, Chapter 11 + ections 17.1 an 17.2 Aitional reference: John Cox an Mark Rubinstein, Options Markets, Chapter 5 1. OnePerio Binomial Moel Creating synthetic options (replicating options)
More information4. Important theorems in quantum mechanics
TFY4215 Kjemisk fysikk og kvantemekanikk  Tillegg 4 1 TILLEGG 4 4. Important theorems in quantum mechanics Before attacking threeimensional potentials in the next chapter, we shall in chapter 4 of this
More informationUsing research evidence in mental health: userrating and focus group study of clinicians preferences for a new clinical questionanswering service
DOI: 10.1111/j.14711842.2008.00833.x Using research evience in mental health: userrating an focus group stuy of clinicians preferences for a new clinical questionanswering service Elizabeth A. Barley*,
More informationRisk Adjustment for Poker Players
Risk Ajustment for Poker Players William Chin DePaul University, Chicago, Illinois Marc Ingenoso Conger Asset Management LLC, Chicago, Illinois September, 2006 Introuction In this article we consier risk
More informationData Center Power System Reliability Beyond the 9 s: A Practical Approach
Data Center Power System Reliability Beyon the 9 s: A Practical Approach Bill Brown, P.E., Square D Critical Power Competency Center. Abstract Reliability has always been the focus of missioncritical
More informationApertureless NearField Optical Microscopy
VI Apertureless NearField Optical Microscopy In recent years, several types of apertureless nearfield optical microscopes have been developed 1,2,3,4,5,6,7. In such instruments, light scattered from
More informationSage Match Terms and Conditions of Use (Last updated: 9 November 2015)
1. Acknowlegement an Acceptance 1.1. This Agreement is between: (1) you, the person or organisation registere to use or using the Sage accountancy network service known as Sage Match ; an (2) us, as follows:
More informationMinimumEnergy Broadcast in AllWireless Networks: NPCompleteness and Distribution Issues
MinimumEnergy Broacast in AllWireless Networks: NPCompleteness an Distribution Issues Mario Čagal LCAEPFL CH05 Lausanne Switzerlan mario.cagal@epfl.ch JeanPierre Hubaux LCAEPFL CH05 Lausanne Switzerlan
More informationMathematics. Circles. hsn.uk.net. Higher. Contents. Circles 119 HSN22400
hsn.uk.net Higher Mathematics UNIT OUTCOME 4 Circles Contents Circles 119 1 Representing a Circle 119 Testing a Point 10 3 The General Equation of a Circle 10 4 Intersection of a Line an a Circle 1 5 Tangents
More information