DOCSLIB.ORG

Quantum Electronics/Laser Physics Chapter 4 Line Shapes and Line

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Quantum Electronics/Laser Physics Chapter 4 Line Shapes and Line Quantum Electronics/Laser Physics Chapter 4 Line Shapes and Line Widths 4.1 The Natural Line Shape 4.2 Collisional Broadening 4.3 Doppler Broadening 4.4 Einstein Treatment of Stimulated Processes Width and Shape of Spectral Lines 1 The Width and Shape of Spectral lines: Natural Line Shape Δ Ek = !Γk I- The Natural Line shape E •Discrete energy levels have finite k € radiative lifetimes and therefore are not infinitely sharp by application of E Heisenberg’s Uncertainty Principle Δ i = !Γi (HUP). The diagram illustrates this. The Ei angular frequency scale is used here, ie € photon energies are given by (with the conversion to frequency unit) The quantum mechanical line shape E ki = !ωki = hν ki The level widths are related to the for the radiative transition radiative lifetimes by HUP: between E and E is a Lorentzian function. k k ΔEk 1 €Δ Ek ⋅τk ≈ ! ⇒ = = ∑Aki The full width at half -maximum is : ! τ k i 1 1 The level widths are given by Γki = Γk + Γi = + τ k τ k ΔEk = !Γk and ΔEi = !Γi Γki 2π τk and τi are the total lifetimes Iki (ω) = I0 × 2 2 and inverse of the transition probabilities A (ω −ωki ) + Γki 4 ki Width and Shape of Spectral Lines 2 € € Spontaneous Emission Probability Aki • Aki= probability per unit • Spontaneous emission is a time for emission of a random process, i.e., one cannot predict when one single photon of energy ℏωki=hνki. atom will radiatively decay. It’s the Einstein A • The measurement of the coefficient. number of photons emitted by • Ei, Ni, gi represent the level a population of atoms over a energy, population and long period of time leads to the statistical weight notion of a radiative lifetime: At initial time t= 0, the population is N 0 respectively. k ( ) dN atoms decay in dt such that dN = − N t A dt Ek, Nk, gk k k ∑ k ( ) ki i< j % t ( Integrating between 0 and t: N k (t) = N k (0)exp'− * & τ k ) 1 τ k = ≡ Radiative lifetime A Ei, Ni, gi ∑ ki i< j Width and Shape of Spectral Lines 3 € Spontaneous Emission Probability Aki • Statistical weight of level Ek = 2Jk + 1 where Jk = total angular momentum of state ‘k’. • E.g., He 1s2p (1P1) state • (1P1) = (2S+1LJ), S = Total spin angular momentum, L = Total orbital angular momentum and J = Total angular momentum (L+S, L+S-1, …..L-S). • Here g = 2J+1 = 2(1) + 1 = 3 ! Width and Shape of Spectral Lines 4 The Width and Shape of Spectral lines Natural Line Shape If Ei is the fundamental level, then τ i → ∞. If E is resonance level just above the fundamental level, •Note: Atomic levels can k also de-excite non- 1 radiatively, e.g collisions, then Aki = . τ k emission of an electron (Auger effect). The total The Einstein Spontaneous emission coefficient Aki should transition probability is be modulated by a normalised line shape function such as thus the sum of radiative € terms and non-radiative I (ω) Γ 2π terms which can be L(ω) = ki = ki I (ω −ω )2 + Γ 2 4 written in the following 0 ki ki form: The transition probability that includes the line shape Total 1 1 A = + is thus A L( ). ki rad non−rad ki ω τ ki τ ki L(ω) is normalised such that € •Usually, one type of de- +∞ L(ω)dω = L(ω)dω = 1 excitation process will ∫−∞ ∫line € dominate I 0 = Total energy radiated in the line (normalisation factor) Width and Shape of Spectral Lines 5 € The Width and Shape of Spectral lines Line Broadening mechanisms in real line sources: Collisional broadening •In a real source, atoms (emitters) are subjected to the interaction forces (i.e., collisions) of neighbouring atoms, ions, electrons, etc…+ possibly external potentials. These perturb the potential energy of the radiating atom which results in a broadening of the line to a value greater than the natural line width. •This type of broadening may take different forms according to the exact nature of the interaction potential: Collisional broadening, Stark broadening, Pressure broadening •Detailed quantum mechanical calculations would show that the collisionally broadened line shape is also Lorentzian of FWHM Δωtotal = ΔΓNatural + ΔΓCollisional Width and Shape of Spectral Lines 6 € The Width and Shape of Spectral lines Line Broadening mechanisms in real line sources: Doppler broadening •A stationary atom of mass m •In a gas in equilibrium there exists a emits a photon of (angular) Maxwell-Boltzmann distribution of frequency ω velocities (controlled by the absolute 0. temperature T, see Y3 Stat.Phys). •The apparent frequency ω ’ 0 •The probability P(vz)dvz that an atom observed by a stationary observer has z-component of velocity between vz when the atom emits a photon ! and vz+dvz is: 1 moving at the relative velocity v : # & 2 # 2 & m mvz P(vz )dvz = % ( exp% − ( dvz ! 2πk T 2k T % v ⋅ rˆ ( $ B ' $ B ' ω' = ω 1− ! 0 0' * v & c ) •Thus the probability of detecting a € wave with angular frequency between ’ and ’+d ’ is given by the ' € ω0 ω0 ω0 ω0 following Gaussian distribution: rˆ ' 2 % ω −ω ( € ' ' % 2 ( ' ( 0 0 ) * ' P(ω0)dω0 = ' * exp −4 dω0 & πΔ ) ' Δ2 * € & ) Width and Shape of Spectral Lines 7 € € € The Width and Shape of Spectral lines Line Broadening mechanisms in real line sources: Doppler broadening Where Δ is the linewidth parameter, from which one obtains the FWHM Δω 1 (Doppler) (see " truncation of 2 Gaussian functions" in "Optical Resonator"): ω 0 2kT Δω 1 (Doppler) = Δ Ln2 = 2 Ln2 2 c m •A measurement of the Doppler width can thus provide an estimation for the temperature of the medium € •Doppler broadened lines are inhomogeneously broadened The total width of any spectral line emitted in a real source is thus: Δω total = ΔΓNatural + ΔΓCollisional + Δω 1 (Doppler) 2 Width and Shape of Spectral Lines 8 € Einstein Treatment of Stimulated Absorption and Emission • Thermal equilibrium of two-level Ek, Nk, gk atoms with radiation Spontaneous • Radiation in thermal equi., ie black- process body radiation model, is given by Stimulated processe s Planck’s radiation law (radiation energy density=energy per unit Ei, Ni, gi volume per unit interval frequency) 8πhν 3 1 Einstein Coefficients ρ(ν ,T ) = 3 hν c A = coefficient of e kT −1 ki spontaneous emission • The atomic populations are in Maxwell-Boltzmann equilibrium, Bik = coefficient of € maintained by a dynamic (stimulated) absorption equilibrium between emission and absorption processes Bki = coefficient of stimulated emission Width and Shape of Spectral Lines 9 Einstein Treatment of Stimulated Absorption and Emission • The upward and downward Maxwell -Boltzmann: transition rates are obtained in N g $ !ω ' terms of the populations and k = k exp&− ki ) coefficients: N i gi % kBT ( Upward rate: From above: dNi N B = −N B ρ k ikρ dt i ik = N i (Aki + Bki ρ) Downward rate: gkAki exp(−!ω ki kBT ) dNk ρ(ω ki ) = = −Nk (Aki + Bki ρ) gi Bik − gkBki exp(−!ω ki kBT ) dt Equilibrium (detailed balance): Using Planck’s radiation law for ρ(ω ki ) : g B = g B dNi dNk i ik k ki = = 0 2 3 dt dt π c gk Bik = Aki N B ρ = N A + B ρ ω 3 g i ik k ( kii ki ) ! ki i Width and Shape of Spectral Lines 10 € Einstein Treatment of Stimulated Absorption and Emission • To have equal rates of spontaneous and stimulated emission requires: A 8πh A = Bρ(ν 0) ⇒ = ρ(ν 0) = B λ3 −6 2 λ ≡ λ0 = 1 µm ⇒ cρ(ν 0) = I(ν 0) ≈ 5x10 W/m Hz For a (Lorentzian) spectral line of width Δν = 107 Hz 2 -2 -2 I(ν 0) = × I 0 ⇒ I 0 = 50 Wm = 5 mWcm πΔν • Stimulated emission typically negligible for laboratory line sources € Width and Shape of Spectral Lines 11 Elementary Interaction Processes N2 N2 N2 h 12 h 12 h 12 h 12 h 12 N1 N1 N1 • Stimulated • Stimulated • Spontaneous absorption: one emission: one emission: photon lost photon gained one photon • Attenuation • Amplification emitted at • Stimulated photon: random same direction and • Noise phaseWidth and Shape of Spectral Lines 12.
Load more

Recommended publications
  • Stark Broadening of Spectral Lines in Plasmas
    atoms Stark Broadening of Spectral Lines in Plasmas Edited by Eugene Oks Printed Edition of the Special Issue Published in Atoms www.mdpi.com/journal/atoms Stark Broadening of Spectral Lines in Plasmas Stark Broadening of Spectral Lines in Plasmas Special Issue Editor Eugene Oks MDPI • Basel • Beijing • Wuhan • Barcelona • Belgrade Special Issue Editor Eugene Oks Auburn University USA Editorial Office MDPI St. Alban-Anlage 66 4052 Basel, Switzerland This is a reprint of articles from the Special Issue published online in the open access journal Atoms (ISSN 2218-2004) in 2018 (available at: https://www.mdpi.com/journal/atoms/special issues/ stark broadening plasmas) For citation purposes, cite each article independently as indicated on the article page online and as indicated below: LastName, A.A.; LastName, B.B.; LastName, C.C. Article Title. Journal Name Year, Article Number, Page Range. ISBN 978-3-03897-455-0 (Pbk) ISBN 978-3-03897-456-7 (PDF) Cover image courtesy of Eugene Oks. c 2018 by the authors. Articles in this book are Open Access and distributed under the Creative Commons Attribution (CC BY) license, which allows users to download, copy and build upon published articles, as long as the author and publisher are properly credited, which ensures maximum dissemination and a wider impact of our publications. The book as a whole is distributed by MDPI under the terms and conditions of the Creative Commons license CC BY-NC-ND. Contents About the Special Issue Editor ...................................... vii Preface to ”Stark Broadening of Spectral Lines in Plasmas” ..................... ix Eugene Oks Review of Recent Advances in the Analytical Theory of Stark Broadening of Hydrogenic Spectral Lines in Plasmas: Applications to Laboratory Discharges and Astrophysical Objects Reprinted from: Atoms 2018, 6, 50, doi:10.3390/atoms6030050 ...................
    [Show full text]
  • Doppler-Free Spectroscopy
    Doppler-Free Spectroscopy MIT Department of Physics (Dated: November 29, 2012) Traditionally, optical spectroscopy had been performed by dispersing the light emitted by excited matter, or by dispersing the light transmitted by an absorber. Alternatively, if one has available a tunable monochromatic source (such as certain lasers), a spectrum can be measured one wave- length at a time' by measuring light intensity (fluorescence or transmission) as a function of the wavelength of the tunable source. In either case, physically important structures in such spectra are often obscured by the Doppler broadening of spectral lines that comes from the thermal motion of atoms in the matter. In this experiment you will make use of an elegant technique known as Doppler-free saturated absorption spectroscopy that circumvents the problem of Doppler broaden- ing. This experiment acquaints the student with saturated absorption laser spectroscopy, a common application of non-linear optics. You will use a diode laser system to measure hyperfine splittings 2 2 85 87 in the 5 S1=2 and 5 P3=2 states of Rb and Rb. I. PREPARATORY PROBLEMS II. LASER SAFETY 1. Suppose you are interested in small variations in You will be using a medium low power (≈ 40 mW) wavelength, ∆λ, about some wavelength, λ. What near-infrared laser in this experiment. The only real is the expression for the associated small variations damage it can do is to your eyes. Infrared lasers are es- in frequency, ∆ν? Now, assuming λ = 780nm (as is pecially problematic because the beam is invisible. You the case in this experiment), what is the conversion would be surprised how frequently people discover they factor between wavelength differences (∆λ) and fre- have a stray beam or two shooting across the room.
    [Show full text]
  • Saturated Absorption Spectroscopy
    Ph 76 ADVANCED PHYSICS LABORATORY —ATOMICANDOPTICALPHYSICS— Saturated Absorption Spectroscopy I. BACKGROUND One of the most important scientificapplicationsoflasersisintheareaofprecisionatomicandmolecular spectroscopy. Spectroscopy is used not only to better understand the structure of atoms and molecules, but also to define standards in metrology. For example, the second is defined from atomic clocks using the 9192631770 Hz (exact, by definition) hyperfine transition frequency in atomic cesium, and the meter is (indirectly) defined from the wavelength of lasers locked to atomic reference lines. Furthermore, precision spectroscopy of atomic hydrogen and positronium is currently being pursued as a means of more accurately testing quantum electrodynamics (QED), which so far is in agreement with fundamental measurements to ahighlevelofprecision(theoryandexperimentagreetobetterthanapartin108). An excellent article describing precision spectroscopy of atomic hydrogen, the simplest atom, is attached (Hänsch et al.1979). Although it is a bit old, the article contains many ideas and techniques in precision spectroscopy that continue to be used and refined to this day. Figure 1. The basic saturated absorption spectroscopy set-up. Qualitative Picture of Saturated Absorption Spectroscopy — 2-Level Atoms. Saturated absorp- tion spectroscopy is one simple and frequently-used technique for measuring narrow-line atomic spectral features, limited only by the natural linewidth Γ of the transition (for the rubidium D lines Γ 6 MHz), ≈ from an atomic vapor with large Doppler broadening of ∆νDopp 1 GHz. To see how saturated absorp- ∼ tion spectroscopy works, consider the experimental set-up shown in Figure 1. Two lasers are sent through an atomic vapor cell from opposite directions; one, the “probe” beam, is very weak, while the other, the “pump” beam, is strong.
    [Show full text]
  • Introduction to Astrophysical Spectra Solar Spectropolarimetry: from Virtual to Real Observations 2019
    Introduction to Astrophysical Spectra Solar spectropolarimetry: From virtual to real observations 2019 Jorrit Leenaarts ([email protected]) Jaime de la Cruz Rodr´ıguez([email protected]) 1 Contents Preface 4 1 Introduction 5 2 Solid angle 6 3 Radiation, intensity and flux 7 3.1 Basic properties of radiation . 7 3.2 Definition of intensity . 7 3.3 Additional radiation quantities . 9 3.4 Flux from a uniformly bright sphere . 11 4 Radiative transfer 12 4.1 Definitions . 12 4.2 The radiative transfer equation . 14 4.3 Formal solution of the transport equation . 16 4.4 Radiation from a homogeneous medium . 17 4.5 Radiation from an optically thick medium . 19 5 Radiation in thermodynamic equilibrium 22 5.1 Black-body radiation . 22 5.2 Transfer equation and source function in thermodynamic equi- librium . 24 6 Matter in thermodynamic equilibrium 25 7 Matter/radiation interaction 26 7.1 Bound-bound transitions . 27 7.2 Einstein relations . 29 7.3 Emissivity and extinction coefficient . 31 7.4 Source function . 33 8 Line broadening 33 8.1 Broadening processes . 34 8.2 Combining broadening mechanisms . 36 8.3 Line widths as a diagnostic . 40 2 9 Bound-free transitions 40 10 Other radiative processes 43 10.1 Elastic scattering . 45 10.2 The H− ion ............................ 46 11 Rate equations 46 11.1 General theory . 46 11.2 The two-level atom . 47 11.3 A three-level atom as a density diagnostic . 49 11.4 A three-level atom as a temperature diagnostic . 52 12 Exercises 53 3 Preface These are a fraction of the lecture notes for the Solarnet Summer School - Solar spectropolarimetry: From virtual to real observations.
    [Show full text]
  • 14 Shape of Spectral Lines
    II ⋅ Stellar Atmospheres Copyright (2003) George W. Collins, II 14 Shape of Spectral Lines . If we take the classical picture of the atom as the definitive view of the formation of spectral lines, we would conclude that these lines should be delta functions of frequency and appear as infinitely sharp black lines on the stellar spectra. However, many processes tend to broaden these lines so that the lines develop a characteristic shape or profile. Some of these effects originate in the quantum mechanical description of the atom itself. Others result from perturbations introduced by the neighboring particles in the gas. Still others are generated by the motions of the atoms giving rise to the line. These motions consist of the random thermal motion of the atoms themselves which are superimposed on whatever large scale motions may be present. The macroscopic motions may be highly ordered, as in the case of stellar rotation, or show a high degree of randomness such as is characteristic of turbulent flow. 348 14 ⋅ Shape of Spectral Lines In practice, all these effects are present and give the line its characteristic shape. The correct representation of these effects allows for the calculation of the observed line profile and in the process reveals a great deal about the conditions in the star that give rise to the spectrum. Of course the photons that give rise to the absorption lines in the stellar spectrum have their origins at different locations in the atmosphere. So the conditions giving rise to a spectral line are really an average of a range of conditions.
    [Show full text]
  • JAP Course Galaxies and ISM Lecture 2
    The Interstellar Medium : JAP course Galaxies and ISM Lecture 2 April 2020 M.Das Indian Institute of Astrophysics, Bangalore Emission from the ISM The ISM can be studied in emission or absorption using spectral lines. It can also be studied using the continuum emission from gas and stars. ● Emission lines are due to the energy emitted when ion/atom/molecule goes from an excited state to a lower energy state. Absorption lines are due to energy absorbed by intervening medium. Both types of lines have intrinsic shapes and also depend on the nature of the source. Continuum emission is the emission spread over a continuous range of frequencies and arises due to the deceleration of charged particles. ● An example of a spectrum (quasar 3c293) showing the 3 types of emission is given below. SDSS DR12 spectrum of 3c293 showing emission lines, absorption lines and a steeply rising continuum spectrum in the red region. Emission Line Continuum Emission Absorption Line Factors affecting emission line shape The shape of a spectral line depends on the following : 1. Natural line shape 2. Doppler broadening 3. Collisional broadening (not important for the ISM ● Natural line shape : We will treat this classically. Let the emitting atom/molecule be an oscillator of natural frequency ω . Then we can apply the equation of damped 0 harmonic oscillator : 2 2 d r/dt + ω r = -γ dr/dt 0 where γ is the damping coefficient and is given by γ = e2ω 2 /6πεc3m 0 ● The solution of this equation is a decaying electric field. The fourier transform gives the amplitude or intensity of the emission to be: 2 2 I(ν) = I γ /2π[ (ω – ω ) + (γ/2) ] 0 0 ● This line shape is called Lorentzian.
    [Show full text]
  • Doppler-Free Saturated Absorption Spectroscopy of Rubidium Using a Tunable Diode Laser
    Doppler-Free Saturated Absorption Spectroscopy of Rubidium Using a Tunable Diode Laser Molly Krogstad University of Colorado at Boulder Physics REU August 7, 2009 Abstract By performing Doppler-free saturated absorption spectroscopy using a tunable diode laser, we 87 2 2 were able to observe the Rb transitions between the 5 S1/2 and 5 P3/2 states from F=2 to F’=1,2, and 3. The tunable diode laser beam has been amplified using slave laser injection, and is now ready to be locked, seed a new tapered amplifier, and used as a source of light for a magneto-optical trap to cool and trap Rb atoms. Introduction and Theory Tunable diode lasers are often used in atomic physics because they’re relatively inexpensive, reliable sources of narrow-band light [1]. By using a diode laser with a high reflectivity coating on its back facet and a reduced reflectivity on the output facet, along with a diffraction grating with a higher reflectivity, the back of the diode laser chip and the grating will form the new laser cavity of a tunable diode laser. The frequency of the tunable diode laser can then be changed by changing the cavity length. This is done in a controlled manner by changing the voltage applied to piezoelectric transducer disks (PZT), which move the grating in response to the applied voltage. However, since changing the cavity length changes the frequency of the laser, one has to be careful to avoid changes in cavity length due to thermal expansion or mechanical vibrations. This can be done by controlling the temperatures of the baseplate and the diode laser using temperature controllers, enclosing the laser in an insulated metal box to avoid air currents, and mounting the cavity on rubber cushions to reduce the movement due to vibrations [1].
    [Show full text]
  • Doppler-Free Saturation Spectroscopy
    Doppler-Free Saturation Spectroscopy Thomas Rieger and Thomas Volz Max-Planck-Institut fÄurQuantenoptik, Garching 1 Introduction With the advent of the laser in the 1960s, precision spectroscopy of atoms and molecules became possible. The laser, being a very narrow, tunable and coherent light source, allowed to resolve features in atomic and molec- ular spectra with an unprecedented resolution and accuracy, which led to a better understanding of the structure of atoms and molecules. Precision spectroscopy became a very active ¯eld and within a short time, a wide range of di®erent spectroscopic techniques were developed. A good review is for instance the article [1] written by T. W. HÄansch, A. L. Schawlow and G. W. Series, which gives an overview of precision spectroscopy of atomic hydrogen. Many of the basic principles and techniques can be understood from this article and are still not outdated. Another very good and com- prehensive introduction on a more detailed basis is given in the book "Laser Spectroscopy" by W. DemtrÄoder[2], one of the pioneers of the ¯eld. Laser spectroscopy also paved the way towards all the exciting developments that took place in the past two decades in the ¯eld of laser cooling and trap- ping of atoms which culminated in 1995 with the realisation of Bose-Einstein condensation in alkali gases [3]. In all the labs dealing with laser cooling and trapping of atoms, the technique of Doppler-free saturated absorption spectroscopy is frequently used as a tool for locking the lasers to particu- lar atomic lines. In this graduate-student lab experiment, this technique is introduced in theory and experiment.
    [Show full text]
  • The Emission Lines of Quasars and Similar Objects
    The erI-iission lines of quasars and siva-filar objects Kris Davidson" Astronomy Department, Uniuersity of Minnesota, Minneapolis, MN 55455 Hagai Netzert Department of Astronomy, University of Texas, Austin, TX 78712 Much of our information about quasars is derived from their emission-line spectra. The analysis of such spectra has become an intricate subject which differs considerably from traditional, low-density nebular astrophysics. This review is intended to explain our present understanding of the situation, including some aspects of galactic nuclei whose luminosities are more modest than quasars. Quasars line-emitting regions are probably photoionized (even if supplementary heating processes also occur). So fax, models have been constructed which include ionization and thermal equilibria, the transfer of resonance-line and related photons, and the likely effects of absorption and scattering by dust grains. From comparisons between emission-line intensities produced in these models and observed quasars spectra, it appears that certain densities and pressures and size scales occur in or around quasars. The relative abundances of elements are not very far from solar values, although it is suspected that heavy elements —carbon, nitrogen, and oxygen in particular —are moderately "overabundant" in quasars. The emission-line intensities also provide indirect information about quasars ultraviolet and soft-x-ray continua; there are hints that photons with energies between 20 and 300 eV—which are not directly observable —may even represent the peak of the luminous output of a typical quasar. Finally, some gas-dynamical questions, while extremely important, are very difficult to answer, because of a lack of observables. CONTENTS 715 VII.
    [Show full text]
  • Broadening of Spectral Lines Due to Dynamic Multiple Scattering and the Tully-Fisher Relation
    View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by CERN Document Server BROADENING OF SPECTRAL LINES DUE TO DYNAMIC MULTIPLE SCATTERING AND THE TULLY-FISHER RELATION Sisir Roy1;2, & Menas Kafatos1 Center for Earth Observing and Space Research Institute for Computational Sciences and Informatics and Department of Physics, George Mason University Fairfax, VA 22030 USA Suman Dutta2 Physics and Applied Mathematics Unit Indian Statistical Institute, Calcutta, INDIA 1;2 e.mail: [email protected] 1 e.mail : [email protected] 2 email : [email protected] Abstract The frequency shift of spectral lines is most often explained by the Doppler Effect in terms of relative motion, whereas theDoppler broadening of a particular line mainly depends on the absolute temperature. The Wolf effect on the other hand deals with the correlation induced spectral change and explains both the broadening and shift of the spectral lines. In this framework a relation between the width of the spectral line is related to the redshift z for the line and hence with the distance. For smaller values of z a relation similar to the Tully-Fisher relation can be obtained and for larger values of z a more general relation can be constructed. The derivation of this kind of relation based on dynamic multiple scattering theory may play a significant role in explaining the overall spectra of quasi stellar objects. We emphasize that this mechanism is not applicable for nearby galaxies, z 1. ≤ Keywords : spectral line broadening, spectral line shift, Tully-Fisher relation. PACS : 32.70.Jz 1 Introduction In studying the motion of astronomical objects, astrophysicists utilize the study of frequency shift of spectral lines.
    [Show full text]
  • 13. DOPPLER-FREE SPECTROSCOPY James C
    13. DOPPLER-FREE SPECTROSCOPY James C. Bergquist National Institute of Standards and Technology Boulder, Colorado 13.1 Introduction Spectroscopy is an important tool for investigating the structure of physical systems such as atoms or molecules. Thermal motion of free atoms and molecules gives rise to Doppler broadening of the characteristic spectral transi- tions, which often blurs important details of the spectra and prevents a deeper understanding of the underlying physics. Long before the appearance of lasers, well before their use in nonlinear, high-resolution spectroscopy, long before laser-cooling, atomic and molecular beams had been used for high-resolution spectroscopy. And, perhaps not surprisingly, beam techniques remain prominent in spectral studies. In the course of this chapter, we will seek a rudimentary appreciation of the methods used to reveal Doppler-free spectra. But first we will begin with a brief discussion of motional effects that produce line broadening and shift. before we address their countermeasures. 13.2 Spectral Line-Broadening Mechanisms Atoms or molecules in gases can be relatively free and undisturbed, but their spectral lines are spread out over a range of frequencies by the Doppler effect because they are moving in all directions with high thermal velocities. Those particles moving toward an observer absorb light at lower frequencies than those at rest; those receding absorb at higher frequencies. The resulting Doppler broadening can often mask spectral fine and hyperfine structure, even though each individual absorber still retains its typically much narrower natural line width. The spectral line of a moving particle is shifted away from its rest-frame .
    [Show full text]
  • Dispersive Extinction Theory of Redshift
    Physics Essays volume 18, number 2, 2005 Dispersive Extinction Theory of Redshift Ling Jun Wang Abstract A dispersive extinction theory is presented to explain the cosmic redshift and the 2.7 K background radiation as an alternative to the currently prevailing Doppler shift theory and the big bang theory. According to this theory, the cosmic redshift and the 2.7 K background radiation are due to the dispersive scattering and ab- sorption of starlight by the space medium. An estimate of the nonlinear absorp- tion constant is given by comparing the result to the Hubble constant derived from the observational data. An experimental method is designed to test the valid- ity of the dispersive extinction theory as opposed to the Doppler shift theory. Key words: redshift, Doppler shift, big bang theory, dispersive extinction theory 1. INTRODUCTION accurate determination of stellar distances, the The spectroscopic redshift of the stars plays a cru- modification of the inverse square law relating cial role in modern cosmology. It has been discovered brightness to distance in a curved space-time, the that the spectroscopic redshift of a star is by and large decrease in the energy of the light brought about by linearly proportional to its distance from Earth. the reduction of the frequency of the light wave, and Hubble proposed that the redshift was caused by a the evolution in the luminosity of galaxies with time Doppler effect due to the receding movement of the since the big bang. The deviation from linearity also stars and galaxies, which logically suggested an ever- depends on the density parameter that discriminates expanding universe.(1,2) It has been further proposed between cosmological models.
    [Show full text]