The Role of Electric Polarization in Nonlinear optics


 Iris Sibyl Barker
 1 years ago
 Views:
Transcription
1 The Role of Electric Polarization in Nonlinear optics Sumith Doluweera Department of Physics University of Cincinnati Cincinnati, Ohio Abstract Nonlinear optics became a very active field of research in both experimental and theoretical physics after the invention of LASER. Nonlinear nature is very important for optical data processing applications and all physics of nonlinear optics can be extracted by studying the behavior of applied optical fieldinduced polarization of the medium. In this article very basic properties of nonlinear electric susceptibilities are discussed qualitatively. 1
2 1 Introduction In linear optics it is assumed that an optical disturbance propagating through an optical medium can be described by a linear wave equation. As a consequence of that assumption regardless of the intensity of light, the principle of superposition is valid in the regime of linear optics. When the intensity of light becomes great enough, linear optics is no longer enough to describe the situation observed experimentally [2]. It seems that light waves interact with one another and optical medium. These nonlinear phenomena require an extension of the linear theory, that allows for a nonlinear response of optical materials to the electromagnetic radiation. It was realized that the electric polarization induced in the medium is the key to study physics of nonlinear optics and so in general the polarization of the medium should be expressed as a power series of applied electric field E. P = ɛ 0 [χ (1) E + χ (2) EE + χ (3) EEE +...]. (1) Where P is the polarization,ɛ 0 is the free space permitivity and χ (i) is the i th order susceptibility tensor(material coefficient) of a given medium. First approximation of this equation gives linear optics and higher order terms contribute for nonlinear optics. 2 Theoretical framework of Nonlinear optics. Two major theoretical approaches can be employed in nonlinear optics as well as laser optics. They are semiclassical theory and quantum electrodynamical theory. In the semiclassical theory the media composed of molecules and atoms are described by quantum mechanics and light radiation is described by Maxwell s theory. The key issue of semiclassical theory is to give the expressions of macroscopic nonlinear electric polarization for optical media. The density matrix method is used to derive the expressions for various orders of susceptibilities and the expressions for various orders of polarization components. Substituting the appropriate nonlinear polarization components into the generalized wave equation, in principle,it is possible to predict many possible nonlinear optical responses of the medium for a given condition of the input intense optical fields[1]. 3 Fundamental understanding of nonlinear polarization. Under the interaction of an applied optical electric field, the atoms or molecules of the medium may respond in two ways: (i) a real transition of a certain amount of atoms or molecules from one quantum eigen state another, and (ii) the perturbation of normal distribution or motion of internal electric charges within an atoms or molecules. The first is predominant for resonant interactions and the second is predominant for non or near resonant interactions. Optical fieldinduced electric dipole moment which, in turn, will act as a new source to emit a secondary electromagnetic wave. This is the fundamental process describing the optical fieldinduced dipole moment of a molecular system and the reemission of a secondary wave radiation. Assuming that the number of molecules in a unit volume is N and induced dipole moment of i th molecule is p i then P is determined by N P(t) = p i (t) (2) i=1 2
3 . From Eq. (2) it can be seen that the electric polarization of a medium is determined by two factors: one is the field induced dipole moment of each individual molecule of the medium, and the other is the statistically averaged property of a great number of molecules. That is the molecular dipole moment is determined by the microscopic structure or their eigen functions; whereas the results of the summation depends on the microscopic symmetry. Now taking the n th order Fourier component of polarization P (n) (t)and the Fourier component of E(t) it can be shown that [1] P (n) (ω) = ɛ 0 χ (n) (ω 1, ω 2,..., ω n )E(ω 1 )E(ω 2 )...E(ω n ). (3). The values and properties of χ (n) can be determined from the semiclassical theory mentioned above and it is very complex and difficult. So By considering special features of interaction between the incident light beam and the given medium and then simplifying the above model it is possible to extract some useful conclusions. 4 Various mechanisms causing Nonlinear polarization in a medium. Depending on the applied field frequency and the phase of the medium one or more of the mechanisms discuss below become the major contributor to the nonlinear behavior of the medium. 4.1 Distortion of electronic cloud The change of the outershell electronic cloud of an atom, ions or molecule compare to the undisturbed status without applying an external optical electric field. This mechanism has very fast response time and approximately less than ( ) seconded: most optical frequency mixing effects such as second harmonic and third harmonic generation, sumfrequency generation, optical parametric oscillation and fourphoton parametric interaction. 4.2 Intramolecular motion It denotes the polarization contribution from an opticalfield induced relative motion (vibration, rotation, etc.) between the nuclei(or ions) within a molecule. The response time of this mechanism is around second. Ex: some Raman resonanceenhanced fourwavemixing effects and Raman enhanced refractive index change. 4.3 Molecular reorientation It denotes the additional electric polarization contribution from an optical field induced reorientation of anisotropic molecules in a liquid. The response time of this process is dependent on the rotational viscosity of molecules in the liquid and is approximately ( ) second. Ex: stimulated Kerr scattering and Kerreffect related refractive index change. 3
4 4.4 Induced acoustic motion It is the polarization contribution from an optical induced macroscopic acoustic motion related to the so called electrostriction interaction. the response time of this mechanism is ( ) second depending on the phase state of the medium. Ex ; Brillouin scattering, self focusing and optical breakdown damage. 4.5 Induced population change The distribution of molecules in their different eigen states may be changed owing to onephoton or twophoton absorption or Raman transition for resonant interaction. the response time of this additional polarization of the medium is strongly depend on the dynamic properties of molecular transition and relaxation of the medium. and in general slower than that of first three mechanisms. 5 Manipulation of nonlinear susceptibilities The main issue of nonlinear optics is to study the interaction between the laser field and media. In many cases, the applied laser field is a coherent monochromatic electromagnetic wave with narrow spectral line width and a small divergent angle. Since the laser field has only one or more monochromatic Fourier components, the fieldinduced nonlinear polarization can also be recognized as a combination of limited number of Fourier components. According to Eq.(3), the linear component is given by Secondorder nonlinear polarization is given by P (1) (ω) = ɛ 0 χ (1) (ω)e(ω) (4) P (2) (ω = ω 1 + ω 2 ) = ɛ 0 χ (2) (ω 1, ω 2 )E(ω 1 )E(ω 2 ) (5) Physical meaning of this equation is that the radiation at new frequency ω = ω 1 + ω 2 can be generated by two incident monochromatic waves with frequencies of ω 1 and ω 2.The χ (2) is a third order tensor having 3 9 = 27 elements. The third order nonlinear polarization is given by P (3) (ω = ω 1 + ω 2 + ω 3 ) = ɛ 0 χ (2) (ω 1, ω 2, ω 3 )E(ω 1 )E(ω 2 )E(ω 3 ) (6). This equation tells that in the third order approximation, the radiation at a new frequency ω = ω 1 +ω 2 +ω 3 can be generated by an intense incident field containing ω 1, ω 2 and ω 3.The χ (3) is a fourth order tensor having 3 27 = 81 elements. The above equations (4),(5) and(6) tell that variousorder of susceptibilities are the key parameters to describe the nonlinear coupling between different incident waves, as well as the generation of new frequency radiation through the induced nonlinear electric polarization of the medium. Based on the theoretical analyses [1] it is understood that various orders of susceptibilities of a medium possess the following basic properties, which help researchers to considerably simplify theoretical work and have a better understanding the related nonlinear optical processes. 4
5 5.1 Relative magnitude of various orders of susceptibilities If the major contribution for polarization is the distortion of electronic cloud of a molecular system, the approximation χ (n) / χ (n 1) 1/ E 0 (7) is valid and where E 0 is the magnitude of average electric field strength inside an atom ( it is about V/m for a hydrogen atom.). according to Eq.(3) the ratio between successive polarization can be roughly estimated by p (n) / p (n 1) χ (n 1) /χ (n) E / E 0. (8) Here E is the magnitude of an applied optical field. For ordinary light sources the ratio of E / E 0 is so small that all nonlinear terms can be neglected. If the applied incident light is of high spectral intensity the ratio E / E 0 is not small and second and third order contributions may play vital roles. 5.2 Spatial symmetry restrictions on susceptibilities The susceptibility tensors must remain unchanged upon the symmetric operation allowed for the medium. This reduces the number of the independent and nonzero elements of the susceptibility tensors. The most important conclusion from this property is that for all centrosymmetric crystals and isotropic media (gases, liquids and amorphous solids), all tensor elements of evenorder susceptibilities (χ (2), χ (4)...) must be zero. Therefore no second order nonlinear effects can be observed for such media. But oddodder susceptibility tensors will not be zero and they provide nonlinear effects. 5.3 Resonance enhancement of susceptibility When one or a combination of several frequency components of the applied electric field approaches a resonant frequency of the medium, the magnitudes of the tensor elements for appropriates orders of susceptibilities can be significantly increased. 5.4 Permutation symmetry of susceptibilities The following permutation symmetry relations of tensor elements (in Cartesian coordinates) for second order and third order susceptibilities hold [1]; χ (2) ijk (ω 1, ω 2 ) = χ (2) ijk (ω 2, ω 1 ) (9) and χ (3) ijkl (ω 1, ω 2, ω 3 ) = χ (3) ikjl (ω 2, ω 1, ω 3 ) = χ (3) iljk (ω 3, ω 1, ω 2 ) =... (10) 5.5 complex conjugation and time reversal symmetry It can be proved that various orders of susceptibilities are complex quantities in general. Since the polarization response must be a real quantity, the manipulation of complex conjugation for χ (n) leads to [χ (n) (ω 1, ω 2,.., ω n )] = χ (n) ( ω 1, ω 2,.., ω n ) 5
6 equation Furthermore if we consider the non resonant case, χ (n) can be approximately viewed as real quantities, and then we obtain [1] And finally considering both of above [χ (n) (ω 1, ω 2,.., ω n )] = χ (n) (ω 1, ω 2,.., ω n ) (12) χ (n) (ω 1, ω 2,.., ω n ) = χ (n) ( ω 1, ω 2,.., ω n ) (13) This implies that susceptibility tensors are invariant for simultaneous change of the sign for all frequency arguments. This is the time reversal symmetry and holds only for nonresonant interaction. By using these symmetries the number of independent and nonzero elements of χ (n) can be further reduced and greatly simplify the analyses. 6 Conclusion Nonlinear phenomena are ultimately due to inability of dipoles in the optical medium to respond in a linear fashion to the alternating electric field associated with a light beam. Understanding the various orders(mainly second and third) of susceptibility tensors and the behavior of their elements of the optical medium subject to given condition is the basic problem of nonlinear optics. References [1] Guang S. He and Song H. Liu, Physics of Nonlinear Optics. [2] Frank L.Pedrotti, S.J.and Leno S. Pedrotti., Introduction to Optics. 6
Frequency Doubling and Second Order Nonlinear Optics
Frequency Doubling and Second Order Nonlinear Optics Paul M. Petersen DTU Fotonik, Risø campus Technical University of Denmark, Denmark (email: paul.michael.petersen@risoe.dk) Outline of the talk The first
More informationF 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 thus, the total number of atoms per second that absorb a photon is
Stimulated Emission of Radiation  stimulated emission is referring to the emission of radiation (a photon) from one quantum system at its transition frequency induced by the presence of other photons
More informationIntroduction to Optics
Second Edition Introduction to Optics FRANK L. PEDROTTI, S.J. Marquette University Milwaukee, Wisconsin Vatican Radio, Rome LENO S. PEDROTTI Center for Occupational Research and Development Waco, Texas
More informationAmplification Atomic (or molecular, or semiconductor) system has energy levels Some higher energy states are stable for a short time (ps to ms)
Part 5: Lasers Amplification Atomic (or molecular, or semiconductor) system has energy levels Some higher energy states are stable for a short time (ps to ms) Incident photon can trigger emission of an
More informationSection 6 Raman Scattering (lecture 10)
Section 6 Scattering (lecture 10) Previously: Quantum theory of atoms / molecules Quantum Mechanics Valence Atomic and Molecular Spectroscopy Scattering The scattering process Elastic (Rayleigh) and inelastic
More informationAssessment Plan for Learning Outcomes for BA/BS in Physics
Department of Physics and Astronomy Goals and Learning Outcomes 1. Students know basic physics principles [BS, BA, MS] 1.1 Students can demonstrate an understanding of Newton s laws 1.2 Students can demonstrate
More informationMASTER OF SCIENCE IN PHYSICS MASTER OF SCIENCES IN PHYSICS (MS PHYS) (LIST OF COURSES BY SEMESTER, THESIS OPTION)
MASTER OF SCIENCE IN PHYSICS Admission Requirements 1. Possession of a BS degree from a reputable institution or, for nonphysics majors, a GPA of 2.5 or better in at least 15 units in the following advanced
More informationThomson and Rayleigh Scattering
Thomson and Rayleigh Scattering Initial questions: What produces the shapes of emission and absorption lines? What information can we get from them regarding the environment or other conditions? In this
More informationNMR for Physical and Biological Scientists Thomas C. Pochapsky and Susan Sondej Pochapsky Table of Contents
Preface Symbols and fundamental constants 1. What is spectroscopy? A semiclassical description of spectroscopy Damped harmonics Quantum oscillators The spectroscopic experiment Ensembles and coherence
More informationPhysics 9e/Cutnell. correlated to the. College Board AP Physics 1 Course Objectives
Physics 9e/Cutnell correlated to the College Board AP Physics 1 Course Objectives Big Idea 1: Objects and systems have properties such as mass and charge. Systems may have internal structure. Enduring
More informationRaman Spectroscopy. 1. Introduction. 2. More on Raman Scattering. " scattered. " incident
February 15, 2006 Advanced Physics Laboratory Raman Spectroscopy 1. Introduction When light is scattered from a molecule or crystal, most photons are elastically scattered. The scattered photons have the
More informationThe excitation in Raman spectroscopy is usually. Practical Group Theory and Raman Spectroscopy, Part II: Application of Polarization
Electronically reprinted from March 214 Molecular Spectroscopy Workbench Practical Group Theory and Raman Spectroscopy, Part II: Application of Polarization In this second installment of a twopart series
More informationWaves  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 informationDOCTOR OF PHILOSOPHY IN PHYSICS
DOCTOR OF PHILOSOPHY IN PHYSICS The Doctor of Philosophy in Physics program is designed to provide students with advanced graduate training in physics, which will prepare them for scientific careers in
More information6 J  vector electric current density (A/m2 )
Determination of Antenna Radiation Fields Using Potential Functions Sources of Antenna Radiation Fields 6 J  vector electric current density (A/m2 ) M  vector magnetic current density (V/m 2 ) Some problems
More informationOptics and Spectroscopy at Surfaces and Interfaces
Vladimir G. Bordo and HorstGunter Rubahn Optics and Spectroscopy at Surfaces and Interfaces WILEY VCH WILEYVCH Verlag GmbH & Co. KGaA Contents Preface IX 1 Introduction 1 2 Surfaces and Interfaces 5
More informationThe Fundamentals of Infrared Spectroscopy. Joe Van Gompel, PhD
TN100 The Fundamentals of Infrared Spectroscopy The Principles of Infrared Spectroscopy Joe Van Gompel, PhD Spectroscopy is the study of the interaction of electromagnetic radiation with matter. The electromagnetic
More informationThomson and Rayleigh Scattering
Thomson and Rayleigh Scattering In this and the next several lectures, we re going to explore in more detail some specific radiative processes. The simplest, and the first we ll do, involves scattering.
More informationChapter 7: Polarization
Chapter 7: Polarization Joaquín Bernal Méndez Group 4 1 Index Introduction Polarization Vector The Electric Displacement Vector Constitutive Laws: Linear Dielectrics Energy in Dielectric Systems Forces
More informationGroup Theory and Chemistry
Group Theory and Chemistry Outline: Raman and infrared spectroscopy Symmetry operations Point Groups and Schoenflies symbols Function space and matrix representation Reducible and irreducible representation
More informationNMR and IR spectra & vibrational analysis
Lab 5: NMR and IR spectra & vibrational analysis A brief theoretical background 1 Some of the available chemical quantum methods for calculating NMR chemical shifts are based on the HartreeFock selfconsistent
More informationRaman Scattering Theory David W. Hahn Department of Mechanical and Aerospace Engineering University of Florida (dwhahn@ufl.edu)
Introduction Raman Scattering Theory David W. Hahn Department of Mechanical and Aerospace Engineering University of Florida (dwhahn@ufl.edu) The scattering of light may be thought of as the redirection
More informationPlate 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 informationBCM 6200  Protein crystallography  I. Crystal symmetry Xray diffraction Protein crystallization Xray sources SAXS
BCM 6200  Protein crystallography  I Crystal symmetry Xray diffraction Protein crystallization Xray sources SAXS Elastic Xray Scattering From classical electrodynamics, the electric field of the electromagnetic
More informationStructure Factors 59553 78
78 Structure Factors Until now, we have only typically considered reflections arising from planes in a hypothetical lattice containing one atom in the asymmetric unit. In practice we will generally deal
More informationA Theoretical Model for Mutual Interaction between Coaxial Cylindrical Coils Lukas Heinzle
A Theoretical Model for Mutual Interaction between Coaxial Cylindrical Coils Lukas Heinzle Page 1 of 15 Abstract: The wireless power transfer link between two coils is determined by the properties of the
More informationProblem Set 3 Solutions CH332 (SP 06) 1. Skoog problem 151 (omit terms (j), (k) and (m)). Draw diagrams as necessary.
Problem Set 3 Solutions CH332 (SP 06) 1. Skoog problem 151 (omit terms (j), (k) and (m)). Draw diagrams as necessary. a) fluorescence Relaxation of an excited state by emission of a photon without a change
More informationInfrared Spectroscopy: Theory
u Chapter 15 Infrared Spectroscopy: Theory An important tool of the organic chemist is Infrared Spectroscopy, or IR. IR spectra are acquired on a special instrument, called an IR spectrometer. IR is used
More informationRaman Spectroscopy Basics
Raman Spectroscopy Basics Introduction Raman spectroscopy is a spectroscopic technique based on inelastic scattering of monochromatic light, usually from a laser source. Inelastic scattering means that
More informationMolecular Velocity Distribution in Air
Molecular Velocity Distribution in Air Abstract The present paper contains a description of how the velocity distribution of a molecular gas can be determined using light scattering by light with a wavelength
More informationMolecular spectroscopy III: Nuclear Magnetic Resonance (NMR)
Molecular spectroscopy III: Nuclear Magnetic Resonance (NMR) Nuclear magnetic resonance (NMR) is a physical phenomenon in which magnetic nuclei in a magnetic field absorb electromagnetic radiation at a
More information1. Radiative Transfer. 2. Spectrum of Radiation. 3. Definitions
1. Radiative Transfer Virtually all the exchanges of energy between the earthatmosphere system and the rest of the universe take place by radiative transfer. The earth and its atmosphere are constantly
More informationConcept 2. A. Description of lightmatter interaction B. Quantitatities in spectroscopy
Concept 2 A. Description of lightmatter interaction B. Quantitatities in spectroscopy Dipole approximation Rabi oscillations Einstein kinetics in twolevel system B. Absorption: quantitative description
More informationDevelopment 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 information7. DYNAMIC LIGHT SCATTERING 7.1 First order temporal autocorrelation function.
7. DYNAMIC LIGHT SCATTERING 7. First order temporal autocorrelation function. Dynamic light scattering (DLS) studies the properties of inhomogeneous and dynamic media. A generic situation is illustrated
More informationRaman spectroscopy Lecture
Raman spectroscopy Lecture Licentiate course in measurement science and technology Spring 2008 10.04.2008 Antti Kivioja Contents  Introduction  What is Raman spectroscopy?  The theory of Raman spectroscopy
More informationMaster Degree Program
SAINT PETERSBURG STATE ELECTROTECHNICAL UNIVERSITY LETI Laser Measurement and Navigation Systems department Master Degree Program ETU LETI TRADITIONS AND INNOVATIONS ETU LETI is the oldest Electrotechnical
More informationState of Stress at Point
State of Stress at Point Einstein Notation The basic idea of Einstein notation is that a covector and a vector can form a scalar: This is typically written as an explicit sum: According to this convention,
More informationFour Wave Mixing In DWDM Optical System
International Journal of Computational Engineering Research Vol, 03 Issue, 6 Four Wave Mixing In DWDM Optical System Gouri Deshmukh 1, Prof.Santosh Jagtap 2 (Vidyalankar Institute Of Technology,Electronics
More informationBlackbody 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 informationAcoustic Velocity, Impedance, Reflection, Transmission, Attenuation, and Acoustic Etalons
Acoustic Velocity, Impedance, Reflection, Transmission, Attenuation, and Acoustic Etalons Acoustic Velocity The equation of motion in a solid is (1) T = ρ 2 u t 2 (1) where T is the stress tensor, ρ is
More informationDoes Quantum Mechanics Make Sense? Size
Does Quantum Mechanics Make Sense? Some relatively simple concepts show why the answer is yes. Size Classical Mechanics Quantum Mechanics Relative Absolute What does relative vs. absolute size mean? Why
More informationTime out states and transitions
Time out states and transitions Spectroscopy transitions between energy states of a molecule excited by absorption or emission of a photon hn = DE = E i  E f Energy levels due to interactions between
More informationAcoustooptic modulator
1 of 3 Acoustooptic modulator F An acoustooptic modulator (AOM), also called a Bragg cell, uses the acoustooptic effect to diffract and shift the frequency of light using sound waves (usually at radiofrequency).
More informationInteraction of Atoms and Electromagnetic Waves
Interaction of Atoms and Electromagnetic Waves Outline  Review: Polarization and Dipoles  Lorentz Oscillator Model of an Atom  Dielectric constant and Refractive index 1 True or False? 1. The dipole
More informationApplication Note AN4
TAKING INVENTIVE STEPS IN INFRARED. MINIATURE INFRARED GAS SENSORS GOLD SERIES UK Patent App. No. 2372099A USA Patent App. No. 09/783,711 World Patents Pending INFRARED SPECTROSCOPY Application Note AN4
More informationLecture 3: Optical Properties of Bulk and Nano. 5 nm
Lecture 3: Optical Properties of Bulk and Nano 5 nm The Previous Lecture Origin frequency dependence of χ in real materials Lorentz model (harmonic oscillator model) 0 e  n( ) n' n '' n ' = 1 + Nucleus
More informationIndiana's Academic Standards 2010 ICP Indiana's Academic Standards 2016 ICP. map) that describe the relationship acceleration, velocity and distance.
.1.1 Measure the motion of objects to understand.1.1 Develop graphical, the relationships among distance, velocity and mathematical, and pictorial acceleration. Develop deeper understanding through representations
More informationLecture 3 Fluid Dynamics and Balance Equa6ons for Reac6ng Flows
Lecture 3 Fluid Dynamics and Balance Equa6ons for Reac6ng Flows 3. 1 Basics: equations of continuum mechanics  balance equations for mass and momentum  balance equations for the energy and the chemical
More informationof transitions from the upper energy level to the lower one per unit time caused by a spontaneous emission of radiation with the frequency ω = (E E
THE EERGY DISTRIBUTIO OF ATOMS I THE FIELD OF THERMAL BLACKBODY RADIATIO Fedor V.Prigara Institute of Microelectronics and Informatics, Russian Academy of Sciences, Universitetskaya, 50007 Yaroslavl, Russia
More informationDO PHYSICS ONLINE FROM QUANTA TO QUARKS QUANTUM (WAVE) MECHANICS
DO PHYSICS ONLINE FROM QUANTA TO QUARKS QUANTUM (WAVE) MECHANICS Quantum Mechanics or wave mechanics is the best mathematical theory used today to describe and predict the behaviour of particles and waves.
More informationBoltzmann Distribution Law
Boltzmann Distribution Law The motion of molecules is extremely chaotic Any individual molecule is colliding with others at an enormous rate Typically at a rate of a billion times per second We introduce
More informationStefan Prorok (Autor) Hybrid SiliconOrganic Resonators for Optical Modulation and Filtering
Stefan Prorok (Autor) Hybrid SiliconOrganic Resonators for Optical Modulation and Filtering https://cuvillier.de/de/shop/publications/6929 Copyright: Cuvillier Verlag, Inhaberin Annette JentzschCuvillier,
More informationMolecular Spectroscopy: Applications
Chapter 6. Molecular Spectroscopy: Applications Notes: Most of the material presented in this chapter is adapted from Stahler and Palla (24), Chap. 6, and Appendices B and C. 6.1 Carbon Monoxyde (CO) Since
More informationMeasuring the Refractive Index of Infrared Materials by DualWavelength FabryPerot Interferometry. A Senior Project. presented to
Measuring the Refractive Index of Infrared Materials by DualWavelength FabryPerot Interferometry A Senior Project presented to the Faculty of the Physics Department California Polytechnic State University,
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 informationSpectroscopy. The Interaction of Electromagnetic Radiation (Light) with Molecules
Spectroscopy. The Interaction of Electromagnetic Radiation (Light) with Molecules (1) Electromagnetic Radiationwave description propagation c = 3 x 10 10 cm/sec magnetic () and electric (E) field vectors
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
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 information1 The water molecule and hydrogen bonds in water
The Physics and Chemistry of Water 1 The water molecule and hydrogen bonds in water Stoichiometric composition H 2 O the average lifetime of a molecule is 1 ms due to proton exchange (catalysed by acids
More informationWAVES AND FIELDS IN INHOMOGENEOUS MEDIA
WAVES AND FIELDS IN INHOMOGENEOUS MEDIA WENG CHO CHEW UNIVERSITY OF ILLINOIS URBANACHAMPAIGN IEEE PRESS Series on Electromagnetic Waves Donald G. Dudley, Series Editor IEEE Antennas and Propagation Society,
More informationNuclear Magnetic Resonance
Nuclear Magnetic Resonance Introduction Atomic magnetism Nuclear magnetic resonance refers to the behaviour of atomic nuclei in the presence of a magnetic field. The first principle required to understand
More information5.33 Lecture Notes: Introduction to Spectroscopy
5.33 Lecture Notes: ntroduction to Spectroscopy What is spectroscopy? Studying the properties of matter through its interaction with different frequency components of the electromagnetic spectrum. Latin:
More informationMODELING AND MEASURING THE POLARIZATION OF LIGHT:
MODELING AND MEASURING THE POLARIZATION OF LIGHT: FROM JONES MATRICES TO ELLIPSOMETRY OVERALL GOALS The Polarization of Light lab strongly emphasizes connecting mathematical formalism with measurable results.
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 informationEnergy Transport. Focus on heat transfer. Heat Transfer Mechanisms: Conduction Radiation Convection (mass movement of fluids)
Energy Transport Focus on heat transfer Heat Transfer Mechanisms: Conduction Radiation Convection (mass movement of fluids) Conduction Conduction heat transfer occurs only when there is physical contact
More information"in recognition of the services he rendered to the advancement of Physics by his discovery of energy quanta". h is the Planck constant he called it
1 2 "in recognition of the services he rendered to the advancement of Physics by his discovery of energy quanta". h is the Planck constant he called it the quantum of action 3 Newton believed in the corpuscular
More informationSecond postulate of Quantum mechanics: If a system is in a quantum state represented by a wavefunction ψ, then 2
. POSTULATES OF QUANTUM MECHANICS. Introducing the state function Quantum physicists are interested in all kinds of physical systems (photons, conduction electrons in metals and semiconductors, atoms,
More informationWaves Sound and Light
Waves Sound and Light r2 c:\files\courses\1710\spr12\wavetrans.doc Ron Robertson The Nature of Waves Waves are a type of energy transmission that results from a periodic disturbance (vibration). They are
More informationChapter 8 Molecules. Some molecular bonds involve sharing of electrons between atoms. These are covalent bonds.
Chapter 8 Molecules (We have only three days for chapter 8!) 8.1 The Molecular Bond A molecule is an electrically neutral group of atoms held together strongly enough to behave as a single particle. A
More informationMultidimensional spectroscopy
Multidimensional spectroscopy GB SE EA Rephasing 1 1 1 2 1 1 1 1 1 t2 1 1 Nonrephasing 1 1 1 2 1 1 1 1 1 1 1 t 2 Thomas la Cour Jansen University of Groningen, 29 Front cover: The double sided Feynman
More informationSelfGuided Intense Laser Pulse Propagation in Air
Nonlinear Analysis: Modelling and Control, 2000, v.6, No, 226 SelfGuided Intense Laser Pulse Propagation in Air R. Danielius, D. Mikalauskas, A. Dubietis and A. Piskarskas Department of Quantum Electronics,
More informationTime out states and transitions
Time out states and transitions Spectroscopy transitions between energy states of a molecule excited by absorption or emission of a photon hν = E = E i E f Energy levels due to interactions between parts
More informationPUMPED Nd:YAG LASER. Last Revision: August 21, 2007
PUMPED Nd:YAG LASER Last Revision: August 21, 2007 QUESTION TO BE INVESTIGATED: How can an efficient atomic transition laser be constructed and characterized? INTRODUCTION: This lab exercise will allow
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 information2, 8, 20, 28, 50, 82, 126.
Chapter 5 Nuclear Shell Model 5.1 Magic Numbers The binding energies predicted by the Liquid Drop Model underestimate the actual binding energies of magic nuclei for which either the number of neutrons
More informationMolecular Symmetry 1
Molecular Symmetry 1 I. WHAT IS SYMMETRY AND WHY IT IS IMPORTANT? Some object are more symmetrical than others. A sphere is more symmetrical than a cube because it looks the same after rotation through
More informationSemiconductor Laser Diode
Semiconductor Laser Diode Outline This student project deals with the exam question Semiconductor laser diode and covers the following questions: Describe how a semiconductor laser diode works What determines
More informationPreview 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 informationLecture 1: Microscopic Theory of Radiation
253a: QFT Fall 2009 Matthew Schwartz Lecture : Microscopic Theory of Radiation Blackbody Radiation Quantum Mechanics began on October 9, 900 with Max Planck s explanation of the blackbody radiation spectrum.
More informationApplications of Quantum Chemistry HΨ = EΨ
Applications of Quantum Chemistry HΨ = EΨ Areas of Application Explaining observed phenomena (e.g., spectroscopy) Simulation and modeling: make predictions New techniques/devices use special quantum properties
More informationElectromagnetically induced transparency and its dispersion properties in a fourlevel invertedy atomic system
Physics Letters A 317 (2003) 370 377 www.elsevier.com/locate/pla Electromagnetically induced transparency and its dispersion properties in a fourlevel invertedy atomic system Amitabh Joshi, Min Xiao
More informationFundamentals of molecular absorption spectroscopy (UV/VIS)
10.2.1.3 Molecular spectroscopy 10.2.1.3.1 Introduction Molecular radiation results from the rotational, vibrational and electronic energy transitions of molecules. Band spectra are the combination of
More informationPolarization Dependence in Xray Spectroscopy and Scattering. S P Collins et al Diamond Light Source UK
Polarization Dependence in Xray Spectroscopy and Scattering S P Collins et al Diamond Light Source UK Overview of talk 1. Experimental techniques at Diamond: why we care about xray polarization 2. How
More informationE. K. A. ADVANCED PHYSICS LABORATORY PHYSICS 3081, 4051 NUCLEAR MAGNETIC RESONANCE
E. K. A. ADVANCED PHYSICS LABORATORY PHYSICS 3081, 4051 NUCLEAR MAGNETIC RESONANCE References for Nuclear Magnetic Resonance 1. Slichter, Principles of Magnetic Resonance, Harper and Row, 1963. chapter
More informationarxiv:astroph/0110525 v4 4 Feb 2002
arxiv:astroph/0110525 v4 4 Feb 2002 The difficult discrimination of Impulse Stimulated Raman Scattering redshift against Doppler redshift J. MoretBailly February 4, 2002 Pacs 42.65.Dr Stimulated Raman
More informationThe Fiber Laser Advantage
The Fiber Laser Advantage White Paper PN 200020000 Revision 1.1 January 2009 Calmar Laser, Inc www.calmarlaser.com Overview With the fiber optics revolution for telecommunications in the 1980s, fiber
More informationMolecular Spectroscopy
Molecular Spectroscopy UVVis Spectroscopy Absorption Characteristics of Some Common Chromophores UVVis Spectroscopy Absorption Characteristics of Aromatic Compounds UVVis Spectroscopy Effect of extended
More informationFiber Optics: Fiber Basics
Photonics Technical Note # 21 Fiber Optics Fiber Optics: Fiber Basics Optical fibers are circular dielectric waveguides that can transport optical energy and information. They have a central core surrounded
More informationPeriodic Wave Phenomena
Name: Periodic Wave Phenomena 1. The diagram shows radar waves being emitted from a stationary police car and reflected by a moving car back to the police car. The difference in apparent frequency between
More informationChapter 8 Maxwell relations and measurable properties
Chapter 8 Maxwell relations and measurable properties 8.1 Maxwell relations Other thermodynamic potentials emerging from Legendre transforms allow us to switch independent variables and give rise to alternate
More informationThe Phenomenon of Photoelectric Emission:
The Photoelectric Effect. The Wave particle duality of light Light, like any other E.M.R (electromagnetic radiation) has got a dual nature. That is there are experiments that prove that it is made up of
More information develop a theory that describes the wave properties of particles correctly
Quantum Mechanics Bohr's model: BUT: In 192526: by 1930s:  one of the first ones to use idea of matter waves to solve a problem  gives good explanation of spectrum of single electron atoms, like hydrogen
More informationEðlisfræði 2, vor 2007
[ Assignment View ] [ Print ] Eðlisfræði 2, vor 2007 30. Inductance Assignment is due at 2:00am on Wednesday, March 14, 2007 Credit for problems submitted late will decrease to 0% after the deadline has
More informationDISTANCE DEGREE PROGRAM CURRICULUM NOTE:
Bachelor of Science in Electrical Engineering DISTANCE DEGREE PROGRAM CURRICULUM NOTE: Some Courses May Not Be Offered At A Distance Every Semester. Chem 121C General Chemistry I 3 Credits Online Fall
More informationarxiv:1111.4354v2 [physics.accph] 27 Oct 2014
Theory of Electromagnetic Fields Andrzej Wolski University of Liverpool, and the Cockcroft Institute, UK arxiv:1111.4354v2 [physics.accph] 27 Oct 2014 Abstract We discuss the theory of electromagnetic
More informationChapter 5 Light and Matter: Reading Messages from the Cosmos
Chapter 5 Light and Matter: Reading Messages from the Cosmos Messages Interactions of Light and Matter The interactions determine everything we see, including what we observe in the Universe. What is light?
More informationDispersion diagrams of a waterloaded cylindrical shell obtained from the structural and acoustic responses of the sensor array along the shell
Dispersion diagrams of a waterloaded cylindrical shell obtained from the structural and acoustic responses of the sensor array along the shell B.K. Jung ; J. Ryue ; C.S. Hong 3 ; W.B. Jeong ; K.K. Shin
More informationVSEPR Model. The ValenceShell Electron Pair Repulsion Model. Predicting Molecular Geometry
VSEPR Model The structure around a given atom is determined principally by minimizing electron pair repulsions. The ValenceShell Electron Pair Repulsion Model The valenceshell electron pair repulsion
More informationphys4.17 Page 1  under normal conditions (pressure, temperature) graphite is the stable phase of crystalline carbon
Covalent Crystals  covalent bonding by shared electrons in common orbitals (as in molecules)  covalent bonds lead to the strongest bound crystals, e.g. diamond in the tetrahedral structure determined
More information