Technique for measuring the parameters of polarization of an ultrasonic wave
|
|
- Dayna Thornton
- 5 years ago
- Views:
Transcription
1 arxiv:physics/ v1 [physics.class-ph] 1 Apr 000 Technique for measuring the parameters of polarization of an ultrasonic wave A. M. Burkhanov, K. B. lasov,.. Gudkov, and B.. Tarasov February, 008 Among physical phenomena consisting in variation of the polarization of a shear ulrasonic wave the acoustic analogs of the Faraday and the Cotton- Mouton effects are investigated at present (see [1] and [] the first theorectical papers, [3] discovery of rotation of the polarization, and [4] [7] some experiments. They are observed when initially linearly polarized ultrasonic wave propagates inside a bulk specimen and are due to interaction between elastic and magnetic subsystems or conduction electrons. Quantitative characteristics of the effects are polarization parameters: ε the ellipticity which modulus is the ratio of the minor and major ellipse axes and φ the angle of rotation of the polarization plane or, more correctly, of the major ellipse axis if ε 0. Most of recent experiments on polarization phenomena were performed with the use of phase-amplitude methods. A review of them is given in Ref. [8]. Besides, a phenomenon is considered as the acoustic analog of magnetooptic Kerr effect if variation of the polarization occurs while reflection of the wave from an interface between magnetic medium and isotropic nonmagnetic one. It was predicted by lasov and Kuleev [9] in 1968, however, there was no papers yet about experiments in which both the parameters characterizing the polarization, ε and φ, were measured. We have completed such an experiment and the results will be published soon. While performing it we found that a very small variations of a high level signal took place and came to a conclusion that amplitude variant of a technique should be more suitable here. First amplitude technique for a precise measurement of φ was introduced by Boyd and Gavenda [10]. Its aplicability was limited to the case ε 0. Though, we developed an amplitude method free of this restriction for measuring φ as well as ε. A description of the technique is the subject of this paper. 1
2 The method consists of measuring the amplitude of the voltage, (H, on the receiving transducer at a certain B 1 relative to an initial B B 0 using three different angles for the receiving transducer ψ with futher processing of the data with the formulas (, (, and (3 presented below. It can be used for investigating the acoustic analogs of the Faraday and the Cotton-Mouton effects as well. A periodic motion of the volume element over an elliptic trajectory can be repersented with the help of amplitudes, u ±, and phases, ϕ ±, of circular elastic vibrations. Introducing a parameter expressions for ε and φ have the form: p (u /u + e i(ϕ ϕ +, (1 ε 1 p 1 + p, φ 1 Im [ln(p]. ( Projection of the elastic vibrations to polarization direction of the receiving transducer can be written as follows: u r (t u e r Re { u + exp [ i(ωt ϕ + ψ ] +u exp [ i(ωt ϕ + ψ ]}, (3 * designates the complex conjugate, e r is unit vector of the direction of the polarization of the receiving transducer, ψ is the angle between this direction and the plane of incidence, ω is frequency, and t is time. u r excite an ac voltage cos(ωtα ηu r ( η is the coefficient of transformation of elastic vibration energy into electric field energy, and α is a phase constant. Using Eq. (3 we have η [cos ωt cosα + sin ωt sin α] [ u + cos(ϕ + + ψ + u cos(ϕ ψ ] cos ωt + [ u + sin(ϕ + + ψ + u sin(ϕ ψ ] sin ωt. (4 Since Eq. (4 is valid for arbitrary t, it may be transformed into two equations: η cos α u+ cos(ϕ + + ψ + u cos(ϕ ψ, (5 η sin α u+ sin(ϕ + + ψ + u sin(ϕ ψ. (6
3 Multiplying Eq. (6 by i and adding the result to Eq. (5 we obtain η eiα u + e i(ϕ+ +ψ + u e i(ϕ ψ. (7 The method suggested here for determining the polarization of the reflected wave consists of measuring the amplitude of the signal at a certain B 1 relative to an initial B B 0 using three different angles for the receiving transducer: ψ 1, ψ, and ψ 3. We assume that ε(b 0 0 and φ(b 0 0. Relevant equations for the two different values of B and three of ψ may be obtained by making the appropriate substitutions into Eq. (7. Introducing indexes j 0, 1 for the two values of B and k 1,, 3 for the three values of ψ for kj, α kj, u ± j, and ϕ ± j we have: 10 + η eiα 10 u + 0 e i(ϕ 0 +ψ 1 + u 0 e i(ϕ 0 ψ 1, (8 11 Dividing Eq. (9 by (8, we obtain F ± 1 + η eiα 11 u + 1 ei(ϕ 1 +ψ 1 + u 1 e i(ϕ 1 ψ 1. ( e i(α 11α 10 F + 1 eiψ 1 + F 1 eiψ 1, (10 u ± 1 e iϕ ± 1 u + 0 exp[i(ϕ ψ 1 ] + u 0 exp[i(ϕ 0 ψ 1 ]. (11 Similar equations for ψ ψ have the form 1 10 e i(α 1α 10 δ e iλ F + 1 eiψ + F 1 eiψ, (1 λ and δ describe variations in phase and amplitude of the signal, respectively, caused by differences in transducer coupling to the sample while changing ψ from ψ 1 to ψ. One more change in ψ gives the following equations in addition to (10 and (1: e i(α 31α 10 δ 3 e iλ 3 F + 1 eiψ 3 + F 1 eiψ 3. (13 Here δ 3 and λ 3 have the same origin as δ and λ, but correspond to changing ψ from ψ 1 to ψ 3. 3
4 After multiplying the left and right sides of Eqs. (10, (1, and (13 by their complex conjugates we obtain ( ( 1 δ 10 ( 31 δ 3 10 F + 1 F + 1 F F 1 F 1 F F 1 + F1 F 1 + F1 F 1 + F1 cos ( ϕ 1 + ψ 1, (14 cos ( ϕ 1 + ψ, (15 cos ( ϕ 1 + ψ 3, (16 ϕ 1 ϕ + (B 1 ϕ (B 1, (17 and, due to the assumption of ε(b 0 0 and φ(b 0 0, δ i 10 cos (ψ i i0 cos (ψ 1. (18 These operations are necessary to remove the phase α kj from our equations since amplitude is the only parameter measured in this variant of a technique. We divide both sides of Eqs. (14 (16 by to obtain p p 1 + cos[(φ 1 ψ 1 ] ( 11/ 10, (19 p p 1 + cos[(φ 1 ψ ] ( 1 δ / 10, (0 p p 1 + cos[(φ 1 ψ 3 ] ( 31 δ 3 / 10, (1 p 1 p(b 1. Thus we have three equations with three unknowns, namely F 1 + F1, p 1, and φ 1. The latter two are the parameters we are interested in and corresponding solutions of the system have the form φ 1 1 tan1{ [ ( 1 δ 31 δ3 cos ψ1 + ( 31 δ3 11 [ ( 1 δ 31 δ 3 F + 1 F + 1 F + 1 F + 1 F 1 F 1 F 1 F 1 cos ψ + ( 11 1 δ cos ψ3 ] sin ψ1 + ( 31 δ 3 11 sin ψ + ( 11 1 δ sin ψ3 ] 1} ( 4
5 and p 1 a 1 c 1 ± [ (a1 c 1 1 ] 1/, (3 a 1 11 sin [(ψ ψ 3 ] + 1 δ sin [((ψ 3 ψ 1 ] + 31 δ3 sin [(ψ 1 ψ ]cos φ 1, c 1 ( 1 δ 31 δ 3 sin ψ1 + ( 31 δ 3 11 sin ψ + ( 11 1 δ sin ψ3. The ( sign should be taken before the square root in Eq.(3, since it alone allows p 1 0 and therefore ε 1. References [1] C. Kittel, Phys. Rev. 110, 836 (1958. [] K. B. lasov, Fizika Metallov i Metallovedenie 7, 447 (1959 [Phys. Met. Metallogr. (USSR 7, 11 (1959]. [3] R. W. Morse and J. D. Gavenda, Phys. Rev. Lett., 50 (1959. [4] H. Matthews and R. C. Le Craw, Phys. Rev. Lett. 8, 397 (196. [5] B. Luthi, Phys. Lett. 3, 85 (1963. [6] A. M. Burkhanov, K. B. lasov,.. Gudkov, and I.. Zhevstovskikh, Akusticheskii zhurnal 34, 991 (1988 [Sov. Phys.-Acoustics 34, 569 (1988] [7] B.. Tarasov A. M. Burkhanov, and K. B. lasov, Fiz. Tver. Tela 38, 135 (1996 [Sov. Phys.-Solid State 38, 1176 (1996]. [8].. Gudkov and B.. Tarasov, J. Acoust. Soc. Am. 104, 756 (1998. [9] K. B. lasov and. G. Kuleev, Fiz. Tver. Tela 10, 076 (1968 [Sov. Phys.-Solid State 10, 167 (1969]. [10] R. J. Boyd and J. D. Gavenda, Phys. Rev. 15, 645 (
Waves in Linear Optical Media
1/53 Waves in Linear Optical Media Sergey A. Ponomarenko Dalhousie University c 2009 S. A. Ponomarenko Outline Plane waves in free space. Polarization. Plane waves in linear lossy media. Dispersion relations
More informationPhysics 214 Midterm Exam Solutions Winter 2017
Physics 14 Midterm Exam Solutions Winter 017 1. A linearly polarized electromagnetic wave, polarized in the ˆx direction, is traveling in the ẑ-direction in a dielectric medium of refractive index n 1.
More informationJones vector & matrices
Jones vector & matrices Department of Physics 1 Matrix treatment of polarization Consider a light ray with an instantaneous E-vector as shown y E k, t = xe x (k, t) + ye y k, t E y E x x E x = E 0x e i
More informationElectromagnetic Waves
May 7, 2008 1 1 J.D.Jackson, Classical Electrodynamics, 2nd Edition, Section 7 Maxwell Equations In a region of space where there are no free sources (ρ = 0, J = 0), Maxwell s equations reduce to a simple
More informationPhysics Letters A 374 (2010) Contents lists available at ScienceDirect. Physics Letters A.
Physics Letters A 374 (2010) 1063 1067 Contents lists available at ScienceDirect Physics Letters A www.elsevier.com/locate/pla Macroscopic far-field observation of the sub-wavelength near-field dipole
More informationElectromagnetic Acoustic Transducers for In and Out of plane Ultrasonic Wave Detection
7th World Conference on Nondestructive Testing, 5-8 Oct 8, Shanghai, China Electromagnetic Acoustic Transducers for In and Out of plane Ultrasonic Wave Detection Xiaoming JIAN, Steve DIXON, Karl QUIK Phoenix
More informationIntroduction to Polarization
Phone: Ext 659, E-mail: hcchui@mail.ncku.edu.tw Fall/007 Introduction to Polarization Text Book: A Yariv and P Yeh, Photonics, Oxford (007) 1.6 Polarization States and Representations (Stokes Parameters
More informationIntroduction to Condensed Matter Physics
Introduction to Condensed Matter Physics Diffraction I Basic Physics M.P. Vaughan Diffraction Electromagnetic waves Geometric wavefront The Principle of Linear Superposition Diffraction regimes Single
More informationMatrices in Polarization Optics. Polarized Light - Its Production and Analysis
Matrices in Polarization Optics Polarized Light - Its Production and Analysis For all electromagnetic radiation, the oscillating components of the electric and magnetic fields are directed at right angles
More informationComplex Numbers. The set of complex numbers can be defined as the set of pairs of real numbers, {(x, y)}, with two operations: (i) addition,
Complex Numbers Complex Algebra The set of complex numbers can be defined as the set of pairs of real numbers, {(x, y)}, with two operations: (i) addition, and (ii) complex multiplication, (x 1, y 1 )
More informationMOKE: Principles and Measurement. Corbyn Mellinger Dr. Xu Group June 10, 2016
MOKE: Principles and Measurement Corbyn Mellinger Dr. Xu Group June 10, 2016 Common Magneto-optical Effects Faraday Effect: magnetization of material affects transmission of polarized light Kerr Effect:
More informationarxiv:cond-mat/ v1 [cond-mat.other] 13 Apr 2006
arxiv:cond-mat/060439v1 cond-mat.other] 13 Apr 006 Spin-wave instability for parallel pumping in ferromagnetic thin films under oblique field Kazue Kudo, Katsuhiro Nakamura Department of Applied Physics,
More informationarxiv:physics/ v2 [physics.optics] 6 Apr 2007
Unified theory for Goos-Hänchen and Imbert-Fedorov effects Chun-Fang Li Department of Physics, Shanghai University, arxiv:physics/0611047v2 [physics.optics] 6 Apr 2007 Shanghai 200444, P. R. China and
More informationBrewster Angle and Total Internal Reflection
Lecture 4: Polarization Outline 1 Polarized Light in the Universe 2 Brewster Angle and Total Internal Reflection 3 Descriptions of Polarized Light 4 Polarizers 5 Retarders Christoph U. Keller, Utrecht
More information2 u 1-D: 3-D: x + 2 u
c 2013 C.S. Casari - Politecnico di Milano - Introduction to Nanoscience 2013-14 Onde 1 1 Waves 1.1 wave propagation 1.1.1 field Field: a physical quantity (measurable, at least in principle) function
More informationarxiv: v2 [nlin.ps] 14 Aug 2016
arxiv:1605.05726v2 [nlin.ps] 14 Aug 2016 Stability of ion acoustic nonlinear waves and solitons in magnetized plasmas Piotr Goldstein and Eryk Infeld Theoretical Physics Division, National Centre for Nuclear
More informationQuestion 1: Some algebra
October 13, 017 Cornell University, Department of Physics PHYS 337, Advance E&M, HW # 6, due: 10/4/017, 11:15 AM Question 1: Some algebra 1. Prove the vector identity used in lecture to derive the energy
More informationLecture 19 Optical MEMS (1)
EEL6935 Advanced MEMS (Spring 5) Instructor: Dr. Huikai Xie Lecture 19 Optical MEMS (1) Agenda: Optics Review EEL6935 Advanced MEMS 5 H. Xie 3/8/5 1 Optics Review Nature of Light Reflection and Refraction
More informationElectromagnetic (EM) Waves
Electromagnetic (EM) Waves Short review on calculus vector Outline A. Various formulations of the Maxwell equation: 1. In a vacuum 2. In a vacuum without source charge 3. In a medium 4. In a dielectric
More informationwhere d is the vibration direction of the displacement and c is the wave velocity. For a fixed time t,
3 Plane waves 3.1 Plane waves in unbounded solid Consider a plane wave propagating in the direction with the unit vector p. The displacement of the plane wave is assumed to have the form ( u i (x, t) =
More informationReflection and Transmission of Light in Structures with Incoherent Anisotropic Layers
Optics and Spectroscopy, Vol. 87, No., 999, pp. 5. Translated from Optika i Spektroskopiya, Vol. 87, No., 999, pp. 2 25. Original Russian Text Copyright 999 by Ivanov, Sementsov. PHYSICAL AND QUANTUM OPTICS
More informationBrewster Angle and Total Internal Reflection
Lecture 5: Polarization Outline 1 Polarized Light in the Universe 2 Brewster Angle and Total Internal Reflection 3 Descriptions of Polarized Light 4 Polarizers 5 Retarders Christoph U. Keller, Leiden University,
More informationLecture 5: Polarization. Polarized Light in the Universe. Descriptions of Polarized Light. Polarizers. Retarders. Outline
Lecture 5: Polarization Outline 1 Polarized Light in the Universe 2 Descriptions of Polarized Light 3 Polarizers 4 Retarders Christoph U. Keller, Leiden University, keller@strw.leidenuniv.nl ATI 2016,
More informationMathematical Review for AC Circuits: Complex Number
Mathematical Review for AC Circuits: Complex Number 1 Notation When a number x is real, we write x R. When a number z is complex, we write z C. Complex conjugate of z is written as z here. Some books use
More informationOn Electromagnetic-Acoustic Analogies in Energetic Relations for Waves Interacting with Material Surfaces
Vol. 114 2008) ACTA PHYSICA POLONICA A No. 6 A Optical and Acoustical Methods in Science and Technology On Electromagnetic-Acoustic Analogies in Energetic Relations for Waves Interacting with Material
More informationOn the study of elastic wave scattering and Rayleigh wave velocity measurement of concrete with steel bar
NDT&E International 33 (2000) 401 407 www.elsevier.com/locate/ndteint On the study of elastic wave scattering and Rayleigh wave velocity measurement of concrete with steel bar T.-T. Wu*, J.-H. Sun, J.-H.
More informationHomework 1. Nano Optics, Fall Semester 2017 Photonics Laboratory, ETH Zürich
Homework 1 Contact: mfrimmer@ethz.ch Due date: Friday 13.10.2017; 10:00 a.m. Nano Optics, Fall Semester 2017 Photonics Laboratory, ETH Zürich www.photonics.ethz.ch The goal of this homework is to establish
More informationMultilayer Reflectivity
Multilayer Reflectivity John E. Davis jed@jedsoft.org January 5, 2014 1 Introduction The purpose of this document is to present an ab initio derivation of the reflectivity for a plane electromagnetic wave
More informationSolutions: Homework 7
Solutions: Homework 7 Ex. 7.1: Frustrated Total Internal Reflection a) Consider light propagating from a prism, with refraction index n, into air, with refraction index 1. We fix the angle of incidence
More informationEnergy Level Sets for the Morse Potential
Energy Level Sets for the Morse Potential Fariel Shafee Department of Physics Princeton University Princeton, NJ 08540 Abstract: In continuation of our previous work investigating the possibility of the
More informationBifurcation of Sound Waves in a Disturbed Fluid
American Journal of Modern Physics 7; 6(5: 9-95 http://www.sciencepublishinggroup.com/j/ajmp doi:.68/j.ajmp.765.3 ISSN: 36-8867 (Print; ISSN: 36-889 (Online Bifurcation of Sound Waves in a Disturbed Fluid
More informationPropagation of EM Waves in material media
Propagation of EM Waves in material media S.M.Lea 09 Wave propagation As usual, we start with Maxwell s equations with no free charges: D =0 B =0 E = B t H = D t + j If we now assume that each field has
More informationOptics and Optical Design. Chapter 6: Polarization Optics. Lectures 11-13
Optics and Optical Design Chapter 6: Polarization Optics Lectures 11-13 Cord Arnold / Anne L Huillier Polarization of Light Arbitrary wave vs. paraxial wave One component in x-direction y x z Components
More informationSelected Topics in Physics a lecture course for 1st year students by W.B. von Schlippe Spring Semester 2007
Selected Topics in Physics a lecture course for st year students by W.B. von Schlippe Spring Semester 7 Lecture : Oscillations simple harmonic oscillations; coupled oscillations; beats; damped oscillations;
More informationQUANTUM MECHANICS I PHYS 516. Solutions to Problem Set # 5
QUANTUM MECHANICS I PHYS 56 Solutions to Problem Set # 5. Crossed E and B fields: A hydrogen atom in the N 2 level is subject to crossed electric and magnetic fields. Choose your coordinate axes to make
More information1. Reflection and Refraction of Spherical Waves
1. Reflection and Refraction of Spherical Waves Our previous book [1.1] was completely focused on the problem of plane and quasi-plane waves in layered media. In the theory of acoustic wave propagation,
More informationCircuit Analysis-III. Circuit Analysis-II Lecture # 3 Friday 06 th April, 18
Circuit Analysis-III Sinusoids Example #1 ü Find the amplitude, phase, period and frequency of the sinusoid: v (t ) =12cos(50t +10 ) Signal Conversion ü From sine to cosine and vice versa. ü sin (A ± B)
More informationOptics and Optical Design. Chapter 6: Polarization Optics. Lectures 11 13
Optics and Optical Design Chapter 6: Polarization Optics Lectures 11 13 Cord Arnold / Anne L Huillier Polarization of Light Arbitrary wave vs. paraxial wave One component in x direction y x z Components
More informationPolarimetry in the E-ELT era. Polarized Light in the Universe. Descriptions of Polarized Light. Polarizers. Retarders. Fundamentals of Polarized Light
Polarimetry in the E-ELT era Fundamentals of Polarized Light 1 Polarized Light in the Universe 2 Descriptions of Polarized Light 3 Polarizers 4 Retarders Christoph U. Keller, Leiden University, keller@strw.leidenuniv.nl
More informationGeneralized reciprocal relations for transmission and reflection of light through a 1D stratified anisotropic metamaterial
Generalized reciprocal relations for transmission and reflection of light through a 1D stratified anisotropic metamaterial Railing Chang 1 and P. T. Leung 1,* 1 Institute of Optoelectronic Sciences, National
More informationSuperposition of electromagnetic waves
Superposition of electromagnetic waves February 9, So far we have looked at properties of monochromatic plane waves. A more complete picture is found by looking at superpositions of many frequencies. Many
More informationPolarization Correlation in the Gamma- Gamma Decay of Positronium
Polarization Correlation in the Gamma- Gamma Decay of Positronium Bin LI Department of Physics & Astronomy, University of Pittsburgh, PA 56, U.S.A April 5, Introduction Positronium is an unstable bound
More information12A Reflection & Transmission (Normal Incidence)
12A Reflection & Transmission (Normal Incidence) Topics: Reflection and transmission, boundary conditions, complex exponentials. Summary: Students begin by expressing in exponential notation the boundary
More informationEM waves: energy, resonators. Scalar wave equation Maxwell equations to the EM wave equation A simple linear resonator Energy in EM waves 3D waves
EM waves: energy, resonators Scalar wave equation Maxwell equations to the EM wave equation A simple linear resonator Energy in EM waves 3D waves Simple scalar wave equation 2 nd order PDE 2 z 2 ψ (z,t)
More informationThe Propagation Peculiarities of Electromagnetic and Acoustical Waves
The Propagation Peculiarities of Electromagnetic and Acoustical Waves Felix F. Gorbatsevich gorich@geoksc.apatity.ru Modern researchers interpret a physical, homogeneous continual medium (gas, liquid,
More informationMagnetohydrodynamic waves in a plasma
Department of Physics Seminar 1b Magnetohydrodynamic waves in a plasma Author: Janez Kokalj Advisor: prof. dr. Tomaž Gyergyek Petelinje, April 2016 Abstract Plasma can sustain different wave phenomena.
More informationHomework 1. Nano Optics, Fall Semester 2018 Photonics Laboratory, ETH Zürich
Homework 1 Contact: mfrimmer@ethz.ch Due date: Friday 12 October 2018; 10:00 a.m. Nano Optics, Fall Semester 2018 Photonics Laboratory, ETH Zürich www.photonics.ethz.ch The goal of this homework is to
More informationRadio Propagation Channels Exercise 2 with solutions. Polarization / Wave Vector
/8 Polarization / Wave Vector Assume the following three magnetic fields of homogeneous, plane waves H (t) H A cos (ωt kz) e x H A sin (ωt kz) e y () H 2 (t) H A cos (ωt kz) e x + H A sin (ωt kz) e y (2)
More informationWAVE PROPAGATION IN ONE- DIMENSIONAL STRUCTURES. Lecture Notes for Day 2
WAVE PROPAGATION IN ONE- DIMENSIONAL STRUCTURES Lecture Notes for Day S. V. SOROKIN Department of Mechanical and Manufacturing Engineering, Aalborg University . BASICS OF THE THEORY OF WAVE PROPAGATION
More informationSignal Loss. A1 A L[Neper] = ln or L[dB] = 20log 1. Proportional loss of signal amplitude with increasing propagation distance: = α d
Part 6 ATTENUATION Signal Loss Loss of signal amplitude: A1 A L[Neper] = ln or L[dB] = 0log 1 A A A 1 is the amplitude without loss A is the amplitude with loss Proportional loss of signal amplitude with
More informationThe electric field produced by oscillating charges contained in a slab
The electric field produced by oscillating charges contained in a slab Ref: Feynman Lectures Vol-1, Chapter 31 1. An accelerated charge produces electromagnetic fields 2. Calculation of the field produced
More informationDouble-distance propagation of Gaussian beams passing through a tilted cat-eye optical lens in a turbulent atmosphere
Double-distance propagation of Gaussian beams passing through a tilted cat-eye optical lens in a turbulent atmosphere Zhao Yan-Zhong( ), Sun Hua-Yan( ), and Song Feng-Hua( ) Department of Photoelectric
More informationPrinciple and application of ultrasonic wave
Topics on ultrasonic wave Principle and application of ultrasonic wave Writer Handong Li ( ) Emendator: Yabin Zhu ( ) 1 brief introduction to the special subject Ultrasonic wave is an acoustic wave whose
More informationPROPAGATION OF WAVES AT AN IMPERFECTLY
Journal of Theoretical and Applied Mechanics, Sofia, 2011, vol. 41, No. 3, pp. 77 92 PROPAGATION OF WAVES AT AN IMPERFECTLY BONDED INTERFACE BETWEEN TWO MONOCLINIC THERMOELASTIC HALF-SPACES Joginder Singh
More informationCritical entanglement and geometric phase of a two-qubit model with Dzyaloshinski Moriya anisotropic interaction
Chin. Phys. B Vol. 19, No. 1 010) 010305 Critical entanglement and geometric phase of a two-qubit model with Dzyaloshinski Moriya anisotropic interaction Li Zhi-Jian 李志坚 ), Cheng Lu 程璐 ), and Wen Jiao-Jin
More informationCoherent states, beam splitters and photons
Coherent states, beam splitters and photons S.J. van Enk 1. Each mode of the electromagnetic (radiation) field with frequency ω is described mathematically by a 1D harmonic oscillator with frequency ω.
More informationElectromagnetic Theory: PHAS3201, Winter Maxwell s Equations and EM Waves
Electromagnetic Theory: PHA3201, Winter 2008 5. Maxwell s Equations and EM Waves 1 Displacement Current We already have most of the pieces that we require for a full statement of Maxwell s Equations; however,
More informationA model for the ultrasonic field radiated by an Electro-Magnetic Acoustic Transducer in a ferromagnetic solid
13th International Symposium on Nondestructive Characterization of Materials (NDCM-XIII), 2-24 May 213, Le Mans, France www.ndt.net/?id=1557 More Info at Open Access Database www.ndt.net/?id=1557 A model
More informationAbsorption suppression in photonic crystals
PHYSICAL REVIEW B 77, 442 28 Absorption suppression in photonic crystals A. Figotin and I. Vitebskiy Department of Mathematics, University of California at Irvine, Irvine, California 92697, USA Received
More informationLongitudinal waves of a finite amplitude in nonlinear elastic media
Longitudinal waves of a finite amplitude in nonlinear elastic media Ivan A. Molotkov 1), Ivan Pšenčík 2) 1) IZMIRAN, Troitsk, Moscow Region, 142190, Russia. E-mail molotkov@izmiran.rssi.ru 2) Geophysical
More informationSupporting Information: Ultraintense. femtosecond magnetic nanoprobes induced by. azimuthally polarized laser beams
Supporting Information: Ultraintense femtosecond magnetic nanoprobes induced by azimuthally polarized laser beams Manuel Blanco, Ferran Cambronero, M. Teresa Flores-Arias, Enrique Conejero Jarque, Luis
More informationPlane Waves Part II. 1. For an electromagnetic wave incident from one medium to a second medium, total reflection takes place when
Plane Waves Part II. For an electromagnetic wave incident from one medium to a second medium, total reflection takes place when (a) The angle of incidence is equal to the Brewster angle with E field perpendicular
More informationPlasma heating in stellarators at the fundamental ion cyclotron frequency
PHYSICS OF PLASMAS VOLUME 7, NUMBER FEBRUARY 000 Plasma heating in stellarators at the fundamental ion cyclotron frequency V. A. Svidzinski and D. G. Swanson Department of Physics, Auburn University, Auburn,
More informationPolarization Mode Dispersion
Unit-7: Polarization Mode Dispersion https://sites.google.com/a/faculty.muet.edu.pk/abdullatif Department of Telecommunication, MUET UET Jamshoro 1 Goos Hänchen Shift The Goos-Hänchen effect is a phenomenon
More informationERRATA AND ADDITIONS FOR "ENGINEERING NOISE CONTROL" 4th Edn. First printing April 23, 2018
ERRATA AND ADDITIONS FOR "ENGINEERING NOISE CONTROL" 4th Edn. First printing April 3, 08 p4, Eq..3 should not have the ± symbol on the RHS p36, 3 lines from the bottom of the page, replace cos b with cos
More informationTHE ACOUSTIC POWER RADIATED BY A CIRCULAR MEMBRANE EXCITED FOR VIBRATION BOTH BY MEANS OF THE EDGE AND BY EXTERNAL SURFACE LOAD
ARCHIVES OF ACOUSTICS 3, 1, 19 119 (25) THE ACOUSTIC POWER RADIATED BY A CIRCULAR MEMBRANE EXCITED FOR VIBRATION BOTH BY MEANS OF THE EDGE AND BY EXTERNAL SURFACE LOAD K SZEMELA, W P RDZANEK Jr, W RDZANEK
More informationMethoden moderner Röntgenphysik II: Streuung und Abbildung
Methoden moderner Röntgenphysik II: Streuung und Abbildung Lecture 4 Location Vorlesung zum Haupt- oder Masterstudiengang Physik, SoSe 2015 G. Grübel, M. Martins, E. Weckert Lecture hall AP, Physics, Jungiusstraße
More informationAvailable online at ScienceDirect. Procedia Engineering 144 (2016 )
Available online at www.sciencedirect.com ScienceDirect Procedia Engineering 44 (06 ) 46 467 th International Conference on Vibration Problems, ICOVP 05 Propagation of Love waves in composite layered structures
More informationI. Rayleigh Scattering. EE Lecture 4. II. Dipole interpretation
I. Rayleigh Scattering 1. Rayleigh scattering 2. Dipole interpretation 3. Cross sections 4. Other approximations EE 816 - Lecture 4 Rayleigh scattering is an approximation used to predict scattering from
More informationarxiv:physics/ v3 [physics.gen-ph] 2 Jan 2006
A Wave Interpretation of the Compton Effect As a Further Demonstration of the Postulates of de Broglie arxiv:physics/0506211v3 [physics.gen-ph] 2 Jan 2006 Ching-Chuan Su Department of Electrical Engineering
More informationMSE 383, Unit 3-3. Joshua U. Otaigbe Iowa State University Materials Science & Engineering Dept.
Dynamic Mechanical Behavior MSE 383, Unit 3-3 Joshua U. Otaigbe Iowa State University Materials Science & Engineering Dept. Scope Why DMA & TTS? DMA Dynamic Mechanical Behavior (DMA) Superposition Principles
More informationProblem Set 10 Solutions
Massachusetts Institute of Technology Department of Physics Physics 87 Fall 25 Problem Set 1 Solutions Problem 1: EM Waves in a Plasma a Transverse electromagnetic waves have, by definition, E = Taking
More informationarxiv: v2 [quant-ph] 14 Mar 2018
God plays coins or superposition principle for classical probabilities in quantum suprematism representation of qubit states. V. N. Chernega 1, O. V. Man ko 1,2, V. I. Man ko 1,3 1 - Lebedev Physical Institute,
More informationRemarks on the tunneling limit of strong-field photoionization
Remarks on the tunneling limit of strong-field photoionization Jarosław H. Bauer * Katedra Fizyki Teoretycznej Uniwersytetu Łódzkiego, Ul. Pomorska 149/153, 90-36 Łódź, Poland Some results from a recent
More informationAcoustic wave reflection from the transition layer of surficial marine sediment
Acoust. Sci. & Tech. 25, 3 (2004) PAPER Acoustic wave reflection from the transition layer of surficial marine sediment Masao Kimura and Takuya Tsurumi School of Marine Science and Technology, Tokai University
More informationRelation between Periodic Soliton Resonance and Instability
Proceedings of Institute of Mathematics of NAS of Ukraine 004 Vol. 50 Part 1 486 49 Relation between Periodic Soliton Resonance and Instability Masayoshi TAJIRI Graduate School of Engineering Osaka Prefecture
More informationA reciprocity relationship for random diffuse fields in acoustics and structures with application to the analysis of uncertain systems.
A reciprocity relationship for random diffuse fields in acoustics and structures with application to the analysis of uncertain systems Robin Langley Example 1: Acoustic loads on satellites Arianne 5 Launch
More informationSnell s law in transversely isotropic media using linearized group velocities and related quantities
Snell's law using group angles and velocities Snell s law in transversely isotropic media using linearized group velocities and related quantities P.F. Daley ABSTRACT Using a linearized approximation for
More informationA novel type of transverse surface wave propagating in a layered structure consisting of a piezoelectric layer attached to an elastic half-space
Acta Mech Sin 2010 26:417 423 DOI 10.1007/s10409-010-0336-5 RESEARCH PAPER A novel type of transverse surface wave propagating in a layered structure consisting of a piezoelectric layer attached to an
More informationAnalysis of a Piezoelectric Sensor to Detect Flexural Waves
Analysis of a Piezoelectric Sensor to Detect Flexural Waves M. Veidt, T. Liu and S. Kitipornchai Department of Mechanical Engineering, The University of Queensland, Brisbane, Qld. 47, Australia Department
More informationTheoretische Physik 2: Elektrodynamik (Prof. A-S. Smith) Home assignment 9
WiSe 202 20.2.202 Prof. Dr. A-S. Smith Dipl.-Phys. Ellen Fischermeier Dipl.-Phys. Matthias Saba am Lehrstuhl für Theoretische Physik I Department für Physik Friedrich-Alexander-Universität Erlangen-Nürnberg
More informationA NEW APPROACH FOR SOLITON SOLUTIONS OF RLW EQUATION AND (1+2)-DIMENSIONAL NONLINEAR SCHRÖDINGER S EQUATION
A NEW APPROACH FOR SOLITON SOLUTIONS OF RLW EQUATION AND (+2-DIMENSIONAL NONLINEAR SCHRÖDINGER S EQUATION ALI FILIZ ABDULLAH SONMEZOGLU MEHMET EKICI and DURGUN DURAN Communicated by Horia Cornean In this
More informationA New Ultrasonic Immersion Technique to Retrieve Anisotropic Stiffness Matrix for Dispersion Curves Algorithms
A New Ultrasonic Immersion Technique to Retrieve Anisotropic Stiffness Matrix for Dispersion Curves Algorithms DARUN BARAZANCHY 1, WILLIAM ROTH 2 and VICTOR GIURGIUTIU 3 ABSTRACT Dispersion curve algorithms
More informationReflection of quasi-p and quasi-sv waves at the free and rigid boundaries of a fibre-reinforced medium
Sādhan ā Vol. 7 Part 6 December 00 pp. 63 630. Printed in India Reflection of quasi-p and quasi-sv waves at the free and rigid boundaries of a fibre-reinforced medium A CHATTOPADHYAYRLKVENKATESWARLU and
More informationAPPLICATION-DIRECTED MODELING OF RADIATION AND PROPAGATION OF ELASTIC WAVES IN ANISOTROPIC MEDIA: GPSS AND OPOSSM
APPLICATION-DIRECTED MODELING OF RADIATION AND PROPAGATION OF ELASTIC WAVES IN ANISOTROPIC MEDIA: GPSS AND OPOSSM M. Spies, F. Walte Fraunhofer-Institute for Nondestructive Testing (IzfP) 66123 Saarbriicken,
More informationLecture 2: Thin Films. Thin Films. Calculating Thin Film Stack Properties. Jones Matrices for Thin Film Stacks. Mueller Matrices for Thin Film Stacks
Lecture 2: Thin Films Outline Thin Films 2 Calculating Thin Film Stack Properties 3 Jones Matrices for Thin Film Stacks 4 Mueller Matrices for Thin Film Stacks 5 Mueller Matrix for Dielectrica 6 Mueller
More informationPhys. 506 Electricity and Magnetism Winter 2004 Prof. G. Raithel Problem Set 5 Total 40 Points. 1. Problem Points
Phys. 56 Electricity and Magnetism Winter 4 Prof. G. Raithel Problem Set 5 Total 4 Points. Problem. Points The partial-wave analysis presented in Chapter.4 applied to the case of a perfectly conducting
More informationNOTE. Application of Contour Dynamics to Systems with Cylindrical Boundaries
JOURNAL OF COMPUTATIONAL PHYSICS 145, 462 468 (1998) ARTICLE NO. CP986024 NOTE Application of Contour Dynamics to Systems with Cylindrical Boundaries 1. INTRODUCTION Contour dynamics (CD) is a widely used
More informationElectromagnetic generation of ultrasound in metals at low temperatures
Pramana-J. Phys., Vol. 28, No. 5, May 1987, pp. 483--488. ~) Printed in India. Electromagnetic generation of ultrasound in metals at low temperatures A N VASIL'EV and Yu P GAIDUKOV Physical Department,
More informationON POSITIVE-OPERATOR-VALUED MEASURE FOR PHASE MEASUREMENTS. Abstract. The unnormalizable Susskind-Glogower (SG) phase eigenstates, which
ON POSITIVE-OPERATOR-VALUED MEASURE FOR PHASE MEASUREMENTS Qianbing Zheng and Takayoshi Kobayashi Department of Physics, Graduate School of Science, The University of Tokyo, Hongo 7-3-1, Bunkyo-ku, Tokyo
More information19 th INTERNATIONAL CONGRESS ON ACOUSTICS MADRID, 2-7 SEPTEMBER 2007 NONLINEAR DYNAMICS IN PARAMETRIC SOUND GENERATION
9 th INTERNATIONAL CONGRESS ON ACOUSTICS MADRID, -7 SEPTEMBER 7 NONLINEAR DYNAMICS IN PARAMETRIC SOUND GENERATION PACS: 43.5.Ts, 43.5.+y V.J. Sánchez Morcillo, V. Espinosa, I. Pérez-Arjona and J. Redondo
More informationElectromagnetic Waves
Physics 8 Electromagnetic Waves Overview. The most remarkable conclusion of Maxwell s work on electromagnetism in the 860 s was that waves could exist in the fields themselves, traveling with the speed
More informationVector attenuation: elliptical polarization, raypaths and the Rayleigh-window effect
Geophysical Prospecting, 6, 54, 399 47 Vector attenuation: elliptical polarization, raypaths and the Rayleigh-window effect José M. Carcione Istituto Nazionale di Oceanografia e di Geofisica Sperimentale
More informationQuantum Condensed Matter Physics Lecture 5
Quantum Condensed Matter Physics Lecture 5 detector sample X-ray source monochromator David Ritchie http://www.sp.phy.cam.ac.uk/drp2/home QCMP Lent/Easter 2019 5.1 Quantum Condensed Matter Physics 1. Classical
More informationDynamic Mechanical Analysis (DMA) of Polymers by Oscillatory Indentation
Dynamic Mechanical Analysis (DMA) of Polymers by Oscillatory Indentation By Jennifer Hay, Nanomechanics, Inc. Abstract This application note teaches the theory and practice of measuring the complex modulus
More informationChapter 1 Mathematical Foundations
Computational Electromagnetics; Chapter 1 1 Chapter 1 Mathematical Foundations 1.1 Maxwell s Equations Electromagnetic phenomena can be described by the electric field E, the electric induction D, the
More informationBackground ODEs (2A) Young Won Lim 3/7/15
Background ODEs (2A) Copyright (c) 2014-2015 Young W. Lim. Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any
More information4. Complex Oscillations
4. Complex Oscillations The most common use of complex numbers in physics is for analyzing oscillations and waves. We will illustrate this with a simple but crucially important model, the damped harmonic
More informationREFLECTION AND REFRACTION OF PLANE EM WAVES
REFLECTION AND REFRACTION OF PLANE EM WAVES When an electromagnetic wave hits a boundary between different materials, some of the wave s energy is reflected back while the rest continues on through the
More informationHomework 3. 1 Coherent Control [22 pts.] 1.1 State vector vs Bloch vector [8 pts.]
Homework 3 Contact: jangi@ethz.ch Due date: December 5, 2014 Nano Optics, Fall Semester 2014 Photonics Laboratory, ETH Zürich www.photonics.ethz.ch 1 Coherent Control [22 pts.] In the first part of this
More information