Frequency Doubling and Second Order Nonlinear Optics

Size: px
Start display at page:

Download "Frequency Doubling and Second Order Nonlinear Optics"

Transcription

1 Frequency Doubling and Second Order Nonlinear Optics Paul M. Petersen DTU Fotonik, Risø campus Technical University of Denmark, Denmark (

2 Outline of the talk The first observation of second harmonic generation Nonlinear optical effects in solids The nonlinear wave equation (formulation of the interaction in nonlinear materials) Second order nonlinear optics Contracted notation for the second order susceptibility Three wave mixing Frequency doubling Phase matching in materials with birefringence

3 The first observation of second harmonic generation Second harmonic generation (SHG) was first demonstrated by P. A. Franken et al. at the University of Michigan in They focused a ruby laser with a wavelength of 694 nm into a quartz sample. They sent the output light through a spectrometer and recording the spectrum on photographic paper, which indicated the production of light at 347 nm. (Note that the SHG spot does not appear in the publication!)

4 Conversion of red lasers into blue lasers

5 Generation of new waves in a nonlinear medium Light interacts with the nonlinear medium. The incident beams are modified and new beams are generated.

6 Optical Polarisation induced in Solids The optical electrical field induces electrical dipole moments in the nonlinear material. The induced dipoles modify the incident beam and for strong optical fields leads to the generation of new k-vectors and new frequencies. P is the dipole moment per unit volume. The optical field vector The induced dipoles represents accelerating charged particles that radiates electromagnetic radiation perpendicular to the acceleration vector.

7 Second Order Nonlinear Polarization The relation between the induced optical polarisation in the material and the electric field. a) In a linear material b) In a crystal without inversion symmetry. The optical polarisation induced by an applied sinussoidal electric field with frequency ω. The polarisation consists of three contributions with frequencies ω, ω and 0 (dc-term)

8 Nonlinear Optical Effects in Solids The nonlinear optical effects are described by the polarization: (1) () (3) ε ε χ χ χ D = E + P, P( E) = ( E + E E + 4 E E E + ) 0 i 0 ij j ijk j k ijkl j k l Linear optics is described by χ ij (1) : The optical properties are independent of the light intensity The frequency of light does not change due to interaction with light The principle of superposion is valid Nonlinear optics is described by χ ijk () and χ ijkl (3) Light can interact with light The principle of superposion is not valid New waves with new k-vectors and new frequencies are generated

9 Nonlinear Optical Effects in Solids The nonlinear optical effects are described by the polarization: D = ε E + P P E = ε χ E + χ E E + χ E E E + (1) () (3) 0, i ( ) ( 0 ij j ijk j k 4 ijkl j k l ) χ (1) ij describes the linear 1. order optical properties: absorption (α) and refraction (n) χ () ijk describes the. order nonlinearities: frequency doubling, electro-optic effect, and parametric oscillation, etc. χ (3) ijkl describes 3. order nonlinearities: quadratic kerr effect, intensity-dependent refractive index, four-wave mixing, self-focusing, etc.

10 Quantum mechanical determination of the susceptibility χ The material response is given by the polarization: iωt iωt P( t) = ½ ε E{ χ( ω) e + χ( ω) e } 0 (1) The susceptibility χ(ω) may be determined by calculating P(t) quantum mechanically and then determine χ(ω) by comparison with Eq.(1). The macroscopic polarization with N atoms in a volume V is: P( t) = Nd( t) / V Where the electric dipole moment is ( ) = Ψ( ) Ψ( ) 3 z, X= x j j=1 d t t ex t d r

11 Formulation of the interaction in nonlinear materials The Maxwell equations: D H H = J +, E=- µ 0, t t D= ε E + P, J = σ E lead to: the nonlinear wave equation The nonlinear polarization term P NL leads to the generation of new waves with new k-vectors, polarization, and frequencies: For a new wave: 0 NL E E P E = µ 0σ + µ 0ε0ε + µ 0 t t t E z t Ae c c i( ωit ki z) i (, ) = ½ i +.. the nonlinear wave equation reduces (SVEA-approximation) to: dai 1 µ µ e + c. c. = σ Ae + c. c. + i dz i( ωit ki z) 0 i( ωit kiz) 0 1 i i ωi ε 0εi ε 0εi P t NL

12 The nonlinear wave equation dai 1 µ µ e + c. c. = σ Ae + c. c. + i dz i( ωit ki z) 0 i( ωit ki z) 0 1 i i ωi ε 0εi ε 0εi P t NL This is the fundamental equation that governs the generation of a i( ωit kiz) new wave E ( z, t) = ½ Ae + c. c. i i

13 Second Order Nonlinear Optics The interaction between light and matter is given by: where P E E E E E E E (1) () (3) i ( ) = ( ε 0χij j + χijk j k + 4 χijkl j k l + ) P ( ), E = χ E E () i NL ijk j k describes the second order nonlinearities. The notation χ = d () ijk ijk is often used in the literature where d ijk is a third order tensor. with 7 elements.

14 Contracted Notation for the Second Order Susceptibility P ( ), E = d E E i NL ijk j k where χ = d () ijk ijk since d ijk = d ikj The third order tensor may be represented by a (3x6) matrix: d with 18 elements. il d11 K d16 = M O M d31 a L 36

15 Generation of new waves using second order nonlinearities Sum frequency generation Second harmonic generation ω 1, ω ω 1 + ω Nonlinear crystal ω, ω Difference frequency generation Nonlinear crystal ω Optical parametric oscillator (OPO) Nonlinear crystal ω 1, ω ω 1 -ω Nonlinear ω crystal ω pump signal, ω idler M M

16 Three Wave Mixing Two waves E(ω 1 ) and E(ω ) may due to the interaction with the second order nonlinear polarization generate a third beam E(ω 3 ) ω 1, ω ω 1, ω, ω 3 Nonlinear crystal The three waves are given by: E A e c c E A e c c E A e c c i ( ω1t + k1z ) i ( ωt+ k z ) i( ω3t + k3z) ( ω ) = ½ +.., ( ω ) = ½ +.., ( ω ) = ½ where we have assumed all waves to be polarized in the same direction. For the three waves the nonlinear wave Equation reduces to: da1 µ σ c iω µ αdc = A A A e dz n n * da µ σ c iω µ αdc = A A A e dz n n 0 0 * 3 1 da µ σ c iω µ αdc = A A A e dz n n where k=k 3 -k 1 -k, α= (- δ ω1 ω )/, and where we have used (δ ω1 ω =1 for ω 1 = ω and δ ω1 ω =0 for ω 1 #ω ) i kz i kz i kz ' The fundamental equations that describes second order nonlinear interaction. µ 0 µ 0c ε ε = n 0 i 3

17 Frequency doubling ω 1 = ω, ω = ω ω, ω 3 =ω Nonlinear crystal The fundamental equation da c i dc = µ σ A ω µ α A A e dz n n i kz reduces to: da( ω) dz iωµ 0dc = n( ω) A ( ω) e i kz where absorption is neglected. If we assume that A 1 =A =A(ω) is undepleted we obtain the second harmonic intensity: 3 3 µ c 0 ω d sin( kl / ) = L I ω I( ω) ( ) n ( ω) n( ω) kl / where L is the length of the nonlinear crystal.

18 Phase matching in materials with birefringence Strong SHG signals are obtained when : ω k=k3-k1-k =k3-k 1 = ( n( ω) n( ω)) = 0 c Phase matching condition It was suggested independently by Giordmaine(ref.1) and Maker et al(ref.)) that index matching may be obtained in birefractive crystals by correct choice of polarisation and angle θ of propagation. The intersection defines the propagation direction. In Ref. phase matching in KDP with an 300-fold increase of blue light intensity was observed in 196 Ref.1: J.A.Giordmaine, Phys. Rev. Letters, 8, 19(196); Ref: P. Maker et. al, Phys. Rev. Letters, 8, 1(196),

19 Type I and II phase matching Type I phase matching: The refractive index of an extraordinary beam is given by: ne ( θ ) = n0 Phase matching is obtained in negative uniaxial crystals (n e <n 0 ) when sin e n e n n o e θ + n cos ( ω, θ ) = n m θ 0 Type II phase matching: In this case the fundamental beam ω consist of both an ordinary beam and an extraordinary beam and in this configuration the beam at ω fulfils the condition: n ( θ, ω) = ½( n ( θ, ω) + n ( ω)) e m e m and the frequency doubled beam will be an extraordinary beam 0

20 Suggested further reading: Nonlinear Optics by R. W. Boyd Academic Press Optical Electronics in Modern Communications by A. Yariv, Oxford University Press The Principles of Nonlinear Optics by Y. R. Shen, Wiley

The simplest implementation is the placing a crystal in the extra-cavity configuration:

The simplest implementation is the placing a crystal in the extra-cavity configuration: Non-Linear optics Lecture 4: Practical SHG and an introduction to χ 3 processes. Learning goals At the end of this lecture you should be able to: Understand and explain intra- and extra-cavity SHG techniques.

More information

The Role of Electric Polarization in Nonlinear optics

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

More information

Coupled Mode Analysis

Coupled Mode Analysis Coupled Mode Analysis Chapter 4 Physics 208, Electro-optics Peter Beyersdorf Document info Ch 4, 1 Class Outline The dielectric tensor Plane wave propagation in anisotropic media The index ellipsoid Phase

More information

Polarized and unpolarised transverse waves

Polarized and unpolarised transverse waves Polarized and unpolarised transverse waves T. Johnson 3-0-5 Electromagnetic Processes In Dispersive Media, Lecture 6 The quarter wave plate Outline Set up coordinate system suitable for transverse waves

More information

Today in Physics 218: dispersion

Today in Physics 218: dispersion Today in Physics 18: dispersion Motion of bound electrons in matter, and the frequency dependence of the dielectric constant Dispersion relations Ordinary and anomalous dispersion The world s largest-selling

More information

Nonlinear Optics Basics: Kramers-Krönig Relations in Nonlinear Optics

Nonlinear Optics Basics: Kramers-Krönig Relations in Nonlinear Optics Nonlinear Optics Basics: Kramers-Krönig Relations in Nonlinear Optics Mansoor Sheik-Bahae Department of Physics and Astronomy and Department of Electrical and Computer Engineering University of New Mexico,

More information

ENERGY METEOROLOGY. UNIT 1: Basics of Radiation. Energy transfer through radiation. Concept of blackbody radiation, Kirchhoff s law

ENERGY METEOROLOGY. UNIT 1: Basics of Radiation. Energy transfer through radiation. Concept of blackbody radiation, Kirchhoff s law UNIT 1: Basics of Radiation Energy transfer through radiation Concept of blackbody radiation, Kirchhoff s law Radiation laws of Planck, Stefan-Boltzmann and Wien Radiation quantities Examples Radiative

More information

Chapter 35. Electromagnetic Fields and Waves

Chapter 35. Electromagnetic Fields and Waves Chapter 35. Electromagnetic Fields and Waves To understand a laser beam, we need to know how electric and magnetic fields change with time. Examples of timedependent electromagnetic phenomena include highspeed

More information

Generation and Application of Terahertz Pulses

Generation and Application of Terahertz Pulses Preparation of the concerne sectors for eucational an R&D activities relate to the Hungarian ELI project Generation an Application of Terahertz Pulses János Hebling Márta Unferorben TÁMOP-4...C-//KONV--5

More information

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

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

More information

Multipole Theory in Electromagnetism

Multipole Theory in Electromagnetism Multipole Theory in Electromagnetism Classical, quantum, and symmetry aspects, with applications R. E. RAAB О. L. DE LANGE School of Chemical and Physical Sciences, University of Natal, Pietermaritzburg,

More information

Frequency doubling of He Ne laser radiation at nm

Frequency doubling of He Ne laser radiation at nm Pure Appl. Opt. 5 (1996) 119 124. Printed in the UK Frequency doubling of He Ne laser radiation at 632.8 nm R Stoleru, M L Pascu and A M Dumitras Institute of Atomic Physics, Laser Department, PO Box MG-6,

More information

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

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

More information

Electromagnetic Waves

Electromagnetic Waves May 4, 2010 1 1 J.D.Jackson, Classical Electrodynamics, 2nd Edition, Section 7 Maxwell Equations A basic feature of Maxwell equations for the EM field is the existence of travelling wave solutions which

More information

April 15. Physics 272. Spring Prof. Philip von Doetinchem

April 15. Physics 272. Spring Prof. Philip von Doetinchem Physics 272 April 15 Spring 2014 http://www.phys.hawaii.edu/~philipvd/pvd_14_spring_272_uhm.html Prof. Philip von Doetinchem philipvd@hawaii.edu Phys272 - Spring 14 - von Doetinchem - 291 Lunar eclipse

More information

Electromagnetic Radiation

Electromagnetic Radiation Electromagnetic Radiation Wave - a traveling disturbance, e.g., displacement of water surface (water waves), string (waves on a string), or position of air molecules (sound waves). [ π λ ] h = h sin (

More information

We consider a hydrogen atom in the ground state in the uniform electric field

We consider a hydrogen atom in the ground state in the uniform electric field Lecture 13 Page 1 Lectures 13-14 Hydrogen atom in electric field. Quadratic Stark effect. Atomic polarizability. Emission and Absorption of Electromagnetic Radiation by Atoms Transition probabilities and

More information

Lecture- POLARISATION Unit-02 02

Lecture- POLARISATION Unit-02 02 Lecture- 02 POLARISATION Unit-02 CONTENTS POLARISATION BY REFRACTION Optic Axis Principal Section of a Crystal Geometry of Calcite Crystal Geometry of Calcite Crystal POLARISATION BY REFRACTION Polarisation

More information

Bloch waves and Bandgaps

Bloch waves and Bandgaps Bloch waves and Bandgaps Chapter 6 Physics 208, Electro-optics Peter Beyersdorf Document info Ch 6, 1 Bloch Waves There are various classes of boundary conditions for which solutions to the wave equation

More information

THE MAGNETO TELLURIC (MT) METHOD

THE MAGNETO TELLURIC (MT) METHOD Presented at Short Course II on Surface Exploration for Geothermal Resources, organized by UNU-GTP and KenGen, at Lake Naivasha, Kenya, -17 November, 007. THE MAGNETO TELLURIC (MT METHOD Knútur Árnason

More information

sinusoidal electromagnetic waves

sinusoidal electromagnetic waves CH32: Electromagnetic Waves Maxwell s equations and electromagnetic waves sinusoidal electromagnetic waves Passage of electromagnetic waves through matter Energy and momentum of electromagnetic waves *(Not

More information

Thomson and Rayleigh Scattering

Thomson 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 information

Acousto-optic modulator

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

More information

Fermi s Golden Rule. Emmanuel N. Koukaras A.M.: 198

Fermi s Golden Rule. Emmanuel N. Koukaras A.M.: 198 Fermi s Golden Rule Emmanuel N. Kouaras A.M.: 198 Abstract We present a proof of Fermi s Golden rule from an educational perspective without compromising formalism. 2 1. Introduction Fermi s Golden Rule

More information

UNIVERSITY OF PAVIA NONLINEAR OPTICAL PROPERTIES OF PLANAR MICROCAVITIES AND PHOTONIC CRYSTAL SLABS

UNIVERSITY OF PAVIA NONLINEAR OPTICAL PROPERTIES OF PLANAR MICROCAVITIES AND PHOTONIC CRYSTAL SLABS UNIVERSITY OF PAVIA DEPARTMENT OF PHYSICS ALESSANDRO VOLTA Dottorato di Ricerca in Fisica XVIII ciclo NONLINEAR OPTICAL PROPERTIES OF PLANAR MICROCAVITIES AND PHOTONIC CRYSTAL SLABS Doctoral thesis by

More information

The Theory of Birefringence

The Theory of Birefringence Birefringence spectroscopy is the optical technique of measuring orientation in an optically anisotropic sample by measuring the retardation of polarized light passing through the sample. Birefringence

More information

( ) = Aexp( iωt ) will look like: = c n R. = ω k R. v p

( ) = Aexp( iωt ) will look like: = c n R. = ω k R. v p Phase Velocity vs. Group Velocity We should perhaps be (at least) a little bit disturbed that the real part of the index of refraction can be less than 1 for some frequencies. When we re working with just

More information

PHYS-2020: General Physics II Course Lecture Notes Section XIII

PHYS-2020: General Physics II Course Lecture Notes Section XIII PHYS-2020: General Physics II Course Lecture Notes Section XIII Dr. Donald G. Luttermoser East Tennessee State University Edition 4.0 Abstract These class notes are designed for use of the instructor and

More information

Lab 8: Polarization of Light

Lab 8: Polarization of Light Lab 8: Polarization of Light 1 Introduction Refer to Appendix D for photos of the apparatus Polarization is a fundamental property of light and a very important concept of physical optics. Not all sources

More information

UNIT 28: ELECTROMAGNETIC WAVES AND POLARIZATION Approximate Time Three 100-minute Sessions

UNIT 28: ELECTROMAGNETIC WAVES AND POLARIZATION Approximate Time Three 100-minute Sessions Name St.No. - Date(YY/MM/DD) / / Section Group # UNIT 28: ELECTROMAGNETIC WAVES AND POLARIZATION Approximate Time Three 100-minute Sessions Hey diddle diddle, what kind of riddle Is this nature of light?

More information

Polarization of Light

Polarization of Light Polarization of Light Thursday, 11/09/2006 Physics 158 Peter Beyersdorf Document info 1 Class Outline Polarization of Light Polarization basis Jones Calculus 16. 2 Polarization The Electric field direction

More information

linearly polarized with polarization axis parallel to the transmission axis of the polarizer.

linearly polarized with polarization axis parallel to the transmission axis of the polarizer. Polarization Light is a transverse wave: the electric and magnetic fields both oscillate along axes that are perpendicular to the direction of wave motion. The simplest kind of radiation is said to be

More information

Stefan Prorok (Autor) Hybrid Silicon-Organic Resonators for Optical Modulation and Filtering

Stefan Prorok (Autor) Hybrid Silicon-Organic Resonators for Optical Modulation and Filtering Stefan Prorok (Autor) Hybrid Silicon-Organic Resonators for Optical Modulation and Filtering https://cuvillier.de/de/shop/publications/6929 Copyright: Cuvillier Verlag, Inhaberin Annette Jentzsch-Cuvillier,

More information

Design and Simulation of DPSS Laser with SHG for Material Processing

Design and Simulation of DPSS Laser with SHG for Material Processing IJAPLett Vol., No. 1, January-March 9 Aseel A. AlSharify Department of Laser and Optoelectronics Engineering, University of Technology, Baghdad, Iraq Design and Simulation of DPSS Laser with SHG for Material

More information

arxiv:cond-mat/ v3 11 Feb 1998

arxiv:cond-mat/ v3 11 Feb 1998 Maxwell-Schrödinger Equation for Polarized Light and Evolution of the Stokes Parameters Hiroshi Kuratsuji and Shouhei Kakigi Department of Physics, Ritsumeikan University-BKC, Kusatsu City 55-8577, Japan

More information

Constructive vs. destructive interference; Coherent vs. incoherent interference

Constructive vs. destructive interference; Coherent vs. incoherent interference Constructive vs. destructive interference; Coherent vs. incoherent interference Waves that combine in phase add up to relatively high irradiance. = Constructive interference (coherent) Waves that combine

More information

Third harmonic frequency generation by Type-I critically phase-matched LiB 3 O 5 crystal by means of optically active quartz crystal

Third harmonic frequency generation by Type-I critically phase-matched LiB 3 O 5 crystal by means of optically active quartz crystal Third harmonic frequency generation by Type-I critically phase-matched LiB 3 O 5 crystal by means of optically active quartz crystal Valentin P. Gapontsev, 1,2 Valentin A. Tyrtyshnyy, 1 Oleg I. Vershinin,

More information

Physics 53. Wave Motion 1

Physics 53. Wave Motion 1 Physics 53 Wave Motion 1 It's just a job. Grass grows, waves pound the sand, I beat people up. Muhammad Ali Overview To transport energy, momentum or angular momentum from one place to another, one can

More information

EXPERIMENT 9 Diffraction Gratings

EXPERIMENT 9 Diffraction Gratings EXPERIMENT 9 Diffraction Gratings 1. How a Diffraction Grating works? Diffraction gratings are optical components with a period modulation on its surface. Either the transmission (or the phase) changes

More information

How to Select a Waveplate

How to Select a Waveplate How to Select a Waveplate A wave retarder is a component that resolves a light wave into two orthogonal polarization components and produces a phase shift between them. The resulting difference in phase

More information

Interference with monochromatic light

Interference with monochromatic light Interference with monochromatic light H. O. Tittel Two beam interference. Division of amplitude For interference at least two beams are needed. Two special situations of interference: two beam interference

More information

Dispersion and Prism

Dispersion and Prism Pre-lab Quiz/PHYS 224 Dispersion and Prism Your name Lab section 1. What do we investigate in this lab? 2. Describe Snell s Law and draw a diagram. 3. As shown in Figure 4, the specific angle of the prism

More information

1. Basics of LASER Physics

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

More information

0.1 Dielectric Slab Waveguide

0.1 Dielectric Slab Waveguide 0.1 Dielectric Slab Waveguide At high frequencies (especially optical frequencies) the loss associated with the induced current in the metal walls is too high. A transmission line filled with dielectric

More information

GRAVITATIONAL FARADAY EFFECT PRODUCED BY A RING LASER

GRAVITATIONAL FARADAY EFFECT PRODUCED BY A RING LASER GRAVITATIONAL FARADAY EFFECT PRODUCED BY A RING LASER DAVID ERIC COX, JAMES G. O BRIEN, RONALD L. MALLETT, AND CHANDRA ROYCHOUDHURI Using the linearized Einstein gravitational field equations and the Maxwell

More information

1D Cubic NLS (CNLS) and Cubic-Quintic NLS (CQNLS)

1D Cubic NLS (CNLS) and Cubic-Quintic NLS (CQNLS) 1D Cubic NLS (CNLS) and Cubic-Quintic NLS (CQNLS) Marcello Sani December 5, 2006 Contents Introduction Physical applications of the CNLS From the Sine-Gordon to the 1D CNLS Single soliton solution for

More information

Lecture 2: Interference

Lecture 2: Interference Lecture 2: Interference λ S 1 d S 2 Lecture 2, p.1 Today Interference of sound waves Two-slit interference Lecture 2, p.2 Review: Wave Summary ( ) ( ) The formula y x,t = Acos kx ωt describes a harmonic

More information

Symbols, conversions, and atomic units

Symbols, conversions, and atomic units Appendix C Symbols, conversions, and atomic units This appendix provides a tabulation of all symbols used throughout this thesis, as well as conversion units that may useful for reference while comparing

More information

Thomson and Rayleigh Scattering

Thomson 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 information

Electromagnetically induced transparency and its dispersion properties in a four-level inverted-y atomic system

Electromagnetically induced transparency and its dispersion properties in a four-level inverted-y atomic system Physics Letters A 317 (2003) 370 377 www.elsevier.com/locate/pla Electromagnetically induced transparency and its dispersion properties in a four-level inverted-y atomic system Amitabh Joshi, Min Xiao

More information

How can I tell what the polarization axis is for a linear polarizer?

How can I tell what the polarization axis is for a linear polarizer? How can I tell what the polarization axis is for a linear polarizer? The axis of a linear polarizer determines the plane of polarization that the polarizer passes. There are two ways of finding the axis

More information

I. MOLECULAR MECHANICS (MM): A CLASSICAL DESCRIPTION OF MOLECULES. A. The conceptual and chemical basis

I. MOLECULAR MECHANICS (MM): A CLASSICAL DESCRIPTION OF MOLECULES. A. The conceptual and chemical basis 2 I. MOLECULAR MECHANICS (MM): A CLASSICAL DESCRIPTION OF MOLECULES A. The conceptual and chemical basis Chemical bonding is a genuinely quantum effect, which cannot be understood on the grounds of classical

More information

Young s Double Slit Experiment Now consider 2 slits width b Separated by space a (centre to centre of slits) Now the pattern created by one slit

Young s Double Slit Experiment Now consider 2 slits width b Separated by space a (centre to centre of slits) Now the pattern created by one slit Young s Double Slit Experiment Now consider 2 slits width b Separated by space a (centre to centre of slits) Now the pattern created by one slit creates interference with other Double Slit Interference

More information

6.1 Electromagnetic Waves

6.1 Electromagnetic Waves 6.1 Electromagnetic Waves electromagnetic radiation can be described as a harmonic wave in either time or distance waves are characterized by their period, frequency, wavelength and wave number Planck's

More information

Fermi s golden rule. 1 Main results

Fermi s golden rule. 1 Main results Fermi s golden rule Andreas Wacker 1 Mathematical Physics, Lund University October 1, 216 Fermi s golden rule 2 is a simple expression for the transition probabilities between states of a quantum system,

More information

Solving the Harmonic Oscillator Equation. Morgan Root NCSU Department of Math

Solving the Harmonic Oscillator Equation. Morgan Root NCSU Department of Math Solving the Harmonic Oscillator Equation Morgan Root NCSU Department of Math Spring-Mass System Consider a mass attached to a wall by means of a spring. Define y to be the equilibrium position of the block.

More information

Modeling solids: Finite Element Methods

Modeling solids: Finite Element Methods Chapter 9 Modeling solids: Finite Element Methods NOTE: I found errors in some of the equations for the shear stress. I will correct them later. The static and time-dependent modeling of solids is different

More information

- thus, the total number of atoms per second that absorb a photon is

- 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 information

Optical Design of Lares Retroreflector Array

Optical Design of Lares Retroreflector Array Optical Design of Lares Retroreflector Array 1. Introduction 2. Retroreflection 3. Diffraction pattern of cube corner 4. Lares cross section 5. Effect of thermal gradients 6. Velocity aberration 7. Range

More information

Physics 53. Rotational Motion 1. We're going to turn this team around 360 degrees. Jason Kidd

Physics 53. Rotational Motion 1. We're going to turn this team around 360 degrees. Jason Kidd Physics 53 Rotational Motion 1 We're going to turn this team around 360 degrees. Jason Kidd Rigid bodies To a good approximation, a solid object behaves like a perfectly rigid body, in which each particle

More information

Spectroscopic Notation

Spectroscopic Notation Spectroscopic Notation Most of the information we have about the universe comes to us via emission lines. However, before we can begin to understand how emission lines are formed and what they tell us,

More information

Chapter 24. Wave Optics

Chapter 24. Wave Optics Chapter 24 Wave Optics Wave Optics The wave nature of light is needed to explain various phenomena. Interference Diffraction Polarization The particle nature of light was the basis for ray (geometric)

More information

From Einstein to Klein-Gordon Quantum Mechanics and Relativity

From Einstein to Klein-Gordon Quantum Mechanics and Relativity From Einstein to Klein-Gordon Quantum Mechanics and Relativity Aline Ribeiro Department of Mathematics University of Toronto March 24, 2002 Abstract We study the development from Einstein s relativistic

More information

Ch 24 Wave Optics. concept questions #8, 11 problems #1, 3, 9, 15, 19, 31, 45, 48, 53

Ch 24 Wave Optics. concept questions #8, 11 problems #1, 3, 9, 15, 19, 31, 45, 48, 53 Ch 24 Wave Optics concept questions #8, 11 problems #1, 3, 9, 15, 19, 31, 45, 48, 53 Light is a wave so interference can occur. Interference effects for light are not easy to observe because of the short

More information

Spectral Imaging by Upconversion

Spectral Imaging by Upconversion 35 Spectral Imaging by Upconversion Jeppe Seidelin Dam 1, Christian Pedersen 1 and Peter Tidemand-Lichtenberg 1, 1 DTU Fotonik, Deparment of Photonics Engineering, Frederiksborgvej 399, 4000 Roskilde,

More information

Stress Optics laboratory practice guide 2012

Stress Optics laboratory practice guide 2012 Stress Optics laboratory practice guide 2012 Transparent materials having internal mechanical stress are found to be birefringent, due to their anisotropic nature. That is, they demonstrate double refraction

More information

Electromagnetic Waves and Polarization

Electromagnetic Waves and Polarization Electromagnetic Waves and Polarization Physics 2415 Lecture 30 Michael Fowler, UVa Today s Topics Measuring the speed of light Wave energy and power: the Poynting vector Light momentum and radiation pressure

More information

University of Illinois at Chicago Department of Physics. Electricity and Magnetism PhD Qualifying Examination

University of Illinois at Chicago Department of Physics. Electricity and Magnetism PhD Qualifying Examination University of Illinois at Chicago Department of Physics Electricity and Magnetism PhD Qualifying Examination January 6, 2015 9.00 am 12:00 pm Full credit can be achieved from completely correct answers

More information

Introduction to Crystal Symmetry and Raman Spectroscopy

Introduction to Crystal Symmetry and Raman Spectroscopy Introduction to Crystal Symmetry and Raman Spectroscopy José A. Flores Livas Thursday 13 th December, 2012 1 of 30 Outline Introduction to Raman spectroscopy Symmetry of crystals and normal modes Experimental

More information

Small oscillations with many degrees of freedom

Small oscillations with many degrees of freedom Analytical Dynamics - Graduate Center CUNY - Fall 007 Professor Dmitry Garanin Small oscillations with many degrees of freedom General formalism Consider a dynamical system with N degrees of freedom near

More information

wavelength λ Amplitude of the wave A λ crest A trough observer speed of the wave v Period of the wave P λ = v P frequency f, f = 1/P v =λ f

wavelength λ Amplitude of the wave A λ crest A trough observer speed of the wave v Period of the wave P λ = v P frequency f, f = 1/P v =λ f Waves Traveling waves: Traveling, periodic, sinusoidal (Shaped like a mathematical sine wave) water waves, sound waves, electromagnetic waves, and others, share certain features shown in the figure. The

More information

Elasticity and Equations of State

Elasticity and Equations of State Elasticity and Equations of State The way planets deform depends primarily upon the elastic properties of the constituent polycrystalline materials. In particular, the speed of body waves passing through

More information

Andrea Borghese The role of photons in Supergravity

Andrea Borghese The role of photons in Supergravity Based on: A.B., A.Guarino, D.Roest, [1209.3003] A.B., G.Dibitetto, A.Guarino, D.Roest, O.Varela, [1211.5335] A.B., A.Guarino, D.Roest, [1302.5067] PLAN Describe the spin-1 sector in supergravity theories

More information

Verdet Constant Measurement of Olive Oil for Magnetic Field Sensor

Verdet Constant Measurement of Olive Oil for Magnetic Field Sensor International Journal of Advances in Electrical and Electronics Engineering 362 Available online at www.ijaeee.com& www.sestindia.org/volume-ijaeee ISSN: 2319-1112 Verdet Constant Measurement of Olive

More information

- the total energy of the system is found by summing up (integrating) over all particles n(ε) at different energies ε

- the total energy of the system is found by summing up (integrating) over all particles n(ε) at different energies ε Average Particle Energy in an Ideal Gas - the total energy of the system is found by summing up (integrating) over all particles n(ε) at different energies ε - with the integral - we find - note: - the

More information

Satellite Remote Sensing SIO 135/SIO 236. Electromagnetic Radiation and Polarization

Satellite Remote Sensing SIO 135/SIO 236. Electromagnetic Radiation and Polarization Satellite Remote Sensing SIO 135/SIO 236 Electromagnetic Radiation and Polarization 1 Electromagnetic Radiation Models «To understand the interaction that the EMR undergoes before it reaches the sensor,

More information

MICROWAVE OPTICS THE MEASUREMENTS OF THE WAVELENGTH OF THE MICROWAVES BASED ON THE INTERFERENTIAL METHODS.

MICROWAVE OPTICS THE MEASUREMENTS OF THE WAVELENGTH OF THE MICROWAVES BASED ON THE INTERFERENTIAL METHODS. MICROWAVE OPICS HE MEASUREMENS OF HE WAVELENGH OF HE MICROWAVES BASED ON HE INERFERENIAL MEHODS. BASIC HEORY Microwaves belong to the band of very short electromagnetic waves. he wavelengths of the microwaves

More information

Light as a wave. VCE Physics.com. Light as a wave - 1

Light as a wave. VCE Physics.com. Light as a wave - 1 Light as a wave Huygen s wave theory Newton s corpuscular theory Young s double slit experiment Double slit interference Diffraction Single slit interference The electromagnetic nature of light The electromagnetic

More information

Polarization. M. Creech-Eakman Radiation and Optics

Polarization. M. Creech-Eakman Radiation and Optics Polarization M. Creech-Eakman Radiation and Optics Basics of Polarization Only possible for transverse waves Conventionally refers to the E part of the EM wave Some materials are isotropic and leave EM

More information

Quadrature frequency doubling

Quadrature frequency doubling University of Ljubljana Faculty of mathematics and physics Seminar Quadrature frequency doubling Gregor Tavčar Mentor Prof. Dr. Irena Drevenšek Olenik Ljubljana, October 2008 Abstract Quadrature frequency

More information

Chapter 7. Plane Electromagnetic Waves and Wave Propagation

Chapter 7. Plane Electromagnetic Waves and Wave Propagation Chapter 7. Plane Electromagnetic Waves and Wave Propagation 7.1 Plane Monochromatic Waves in Nonconducting Media One of the most important consequences of the Maxwell equations is the equations for electromagnetic

More information

Chemistry 431. Lecture 28

Chemistry 431. Lecture 28 Chemistry 43 Lecture 28 Introduction to electrostatics Charge and dipole moment Polarizability van der Waal s forces Review of transition dipole NC State University Review of Electrostatics The Coulombic

More information

15 Molecular symmetry

15 Molecular symmetry 5 Molecular symmetry Solutions to exercises Discussion questions E5.(b) Symmetry operations Symmetry elements. Identity, E. The entire object 2. n-fold rotation 2. n-fold axis of symmetry, C n 3. Reflection

More information

MODERN PHYSICS. CET questions from Bohr s atom model, Lasers and Scattering

MODERN PHYSICS. CET questions from Bohr s atom model, Lasers and Scattering MODERN PHYSICS CET questions from Bohr s atom model, Lasers and Scattering 1. For the electron to revolve around the atomic nucleus without radiating energy, the electronic orbit should be : (1) Circular

More information

not to be republished NCERT WAVE OPTICS Chapter Ten MCQ I

not to be republished NCERT WAVE OPTICS Chapter Ten MCQ I Chapter Ten WAVE OTICS MCQ I 10.1 Consider a light beam incident from air to a glass slab at Brewster s angle as shown in Fig. 10.1. A polaroid is placed in the path of the emergent ray at point and rotated

More information

CfE. Unit 3 Electromagnetism. Topic 3 Electromagnetic Radiation. Advanced Higher. Physics Department. Useful Websites.

CfE. Unit 3 Electromagnetism. Topic 3 Electromagnetic Radiation. Advanced Higher. Physics Department. Useful Websites. CfE Advanced Higher Physics Department Unit 3 Electromagnetism Topic 3 Electromagnetic Radiation Useful Websites www.scholar.hw.ac.uk http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html Advanced Higher

More information

Crystal Optics of Visible Light

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

More information

CHAPTER 2 DRUG SUBSTANCES AND INSTRUMENTS EMPLOYED

CHAPTER 2 DRUG SUBSTANCES AND INSTRUMENTS EMPLOYED CHAPTER 2 DRUG SUBSTANCES AND INSTRUMENTS EMPLOYED 2.1 Preparation of Pure polymorphic forms Lamivudine polymorphic Form I and Form II drug substances were prepared in Aurobindo Pharma Limited Research

More information

Lecture 18 Time-dependent perturbation theory

Lecture 18 Time-dependent perturbation theory Lecture 18 Time-dependent perturbation theory Time-dependent perturbation theory So far, we have focused on quantum mechanics of systems described by Hamiltonians that are time-independent. In such cases,

More information

Penetration depth of Synthetic Aperture Radar signals in ice and snow: an analytical approach

Penetration depth of Synthetic Aperture Radar signals in ice and snow: an analytical approach Penetration depth of Synthetic Aperture Radar signals in ice and snow: an analytical approach Michel Gay1, Laurent Ferro-Famil2 1 Grenoble Images Speech Signal and Control laboratory d Electronique et

More information

Boardworks AS Physics

Boardworks AS Physics Boardworks AS Physics Vectors 24 slides 11 Flash activities Prefixes, scalars and vectors Guide to the SI unit prefixes of orders of magnitude Matching powers of ten to their SI unit prefixes Guide to

More information

Standard Expression for a Traveling Wave

Standard Expression for a Traveling Wave Course PHYSICS260 Assignment 3 Due at 11:00pm on Wednesday, February 20, 2008 Standard Expression for a Traveling Wave Description: Identify independant variables and parameters in the standard travelling

More information

ConcepTest Superposition. If waves A and B are superposed (that is, their amplitudes are added) the resultant wave is

ConcepTest Superposition. If waves A and B are superposed (that is, their amplitudes are added) the resultant wave is ConcepTest 24.1 Superposition If waves A and B are superposed (that is, their amplitudes are added) the resultant wave is 1) 2) 3) 4) ConcepTest 24.1 Superposition If waves A and B are superposed (that

More information

Chapter Four: Interference

Chapter Four: Interference Chapter Four Interference CHAPTER OUTLINE 4.1 Superposition of Waves 4.2 Interference 4.2.1Theory of Interference 4.2.2Intensity Distribution 4.2.3Superposition of Incoherent Waves 4.2.4Superposition of

More information

Amplification Atomic (or molecular, or semiconductor) system has energy levels Some higher energy states are stable for a short time (ps to ms)

Amplification 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 information

Lecture 1. The nature of electromagnetic radiation.

Lecture 1. The nature of electromagnetic radiation. Lecture 1. The nature of electromagnetic radiation. 1. Basic introduction to the electromagnetic field: Dual nature of electromagnetic radiation Electromagnetic spectrum. Basic radiometric quantities:

More information

Four Wave Mixing In DWDM Optical System

Four 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 information

1. Examples: Wave motion is generating, when disturbance is generating in a wave source and the disturbance is propagating in time and in space.

1. Examples: Wave motion is generating, when disturbance is generating in a wave source and the disturbance is propagating in time and in space. Wave motion 1. Examples: Wave motion can be observed when a water surface is disturbed. In this case waves move outwards across the water surface from the point of disturbance. Wave motion along the string.

More information

Measurement of the Wavelength of Light

Measurement of the Wavelength of Light Measurement of the Wavelength of ight Phys 303 ab Experiment 0 Justin M. Sanders January 15, 2013 Abstract ight waves diffract when reflecting off a grated surface and the diffraction angles are related

More information

Frequency doubling in SBN crystal affected by poling and thermal treatment

Frequency doubling in SBN crystal affected by poling and thermal treatment MSc in Photonics Universitat Politè cnica de Catalunya (UPC) Universitat Autò noma de Barcelona (UAB) Universitat de Barcelona (UB) Institut de Ciè ncies Fotò niques (ICFO) PHOTONICSBCN http://www.photonicsbcn.eu

More information