DOCSLIB.ORG

Coherence in Beams

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Coherence in Beams Coherence in Beams Jörg Rossbach University of Hamburg & DESY CERN Accelerator School (CAS) on Free-Electron Laser and Energy Recovery Linac 31 May – 10 June, 2016, Hamburg Contents This lecture will address some basic issues -- details and solutions will be given in later lectures --- or (even better) in your own studies • Why coherence ? • Basics on wave propagation • Interference • Transverse coherence • Longitudinal coherence • Correlation functions • Coherent matter waves 0 p o s itio n / m m CAS on FELs and ERLs, Hamburg 2016 Jörg Rossbach, Univ HH 2 Why coherence? Electro-magnetic radiation comes in waves: amplitudes and phases -- and we have to cope with it ! Structure of biological macromolecule reconstructed from diffraction pattern of protein crystal: LYSOZYME , MW=19,806 Images courtesy Janos Hajdu CAS on FELs and ERLs, Hamburg 2016 Jörg Rossbach, Univ HH 3 Coherence of a single photon pulse from an FEL courtesy Janos Hajdu SINGLE MACROMOLECULE simulated image Needs very high radiation power @ λ ≈1Å CAS on FELs and ERLs, Hamburg 2016 Jörg Rossbach, Univ HH 4 CAS on FELs and ERLs, Hamburg 2016 Jörg Rossbach, Univ HH 4 Why Coherence ? Diffraction from LCLS X-ray FEL/Stanford: D. Li, et al., DOI: 10.1038/ncomms10140 (2016) CAS on FELs and ERLs, Hamburg 2016 Jörg Rossbach, Univ HH 5 Basics on wave propagation 1. At some distance from the source, a wave front propagates indepentently Huygens Principle: Each point on the wave front can be considered the origin of a spherical wave, the new wave front being the envelope of these wavelets applicable for e.m., water, acoustic, matter waves Basics for diffraction 2. The e.m. wave equation is linear If two waves , are solutions, then will be a solution as well ! Basics for interference CAS on FELs and ERLs, Hamburg 2016 Jörg Rossbach, Univ HH 6 Diffraction from a slit ˆ Consider a plane wave (complex amplitude E 0 ) to screen of arriving from the left at slit of width a observation We use Huygens principle and consider the radiation field consisting of wavelets from tiny areas of size ∆y . We observe under an angle θ from a “very far distance”. We call the complex electric wave vector of the first wavelet ˆ . E1 ∆δ ∆y sin θ The next wavelet is: ˆ ⋅ i with ∆δ = 2 π E1 e λ δ a ⋅sin θ And the last wavelet: ˆ ⋅ i N with δ= 2 π E1 e N λ 2 ∆δ δ 2 ∝ˆˆˆ =++in ++ ˆ i N The intensity at the screen is IEsum E1KK Ee 1 Ee 1 ∆y λ The amplitude of each wavelet is E ˆ = E ˆ = E ˆ ∆ δ 1a 0 0 2π a sin θ CAS on FELs and ERLs, Hamburg 2016 Jörg Rossbach, Univ HH 7 Diffraction from a slit Intensity at the screen: 2 2 λ 2 ∆δ iδ IE∝ˆ = E ˆ ∆++++δ ()1 KK eein N sum 2πa sin θ 0 δ= δ 2 2 N 2 λδ λ δ 2 ⇒ Eedˆi δ = − Eie ˆ ()i N − 1 πθ0 ∫ πθ 0 2sinaδ =0 2sin a λ2 λ 2 iδ∗ − i δ I∝ EeEeˆ()()N −−=1 ˆ N 1 21cos E 2 () −=δ 2πθa sin0 0 2 πθ a sin 0 N π θ 2 asin 2 sin λ δ λ π θ =2 2 N = 2 ∝ 2 asin 4 E0 sin E0 sinc 2sinπa θ 2 πasin θ 2 λ λ Can be interpreted as a Fourier transform of the transmission function of the slit (note δ ≈ 2πyθ/λ is a linear function of y): δ= δ = N iδ y y 2 2πθ+∞ 2 πθ e iy iy dδ∝ eλ dy = τ() ye λ dyFT = () τ () y ∫θ ∫ ∫ slit δ = = −∞ 0 y y 1 CAS on FELs and ERLs, Hamburg 2016 Jörg Rossbach, Univ HH 8 Diffraction from two narrow slits Makes it simple to calculate more complicated slit systems: e.g. Young’s double slit experiment (1801) τ Fourier transform of two delta functions at ±a/2: 2δ +∞ 2πθ a ai y πθλ− πθλ π a θ δy++− δ y edyeλ =+ia/ e ia / = 2cos ∫ λ −∞ 1444244432 2 τ 2δ θ∝ () τ 2 I() FT2δ () y 2 πθa 2 πθ a ∝cos =1 1 + cos : λ 2 λ CAS on FELs and ERLs, Hamburg 2016 Jörg Rossbach, Univ HH 9 Diffraction from two real slits We can even take into account the finite width of the slits: τ= τ′ − ⋅ τ ′ ′ realistic()y∫ 2δ ( yy ) slit () ydy The Fourier transform of such a convolution integral is just the product of the Fourier transforms: θτ∝() 2 = ττ ⋅ 2 I() FTrealistic () y FT ()():2δ FT slit Note 1: “diffraction from two slits” (or of a finite number of separated waves) is mostly called “ interference ”. Interference from a continuum of waves is called “diffraction ”. There is no fundamental difference ! Note 2: Due to interference of two waves, there are suddenly locations of permanently ZERO intensity (energy density) where each individual wave did generate intensity. Energy density is re-distributed in space due to interference ! CAS on FELs and ERLs, Hamburg 2016 Jörg Rossbach, Univ HH 10 Far field condition We have assumed a plane wave arriving at the slits. Typically realized by a point source in very far distance L. How far is “far”? There should be no significant phase difference of the wave between the two slits (or the illuminated object) Compare the optical path lengths ! a2 L− L = << λ 1 2 8L Point source a2 L >> distance should be 8λ The same condition holds for the distance from object to observation screen ! Fraunhofer diffraction Otherwise: Fresnel diffraction (no fun) 11 CAS on FELs and ERLs, Hamburg 2016 Jörg Rossbach, Univ HH transverse coherence What matters for interference is the superposition of (two) e.m. waves. So far we assumed they both come from the same source. This is not realistic. Let’s now drop this assumption but let’s still consider monochromatic waves. iδ i δ =+=1 + 2 (Let’s assume A 1 = A 2) E E121 E Ae Ae 1 Intensity: 2 2 ? ∝ =+()δ − δ I E2 A 1 1 cos( 2 1 ) period =() + ∆ δ ⇒ I I 0 1 cos asin θ ∆=δ2 π +const ∝⋅+ a x const λ ? ? ? Such radiation from slits is called transversely coherent CAS on FELs and ERLs, Hamburg 2016 Jörg Rossbachsely, Univ HH 12 transverse coherence =( + ∆ δ ) I I 0 1 cos Moving along the screen, the cos ∆δ - term oscillates between +1 and -1 (see page 9) The interference contrast (=“visibility”) is then V=1: I− I V ≡max min →1 (perfect coherence and A =A ) + 1 2 Imax I min 2πa θ 2 π c Phase difference ∆δ can be expressed as time delay, e.g.: ∆=δ = τωτ = λ λ 0 Imagine, the two fields E1 and E2 do NOT stem from the same point source. We can still calculate the intensity on the screen according to p.9, but the phase difference on the screen does NOT only stem from the time delay τ (due to the observation angle), but there may be a further time difference τ’ between E1 and E2 : ∆δ ωτ′ ωττ+ ′ =i i0 = i 0 ( ) E2 Eee 1 Ee 1 E() tE⋅∗ ( t − τ ) O,1 O ,2 T ≡ γc τ 12 (a , ) normalized complex correlation function 2⋅ 2 EO,1 E O ,2 We consider intensities need to average over osc. period CAS on FELs and ERLs, Hamburg 2016 Jörg Rossbach, Univ HH 13 transverse coherence E() tE⋅∗ ( t − τ ) O,1 O ,2 ≡ γc τ 12 (a , ) 2 2 normalized complex correlation function E⋅ E 2πa θ a θ O,1 O 2 - depends on observation angle through τ = = λω 0 c In our simple case A 1 = A 2: =( + ∆δ) +ℜ γc =( + γ ) II01 cos⇒ I 0( 1 12) I 0 1 12 ω∗ − ωττ +′ − it0 it 0 ( ) Ae1 Ae 1 −ω τ′ − τ Indeed: γc τ = = i 0 ( ) 12 (a , ) 2 e A1 ω τ ∆δ γc τ 0 = 12 (a , ) ⇒ e e γ=ℜ γc =ℜ∆δ = ∆ δ 12 12 e cos γ c The visibility of interference is determined by: 12 =γ c = In this case (A 1 = A 2): V 12 1 q.e.d. CAS on FELs and ERLs, Hamburg 2016 Jörg Rossbach, Univ HH 14 transverse coherence E() tE⋅∗ ( t − τ ) O,1 O ,2 ≡ γc τ 12 (a , ) 2 normalized complex correlation function ⋅ 2 EO,1 E O 2 ≠ If I 1 I 2 2 ω ωττ+′ − 2 ωττ′− − ωττ ′ − ∝=+i0 t i 0 () t =++2 2 i0 ()() + i 0 Itotal E sum Ae1 Ae 2 AAAAe 1212 ( e ) =++()ωττ′ − + + ℜ γ c ⇒ IIIIItotal 12 12cos 0 ( ) ⇒ IIII 12 1212 I− I 2 I I V ≡max min =1 2 γc ≡ γ eff + + 12 12 Imax I min II 1 2 CAS on FELs and ERLs, Hamburg 2016 Jörg Rossbach, Univ HH 15 transverse coherence ∗ 2 E( y ,0)⋅ E ( y ,0) dy dy This is a single number describing the entire beam ς ≡ ∫ 11 22 12 2 from slit (object), independent of angle of observation. ()E( y ,0) dy ∫ 1 1 1 ς →1 for perfectly coherent radiation. Example from FLASH FEL: From: A. Singer, et. al: Opt.Express 20, No.16 (2012) ς = ± x 0.59 0.1 ς = ± y 0.72 0.08 CAS on FELs and ERLs, Hamburg 2016 Jörg Rossbach, Univ HH 16 Transverse coherence S. Reiche Z=25 m Z=37.5 m Z=50 m Z=62.5 m Z=75 m Z=87.5 m m Single mode dominates close to 100% transverse coherence CAS on FELs and ERLs, Hamburg Jörg Rossbach, Univ HH 17 2016 impact of focusing (needed for most experiments) CAS on FELs and ERLs, Hamburg 2016 Jörg Rossbach, Univ HH 18 transverse coherence Why are the phases in 1 and 2 uncorrelated? Probably because the source is extended ! Consider a ray arriving at double slit at an angle ϕ and with intensity I(ϕ ) It contributes a phase difference π ϕ to double slit of: ∆δ = 2 a ϕ λ The averaged phase difference between the ω∗ − ωττ +′ − it0 it 0 ( ) Ae1 Ae 1 −ω τ′ − τ γc τ = = i 0 ( ) extended source to the double slit is: 12 (a , ) 2 e A1 +∞ 2πa ϕ 1−i I (ϕ ) a a Van Zitter-Zernicke-Theorem: IedFT(ϕ ) λ ϕ = ≡ I⇒ VI= Visibility of interference pattern corresponds to ∫ λ λ Fourier Transform of source distribution function Itotal −∞ I total CAS on FELs and ERLs, Hamburg 2016 Jörg Rossbach, Univ HH 19 temporal coherence 2 2 −π t − π t ()∆τ 2 πν ()∆ τ 2 =i2 0 t ℜ = πν EtEe( )0 e ; EtEe( )0 cos(2 0 t ) ν− ν 2 −π (0 ) −∆−πτνν()()22 ∆ ν 2 FT( E ( t )) ∝ e(0 ) = e Phase information will be lost after longitudinal coherence time: τ ≈ 1 c ∆ν CAS on FELs and ERLs, Hamburg 2016 Jörg Rossbach, Univ HH 20 .
Load more

Recommended publications
  • Properties of Laser Beams
    Properties of Laser Beams 1. Laser light is highly monochromatic Monochromaticity refers to a pure spectral color of a single wavelength. A beam is more and more monochromatic if the line spread in frequency is narrow or small. This line width is an outcome of the homogeneous broadening factors and inhomogeneous broadening factors. Despite these broadening mechanisms the line width in a laser is generally very small as compared to the normal lights. A laser cavity forms a resonant system. The photons are emitted by the stimulated emission where in all the photons are in same phase and in the same state of polarization. Oscillations can sustain only at the resonance frequency of the cavity. This leads to the narrowing of the laser line width. So, the laser light is usually very pure in wavelength, and the laser is said to have the property of monochromaticity. 2. Laser light is highly coherent Two beams of light are coherent when there is a constant phase relation between the two beams or the phase difference between their waves is constant; they are incoherent if there is a random or changing phase relationship, or the phase difference is not constant. Sustained interference patterns are formed only by radiation emitted by coherent sources, generally produced by splitting a single beam into two or more beams. A laser, unlike an incandescent light source, produces a beam in which all the components bear a fixed relationship to each other i.e. the laser beam is generally coherent. For any electromagnetic (em) wave, there are two kinds of coherence viz.
    [Show full text]
  • Visualizing and Manipulating the Spatial and Temporal Coherence of Light with an Adjustable Light Source in an Undergraduate Experiment
    European Journal of Physics PAPER • OPEN ACCESS Visualizing and manipulating the spatial and temporal coherence of light with an adjustable light source in an undergraduate experiment To cite this article: K Pieper et al 2019 Eur. J. Phys. 40 055302 View the article online for updates and enhancements. This content was downloaded from IP address 141.52.96.103 on 10/09/2019 at 16:03 European Journal of Physics Eur. J. Phys. 40 (2019) 055302 (11pp) https://doi.org/10.1088/1361-6404/ab3035 Visualizing and manipulating the spatial and temporal coherence of light with an adjustable light source in an undergraduate experiment K Pieper1,2 , A Bergmann1, R Dengler2 and C Rockstuhl1,3 1 Institute of Theoretical Solid State Physics, Karlsruhe Institute of Technology, Wolfgang-Gaede-Str. 1, D-76131 Karlsruhe, Germany 2 Institute of Physics and Technical Education, Karlsruhe University of Education, D-76133 Karlsruhe, Germany 3 Institute of Nanotechnology, Karlsruhe Institute of Technology, PO Box 3640, D-76021 Karlsruhe, Germany E-mail: [email protected] Received 14 May 2019, revised 25 June 2019 Accepted for publication 5 July 2019 Published 23 August 2019 Abstract Coherence expresses the ability of light to form interference patterns sta- tionary in time and extended over a spatial domain. The importance of coherence is undoubted but teaching coherence constitutes a challenge. In particular, there are only a few simple and clear experiments to illustrate coherence. To render the phenomena of coherence more accessible and to point out the difference between spatial and temporal coherence, we intro- duce an undergraduate experiment consisting of a light source illuminating a double-slit and a Michelson interferometer.
    [Show full text]
  • 1.2.5 Temporal Coherence We Have Seen That Spatial Coherence Measures the Correlation of the field at Two Separate Spatial Locations
    28 Preliminary concepts 1.2.5 Temporal coherence We have seen that spatial coherence measures the correlation of the field at two separate spatial locations. In a similar manner, temporal coherence specifies the extent to which the radiation maintains a definite phase relationship at two dif- ferent times. Temporal coherence is characterized by the coherence time, which can be experimentally determined by measuring the path length difference over which fringes can be observed in a Michelson interferometer. A simple represen- tation of a coherent wave in time is given by t2 E t e − − iω t . 0( )= 0 exp 2 1 (1.100) 4στ 2 Here στ is the rms temporal width of the intensity profile |E0(t) |. The coherence time tcoh can be defined as 2 tcoh ≡ dτ |C(τ)| , (1.101) where C(τ) is the normalized, first order correlation function (or complex degree of temporal coherence) given by dt E(t)E∗(t + τ) C(τ) ≡ , (1.102) dt |E(t)|2 and the brackets denote ensemble averaging.√ In the simple Gaussian model of Eq. (1.100), the coherence time tcoh =2 πστ . In the frequency domain, we have √ e π (ω − ω )2 E0 dt eiωtE t 0 − 1 , ω = 0( )= exp 2 (1.103) σω 4σω −1 2 where σω =(2στ ) is the rms width of the frequency profile |Eω| .Letus introduce the temporal (longitudinal) phase space variables ct and (ω−ω1)/ω1 = Δω/ω1. The Gaussian wave packet then satisfies σω λ1 cστ · = , (1.104) ω1 4π which is the same phase space area relationship as (1.58) obtained for a trans- versely coherent Gaussian beam.
    [Show full text]
  • A Lower Bound for the Coherence Block Length in Mobile Radio Channels
    electronics Article A Lower Bound for the Coherence Block Length in Mobile Radio Channels Rafael P. Torres * and Jesús R. Pérez * Departamento de Ingeniería de Comunicaciones, Universidad de Cantabria, 39005 Santander, Spain * Correspondence: [email protected] (R.P.T.); [email protected] (J.R.P.) Abstract: A lower bound for the coherence block (ChB) length in mobile radio channels is derived in this paper. The ChB length, associated with a certain mobile radio channel, is of great practical importance in future wireless systems, mainly those based on massive multiple input and multiple output (M-MIMO) technology. In fact, it is one of the factors that determines the achievable spectral efficiency. Firstly, theoretical aspects regarding the mobile radio channels are summarized, focusing on the rigorous definition of coherence bandwidth (BC) and coherence time (TC) parameters. Secondly, the uncertainty relations developed by B. H. Fleury, involving both BC and TC, are presented. Afterwards, a lower bound for the product BCTC is derived, i.e., the ChB length. The obtained bound is an explicit function of easily measurable parameters, such as the delay spread, mobile speed and carrier frequency. Furthermore, and especially important, this bound is also a function of the degree of coherence with which we define both BC and TC. Finally, an application example that illustrates the practical possibilities of the bound obtained is presented. As a further conclusion, the need to determine what degree of correlation is required to consider mobile channels as effectively flat-fading and stationary is highlighted. Keywords: 5G mobile systems; mobile radio channels; coherence bandwidth; coherence time; coherence block; massive MIMO; spectral efficiency Citation: Torres, R.P.; Pérez, J.R.
    [Show full text]
  • Coherent X-Rays: Overview by Malcolm Howells
    Coherent x-rays: overview by Malcolm Howells Lecture 1 of the series COHERENT X-RAYS AND THEIR APPLICATIONS A series of tutorial–level lectures edited by Malcolm Howells* *ESRF Experiments Division ESRF Lecture Series on Coherent X-rays and their Applications, Lecture 1, Malcolm Howells CONTENTS Introduction to the series Books History The idea of coherence - temporal, spatial Young's slit experiment Coherent experiment design Coherent optics The diffraction integral Linear systems - convolution Wave propagation and passage through a transparency Optical propagators - examples Future lectures: 1. Today 2. Quantitative coherence and application to x-ray beam lines (MRH) 3. Optical components for coherent x-ray beams (A. Snigirev) 4. Coherence and x-ray microscopes (MRH) 5. Phase contrast and imaging in 2D and 3D (P. Cloetens) 6. Scanning transmission x-ray microscopy: principles and applications (J. Susini) 7. Coherent x-ray diffraction imaging: history, principles, techniques and limitations (MRH) 8. X-ray photon correlation spectroscopy (A. Madsen) 9. Coherent x-ray diffraction imaging and other coherence techniques: current achievements, future projections (MRH) ESRF Lecture Series on Coherent X-rays and their Applications, Lecture 1, Malcolm Howells COHERENT X-RAYS AND THEIR APPLICATIONS A series of tutorial–level lectures edited by Malcolm Howells* Mondays 5.00 pm in the Auditorium except where otherwise stated 1. Coherent x-rays: overview (Malcolm Howells) (April 7) (5.30 pm) 2. Coherence theory: application to x-ray beam lines (Malcolm Howells) (April 21) 3. Optical components for coherent x-ray beams (Anatoli Snigirev) (April 28) 4. Coherence and x-ray microscopes (Malcolm Howells) (May 26) (CTRL room ) 5.
    [Show full text]
  • Proposal for a Room-Temperature Diamond Maser
    ARTICLE Received 27 Nov 2014 | Accepted 3 Aug 2015 | Published 23 Sep 2015 DOI: 10.1038/ncomms9251 OPEN Proposal for a room-temperature diamond maser Liang Jin1, Matthias Pfender2, Nabeel Aslam2, Philipp Neumann2, Sen Yang2,Jo¨rg Wrachtrup2 & Ren-Bao Liu1 The application of masers is limited by its demanding working conditions (high vacuum or low temperature). A room-temperature solid-state maser is highly desirable, but the lifetimes of emitters (electron spins) in solids at room temperature are usually too short (Bns) for population inversion. Masing from pentacene spins in p-terphenyl crystals, which have a long spin lifetime (B0.1 ms), has been demonstrated. This maser, however, operates only in the pulsed mode. Here we propose a room-temperature maser based on nitrogen-vacancy centres in diamond, which features the longest known solid-state spin lifetime (B5 ms) at room temperature, high optical pumping efficiency (B106 s À 1) and material stability. Our numerical simulation demonstrates that a maser with a coherence time of approximately minutes is feasible under readily accessible conditions (cavity Q-factor B5 Â 104, diamond size B3 Â 3 Â 0.5 mm3 and pump power o10 W). A room-temperature diamond maser may facilitate a broad range of microwave technologies. 1 Department of Physics and Centre for Quantum Coherence, The Chinese University of Hong Kong, Shatin, New Territories, Hong Kong, China. 2 3rd Institute of Physics, University of Stuttgart, 70569 Stuttgart, Germany. Correspondence and requests for materials should be addressed to R.-B.L. (email: [email protected]). NATURE COMMUNICATIONS | 6:8251 | DOI: 10.1038/ncomms9251 | www.nature.com/naturecommunications 1 & 2015 Macmillan Publishers Limited.
    [Show full text]
  • Coherence Length Measurement System Design Description Document
    Coherence Length Measurement System Design Description Document Coherence Length Measurement System Design Description Document ASML / Tao Chen Faculty Advisor: Professor Thomas Brown Pellegrino Conte (Scribe & Document Handler) Lei Ding (Customer Liaison) Maxwell Wolfson (Project Coordinator) Document Number 00007 Revisions Level Date G 5-06-2018 This is a computer-generated document. The electronic Authentication Block master is the official revision. Paper copies are for reference only. Paper copies may be authenticated for specifically stated purposes in the authentication block. 00007 Rev G page 1 Coherence Length Measurement System Design Description Document Rev Description Date Authorization A Initial DDD 1-22-2018 All B Edited System Overview 2-05-2018 All Added Lab Results C Edited System Overview 2-19-2018 All Added New Results D Added New Lab Results 2-26-2018 All Updated FRED Progress E Edited System overview 4-02-2018 All Finalized cost analysis Added new results F Edited Cost Analysis 4-20-2018 All Added new results Added to code analysis G Added Final Results 5-06-2018 All Added Customer Instructions Added to Code 00007 Rev G page 2 Coherence Length Measurement System Design Description Document Table of Contents Revision History 2 Table of Contents 3 Vision Statement 4 Project Scope 4 Theoretical Background 5-7 System Overview 8-10 Cost Analysis 11-13 Spring Semester Timeline 14-15 Lab Results 16-22 FRED Analysis 23-26 Visibility Analysis 27 Design Day Description 28 Conclusions and Future Work 29 Appendix A: Table of All Lab Results 30-40 Appendix B: Visibility Processing Code 41-43 Appendix C: Customer Instructions 44-49 References 50 00007 Rev G page 3 Coherence Length Measurement System Design Description Document Vision Statement: This projects’ goal is to design and assemble an interferometer capable of measuring and reporting information regarding the coherence length of a laser.
    [Show full text]
  • 4. Development of Angle Resolved Low Coherence Interferometry (A/LCI) Using the T- Matrix Method
    Diagnostic Imaging and Assessment Using Angle Resolved Low Coherence Interferometry by Michael G. Giacomelli Department of Biomedical Engineering Duke University Date:_______________________ Approved: ___________________________ Adam Wax, Supervisor ___________________________ Joseph Izatt ___________________________ David Brady ___________________________ Tuan Vo- Dinh ___________________________ Sina Farsiu Dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the Department of Biomedical Engineering in the Graduate School of Duke University 2012 i v ABSTRACT Diagnostic Imaging and Detection using Angle Resolved Low Coherence Interferometry by Michael Giacomelli Department of Biomedical Engineering Duke University Date:_______________________ Approved: ___________________________ Adam Wax, Supervisor ___________________________ Joseph Izatt ___________________________ David Brady ___________________________ Tuan Vo- Dinh ___________________________ Sina Farsiu An abstract of a dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the Department of Biomedical Engineering in the Graduate School of Duke University 2012 Copyright by Michael G. Giacomelli 2012 Abstract The redistribution of incident light into scattered fields ultimately limits the ability to image into biological media. However, these scattered fields also contain information about the structure and distribution of protein complexes, organelles, cells and whole tissues
    [Show full text]
  • Light Scattering from Solid-State Quantum Emitters: Beyond the Atomic Picture
    Light Scattering from Solid-State Quantum Emitters: Beyond the Atomic Picture 1, 1, 2, 1 3 1 Alistair J. Brash, ∗ Jake Iles-Smith, † Catherine L. Phillips, Dara P. S. McCutcheon, John O’Hara, Edmund Clarke,4 Benjamin Royall,1 Jesper Mørk,5 Maurice S. Skolnick,1 A. Mark Fox,1 and Ahsan Nazir2 1Department of Physics and Astronomy, University of Sheffield, Sheffield, S3 7RH, United Kingdom 2School of Physics and Astronomy, The University of Manchester, Oxford Road, Manchester M13 9PL, UK 3Quantum Engineering Technology Labs, H. H. Wills Physics Laboratory and Department of Electrical and Electronic Engineering, University of Bristol, Bristol BS8 1FD, UK 4EPSRC National Epitaxy Facility, Department of Electronic and Electrical Engineering, University of Sheffield, Sheffield, UK 5Department of Photonics Engineering, DTU Fotonik, Technical University of Denmark, Building 343, 2800 Kongens Lyngby, Denmark (Dated: April 12, 2019) Coherent scattering of light by a single quantum emitter is a fundamental process at the heart of many proposed quantum technologies. Unlike atomic systems, solid-state emitters couple to their host lattice by phonons. Using a quantum dot in an optical nanocavity, we resolve these interactions in both time and frequency domains, going beyond the atomic picture to develop a comprehensive model of light scattering from solid-state emitters. We find that even in the presence of a cavity, phonon coupling leads to a sideband that is completely insensitive to excitation conditions, and to a non-monotonic relationship between laser detuning and coherent fraction, both major deviations from atom-like behaviour. Scattering of light by a single quantum emitter is one of atoms, SSEs can experience significant dephasing from the fundamental processes of quantum optics.
    [Show full text]
  • Optics, IDC202 G R O U P
    Optics, IDC202 G R O U P Lecture 3. Rejish Nath Contents 1. Coherence and interference 2. Youngs double slit experiment 3. Alternative setups 4. Theory of coherence 5. Coherence time and length 6. A finite wave train 7. Spatial coherence Literature: 1. Optics, (Eugene Hecht and A. R. Ganesan) 2. Optical Physics, (A. Lipson, S. G. Lipson and H. Lipson) 3. The Optics of Life, (Sönke Johnsen) 4. Modern Optics, (Grant R. Fowles) Course Contents 1. Nature of light (waves and particles) 2. Maxwells equations and wave equation 3. Poynting vector 4. Polarization of light 5. Law of reflection and snell's law 6. Total Internal Reflection and Evanescent waves 7. Concept of coherence and interference 8. Young's double slit experiment 9. Single slit, N-slit Diffraction 10. Grating, Birefringence, Retardation plates 11. Fermat's Principle 12. Optical instruments 13. Human Eye 14. Spontaneous and stimulated emission 15. Concept of Laser 3 Coherence and interference Optical interference is based on the superposition principle. (This is because the Maxwell’s equations are linear differential equations.) The electric field at a point in vacuum: E = E1 + E2 + E3 + E4 + ... is the vector sum of that from the different sources. The same is true for magnetic fields. Remark: This may not be generally true, deviations from linear superposition is the study of nonlinear optical phenomena or simply non-linear optics. Coherence and interference Consider two harmonic, monochromatic, linearly polarised waves = E exp [i(k r !t + φ )] E1 1 1 · − 1 = E exp [i(k r !t + φ )] E2 2 2 · − 2 If the phase difference φ 1 φ 2 is constant, the two sources are said to be mutually coherent.
    [Show full text]
  • 1051-455-20073 Homework #6 Due 8 May 2008 (Th)
    1051-455-20073 Homework #6 Due 8 May 2008 (Th) 1. “White” light includes equal “amounts” of each wavelength in the interval 400 nm λ 700 nm. ≤ ≤ (a) Determine the frequency bandwidth for this wavelength range c c ∆ν ν1 ν2 = ≡ | − | λ − λ ¯ 1 2 ¯ 1 1 ¯ ¯ = c ¯ ¯ λ − λ ¯ ¯ ¯ 1 2 ¯ ¯ ¯ 8 1 1 1 = 2.¯99792458¯ 10 ms− ∼ ¯ ¯× · 400 nm − 700 nm ¯ ¯ ¯ ¯ ∆ν = 3.212 1014 Hz ¯ ¯ ∼ × ¯ ¯ (b) Compute the associated coherence time and coherence length of white light. 1 1 15 coherence time ∆t = = 3.113 10− s ≡ ∆ν ∼ 3.212 1014 Hz ∼ × × c 7 coherence length c ∆t = = 9.334 10− m = 93.34 μm ≡ · ∆ν ∼ × ∼ 2. The range of angular temporal frequencies by a light source is ∆ω: (a) Find an expression for ∆ν ∆ω ω =2πν = ∆ω =2π∆ν = ∆ν = ⇒ ⇒ 2π (b) Derive an expression for the linewidth ∆λ λν = c = ∆c =0=λ ∆ν + ν ∆λ ∆ν ⇒ ∆λ · λ· c = = = ∆λ = ∆ν = ∆ν = ∆λ ⇒ ν − λ ⇒ −ν −ν2 (c) Use the result of (a) to find an expression for the coherence length of the source. c 2πc = = ∆ν ∆ω 15 radians (d) If the light source is a sodium arc that emits two narrow spectral lines with ω1 =3.195 10 sec 15 radians × and ω2 =3.198 10 , find the coherence length. × sec 8 1 2πc 2.99792458 10 ms− = =2π × ∆ω 3.195 1015 radians 3.198 1015 radians × sec − × sec = +62.8mm¯ ¯ ∼ ¯ ¯ 15 radians (e) If the light source is a He:Ne “greenie” laser with ω1 =3.171 10 sec and ω2 =3.469 15 radians × × 10 sec , find the coherence length.
    [Show full text]
  • New Plasma Diagnosis by Coherence Length Spectroscopy
    New Plasma Diagnosis by Coherence Length Spectroscopy Nopporn Poolyarata and Young W. Kimb aThe Development and Promotion of Science and Technology (DPST), Thailand bDepartment of Physics, Lehigh University 16 Memorial Dr. East, Bethlehem, PA 18015 , USA Abstract A new methodology and instrumentation have been developed for diagnosis of dense high temperature plasmas. In a plasma medium, collision processes shorten the optical coherence length at a given emission wavelength. By measuring the coherence length, the rate of collisions a radiating particle experiences can be determined. A map of the collision rates throughout the plasma can speak volumes about the atomic and thermal state of the plasma. Both the time-integrated and time-resolved interference fringes are obtained 252o using emissions due to the transition between 33sp( P32) 4 p and 252o 33sp() P32 7 d. We have observed that the coherence length indeed decreases with increasing collision rate, and in addition, as a function of time as a result of cumulative collisions. The coherence length was found to be 4200 ± 800 nm at 50 torr where the collision frequency is 2.14× 1011 s -1 , and 2400± 130 nm at 140 torr where the collision frequency is8.13× 1011 s -1 . We have also discovered that the coherence length varies with the direction of the viewing line of sight into the discharge plasma. The anisotropy results from the non-uniform structure in the discharge current, and this is further investigated by intentionally deforming the tip of the cathode. A photographic examination of both the cathode and the anode disc confirms the non-axis-symmetric structure of the plasma, which leads to the asymmetry in the plasma, in agreement with the angular dependence of the coherence length.
    [Show full text]