Reflectance of a layered system with a gaussian distribution of the refractive index and inserted metamaterial

Size: px
Start display at page:

Download "Reflectance of a layered system with a gaussian distribution of the refractive index and inserted metamaterial"

Transcription

1 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 David Armando Contreras Solorio Agustín Enciso uñoz Jesús adrigal elchor Unidad Académica de Física Universidad Autónoma de acatecas E mail:dacs10@yahoo.com.mx Resumen Calculamos la reflectancia de una estructura dieléctrica con 41 capas dispuestas alternadamente con índices de refracción positivos y negativos. El índice de refracción de las capas impares es positivo y sigue una distribución de valores gaussiana, mientras que las capas pares intercaladas tienen un índice de refracción negativo constante n = -1. Para varios ángulos de incidencia, realizamos un estudio de la reflectancia variando la longitud de onda, para ambas polarizaciones TE y T. Comparamos este estudio con otro realizado cuando las capas pares tienen índice de refracción positivo constante n = 1. La reflectancia para ondas TE en ambos casos es excelente para longitudes de onda largas, siendo mucho meor en longitudes de onda cortas para capas intercaladas con n = -1. Para ondas T no es buena la reflectancia en ambos casos. Palabras clave: ateriales izquierdos, Reflectancia, ulticapas. Abstract We calculate the electromagnetic reflectance for a dielectric structure made by stacking alternately 41 layers of positive and negative refractive indices. The refractive index of the odd layers is positive and follows a Gaussian distribution, while the inserted 1

2 even layers have a negative refractive index n = -1. For several incident angles, we carry out a study of the reflectance varying the wavelength, for both polarizations TE and T. We compare this study with another one when the even layers have positive refractive index n = 1. The reflectance for TE waves in both cases is excellent for long wavelengths, but for inserted layers with negative refraction the reflectance for short wavelengths is much better. For T waves the reflectance is not good for both cases. Keywords: Left-handed materials, Reflectance, Layered systems. Introduction V. Veselago predicted the possibility to have materials with negative refractive index [1], for which both the magnetic permeability and the electric permittivity were simultaneously negative. If ever found these materials, they would exhibit extraordinary electromagnetic properties. These materials, also known as left-handed materials or metamaterials, were only a theoretical curiosity for 30 years. At the end of the decade of the 90, materials with negative refraction were fabricated [2-5], confirming the predictions of Veselago. Initially, these materials had negative refraction for frequencies in the range of microwaves. However, there are recent reports of materials with negative refraction for optical frequencies [6]. On the other hand, there are proposals of electronic filters using quantum superlattices where the height, or the width, of the barriers potentials follows a Gaussian distribution [7,8]. The transmittance for these superlattices is practically perfect for an interval of electron energies. Out of that interval, the transmittance is zero, i. e. the reflectance is perfect. The interval can be adusted modifying the parameters of the superlattice or of the Gaussian distribution. Therefore, for other type of waves it is reasonable that a layered system with a Gaussian distribution of some property could also have excellent transmittance or reflectance. In this work, we calculate the electromagnetic reflectance for a structure of 41 dielectric layers made by stacking alternately layers of positive and negative refractive 2

3 indices. The index for the odd positive refraction layers is modulated by a Gaussian function, while the even inserted layers have a constant negative refractive index n = -1. For a fixed width of the structure, and for several incident angles of the electromagnetic radiation, we made a study of the dependence of the reflectance with the wavelength, for both polarizations TE and T. In order to compare, we also made the study inserting even layers with constant positive refractive index n = 1. The calculations were made following the procedure described in the book of P. Yeh [9]. Theoretical model and calculation method To calculate the transmittance, we use the theory of Ref. [9]. We consider a structure of N plane dielectric multilayers. The layers are perpendicular to the x axis. Each layer has a width d, electric permitivity ε, and magnetic permeability μ. Each medium is homogeneous and isotropic. For each layer the refractive index n is given by n ± ε μ = (1) ε 0 μ 0 Where ε 0 and μ 0 are, respectively, the permittivity and the permeability of the vacuum. In Eq. 1 the plus sign is for normal materials with positive refraction which have ε and μ simultaneously positive. The minus sign is taken for metamaterials, which is congruent with the boundary conditions for the electromagnetic fields when both ε and μ are simultaneously negative. We consider an electromagnetic plane wave propagating in the xz plane, coming from the left in a medium with refraction index n 0. The plane wave is incident on the structure of N plane multilayers. In the right side of the structure, the wave propagates in a medium S with refraction index n S. We can write the wave function for each layer in the following form i( k r ωt) i( k' r ωt) Ae Be Ψ = + (3) 3

4 Ψ represents the electric or magnetic field. The first and the second terms on the righthand side of Eq. 3 represent propagation to the right and to the left, respectively, i.e. the forward and the backward waves. The index = 0 represents the medium at the left side of the structure with refractive index n 0. In the medium S with = N + 1 we consider only propagation to the right, consequently B S = 0. k y k are the forward and backward wavevectors for medium, t is the time, ω the angular frequency, and i the imaginary unit. If the wave is incident at an angle θ 0 with the normal to the structure, the Law of Snell gives n sinθ = n sin θ =... = n sin θ =... n sinθ. (4) S S The wave propagation from medium 0 to medium S through the multilayer structure is described by A B = S A. (5) 0 Where the (2 2) transfer matrix is given by = D 1 0 N l= 1 D P D l l 1 l D S. (6) The matrix D is called the dynamical or transmission matrix, and arises from the continuity conditions on the electric and magnetic fields at the interface between media 1 and. The matrix P is the kinematical or propagation matrix inside the layer. If it is supposed that the media are lossless, the matrices are given by D TE 1 1 =, D T = 1 1, (7) P ik d e 0 =. ik d 0 e 4

5 The two different polarizations TE and T are indicated. is the wave impedance, given by. μ = (8) ε The transmittance T is given by the ratio of the Poynting power flow of the transmitted wave to that of the incident wave, and is given in terms of the transfer matrix by T = 0 S S (9) The reflectance R is given by R = 1 T (10) The structure we consider has 41 layers and is situated in the vacuum. The refractive index for the odd layers is positive and modulated by the Gaussian function n ( x) = ( n σ + n (11) 2 2 max nmin )exp( ( x x0 ) / ) min Results and discussion We use in Eq. (11) n max = 3.5 and n min = The total width of the structure is D tot = 10 arbitrary units of length (meters, nm, Å, etc.). We use the value σ = D tot / 4. The thickness for all the odd and even layers is the same. The reflectance is calculated using Eqs. (9) and (10) when the inserted even layers have positive refractive index n = 1 or negative refraction index n = -1, in order to compare the reflectances for both cases. In Fig. 1 is shown the profile of refractive indices for the structure, when the inserted layers have positive refraction. 5

6 Figure 1. Diagram of the Gaussian distribution of refractive indices for the structure with even inserted layers of n = 1. Fig. 2 shows the results for the calculations of the dependence of the reflectance with wavelength for incident angles 0 O, 45º y 85º, when the even inserted layers have positive refraction. We observe that the reflectance por TE waves is practically perfect for the three angles, for extensive intervals of long wavelengths. However, the reflectance is poor for short wavelengths, around the value D tot. (a) (b) 6

7 (c) Figure 2. Reflectance vs. wavelength for inserted layers with n = 1. (a) incident angle of 0 O, (b) incident angle of 45 O, (c) incident angle of 85º. In Fig. 3 we show the results for the dependence of the reflectance with the wavelength, when the even layers have negative refraction, for the same angles than in Fig. 2. In this case, we notice that the reflectance for TE waves also is practically perfect for long wavelengths, but is good for short wavelengths as well. For inserted layers with positive or negative refraction, the reflectance is not good for T waves.. (a) (b) 7

8 (c ) Figure 3. Reflectance vs. wavelength for inserted layers with n = -1. (a) incident angle of 0 O, (b) incident angle of 45 O, (c) incident angle of 85º. Conclusion We have made a theoretical study of the reflectance for a structure of 41 dielectric layers where the odd layers have a positive refractive index modulated by a Gaussian distribution, while the even inserted layers can have positive refraction index n = 1 or negative refraction index n = -1. For several incident angles, the reflectance for TE waves is excellent for both cases of even layers with negative or positive refraction for long wavelengths. However, the reflectance for short wavelengths is much better for inserted layers with negative refraction than that produced by inserted layers with positive refraction. The reflectance for T waves is not good for both cases. Therefore, for inserted layers with negative refraction, the structure acts as an omnidirectional mirror for TE waves. Acknowledgments This work has been supported partially by Proect 37/EXC/G/06VIEP-BUAP and by Secretaría General de la Universidad Autónoma de acatecas. 8

9 References 1. V. G. Veselago, The electrodynamics of substances with simultaneously negative values of ε and μ, Sov. Phys. Usp. 10 (1968) J. B. Pendry, A. J. Holden, D. J. Robbins, W. J. Stewart, agnetism from conductors and enhanced nonlinear phenomena, IEEE Trans. icrowave Theory Tech. 47 (1999) D.R. Smith, W.J. Padilla, D.C. Vier, S.C. Nemat-Nasser, and S. Schultz, Composite medium with simultaneously negative permeability and permittivity, Phys. Rev. Lett. 84 (2000) R.A. Shelby, D.R.Smith, S.Schultz, Experimental verification of a negative index of refraction, Science 292 (2001) R. Ruppin, Surface polaritons of a left-handed medium, Phys. Lett. A 277 (2000) C.. Soukoulis, S. Linden, and. Wegener, Negative refractive index at optical wavelengths, Science 315 (2007) H. H. Tung and C. P. Lee, An energy band-pass filter using superlattice structures, IEEE J. Quantum Electron. 32 (1996) I. Gómez, F. Domínguez-Adame, E. Diez, and V. Bellani, Electron transport across a Gaussian superlattice, J. Appl. Phys. 85(7) (1999) P. Yeh, Optical Waves in Layered edia (Wiley, New York, 1988). 9

arxiv:physics/0311029v1 [physics.optics] 6 Nov 2003

arxiv:physics/0311029v1 [physics.optics] 6 Nov 2003 arxiv:physics/031109v1 [physics.optics] 6 Nov 003 A NEW CONDITION TO IDENTIFY ISOTROPIC DIELECTRIC MAGNETIC MATERIALS DISPLAYING NEGATIVE PHASE VELOCITY Ricardo A. Depine 1 and Akhlesh Lakhtakia 1 Grupo

More information

Near Field Imaging with Magnetic Wires

Near 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 information

Ultra-broadband Microwave Metamaterial Absorber

Ultra-broadband Microwave Metamaterial Absorber Ultra-broadband 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 information

2 Metamaterials: Fundamental Revolution and Potential Future

2 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 information

Experimental 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 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 information

SAR REDUCTION IN HUMAN HEAD FROM MOBILE PHONE RADIATION USING SINGLE NEGATIVE META- MATERIALS

SAR 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 information

BACKWARD WAVES AND NEGATIVE REFRACTION IN UNIAXIAL DIELECTRICS WITH NEGATIVE DIELECTRIC PERMITTIVITY ALONG THE ANISOTROPY AXIS

BACKWARD 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. 259-263, 2003. mere prototype; the same method can be extended to

More information

FDTD Analysis of Site Free Space VSWR in Test Site Used for Disturbance Measurement above 1 GHz

FDTD Analysis of Site Free Space VSWR in Test Site Used for Disturbance Measurement above 1 GHz 九 州 工 業 大 学 学 術 機 関 リポジトリ Title FDTD analysis of site free space VS disturbance measurement above 1 GHz Author(s) Kuwabara N; Midori M; Kawabata M Issue Date 9-8 URL http://hdl.handle.net/8/368 9 IEEE.

More information

MODELING OF PLANAR METAMATERIAL STRUCTURE AND ITS EFFECTIVE PARAMETER EXTRACTION

MODELING OF PLANAR METAMATERIAL STRUCTURE AND ITS EFFECTIVE PARAMETER EXTRACTION International Journal of Electronics and Communication Engineering & Technology (IJECET) Volume 7, Issue 1, Jan-Feb 2016, pp. 55-62, Article ID: IJECET_07_01_006 Available online at http://www.iaeme.com/ijecetissues.asp?jtype=ijecet&vtype=7&itype=1

More information

DESIGN AND SIMULATION OF MULTIBAND CHAUCER FRACTAL PATCH ANTENNA LOADED WITH DUMBBELL

DESIGN AND SIMULATION OF MULTIBAND CHAUCER FRACTAL PATCH ANTENNA LOADED WITH DUMBBELL International Journal of Electronics and Communication Engineering & Technology (IJECET) Volume 7, Issue 1, Jan-Feb 216, pp. 45-54, Article ID: IJECET_7_1_5 Available online at http://www.iaeme.com/ijecet/issues.asp?jtype=ijecet&vtype=7&itype=1

More information

MINIMUM USAGE OF FERRITE TILES IN ANECHOIC CHAMBERS

MINIMUM USAGE OF FERRITE TILES IN ANECHOIC CHAMBERS Progress In Electromagnetics Research B, Vol. 19, 367 383, 2010 MINIMUM USAGE OF FERRITE TILES IN ANECHOIC CHAMBERS S. M. J. Razavi, M. Khalaj-Amirhosseini, and A. Cheldavi College of Electrical Engineering

More information

arxiv:1111.4354v2 [physics.acc-ph] 27 Oct 2014

arxiv:1111.4354v2 [physics.acc-ph] 27 Oct 2014 Theory of Electromagnetic Fields Andrzej Wolski University of Liverpool, and the Cockcroft Institute, UK arxiv:1111.4354v2 [physics.acc-ph] 27 Oct 2014 Abstract We discuss the theory of electromagnetic

More information

Antennas. Antennas are transducers that transfer electromagnetic energy between a transmission line and free space. Electromagnetic Wave

Antennas. Antennas are transducers that transfer electromagnetic energy between a transmission line and free space. Electromagnetic Wave Antennas Transmitter I Transmitting Antenna Transmission Line Electromagnetic Wave I Receiver I Receiving Antenna Transmission Line Electromagnetic Wave I Antennas are transducers that transfer electromagnetic

More information

Metamaterials and Transformation Optics

Metamaterials and Transformation Optics AFRL-AFOSR-UK-TR-2011-0021 Metamaterials and Transformation Optics John Pendry Imperial College London Physics Department South Kensington Campus Exhibition Road London, United Kingdom SW7 2AZ EOARD GRANT

More information

Characterization of excited states of 15 N through 14 C(p,p) 14 C using polarized proton beam

Characterization of excited states of 15 N through 14 C(p,p) 14 C using polarized proton beam REVISTA MEXICANA DE FÍSICA S 57 (1) 55 59 FEBRERO 2011 Characterization of excited states of 15 N through 14 C(p,p) 14 C using polarized proton beam G. Murillo, M. Fernández, J. Ramírez, M.G. Mejia-Gil,

More information

Examples of Uniform EM Plane Waves

Examples of Uniform EM Plane Waves Examples of Uniform EM Plane Waves Outline Reminder of Wave Equation Reminder of Relation Between E & H Energy Transported by EM Waves (Poynting Vector) Examples of Energy Transport by EM Waves 1 Coupling

More information

Polarization of Light

Polarization of Light Polarization of Light References Halliday/Resnick/Walker Fundamentals of Physics, Chapter 33, 7 th ed. Wiley 005 PASCO EX997A and EX999 guide sheets (written by Ann Hanks) weight Exercises and weights

More information

Experimental realization of a broadband illusion optics device

Experimental realization of a broadband illusion optics device Experimental realization of a broadband illusion optics device Chao Li, Xiankun Meng, Xiao Liu, Fang Li, Guangyou Fang Key Laboratory of Microwave and Electromagnetic adiation, Institute of Electronics,

More information

Plate waves in phononic crystals slabs

Plate waves in phononic crystals slabs Acoustics 8 Paris Plate waves in phononic crystals slabs J.-J. Chen and B. Bonello CNRS and Paris VI University, INSP - 14 rue de Lourmel, 7515 Paris, France chen99nju@gmail.com 41 Acoustics 8 Paris We

More information

Interferometers. OBJECTIVES To examine the operation of several kinds of interferometers. d sin = n (1)

Interferometers. OBJECTIVES To examine the operation of several kinds of interferometers. d sin = n (1) Interferometers The true worth of an experimenter consists in his pursuing not only what he seeks in his experiment, but also what he did not seek. Claude Bernard (1813-1878) OBJECTIVES To examine the

More information

Experimental results for the focal waveform and beam width in the focusing lens with a 100 ps filter

Experimental results for the focal waveform and beam width in the focusing lens with a 100 ps filter EM Implosion Memos Memo 51 July, 2010 Experimental results for the focal waveform and beam width in the focusing lens with a 100 ps filter Prashanth Kumar, Carl E. Baum, Serhat Altunc, Christos G. Christodoulou

More information

Longwave IR focal-plane binary optics

Longwave IR focal-plane binary optics Longwave IR focal-plane binary optics Z. Sikorski, H. Polakowski Institute of Optoelectronics, Military University of Technology, 2 Kaliskiego Str., -98 Warsaw, e-mail: zsikorsk@wat.waw.pl Abstract In

More information

GRID AND PRISM SPECTROMETERS

GRID AND PRISM SPECTROMETERS FYSA230/2 GRID AND PRISM SPECTROMETERS 1. Introduction Electromagnetic radiation (e.g. visible light) experiences reflection, refraction, interference and diffraction phenomena when entering and passing

More information

An equivalent circuit of a loop antenna.

An equivalent circuit of a loop antenna. 3.2.1. Circuit Modeling: Loop Impedance A loop antenna can be represented by a lumped circuit when its dimension is small with respect to a wavelength. In this representation, the circuit parameters (generally

More information

A wave lab inside a coaxial cable

A wave lab inside a coaxial cable INSTITUTE OF PHYSICS PUBLISHING Eur. J. Phys. 25 (2004) 581 591 EUROPEAN JOURNAL OF PHYSICS PII: S0143-0807(04)76273-X A wave lab inside a coaxial cable JoãoMSerra,MiguelCBrito,JMaiaAlves and A M Vallera

More information

Fundamentals of Electromagnetic Fields and Waves: I

Fundamentals of Electromagnetic Fields and Waves: I Fundamentals of Electromagnetic Fields and Waves: I Fall 2007, EE 30348, Electrical Engineering, University of Notre Dame Mid Term II: Solutions Please show your steps clearly and sketch figures wherever

More information

Spectroscopic Ellipsometry:

Spectroscopic Ellipsometry: Spectroscopic : What it is, what it will do, and what it won t do by Harland G. Tompkins Introduction Fundamentals Anatomy of an ellipsometric spectrum Analysis of an ellipsometric spectrum What you can

More information

Keysight Technologies Understanding the Fundamental Principles of Vector Network Analysis. Application Note

Keysight Technologies Understanding the Fundamental Principles of Vector Network Analysis. Application Note Keysight Technologies Understanding the Fundamental Principles of Vector Network Analysis Application Note Introduction Network analysis is the process by which designers and manufacturers measure the

More information

Amplification of the Radiation from Two Collocated Cellular System Antennas by the Ground Wave of an AM Broadcast Station

Amplification of the Radiation from Two Collocated Cellular System Antennas by the Ground Wave of an AM Broadcast Station Amplification of the Radiation from Two Collocated Cellular System Antennas by the Ground Wave of an AM Broadcast Station Dr. Bill P. Curry EMSciTek Consulting Co., W101 McCarron Road Glen Ellyn, IL 60137,

More information

Composite Electromagnetic Wave Absorber Made of Permalloy or Sendust and Effect of Sendust Particle Size on Absorption Characteristics

Composite Electromagnetic Wave Absorber Made of Permalloy or Sendust and Effect of Sendust Particle Size on Absorption Characteristics PIERS ONLINE, VOL. 4, NO. 8, 2008 846 Composite Electromagnetic Wave Absorber Made of Permalloy or Sendust and Effect of Sendust Particle Size on Absorption Characteristics K. Sakai, Y. Wada, and S. Yoshikado

More information

Development of Optical Wave Microphone Measuring Sound Waves with No Diaphragm

Development of Optical Wave Microphone Measuring Sound Waves with No Diaphragm Progress In Electromagnetics Research Symposium Proceedings, Taipei, March 5 8, 3 359 Development of Optical Wave Microphone Measuring Sound Waves with No Diaphragm Yoshito Sonoda, Takashi Samatsu, and

More information

Experiment #2: Determining Sugar Content of a Drink. Objective. Introduction

Experiment #2: Determining Sugar Content of a Drink. Objective. Introduction Experiment #2: Determining Sugar Content of a Drink Objective How much sugar is there in your drink? In this experiment, you will measure the amount of sugar dissolved in a soft drink by using two different

More information

GPR Polarization Simulation with 3D HO FDTD

GPR Polarization Simulation with 3D HO FDTD Progress In Electromagnetics Research Symposium Proceedings, Xi an, China, March 6, 00 999 GPR Polarization Simulation with 3D HO FDTD Jing Li, Zhao-Fa Zeng,, Ling Huang, and Fengshan Liu College of Geoexploration

More information

Optical Communications

Optical Communications Optical Communications Telecommunication Engineering School of Engineering University of Rome La Sapienza Rome, Italy 2005-2006 Lecture #2, May 2 2006 The Optical Communication System BLOCK DIAGRAM OF

More information

ELECTROMAGNETIC 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 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 information

Refractive Index Measurement Principle

Refractive Index Measurement Principle Refractive Index Measurement Principle Refractive index measurement principle Introduction Detection of liquid concentrations by optical means was already known in antiquity. The law of refraction was

More information

Right- and left-handed twist in optical fibers

Right- and left-handed twist in optical fibers RESEARCH Revista Mexicana de Física 60 (2014) 69 74 JANUARY-FEBRUARY 2014 Right- and left-handed twist in optical fibers D. Tentori and A. Garcia-Weidner* Centro de Investigación Científica y Educación

More information

Physics 25 Exam 3 November 3, 2009

Physics 25 Exam 3 November 3, 2009 1. A long, straight wire carries a current I. If the magnetic field at a distance d from the wire has magnitude B, what would be the the magnitude of the magnetic field at a distance d/3 from the wire,

More information

How To Understand Light And Color

How To Understand Light And Color PRACTICE EXAM IV P202 SPRING 2004 1. In two separate double slit experiments, an interference pattern is observed on a screen. In the first experiment, violet light (λ = 754 nm) is used and a second-order

More information

Optical Storage Technology. Optical Disc Storage

Optical Storage Technology. Optical Disc Storage Optical Storage Technology Optical Disc Storage Introduction Since the early 1940s, magnetic recording has been the mainstay of electronic information storage worldwide. Magnetic tape has been used extensively

More information

Consideration of a high-capacity foil cable:

Consideration of a high-capacity foil cable: Consideration of a high-capacity foil cable: Newly discovered ancient knowledge. The old RF-developers already knew the benefits of longplanar lines and have been used (electronic) Eonen (times) thin flat

More information

Technician Licensing Class

Technician Licensing Class Technician Licensing Class Antennas Presented by Amateur Radio Technician Class Element 2 Course Presentation ELEMENT 2 SUB-ELEMENTS (Groupings) About Ham Radio Call Signs Control Mind the Rules Tech Frequencies

More information

Crystal Optics of Visible Light

Crystal Optics of Visible Light Crystal Optics of Visible Light This can be a very helpful aspect of minerals in understanding the petrographic history of a rock. The manner by which light is transferred through a mineral is a means

More information

Selecting Receiving Antennas for Radio Tracking

Selecting Receiving Antennas for Radio Tracking Selecting Receiving Antennas for Radio Tracking Larry B Kuechle, Advanced Telemetry Systems, Inc. Isanti, Minnesota 55040 lkuechle@atstrack.com The receiving antenna is an integral part of any radio location

More information

Broadband THz Generation from Photoconductive Antenna

Broadband THz Generation from Photoconductive Antenna Progress In Electromagnetics Research Symposium 2005, Hangzhou, China, August 22-26 331 Broadband THz Generation from Photoconductive Antenna Qing Chang 1, Dongxiao Yang 1,2, and Liang Wang 1 1 Zhejiang

More information

Antenna A mean for radiating and receiving radio waves Transitional structure between free-space and a guiding device. Application: Radiation

Antenna A mean for radiating and receiving radio waves Transitional structure between free-space and a guiding device. Application: Radiation Antenna A mean for radiating and receiving radio waves Transitional structure between free-space and a guiding device Application: adiation Introduction An antenna is designed to radiate or receive electromagnetic

More information

Acousto-optic modulator

Acousto-optic modulator 1 of 3 Acousto-optic modulator F An acousto-optic modulator (AOM), also called a Bragg cell, uses the acousto-optic effect to diffract and shift the frequency of light using sound waves (usually at radio-frequency).

More information

Analysis of Electromagnetic Propulsion on a Two-Electric-Dipole System

Analysis of Electromagnetic Propulsion on a Two-Electric-Dipole System Electronics and Communications in Japan, Part 2, Vol. 83, No. 4, 2000 Translated from Denshi Joho Tsushin Gakkai Ronbunshi, Vol. J82-C-I, No. 6, June 1999, pp. 310 317 Analysis of Electromagnetic Propulsion

More information

DETERMINING THE POLARIZATION STATE OF THE RADIATION CROSSING THROUGH AN ANISOTROPIC POLY (VINYL ALCOHOL) FILM

DETERMINING THE POLARIZATION STATE OF THE RADIATION CROSSING THROUGH AN ANISOTROPIC POLY (VINYL ALCOHOL) FILM DETERMINING THE POLARIZATION STATE OF THE RADIATION CROSSING THROUGH AN ANISOTROPIC POLY (VINYL ALCOHOL) FILM ECATERINA AURICA ANGHELUTA Faculty of Physics,,,Al.I. Cuza University, 11 Carol I Bd., RO-700506,

More information

Physics 202 Problems - Week 8 Worked Problems Chapter 25: 7, 23, 36, 62, 72

Physics 202 Problems - Week 8 Worked Problems Chapter 25: 7, 23, 36, 62, 72 Physics 202 Problems - Week 8 Worked Problems Chapter 25: 7, 23, 36, 62, 72 Problem 25.7) A light beam traveling in the negative z direction has a magnetic field B = (2.32 10 9 T )ˆx + ( 4.02 10 9 T )ŷ

More information

F en = mω 0 2 x. We should regard this as a model of the response of an atom, rather than a classical model of the atom itself.

F en = mω 0 2 x. We should regard this as a model of the response of an atom, rather than a classical model of the atom itself. The Electron Oscillator/Lorentz Atom Consider a simple model of a classical atom, in which the electron is harmonically bound to the nucleus n x e F en = mω 0 2 x origin resonance frequency Note: We should

More information

DOING PHYSICS WITH MATLAB COMPUTATIONAL OPTICS RAYLEIGH-SOMMERFELD DIFFRACTION INTEGRAL OF THE FIRST KIND

DOING PHYSICS WITH MATLAB COMPUTATIONAL OPTICS RAYLEIGH-SOMMERFELD DIFFRACTION INTEGRAL OF THE FIRST KIND DOING PHYSICS WITH MATLAB COMPUTATIONAL OPTICS RAYLEIGH-SOMMERFELD DIFFRACTION INTEGRAL OF THE FIRST KIND THE THREE-DIMENSIONAL DISTRIBUTION OF THE RADIANT FLUX DENSITY AT THE FOCUS OF A CONVERGENCE BEAM

More information

The waveguide adapter consists of a rectangular part smoothly transcending into an elliptical part as seen in Figure 1.

The 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 information

Question based on Refraction and Refractive index. Glass Slab, Lateral Shift.

Question based on Refraction and Refractive index. Glass Slab, Lateral Shift. Question based on Refraction and Refractive index. Glass Slab, Lateral Shift. Q.What is refraction of light? What are the laws of refraction? Ans: Deviation of ray of light from its original path when

More information

DIAGNOSTICS OF HETEROGENEOUS POLYMER MATERIALS USING NOISE-LIKE MM-WAVE RADIATION

DIAGNOSTICS OF HETEROGENEOUS POLYMER MATERIALS USING NOISE-LIKE MM-WAVE RADIATION DIAGNOSTICS OF HETEROGENEOUS POLYMER MATERIALS USING NOISE-LIKE MM-WAVE RADIATION B. Kapilevich, B. Litvak, T. Ben Yehuda and O. Shotman The College of J&S, Dept. of Electrical and Electronics Eng. The

More information

Waves in Metamaterials

Waves in Metamaterials Waves in Metamaterials This page intentionally left blank Waves in Metamaterials L. Solymar Imperial College, London E. Shamonina University of Erlangen-Nürnberg 1 3 Great Clarendon Street, Oxford OX2

More information

T-slot Broadband Rectangular Patch Antenna

T-slot Broadband Rectangular Patch Antenna International Journal of Electronic and Electrical Engineering. ISSN 0974-2174 Volume 4, Number 1 (2011), pp.43-47 International Research Publication House http://www.irphouse.com T-slot Broadband Rectangular

More information

Regularities of Signal and Sensitivity Variation of a Reflection Fiber Optopair Sensor Dependent on the Angle between Axes of Fiber Tips

Regularities of Signal and Sensitivity Variation of a Reflection Fiber Optopair Sensor Dependent on the Angle between Axes of Fiber Tips Nonlinear Analysis: Modelling and Control, 9, Vol., No., 9 Regularities of Signal and Sensitivity Variation of a Reflection Fiber Optopair Sensor Dependent on the Angle between Axes of Fiber Tips V. Kleiza,

More information

Scanning Near Field Optical Microscopy: Principle, Instrumentation and Applications

Scanning Near Field Optical Microscopy: Principle, Instrumentation and Applications Scanning Near Field Optical Microscopy: Principle, Instrumentation and Applications Saulius Marcinkevičius Optics, ICT, KTH 1 Outline Optical near field. Principle of scanning near field optical microscope

More information

PHYS 222 Spring 2012 Final Exam. Closed books, notes, etc. No electronic device except a calculator.

PHYS 222 Spring 2012 Final Exam. Closed books, notes, etc. No electronic device except a calculator. PHYS 222 Spring 2012 Final Exam Closed books, notes, etc. No electronic device except a calculator. NAME: (all questions with equal weight) 1. If the distance between two point charges is tripled, the

More information

Since the middle of the 20 th century, the variety of applications

Since the middle of the 20 th century, the variety of applications Since the middle of the 0 th century, the variety of applications requiring electromagnetic absorbers has been increasing rapidly. Therefore, new materials had to be developed, each targeting a specific

More information

Antennas & Propagation. CS 6710 Spring 2010 Rajmohan Rajaraman

Antennas & Propagation. CS 6710 Spring 2010 Rajmohan Rajaraman Antennas & Propagation CS 6710 Spring 2010 Rajmohan Rajaraman Introduction An antenna is an electrical conductor or system of conductors o Transmission - radiates electromagnetic energy into space o Reception

More information

Ultraviolet index estimated in Badajoz (Spain) using a multiband radiometer

Ultraviolet index estimated in Badajoz (Spain) using a multiband radiometer ÓPTICA PURA Y APLICADA. www.sedoptica.es Sección Especial: 37 th AMASOM / Special Section: 37 th AMASOM Radiation and Atmospheric Components Ultraviolet index estimated in Badajoz (Spain) using a multiband

More information

Electromagnetic Wave Simulation Software Poynting

Electromagnetic Wave Simulation Software Poynting Electromagnetic Wave Simulation Software Poynting V Takefumi Namiki V Yoichi Kochibe V Takatoshi Kasano V Yasuhiro Oda (Manuscript received March 19, 28) The analysis of electromagnetic behavior by computer

More information

Voltage Across the Terminals of a Receiving Antenna

Voltage Across the Terminals of a Receiving Antenna Voltage Across the Terminals of a Receiving Antenna 1 Problem Kirk T. McDonald Joseph Henry Laboratories, Princeton University, Princeton, NJ 08544 (June 25, 2007; updated June 27, 2013) Deduce the no-load

More information

Reflection & Transmission of EM Waves

Reflection & Transmission of EM Waves Reflection & Transmission of EM Waves Reading Shen and Kong Ch. 4 Outline Everyday Reflection Reflection & Transmission (Normal Incidence) Reflected & Transmitted Power Optical Materials, Perfect Conductors,

More information

Lecture 3: Fibre Optics

Lecture 3: Fibre Optics Lecture 3: Fibre Optics Lecture aims to explain: 1. Fibre applications in telecommunications 2. Principle of operation 3. Single- and multi-mode fibres 4. Light losses in fibres Fibre is a transparent

More information

WAVELENGTH OF LIGHT - DIFFRACTION GRATING

WAVELENGTH OF LIGHT - DIFFRACTION GRATING PURPOSE In this experiment we will use the diffraction grating and the spectrometer to measure wavelengths in the mercury spectrum. THEORY A diffraction grating is essentially a series of parallel equidistant

More information

1 Introduction. JS'12, Cnam Paris, 3-4 Avril 2012. Ourouk Jawad 1, David Lautru 2, Jean Michel Dricot, François Horlin, Philippe De Doncker 3

1 Introduction. JS'12, Cnam Paris, 3-4 Avril 2012. Ourouk Jawad 1, David Lautru 2, Jean Michel Dricot, François Horlin, Philippe De Doncker 3 Statistical Study of SAR under Wireless Channel Exposure in Indoor Environment Etude Statistique du DAS sous Exposition d un Canal sans Fils en Environnement Intérieur Ourouk Jawad 1, David Lautru 2, Jean

More information

Multilayer Film Applications

Multilayer Film Applications 4 8. Multilayer Film Applications 8 Multilayer Film Applications δ i ω n i l i cos θ i π c λ n il i cos θ i π λ l n in i a sin θ a n i 8.. where we used Eq. 8.. to write cos θ i sin θ i n a sin θ a /n

More information

Copyright 1996 IEEE. Reprinted from IEEE MTT-S International Microwave Symposium 1996

Copyright 1996 IEEE. Reprinted from IEEE MTT-S International Microwave Symposium 1996 Copyright 1996 IEEE Reprinted from IEEE MTT-S International Microwave Symposium 1996 This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE

More information

PHOTOELECTRIC EFFECT AND DUAL NATURE OF MATTER AND RADIATIONS

PHOTOELECTRIC EFFECT AND DUAL NATURE OF MATTER AND RADIATIONS PHOTOELECTRIC EFFECT AND DUAL NATURE OF MATTER AND RADIATIONS 1. Photons 2. Photoelectric Effect 3. Experimental Set-up to study Photoelectric Effect 4. Effect of Intensity, Frequency, Potential on P.E.

More information

Mode Patterns of Parallel plates &Rectangular wave guides Mr.K.Chandrashekhar, Dr.Girish V Attimarad

Mode Patterns of Parallel plates &Rectangular wave guides Mr.K.Chandrashekhar, Dr.Girish V Attimarad International Journal of Scientific & Engineering Research Volume 3, Issue 8, August-2012 1 Mode Patterns of Parallel plates &Rectangular wave guides Mr.K.Chandrashekhar, Dr.Girish V Attimarad Abstract-Parallel

More information

Omni Antenna vs. Directional Antenna

Omni Antenna vs. Directional Antenna Omni Antenna vs. Directional Antenna Document ID: 82068 Contents Introduction Prerequisites Requirements Components Used Conventions Basic Definitions and Antenna Concepts Indoor Effects Omni Antenna Pros

More information

Transmission Lines. Smith Chart

Transmission Lines. Smith Chart Smith Chart The Smith chart is one of the most useful graphical tools for high frequency circuit applications. The chart provides a clever way to visualize complex functions and it continues to endure

More information

v = fλ PROGRESSIVE WAVES 1 Candidates should be able to :

v = fλ PROGRESSIVE WAVES 1 Candidates should be able to : PROGRESSIVE WAVES 1 Candidates should be able to : Describe and distinguish between progressive longitudinal and transverse waves. With the exception of electromagnetic waves, which do not need a material

More information

A Guide to Acousto-Optic Modulators

A Guide to Acousto-Optic Modulators A Guide to Acousto-Optic Modulators D. J. McCarron December 7, 2007 1 Introduction Acousto-optic modulators (AOMs) are useful devices which allow the frequency, intensity and direction of a laser beam

More information

Physics 116. Nov 4, 2011. Session 22 Review: ray optics. R. J. Wilkes Email: ph116@u.washington.edu

Physics 116. Nov 4, 2011. Session 22 Review: ray optics. R. J. Wilkes Email: ph116@u.washington.edu Physics 116 Session 22 Review: ray optics Nov 4, 2011 R. J. Wilkes Email: ph116@u.washington.edu ! Exam 2 is Monday!! All multiple choice, similar to HW problems, same format as Exam 1!!! Announcements

More information

Design and Electromagnetic Modeling of E-Plane Sectoral Horn Antenna For Ultra Wide Band Applications On WR-137 & WR- 62 Waveguides

Design and Electromagnetic Modeling of E-Plane Sectoral Horn Antenna For Ultra Wide Band Applications On WR-137 & WR- 62 Waveguides International Journal of Engineering Science Invention ISSN (Online): 2319 6734, ISSN (Print): 2319 6726 Volume 3 Issue 7ǁ July 2014 ǁ PP.11-17 Design and Electromagnetic Modeling of E-Plane Sectoral Horn

More information

Blackbody radiation derivation of Planck s radiation low

Blackbody radiation derivation of Planck s radiation low Blackbody radiation derivation of Planck s radiation low 1 Classical theories of Lorentz and Debye: Lorentz (oscillator model): Electrons and ions of matter were treated as a simple harmonic oscillators

More information

Agilent De-embedding and Embedding S-Parameter Networks Using a Vector Network Analyzer. Application Note 1364-1

Agilent De-embedding and Embedding S-Parameter Networks Using a Vector Network Analyzer. Application Note 1364-1 Agilent De-embedding and Embedding S-Parameter Networks Using a Vector Network Analyzer Application Note 1364-1 Introduction Traditionally RF and microwave components have been designed in packages with

More information

Has profound implications for the efficiency with which non-linear light is generated!

Has profound implications for the efficiency with which non-linear light is generated! Non-Linear Optics Lecture 3: Achieving Phase Matching Learning goals By the end of this lecture you should: Show that we can use refractive index ellipsoids to define particular directions for phase matching.

More information

Antennas 101 The Basics. Ward Silver NØAX

Antennas 101 The Basics. Ward Silver NØAX Antennas 101 The Basics Ward Silver NØAX The Basics - 1 Antennas radiate (or receive) because electrons are accelerated (or are caused to accelerate) in the antenna s elements Radio or electromagnetic

More information

Preview of Period 3: Electromagnetic Waves Radiant Energy II

Preview of Period 3: Electromagnetic Waves Radiant Energy II Preview of Period 3: Electromagnetic Waves Radiant Energy II 3.1 Radiant Energy from the Sun How is light reflected and transmitted? What is polarized light? 3.2 Energy Transfer with Radiant Energy How

More information

A PRACTICAL MINIATURIZED U-SLOT PATCH ANTENNA WITH ENHANCED BANDWIDTH

A PRACTICAL MINIATURIZED U-SLOT PATCH ANTENNA WITH ENHANCED BANDWIDTH Progress In Electromagnetics Research B, Vol. 3, 47 62, 2008 A PRACTICAL MINIATURIZED U-SLOT PATCH ANTENNA WITH ENHANCED BANDWIDTH G. F. Khodaei, J. Nourinia, and C. Ghobadi Electrical Engineering Department

More information

Development of EM simulator for sea bed logging applications using MATLAB

Development of EM simulator for sea bed logging applications using MATLAB Indian Journal of Geo-Marine Sciences Vol. 40 (2), April 2011, pp. 267-274 Development of EM simulator for sea bed logging applications using MATLAB Hanita Daud 1*, Noorhana Yahya 2, & Vijanth Asirvadam

More information

AP Physics B Ch. 23 and Ch. 24 Geometric Optics and Wave Nature of Light

AP Physics B Ch. 23 and Ch. 24 Geometric Optics and Wave Nature of Light AP Physics B Ch. 23 and Ch. 24 Geometric Optics and Wave Nature of Light Name: Period: Date: MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) Reflection,

More information

Bandwidth analysis of multimode fiber passive optical networks (PONs)

Bandwidth analysis of multimode fiber passive optical networks (PONs) Optica Applicata, Vol. XXXIX, No. 2, 2009 Bandwidth analysis of multimode fiber passive optical networks (PONs) GRZEGORZ STEPNIAK *, LUKASZ MAKSYMIUK, JERZY SIUZDAK Institute of Telecommunications, Warsaw

More information

1. Basics of LASER Physics

1. Basics of LASER Physics 1. Basics of LASER Physics Dr. Sebastian Domsch (Dipl.-Phys.) Computer Assisted Clinical Medicine Medical Faculty Mannheim Heidelberg University Theodor-Kutzer-Ufer 1-3 D-68167 Mannheim, Germany sebastian.domsch@medma.uni-heidelberg.de

More information

1 Basic Optics (1.2) Since. ε 0 = 8.854 10 12 C 2 N 1 m 2 and μ 0 = 4π 10 7 Ns 2 C 2 (1.3) Krishna Thyagarajan and Ajoy Ghatak. 1.

1 Basic Optics (1.2) Since. ε 0 = 8.854 10 12 C 2 N 1 m 2 and μ 0 = 4π 10 7 Ns 2 C 2 (1.3) Krishna Thyagarajan and Ajoy Ghatak. 1. 1 1 Basic Optics Krishna Thyagarajan and Ajoy Ghatak 1.1 Introduction This chapter on optics provides the reader with the basic understanding of light rays and light waves, image formation and aberrations,

More information

Human Exposure to Outdoor PLC System

Human Exposure to Outdoor PLC System 1602 PIERS Proceedings, Marrakesh, MOROCCO, March 20 23, 2011 Human Exposure to Outdoor PLC System Vicko Doric 1, Dragan Poljak 1, and Khalil El Khamlichi Drissi 2 1 University of Split, Croatia 2 Blaise

More information

Phase singularities of the longitudinal field components in the focal region of a high-aperture optical system

Phase singularities of the longitudinal field components in the focal region of a high-aperture optical system D. W. Diehl and T. D. Visser Vol. 21, No. 11/November 2004/J. Opt. Soc. Am. A 2103 Phase singularities of the longitudinal field components in the focal region of a high-aperture optical system Damon W.

More information

Design, realization, and characterization of optical negative index metamaterials

Design, realization, and characterization of optical negative index metamaterials Design, realization, and characterization of optical negative index metamaterials Dissertation zur Erlangung des akademischen Grades doctor rerum naturalium (Dr. rer. nat.) vorgelegt dem Rat der Physikalisch-Astronomischen

More information

Does Destructive Interference Destroy Energy?

Does Destructive Interference Destroy Energy? Does Destructive Interference Destroy Energy? 1 Problem Kirk T. McDonald Joseph Henry Laboratories, Princeton University, Princeton, NJ 08544 (January 7, 014; updated January 15, 014) In principle, a pair

More information

- particle with kinetic energy E strikes a barrier with height U 0 > E and width L. - classically the particle cannot overcome the barrier

- particle with kinetic energy E strikes a barrier with height U 0 > E and width L. - classically the particle cannot overcome the barrier Tunnel Effect: - particle with kinetic energy E strikes a barrier with height U 0 > E and width L - classically the particle cannot overcome the barrier - quantum mechanically the particle can penetrated

More information

Ionosphere Properties and Behaviors - Part 2 By Marcel H. De Canck, ON5AU

Ionosphere Properties and Behaviors - Part 2 By Marcel H. De Canck, ON5AU Ionosphere Properties and Behaviors - Part 2 By Marcel H. De Canck, ON5AU I n the previous issue I explained that gyrofrequency depends on the earth s magnetic field and mentioned that this magnetic field

More information

Efficiency, Dispersion and Straylight Performance Tests of Immersed Gratings for High Resolution Spectroscopy in the Near Infra-red

Efficiency, Dispersion and Straylight Performance Tests of Immersed Gratings for High Resolution Spectroscopy in the Near Infra-red Changing the economics of space Efficiency, Dispersion and Straylight Performance Tests of Immersed Gratings for High Resolution Spectroscopy in the Near Infra-red J. Fernandez-Saldivar 1, F. Culfaz 1,

More information

The Role of Electric Polarization in Nonlinear optics

The Role of Electric Polarization in Nonlinear optics The Role of Electric Polarization in Nonlinear optics Sumith Doluweera Department of Physics University of Cincinnati Cincinnati, Ohio 45221 Abstract Nonlinear optics became a very active field of research

More information

National Laboratory of Antennas and Microwave Technology Xidian University Xi an, Shaanxi 710071, China

National Laboratory of Antennas and Microwave Technology Xidian University Xi an, Shaanxi 710071, China Progress In Electromagnetics Research, PIER 76, 237 242, 2007 A BROADBAND CPW-FED T-SHAPE SLOT ANTENNA J.-J. Jiao, G. Zhao, F.-S. Zhang, H.-W. Yuan, and Y.-C. Jiao National Laboratory of Antennas and Microwave

More information

Waves - Transverse and Longitudinal Waves

Waves - Transverse and Longitudinal Waves Waves - Transverse and Longitudinal Waves wave may be defined as a periodic disturbance in a medium that carries energy from one point to another. ll waves require a source and a medium of propagation.

More information