Plan of the lectures
|
|
- Rosa Lyons
- 5 years ago
- Views:
Transcription
1 Plan of the lectures 1. Introductory remarks on metallic nanostructures Relevant quantities and typical physical parameters Applications. Linear electron response: Mie theory and generalizations 3. Nonlinear response Survey of various models from N-body to macroscopic Mean-field approximation (Hartree and Vlasov equations) 4. Beyond the mean-field approximation Hartree-Fock equations Time-dependent density functional theory (DFT) and local-density approximation (LDA) 5. Macroscopic models: quantum hydrodynamics Linear theory and comparison of various models 6. Spin dynamics: experimental results and recent theoretical advances 7. Illustration: the nonlinear electron dynamics in thin metal films Master Lecture 1
2 Electron dynamics qualitative aspects We have seen that the typical timescale of collective phenomena is πω 1 p 1 fs We need short laser pulses to probe this timescale. Pump-probe experiments Master Lecture
3 Linear response: driven-damped harmonic oscillator β damping oscillations forcing Steady state solution (t ): Resonance becomes broader with increasing damping Master Lecture 3
4 The response is directly proportional to the excitation For instance, variation of the electron density is proportional to laser field When the frequency ω of the excitation is close to the natural frequency of the system, we have resonance enhanced absorption For electron gas, natural frequency ~ ω p In the presence of damping, the resonance becomes «broad» Damping rate Resonant energy = ħω Main purpose of linear theory: determine resonant frequency and damping rate Master Lecture 4
5 Mie theory 1D model Def. of electric dipole n 0 n i Ehrenfest theorem n 0 (x) Poisson s equation Initial shift of the electron density by a distance d(0): Induced change in electric field (from Poisson s equation) δn We obtain: Master Lecture 5
6 ω Finally the dipole obeys the harmonic oscillator equation: If n 0 = const. = n i it can be taken out of the integral: We obtain oscillations at the plasma frequency. This is the fundamental result of Mie theory No dependence on size, temperature, The metal species (Au, Ag, ) appears only in the plasma frequency, through the electron density. No damping: purely oscillatory mode at a single frequency Limitations Derivation in 1D and, of course, purely linear response Master Lecture 6
7 Spill-out effect: illustration Numerical computation of the ground state at zero temperature Sodium nanoparticle n e (r) / n 0 n i Spill-out r / a G. Weick, PhD thesis, IPCMS, Strasbourg, (006) Master Lecture 7
8 Spill-out effect: qualitative picture The electron density at equilibrium is not equal to the ion density n 0 The electrons spill out of a length δ n 0 / This leads to a reduction of the oscillation frequency -a a a+δ x Master Lecture 8
9 The correction to the frequency goes as 1/a This is the first correction we have found to the simple plasmon frequency It is true in any number of dimensions It s just the surface to volume ratio For instance, in 3D: Lithium clusters ħω (ev) Assuming δr does not depend on R N 1/3 Data : C. Brechignac et al, PRL 70, 036 (1993) Graph : G. Weick, PhD thesis, IPCMS, Strasbourg, (006) Master Lecture 9
10 Thomas-Fermi theory of spill-out Valid at Te = 0 Kinetic energy electrostatic energy = We obtain the density as a function of the electrostatic potential V(x) Poisson s equation: Linearize Poisson s equation, assuming ev << µ λ ( µ E F at T = 0) = e The spill-out is a screening effect λdoes not depend on particle s size Master Lecture 10
11 General Mie theory of the surface plasmon (1908) Spherical nanoparticle immersed in external field E 0 Electrostatic response: free charges tend to shield the external field Inside the sphere the electric field is* E int = E 0 3ε m ε + ε m < E ε > ε We make the following assumptions: No magnetic field effect (E/B ~ c) Electric field wavelength >> R = radius of nanoparticle For visible-light lasers λ nm Thus, we consider only the time variation of the field E = E 0 exp( iωt) The dielectric constant depends on the frequency 0 if m * J. D. Jackson, Classical Electrodynamics Master Lecture 11
12 The dielectric constant has a real and an imaginary part ε ( ω) = ε1( ω) + iε( ω) E int = E 0 3ε m ε + ε m When ε << ε 1, the resonance condition is ε 1 = ε m The dielectric constant also determines the photo-absorption cross-section It remains to be determined the frequency dependence of ε 1 (ω). Master Lecture 1
13 Frequency-dependent dielectric constant Drude theory for time-dependent electric field Equation of motion j = electric current Fourier transform: p p exp( iωt) microscopic Ohm s law σ (ω) = conductivity Master Lecture 13
14 Maxwell s equations Use: J = σ E iω t ε b ( ω) = ε ε 0 Bound electrons Free electrons Master Lecture 14
15 Mie resonance E int = E 0 3ε m ε + ε m < E 0 if ε > ε m When ε << ε 1, the resonance condition is ε 1 = ε m Remember the frequency-dependent dielectric constant If Γ << ω, the real part of ε is: = ε m Finally, we obtain the Mie frequency: if ε m ε 1 b Surface plasmon Master Lecture 15
16 Mie resonance in 1D, D, and 3D Dimensionality Geometry Resonant frequency 1D Thin film ω p D Planar surface ω p / 3D Sphere ω p / 3 Master Lecture 16
17 Does Mie theory work? 1. Pure Mie: ω = ω p / 3 ω Mie spill-out. Spill-out correction ω ω Mie 3 ( 1 K N 1/ ) ω / ω Mie spill-out Numerics (TDLDA) TDLDA 3. Self-consistent calculation using TDLDA (time-dependent local density approximation) Na 83 N 1/3 Spill-out ω ω Mie ( 3) 1 N 1/ K ; K > K TDLDA Mie ħω (ev) G. Weick, PhD thesis, IPCMS, Strasbourg (006) Master Lecture 17
18 Experiment vs. Mie theory and TDLDA simulations Experiment Recover Mie value for large N Simulation C. Yannouleas et al., Phys. Rev. B 47, 9849 (1993) Master Lecture 18
19 Linewidth of the Mie resonance damping Sources of damping 1. Electron-electron collisions (e-e). Electron-phonons collisions (e-ph): interactions with lattice 3. Coupling between collective modes (plasmon) and singleparticle modes: Landau damping 4. Radiation damping 5. Master Lecture 19
20 Linewidth of the Mie resonance damping Collision rate in the bulk material Γ = V F / L L is the bulk mean free path: L (Na) = 34 nm; L (Ag) = 5 nm (at T=73K) When L > R (size of the particle) then one should replace L with R Collisions with the particle s surfaces This picture is not quite correct quantum-mechanically The boundaries determine the shape of the wave functions everywhere Kawabata and Kubo (1966) computed the quantum damping rate Still obtain 1/R behavior. Physically: coupling of the collective plasmon excitation to single-particle modes ( Landau damping ) Γ = Γ V + A F R Master Lecture 0
21 Linewidth experimental and numerical results Num. C. Yannouleas et al., Phys. Rev. B 47, 9849 (1993) Exp. R. H. Doremus, J. Chem. Phys. 4, 414 (1965). Numerics ~ Γ 1 Silver ~ R 1/R theory Master Lecture 1
22 Radiation damping An oscillating electric dipole radiates electromagnetic energy This is a source of damping of the electronic energy W: W = 1 Nmv = The total radiated power is (see Jackson, Classical Electrodynamics) dw dt 1 = 4πε 0 I ( kd ) 1 c 1 Nm I k = p e ω ω = Qω sp sp sp : / c current : wave v = dω vector sp = p e ω sp Electric dipole: p=ed d + dw dt Q e 4 sp 0 4 sp ω p N ω p 3 3 4πε c 4πε c 0 W = Γ rad This yields Γ rad e 0 4πε mc 3 ω sp N R 3 Proportional to the volume: significant only for large nanoparticles Γ e hω rad sp 1 3 ev N N N sp hc 10 8 (4 ) ω mc ε kev Master Lecture
Lecture 3: Optical Properties of Insulators, Semiconductors, and Metals. 5 nm
Metals Lecture 3: Optical Properties of Insulators, Semiconductors, and Metals 5 nm Course Info Next Week (Sept. 5 and 7) no classes First H/W is due Sept. 1 The Previous Lecture Origin frequency dependence
More information7. Localized surface plasmons (Particle plasmons)
7. Localized surface plasmons (Particle plasmons) ( Plasmons in metal nanostructures, Dissertation, University of Munich by Carsten Sonnichsen, 2001) Lycurgus cup, 4th century (now at the British Museum,
More informationECE280: Nano-Plasmonics and Its Applications. Week8
ECE280: Nano-Plasmonics and Its Applications Week8 Surface Enhanced Raman Scattering (SERS) and Surface Plasmon Amplification by Stimulated Emission of Radiation (SPASER) Raman Scattering Chandrasekhara
More informationNanophysics: Main trends
Nano-opto-electronics Nanophysics: Main trends Nanomechanics Main issues Light interaction with small structures Molecules Nanoparticles (semiconductor and metallic) Microparticles Photonic crystals Nanoplasmonics
More informationOne-step Solution Processing of Ag, Au and Hybrids for SERS
1 2 3 Supplementary Information One-step Solution Processing of Ag, Au and Pd@MXene Hybrids for SERS 4 5 6 Elumalai Satheeshkumar 1, Taron Makaryan 2, Armen Melikyan 3, Hayk Minassian 4, Yury Gogotsi 2*
More informationLocalized surface plasmons (Particle plasmons)
Localized surface plasmons (Particle plasmons) ( Plasmons in metal nanostructures, Dissertation, University of Munich by Carsten Sonnichsen, 2001) Lycurgus cup, 4th century (now at the British Museum,
More information( ) /, so that we can ignore all
Physics 531: Atomic Physics Problem Set #5 Due Wednesday, November 2, 2011 Problem 1: The ac-stark effect Suppose an atom is perturbed by a monochromatic electric field oscillating at frequency ω L E(t)
More informationPhotonic/Plasmonic Structures from Metallic Nanoparticles in a Glass Matrix
Excerpt from the Proceedings of the COMSOL Conference 2008 Hannover Photonic/Plasmonic Structures from Metallic Nanoparticles in a Glass Matrix O.Kiriyenko,1, W.Hergert 1, S.Wackerow 1, M.Beleites 1 and
More informationSurface plasmon in metallic nanoparticles: Renormalization effects due to electron-hole excitations
PHYSICAL REVIEW B 74, 165421 2006 Surface plasmon in metallic nanoparticles: Renormalization effects due to electron-hole excitations Guillaume Weick, 1,2, * Gert-Ludwig Ingold, 2 Rodolfo A. Jalabert,
More informationSolid State Physics FREE ELECTRON MODEL. Lecture 17. A.H. Harker. Physics and Astronomy UCL
Solid State Physics FREE ELECTRON MODEL Lecture 17 A.H. Harker Physics and Astronomy UCL Magnetic Effects 6.7 Plasma Oscillations The picture of a free electron gas and a positive charge background offers
More informationEnergy transport in metal nanoparticle plasmon waveguides
Energy transport in metal nanoparticle plasmon waveguides Stefan A. Maier, Pieter G. Kik, and Harry A. Atwater California Institute of Technology Thomas J. Watson Laboratory of Applied Physics, Pasadena,
More informationSupporting information for Metal-semiconductor. nanoparticle hybrids formed by self-organization: a platform to address exciton-plasmon coupling
Supporting information for Metal-semiconductor nanoparticle hybrids formed by self-organization: a platform to address exciton-plasmon coupling Christian Strelow, T. Sverre Theuerholz, Christian Schmidtke,
More informationOptical Properties of Solid from DFT
Optical Properties of Solid from DFT 1 Prof.P. Ravindran, Department of Physics, Central University of Tamil Nadu, India & Center for Materials Science and Nanotechnology, University of Oslo, Norway http://folk.uio.no/ravi/cmt15
More informationSCATTERING OF ELECTROMAGNETIC WAVES ON METAL NANOPARTICLES. Tomáš Váry, Juraj Chlpík, Peter Markoš
SCATTERING OF ELECTROMAGNETIC WAVES ON METAL NANOPARTICLES Tomáš Váry, Juraj Chlpík, Peter Markoš ÚJFI, FEI STU, Bratislava E-mail: tomas.vary@stuba.sk Received xx April 2012; accepted xx May 2012. 1.
More informationLight Interaction with Small Structures
Light Interaction with Small Structures Molecules Light scattering due to harmonically driven dipole oscillator Nanoparticles Insulators Rayleigh Scattering (blue sky) Semiconductors...Resonance absorption
More informationNonlinear Electrodynamics and Optics of Graphene
Nonlinear Electrodynamics and Optics of Graphene S. A. Mikhailov and N. A. Savostianova University of Augsburg, Institute of Physics, Universitätsstr. 1, 86159 Augsburg, Germany E-mail: sergey.mikhailov@physik.uni-augsburg.de
More informationPlasmonics. The long wavelength of light ( μm) creates a problem for extending optoelectronics into the nanometer regime.
Plasmonics The long wavelength of light ( μm) creates a problem for extending optoelectronics into the nanometer regime. A possible way out is the conversion of light into plasmons. They have much shorter
More informationare the eigenvalues of the permittivity tensor in Cartesian coordinates, written as, 3 " xx + i" xy ( , which gives
Supplemental Material for Faraday rotation enhancement of gold coated Fe2O3 nanoparticles: Comparison of experiment and theory Raj Kumar Dani, Hongwang Wang, Stefan H. Bossmann, Gary Wysin and Viktor Chikan,
More informationSpring 2009 EE 710: Nanoscience and Engineering
Spring 009 EE 710: Nanoscience and Engineering Part 10: Surface Plasmons in Metals Images and figures supplied from Hornyak, Dutta, Tibbals, and Rao, Introduction to Nanoscience, CRC Press Boca Raton,
More informationSupporting Online Material. Highly Sensitive Plasmonic Silver Nanorods
Supporting Online Material Highly Sensitive Plasmonic Silver Nanorods Arpad Jakab, Christina Rosman, Yuriy Khalavka, Jan Becker, Andreas Trügler+, Ulrich Hohenester+, and Carsten Sönnichsen * MAINZ graduate
More information60 a) b) Energy [ev]
% % 6 6 a b 5 5 δ 4 3 2 δ 4 3 2 2.5 7.5 2.5 7.5 22.5 2.5 7.5 2.5 7.5 22.5 Number of mesh elements 4 Number of mesh elements 4 Supplementary Figure : Panel a Relative error δ of the absorption cross section
More informationPlasmonics: elementary excitation of a plasma (gas of free charges) nano-scale optics done with plasmons at metal interfaces
Plasmonics Plasmon: Plasmonics: elementary excitation of a plasma (gas of free charges) nano-scale optics done with plasmons at metal interfaces Femius Koenderink Center for Nanophotonics AMOLF, Amsterdam
More informationUnderstanding Nanoplasmonics. Greg Sun University of Massachusetts Boston
Understanding Nanoplasmonics Greg Sun University of Massachusetts Boston Nanoplasmonics Space 100pm 1nm 10nm 100nm 1μm 10μm 100μm 1ns 100ps 10ps Photonics 1ps 100fs 10fs 1fs Time Surface Plasmons Surface
More informationLecture 4 Recap: normal metals and the clectron-phonon interaction *
Phys. 598SC Fall 2015 Prof. A. J. Leggett Lecture 4 Recap: normal metals and the clectron-phonon interaction * 1. Normal metals: Sommerfeld-Bloch picture 2. Screening 3. Fermi liquid theory 4. Electron-phonon
More informationObservation of coupled plasmon-polariton modes of plasmon waveguides for electromagnetic energy transport below the diffraction limit
Mat. Res. Soc. Symp. Proc. Vol. 722 2002 Materials Research Society Observation of coupled plasmon-polariton modes of plasmon waveguides for electromagnetic energy transport below the diffraction limit
More informationOptical Properties of Semiconductors. Prof.P. Ravindran, Department of Physics, Central University of Tamil Nadu, India
Optical Properties of Semiconductors 1 Prof.P. Ravindran, Department of Physics, Central University of Tamil Nadu, India http://folk.uio.no/ravi/semi2013 Light Matter Interaction Response to external electric
More informationSize dependence of multipolar plasmon resonance frequencies and damping rates in simple metal spherical nanoparticles
The original publication is available at www.eurphysj.org: http://www.epjst-journal.org/index.php?option=article&access=standard&itemid=9&url= /articles/epjst/pdf/7/5/st44.pdf EPJ manuscript No. (will
More informationPart VIII. Interaction with Solids
I with Part VIII I with Solids 214 / 273 vs. long pulse is I with Traditional i physics (ICF ns lasers): heating and creation of long scale-length plasmas Laser reflected at critical density surface Fast
More informationPreface Introduction to the electron liquid
Table of Preface page xvii 1 Introduction to the electron liquid 1 1.1 A tale of many electrons 1 1.2 Where the electrons roam: physical realizations of the electron liquid 5 1.2.1 Three dimensions 5 1.2.2
More informationPlasmons, Surface Plasmons and Plasmonics
Plasmons, Surface Plasmons and Plasmonics Plasmons govern the high frequency optical properties of materials since they determine resonances in the dielectric function ε(ω) and hence in the refraction
More informationPlasmons, polarons, polaritons
Plasmons, polarons, polaritons Dielectric function; EM wave in solids Plasmon oscillation -- plasmons Electrostatic screening Electron-electron interaction Mott metal-insulator transition Electron-lattice
More informationAndrea Morello. Nuclear spin dynamics in quantum regime of a single-molecule. magnet. UBC Physics & Astronomy
Nuclear spin dynamics in quantum regime of a single-molecule magnet Andrea Morello UBC Physics & Astronomy Kamerlingh Onnes Laboratory Leiden University Nuclear spins in SMMs Intrinsic source of decoherence
More informationII Theory Of Surface Plasmon Resonance (SPR)
II Theory Of Surface Plasmon Resonance (SPR) II.1 Maxwell equations and dielectric constant of metals Surface Plasmons Polaritons (SPP) exist at the interface of a dielectric and a metal whose electrons
More informationB2.III Revision notes: quantum physics
B.III Revision notes: quantum physics Dr D.M.Lucas, TT 0 These notes give a summary of most of the Quantum part of this course, to complement Prof. Ewart s notes on Atomic Structure, and Prof. Hooker s
More informationPHYSICAL SCIENCES PART A
PHYSICAL SCIENCES PART A 1. The calculation of the probability of excitation of an atom originally in the ground state to an excited state, involves the contour integral iωt τ e dt ( t τ ) + Evaluate the
More informationSpace Plasma Physics Thomas Wiegelmann, 2012
Space Plasma Physics Thomas Wiegelmann, 2012 1. Basic Plasma Physics concepts 2. Overview about solar system plasmas Plasma Models 3. Single particle motion, Test particle model 4. Statistic description
More informationFundamentals of wave kinetic theory
Fundamentals of wave kinetic theory Introduction to the subject Perturbation theory of electrostatic fluctuations Landau damping - mathematics Physics of Landau damping Unmagnetized plasma waves The plasma
More informationThe interaction of light and matter
Outline The interaction of light and matter Denise Krol (Atom Optics) Photon physics 014 Lecture February 14, 014 1 / 3 Elementary processes Elementary processes 1 Elementary processes Einstein relations
More informationSupporting Information
Supporting Information Improved Working Model for Interpreting the Excitation Wavelength- and Fluence-Dependent Response in Pulsed aser-induced Size Reduction of Aqueous Gold Nanoparticles Daniel Werner
More informationSummary lecture IX. The electron-light Hamilton operator reads in second quantization
Summary lecture IX The electron-light Hamilton operator reads in second quantization Absorption coefficient α(ω) is given by the optical susceptibility Χ(ω) that is determined by microscopic polarization
More informationMany-Body Problems and Quantum Field Theory
Philippe A. Martin Francois Rothen Many-Body Problems and Quantum Field Theory An Introduction Translated by Steven Goldfarb, Andrew Jordan and Samuel Leach Second Edition With 102 Figures, 7 Tables and
More informationScattering of Electromagnetic Radiation. References:
Scattering of Electromagnetic Radiation References: Plasma Diagnostics: Chapter by Kunze Methods of experimental physics, 9a, chapter by Alan Desilva and George Goldenbaum, Edited by Loveberg and Griem.
More informationUsama Anwar. June 29, 2012
June 29, 2012 What is SPR? At optical frequencies metals electron gas can sustain surface and volume charge oscillations with distinct resonance frequencies. We call these as plasmom polaritons or plasmoms.
More informationDEPARTMENT OF PHYSICS UNIVERSITY OF PUNE PUNE SYLLABUS for the M.Phil. (Physics ) Course
DEPARTMENT OF PHYSICS UNIVERSITY OF PUNE PUNE - 411007 SYLLABUS for the M.Phil. (Physics ) Course Each Student will be required to do 3 courses, out of which two are common courses. The third course syllabus
More information5.74 Introductory Quantum Mechanics II
MIT OpenCourseWare http://ocw.mit.edu 5.74 Introductory Quantum Mechanics II Spring 009 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms. Andrei Tokmakoff,
More informationMathematical Pattern of Plasmon Surface Selection Rules According to DrudeModel
International Journal of Recent Research and Review, Vol. X, Issue 1, March 2017 ISSN 2277 8322 Mathematical Pattern of Plasmon Surface Selection Rules According to DrudeModel Raad A. Khamis 1,Hussam N.
More informationSupplementary Figure 1 Schematics of an optical pulse in a nonlinear medium. A Gaussian optical pulse propagates along z-axis in a nonlinear medium
Supplementary Figure 1 Schematics of an optical pulse in a nonlinear medium. A Gaussian optical pulse propagates along z-axis in a nonlinear medium with thickness L. Supplementary Figure Measurement of
More informationNanomaterials and their Optical Applications
Nanomaterials and their Optical Applications Winter Semester 2013 Lecture 02 rachel.grange@uni-jena.de http://www.iap.uni-jena.de/multiphoton Lecture 2: outline 2 Introduction to Nanophotonics Theoretical
More informationThe effect of surface plasmon resonance on optical response in dielectric (core) metal (shell) nanoparticles
PRAMANA c Indian Academy of Sciences Vol. 85, No. 6 journal of December 2015 physics pp. 1245 1255 The effect of surface plasmon resonance on optical response in dielectric (core) metal (shell) nanoparticles
More informationPlasmonics: elementary excitation of a plasma (gas of free charges) nano-scale optics done with plasmons at metal interfaces
Plasmonics Plasmon: Plasmonics: elementary excitation of a plasma (gas of free charges) nano-scale optics done with plasmons at metal interfaces Femius Koenderink Center for Nanophotonics AMOLF, Amsterdam
More informationMASTER OF SCIENCE IN PHYSICS
MASTER OF SCIENCE IN PHYSICS The Master of Science in Physics program aims to develop competent manpower to fill the demands of industry and academe. At the end of the program, the students should have
More informationDiffusion of silver in silicate glass and clustering in hydrogen atmosphere
Defect and Diffusion Forum Vols. 7-4 (5) pp. 689-694 online at http://www.scientific.net 5 Trans Tech Publications, Switzerland Diffusion of silver in silicate glass and clustering in hydrogen atmosphere
More informationLast Lecture. Overview and Introduction. 1. Basic optics and spectroscopy. 2. Lasers. 3. Ultrafast lasers and nonlinear optics
Last Lecture Overview and Introduction 1. Basic optics and spectroscopy. Lasers 3. Ultrafast lasers and nonlinear optics 4. Time-resolved spectroscopy techniques Jigang Wang, Feb, 009 Today 1. Spectroscopy
More informationECE 240a - Notes on Spontaneous Emission within a Cavity
ECE 0a - Notes on Spontaneous Emission within a Cavity Introduction Many treatments of lasers treat the rate of spontaneous emission as specified by the time constant τ sp as a constant that is independent
More informationLocal and regular plasma oscillations in bulk donor type semiconductors
Local and regular plasma oscillations in bulk donor type semiconductors Yuri Kornyushin Maître Jean Brunschvig Research Unit, Chalet Shalva, Randogne, CH-3975 Abstract Restoring force acts on the electronic
More informationNanomaterials and their Optical Applications
Nanomaterials and their Optical Applications Winter Semester 2012 Lecture 04 rachel.grange@uni-jena.de http://www.iap.uni-jena.de/multiphoton Lecture 4: outline 2 Characterization of nanomaterials SEM,
More informationIntroduction to Plasma Physics
Mitglied der Helmholtz-Gemeinschaft Introduction to Plasma Physics CERN School on Plasma Wave Acceleration 24-29 November 2014 Paul Gibbon Outline Lecture 1: Introduction Definitions and Concepts Lecture
More informationSolid State Physics Byungwoo Park Department of Materials Science and Engineering Seoul National University
Solid State Physics Byungwoo Park Department of Materials Science and Engineering Seoul National University http://bp.snu.ac.kr Types of Crystal Binding Kittel, Solid State Physics (Chap. 3) Solid State
More informationOrigin of Optical Enhancement by Metal Nanoparticles. Greg Sun University of Massachusetts Boston
Origin of Optical Enhancement by Metal Nanoparticles Greg Sun University of Massachusetts Boston Nanoplasmonics Space 100pm 1nm 10nm 100nm 1μm 10μm 100μm Photonics 1ns 100ps 10ps 1ps 100fs 10fs 1fs Time
More informationList of Comprehensive Exams Topics
List of Comprehensive Exams Topics Mechanics 1. Basic Mechanics Newton s laws and conservation laws, the virial theorem 2. The Lagrangian and Hamiltonian Formalism The Lagrange formalism and the principle
More informationMacroscopic dielectric theory
Macroscopic dielectric theory Maxwellʼs equations E = 1 c E =4πρ B t B = 4π c J + 1 c B = E t In a medium it is convenient to explicitly introduce induced charges and currents E = 1 B c t D =4πρ H = 4π
More informationSimulating experiments for ultra-intense laser-vacuum interaction
Simulating experiments for ultra-intense laser-vacuum interaction Nina Elkina LMU München, Germany March 11, 2011 Simulating experiments for ultra-intense laser-vacuum interaction March 11, 2011 1 / 23
More information= qe cos(kz ωt). ω sin(αt) This is further averaged over the distribution of initial ( ) α + ω. = 2m k P g(α) sin(αt) g(α) = g(0) + αg (0) + α2 2 g +
6 Landau Damping 61 Physical Picture of Landau Damping Consider a 1-dimensional electrostatic (longitudinal) wave with k E in the absence of magnetic field Taking v = ẑv and E = ẑe cos(kz ωt), the singleparticle
More informationNanoscale Energy Transport and Conversion A Parallel Treatment of Electrons, Molecules, Phonons, and Photons
Nanoscale Energy Transport and Conversion A Parallel Treatment of Electrons, Molecules, Phonons, and Photons Gang Chen Massachusetts Institute of Technology OXFORD UNIVERSITY PRESS 2005 Contents Foreword,
More information(a) Write down the total Hamiltonian of this system, including the spin degree of freedom of the electron, but neglecting spin-orbit interactions.
1. Quantum Mechanics (Spring 2007) Consider a hydrogen atom in a weak uniform magnetic field B = Bê z. (a) Write down the total Hamiltonian of this system, including the spin degree of freedom of the electron,
More informationGeometries and materials for subwavelength surface plasmon modes
Geometries and materials for subwavelength surface plasmon modes Plasmon slot waveguides : Metal-Insulator-Metal (MIM) Metal nanorods and nanotips Metal nanoparticles Metal Dielectric Dielectric Metal
More informationPHYSICS OF HOT DENSE PLASMAS
Chapter 6 PHYSICS OF HOT DENSE PLASMAS 10 26 10 24 Solar Center Electron density (e/cm 3 ) 10 22 10 20 10 18 10 16 10 14 10 12 High pressure arcs Chromosphere Discharge plasmas Solar interior Nd (nω) laserproduced
More informationOptical and Photonic Glasses. Lecture 39. Non-Linear Optical Glasses III Metal Doped Nano-Glasses. Professor Rui Almeida
Optical and Photonic Glasses : Non-Linear Optical Glasses III Metal Doped Nano-Glasses Professor Rui Almeida International Materials Institute For New Functionality in Glass Lehigh University Metal-doped
More information7. FREE ELECTRON THEORY.
7. FREE ELECTRON THEORY. Aim: To introduce the free electron model for the physical properties of metals. It is the simplest theory for these materials, but still gives a very good description of many
More informationxkcd.com It IS about physics. It ALL is.
xkcd.com It IS about physics. It ALL is. Introduction to Space Plasmas! The Plasma State What is a plasma? Basic plasma properties: Qualitative & Quantitative Examples of plasmas! Single particle motion
More informationis the minimum stopping potential for which the current between the plates reduces to zero.
Module 1 :Quantum Mechanics Chapter 2 : Introduction to Quantum ideas Introduction to Quantum ideas We will now consider some experiments and their implications, which introduce us to quantum ideas. The
More informationPhysics of Condensed Matter I
Physics of Condensed Matter I 1100-4INZ`PC Faculty of Physics UW Jacek.Szczytko@fuw.edu.pl Dictionary D = εe ε 0 vacuum permittivity, permittivity of free space (przenikalność elektryczna próżni) ε r relative
More informationDoctor of Philosophy
FEMTOSECOND TIME-DOMAIN SPECTROSCOPY AND NONLINEAR OPTICAL PROPERTIES OF IRON-PNICTIDE SUPERCONDUCTORS AND NANOSYSTEMS A Thesis Submitted for the degree of Doctor of Philosophy IN THE FACULTY OF SCIENCE
More informationIV. Surface analysis for chemical state, chemical composition
IV. Surface analysis for chemical state, chemical composition Probe beam Detect XPS Photon (X-ray) Photoelectron(core level electron) UPS Photon (UV) Photoelectron(valence level electron) AES electron
More informationLong-Wavelength Optical Properties of a Plasmonic Crystal
Long-Wavelength Optical Properties of a Plasmonic Crystal Cheng-ping Huang 1,2, Xiao-gang Yin 1, Qian-jin Wang 1, Huang Huang 1, and Yong-yuan Zhu 1 1 National Laboratory of Solid State Microstructures,
More informationThe Dielectric Function of a Metal ( Jellium )
The Dielectric Function of a Metal ( Jellium ) Total reflection Plasma frequency p (10 15 Hz range) Why are Metals Shiny? An electric field cannot exist inside a metal, because metal electrons follow the
More informationAN EVALUATION OF OPTICAL CONDUCTIVITY OF PROTOTYPE NON-FERMI LIQUID KONDO ALLOYS
Int. J. Chem. Sci.: 10(3), 01, 1419-147 ISSN 097-768X www.sadgurupublications.com AN EVALUATION OF OPTICAL CONDUCTIVITY OF PROTOTYPE NON-FERMI LIQUID KONDO ALLOYS A. K. SINGH * and L. K. MISHRA a Department
More informationElectromagnetism Phys 3230 Exam 2005
Electromagnetism Phys Exam 5 All four questions in Phys should be addressed. If one is not certain in maths, one should try to present explanations in words. 1. Maxwell s equations (5% from 1 given for
More informationEELS, Surface Plasmon and Adsorbate Vibrations
EELS, Surface Plasmon and Adsorbate Vibrations Ao Teng 2010.10.11 Outline I. Electron Energy Loss Spectroscopy(EELS) and High Resolution EELS (HREELS) II. Surface Plasmon III. Adsorbate Vibrations Surface
More informationIntroduction. Chapter Plasma: definitions
Chapter 1 Introduction 1.1 Plasma: definitions A plasma is a quasi-neutral gas of charged and neutral particles which exhibits collective behaviour. An equivalent, alternative definition: A plasma is a
More informationxkcd.com It IS about physics. It ALL is.
xkcd.com It IS about physics. It ALL is. Introduction to Space Plasmas The Plasma State What is a plasma? Basic plasma properties: Qualitative & Quantitative Examples of plasmas Single particle motion
More information4 Electric Fields in Matter
4 Electric Fields in Matter 4.1 Parity and Time Reversal: Lecture 10 (a) We discussed how fields transform under parity and time reversal. A useful table is Quantity Parity Time Reversal t Even Odd r Odd
More informationFourier transforms, Generalised functions and Greens functions
Fourier transforms, Generalised functions and Greens functions T. Johnson 2015-01-23 Electromagnetic Processes In Dispersive Media, Lecture 2 - T. Johnson 1 Motivation A big part of this course concerns
More informationLecture 10 Light-Matter Interaction Part 4 Surface Polaritons 2. EECS Winter 2006 Nanophotonics and Nano-scale Fabrication P.C.
Lecture 10 Light-Matter Interaction Part 4 Surface Polaritons 2 EECS 598-002 Winter 2006 Nanophotonics and Nano-scale Fabrication P.C.Ku Schedule for the rest of the semester Introduction to light-matter
More information3 Constitutive Relations: Macroscopic Properties of Matter
EECS 53 Lecture 3 c Kamal Sarabandi Fall 21 All rights reserved 3 Constitutive Relations: Macroscopic Properties of Matter As shown previously, out of the four Maxwell s equations only the Faraday s and
More information(002)(110) (004)(220) (222) (112) (211) (202) (200) * * 2θ (degree)
Supplementary Figures. (002)(110) Tetragonal I4/mcm Intensity (a.u) (004)(220) 10 (112) (211) (202) 20 Supplementary Figure 1. X-ray diffraction (XRD) pattern of the sample. The XRD characterization indicates
More informationPHYSICS (PHYS) Physics (PHYS) 1. PHYS 5880 Astrophysics Laboratory
Physics (PHYS) 1 PHYSICS (PHYS) PHYS 5210 Theoretical Mechanics Kinematics and dynamics of particles and rigid bodies. Lagrangian and Hamiltonian equations of motion. PHYS 5230 Classical Electricity And
More informationLecture 21 Reminder/Introduction to Wave Optics
Lecture 1 Reminder/Introduction to Wave Optics Program: 1. Maxwell s Equations.. Magnetic induction and electric displacement. 3. Origins of the electric permittivity and magnetic permeability. 4. Wave
More informationNanoscale antennas. Said R. K. Rodriguez 24/04/2018
Nanoscale antennas Said R. K. Rodriguez 24/04/2018 The problem with nanoscale optics How to interface light emitters & receivers with plane waves? Ε ii(kkkk ωωωω) ~1-10 nm ~400-800 nm What is an antenna?
More informationCondensed matter theory Lecture notes and problem sets 2012/2013
Condensed matter theory Lecture notes and problem sets 2012/2013 Dmitri Ivanov Recommended books and lecture notes: [AM] N. W. Ashcroft and N. D. Mermin, Solid State Physics. [Mar] M. P. Marder, Condensed
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 informationBasics of electromagnetic response of materials
Basics of electromagnetic response of materials Microscopic electric and magnetic field Let s point charge q moving with velocity v in fields e and b Force on q: F e F qeqvb F m Lorenz force Microscopic
More informationIntroduction to Nonlinear Optics
Introduction to Nonlinear Optics Prof. Cleber R. Mendonca http://www.fotonica.ifsc.usp.br Outline Linear optics Introduction to nonlinear optics Second order nonlinearities Third order nonlinearities Two-photon
More informationCLASSICAL ELECTRICITY
CLASSICAL ELECTRICITY AND MAGNETISM by WOLFGANG K. H. PANOFSKY Stanford University and MELBA PHILLIPS Washington University SECOND EDITION ADDISON-WESLEY PUBLISHING COMPANY Reading, Massachusetts Menlo
More informationLecture 10: Surface Plasmon Excitation. 5 nm
Excitation Lecture 10: Surface Plasmon Excitation 5 nm Summary The dispersion relation for surface plasmons Useful for describing plasmon excitation & propagation This lecture: p sp Coupling light to surface
More informationTheoretical Photochemistry WiSe 2016/17
Theoretical Photochemistry WiSe 2016/17 Lecture 8 Irene Burghardt burghardt@chemie.uni-frankfurt.de) http://www.theochem.uni-frankfurt.de/teaching/ Theoretical Photochemistry 1 Topics 1. Photophysical
More informationSupplementary Figure 1
Supplementary Figure 1 XRD patterns and TEM image of the SrNbO 3 film grown on LaAlO 3(001) substrate. The film was deposited under oxygen partial pressure of 5 10-6 Torr. (a) θ-2θ scan, where * indicates
More informationAdvanced Spectroscopies of Modern Quantum Materials
Advanced Spectroscopies of Modern Quantum Materials The part about Advanced spectroscopies Some course goals: Better understand the link between experiment and the microscopic world of quantum materials.
More informationLaser Induced Control of Condensed Phase Electron Transfer
Laser Induced Control of Condensed Phase Electron Transfer Rob D. Coalson, Dept. of Chemistry, Univ. of Pittsburgh Yuri Dakhnovskii, Dept. of Physics, Univ. of Wyoming Deborah G. Evans, Dept. of Chemistry,
More informationPlasmonic properties and sizing of core-shell Cu-Cu 2 O nanoparticles fabricated by femtosecond laser ablation in liquids ABSTRACT
Plasmonic properties and sizing of core-shell Cu-Cu O nanoparticles fabricated by femtosecond laser ablation in liquids J. M. J. Santillán 1, F. A. Videla 1,, D. C. Schinca 1, and L. B. Scaffardi 1, 1
More information