Development of an Ultrasensitive Cavity Ring Down Spectrometer in the 2.10-2.35 Μm Region : Application to Water Vapor and Carbon Dioxide Semen Vasilchenko

Total Page:16

File Type:pdf, Size:1020Kb

Development of an Ultrasensitive Cavity Ring Down Spectrometer in the 2.10-2.35 Μm Region : Application to Water Vapor and Carbon Dioxide Semen Vasilchenko Development of an ultrasensitive cavity ring down spectrometer in the 2.10-2.35 µm region : application to water vapor and carbon dioxide Semen Vasilchenko To cite this version: Semen Vasilchenko. Development of an ultrasensitive cavity ring down spectrometer in the 2.10- 2.35 µm region : application to water vapor and carbon dioxide. Instrumentation and Detectors [physics.ins-det]. Université Grenoble Alpes, 2017. English. NNT : 2017GREAY037. tel-01704680 HAL Id: tel-01704680 https://tel.archives-ouvertes.fr/tel-01704680 Submitted on 8 Feb 2018 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. THÈSE Pour obtenir le grade de DOCTEUR DE LA COMMUNAUTE UNIVERSITE GRENOBLE ALPES Spécialité : Physique de la Matière Condensée et du Rayonnement Arrêté ministériel : 25 mai 2016 Présentée par Semen VASILCHENKO Thèse dirigée par Didier MONDELAIN codirigée par Alain CAMPARGUE préparée au sein du Laboratoire Interdisciplinaire de Physique dans l'École Doctorale Physique Development of an ultrasensitive cavity ring down spectrometer in the 2.10-2.35 µm region. Application to water vapor and carbon dioxide. Thèse soutenue publiquement le 8 juin 2017, devant le jury composé de : Madame Muriel LEPÈRE Professeur, Université de Namur, Rapporteur Monsieur Robert GEORGES Professeur, Université Rennes 1, Rapporteur Monsieur Hugues GUILLET DE CHATELLUS Chargé de recherche, CNRS LIPhy UMR5588, Examinateur Monsieur Olivier PIRALI Chargé de recherche, Institut des Sciences Moléculaires d'Orsay - UMR8214, Examinateur Monsieur Jean-Michel HARTMANN Directeur de recherche, Laboratoire de Météorologie Dynamique (UMR 8539), Président Monsieur Leonid SINITSA Professeur, V.E. Zuev Institute of Atmospheric Optics SB RAS (IAO SB RAS), Examinateur Acknowledgments First and foremost, I would like to express sincere gratitude to my supervisor Didier Mondelain for guidance, patience, and the experience he shared; he handled my pro- fessional and personal issues and read, and corrected the manuscripts of the thesis a multitude of times. I would also like to thank my co-supervisor Alain Campargue, who was always open to discussions and questions and created the perfect working conditions as the head of the scientific group. I am grateful to Peter Cerm´akforˇ tutoring me, giving advice, a great many fruitful discussions and being sociable Heartfelt thanks to all of the LAsers, Mol´eculeset Environnement group for a pleasant atmosphere at work. I am honored to be working with such a strong and productive scientific group. Samir Kassi, Jean-Luc Martin, Serge B´eguier,Semen Mikhailenko and Daniele Romanini deserve a special mention in the acknowledgments list for their help, advice, and useful discussions. Special thanks to my fellow PhD students Magdalena Konefal and Ekaterina Karlovets for sharing the same office and becoming good friends with me. I would like to thank the Universit´eGrenoble Alpes for a 3 years support of my PhD. This support was obtained in the relation of the strong collaboration between our group at LIPhy and my home institute, the Institute of Atmospheric Optics in Tomsk in the frame of the LIA SAMIA (Laboratoire International Associ´e\Spectro- scopie de Mol´eculesd'Int´er^etAtmosph´erique") But for the endeavor of Leonid Sinitsa, carrying out this research of mine would have been impossible. I am grateful to Gleb Lantsman for correcting the style and the language of this manuscript. Last but not least, I would like to give my warmest thanks to my family and friends for their support, communication, and genuine interest in my research. iii Abstract A cavity ring down spectrometer has been developed in the 2.00{2.35 µm spectral range to achieve highly sensitive absorption spectroscopy of molecules of atmospheric and planetologic interest and at high spectral resolution. This spectral region corre- sponds to a transparency window for water vapor and carbon dioxide. Atmospheric windows, where absorption is weak, are used to sound the Earth's and Venus' atmo- spheres where water vapor and carbon dioxide represent the main gaseous absorbers in the infrared, respectively. The CRDS technique consists in injecting photons inside a high finesse optical cavity and measuring the photon's life time of this cavity. This life-time depends on the mirror reflectivity and on the intra-cavity losses due to the absorbing gas in the cavity. Measuring these losses versus the wavelength allow obtaining the absorption spectrum of the gas. The extreme reflectivity of the mirrors allows reaching, for a 1-meter long cavity, a sensitivity equivalent to the one obtained classically with absorption cells of several thousands of kilometers. Three DFB laser diodes emitting around 2.35, 2.26, 2.21 µm were used with this spectrometer giving access to the 4249-4257, 4422-4442 and 4516-4534 cm−1 interval, respectively. Thanks to optical feedback from an external cavity, two of these diodes were spectrally narrowed leading to a better injection of the high finesse cavity thus reducing the noise level of the spectrometer. In parallel, we tested a VECSEL (Vertical-external-Cavity, Surface Emitting laser) through a collaboration with the Institut d'Electronique (IES, UMR 5214) in Montpellier and the Innoptics firm. This laser source is able to cover a 80 cm−1 spectral range centered at 4340 cm−1, equivalent to four DFB laser diodes. In routine the achieved sensitivity with this spectrometer, corresponding to the minimum detectable coefficient is typically of 1×10−10 cm−1. The introductive chapter (Chapter 1) makes the point on the different techniques allowing absorption spectra recordings in the studied spectral region and on their sensitivity. The experimental set-up, the characteristics and performances by the CRD spectrometer developed in this work are detailed in Chapter 2. To our knowledge this instrument is the most sensitive in the considered spectral region. In Chapter 3, detection of quadrupolar electric transitions of HD and N2 illustrate the level of sensitivity reached: (i) the S(3) transition in the 1{0 band of HD has been recorded for the first time and its intensity measured (s = 2:5 × 10−27 cm/molecule), (ii) the position and intensity of the highly forbidden O(14) quadrupolar electric transition of the 2{0 band of N2 have also been newly determined. The two last chapters are devoted to the characterization of the CO2 absorption, in the centre of the transparency window, and of the water vapor absorption. In both cases, we not only studied the allowed transitions of the monomer, but also v the continuum absorption. This latter correspond to a weak background absorption varying slowly with the wave length. The self-continuum cross-sections of the water vapor continuum were measured in many spectral points through the transparency window with a much better accuracy compared to existing measurements. These CRDS data constitute a valuable data set to validate the reference model (MT CKD) for the continuum which is implemented in most of the atmospheric radiative transfer codes. vi R´esum´e Un spectrom`etreutilisant la technique CRDS a ´et´ed´evelopp´eentre 2.00 et 2.35 µm afin de r´ealiserla spectroscopie en absorption de mol´eculesd'int´er^etatmosph´eriqueet plan´etologiqueavec une tr`esgrande sensibilit´eet `ahaute r´esolutionspectrale. Cette r´egiondu spectre correspond `aune fen^etrede transparence de la vapeur d'eau et du dioxyde de carbone. Ces fen^etressont des zones de tr`esfaible absorption utilis´eespour le sondage des atmosph`eresterrestre et v´enusienne dans lesquelles la vapeur d'eau et le dioxyde de carbone repr´esentent respectivement les absorbants gazeux principaux dans l'infrarouge. La technique CRDS consiste `ainjecter des photons dans une cavit´eoptique de haute finesse et `amesurer la dur´eede vie des photons dans cette cavit´e. Celle-ci est mesur´eeen interrompant l'injection des photons dans la cavit´eoptique lors du passage en r´esonancedu laser avec l'un des modes longitudinaux. Cette dur´eede vie d´epend de la r´eflectivit´edes miroirs et des pertes intra-cavit´ecomme celles induites par un gaz qui absorbe. Mesurer ces pertes en fonction de la longueur d'onde permet d'obtenir le spectre d'absorption du gaz en question. L'extr^emer´eflectivit´edes miroirs permet d'atteindre dans une cavit´ed'un peu plus d'1 m de longueur une sensibilit´e ´equivalente `acelle qui serait obtenue classiquement avec une cellule d'absorption longue de plusieurs milliers de kilom`etres. Trois diodes laser DFB ´emettant autour de 2.35, 2.26 et 2.21 µm ont ´et´eutilis´ees avec ce spectrom`etre. Gr^ace`aune r´etro-actionoptique provenant d'une cavit´eex- terne, certaines de ces diodes ont pu ^etre affin´ees,ce qui a permis de mieux injecter la cavit´ehaute finesse et ainsi de r´eduirele niveau de bruit du spectrom`etre. Par- all`element gr^ace`aune collaboration avec l'Institut d'Electronique (IES, UMR 5214) `aMontpellier et la soci´et´eInnoptics nous avons pu tester le prototype d'un VECSEL (Vertical-External-Cavity Surface-Emitting-Laser). Ce laser a permis de couvrir une gamme spectrale de 80 cm−1, entre 4300 et 4380 cm−1, ´equivalente `aquatre diodes laser DFB. La sensibilit´eobtenue en routine avec ce spectrom`etre,correspondant au coefficient minimum d´etectable,est typiquement de 1×10−10 cm−1. Le chapitre intro- ductif (Chapitre 1) fait le point sur les diff´erentes techniques permettant d'acqu´erir des spectres en absorption dans la gamme spectrale ´etudi´eeet sur les sensibilit´esat- teintes.
Recommended publications
  • Modern Quantum Kinetic Theory and Spectral Line Shapes
    LOUIS MONCHICK MODERN QUANTUM KINETIC THEORY AND SPECTRAL LINE SHAPES The modern quantum kinetic theory of spectral line hapes i outlined and a typical calculation of a Ra­ man scattered line hape described. The distingui hing feature of thi calculation i that it was completely ab initio and therefore con tituted a test of modern quantum kinetic theor ,the tate of the art in computing molecular-scattering cross sections, and novel method of olving kinetic equation. The computation em­ ployed a large assortment of tools: group theory finite-element method. cIa ic method of solving cou­ pled sets of ordinary differential equations, graph method of combining angular momenta, and matrix methods of solving integral equations. Agreement with experimental re ult wa excellent. THE PROBLEM Almo t with the inception of quantum mechanics, parison. 1 the a ailability of an extremely good model of theorists-mostly nuclear and atomic physici t -had the interaction of helium ith two deuterium atoms, and developed the general scattering equations neces ary to the feasibilit of carrying out the calculation in a finite describe collision between fundamental particles. With time and at a rea onable co t. The goal which we did not almost no exception, however, only a few angular quite reach. a an entirely ab initio computation con­ momentum and spin states were invol ed; as a re ult, taining a umption only about the rate of convergence these calculations were not computationally intensive. In of the numerical procedure u ed, ith no e peri mental principle, the general methodology was applicable to the quantitie except Planck' and Boltzmann' con tant calculation of molecular inela tic and reactive colli ion, and the electronic charg and mas of the electron, deuter­ which are important ingredients of reaction rates.
    [Show full text]
  • Beam Profiling by Michael Scaggs
    Beam Profiling by Michael Scaggs Haas Laser Technologies, Inc. Introduction Lasers are ubiquitous in industry today. Carbon Dioxide, Nd:YAG, Excimer and Fiber lasers are used in many industries and a myriad of applications. Each laser type has its own unique properties that make them more suitable than others. Nevertheless, at the end of the day, it comes down to what does the focused or imaged laser beam look like at the work piece? This is where beam profiling comes into play and is an important part of quality control to ensure that the laser is doing what it intended to. In a vast majority of cases the laser beam is simply focused to a small spot with a simple focusing lens to cut, scribe, etch, mark, anneal, or drill a material. If there is a problem with the beam delivery optics, the laser or the alignment of the system, this problem will show up quite markedly in the beam profile at the work piece. What is Beam Profiling? Beam profiling is a means to quantify the intensity profile of a laser beam at a particular point in space. In material processing, the "point in space" is at the work piece being treated or machined. Beam profiling is accomplished with a device referred to a beam profiler. A beam profiler can be based upon a CCD or CMOS camera, a scanning slit, pin hole or a knife edge. In all systems, the intensity profile of the beam is analyzed within a fixed or range of spatial Haas Laser Technologies, Inc.
    [Show full text]
  • Pulse Shaping and Ultrashort Laser Pulse Filamentation for Applications in Extreme Nonlinear Optics Antonio Lotti
    Pulse shaping and ultrashort laser pulse filamentation for applications in extreme nonlinear optics Antonio Lotti To cite this version: Antonio Lotti. Pulse shaping and ultrashort laser pulse filamentation for applications in extreme nonlinear optics. Optics [physics.optics]. Ecole Polytechnique X, 2012. English. pastel-00665670 HAL Id: pastel-00665670 https://pastel.archives-ouvertes.fr/pastel-00665670 Submitted on 2 Feb 2012 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. UNIVERSITA` DEGLI STUDI DELL’INSUBRIA ECOLE´ POLYTECHNIQUE THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF PHILOSOPHIÆ DOCTOR IN PHYSICS Pulse shaping and ultrashort laser pulse filamentation for applications in extreme nonlinear optics. Antonio Lotti Date of defense: February 1, 2012 Examining committee: ∗ Advisor Daniele FACCIO Assistant Prof. at University of Insubria Advisor Arnaud COUAIRON Senior Researcher at CNRS Reviewer John DUDLEY Prof. at University of Franche-Comte´ Reviewer Danilo GIULIETTI Prof. at University of Pisa President Antonello DE MARTINO Senior Researcher at CNRS Paolo DI TRAPANI Associate Prof. at University of Insubria Alberto PAROLA Prof. at University of Insubria Luca TARTARA Assistant Prof. at University of Pavia ∗ current position: Reader in Physics at Heriot-Watt University, Edinburgh Abstract English abstract This thesis deals with numerical studies of the properties and applications of spatio-temporally coupled pulses, conical wavepackets and laser filaments, in strongly nonlinear processes, such as harmonic generation and pulse reshap- ing.
    [Show full text]
  • Stark Broadening Measurements in Plasmas Produced by Laser Ablation of Hydrogen Containing Compounds Miloš Burger, Jorg Hermann
    View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by Archive Ouverte en Sciences de l'Information et de la Communication Stark broadening measurements in plasmas produced by laser ablation of hydrogen containing compounds Miloš Burger, Jorg Hermann To cite this version: Miloš Burger, Jorg Hermann. Stark broadening measurements in plasmas produced by laser ablation of hydrogen containing compounds. Spectrochimica Acta Part B: Atomic Spectroscopy, Elsevier, 2016, 122, pp.118-126. 10.1016/j.sab.2016.06.005. hal-02348424 HAL Id: hal-02348424 https://hal.archives-ouvertes.fr/hal-02348424 Submitted on 5 Nov 2019 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Stark broadening measurements in plasmas produced by laser ablation of hydrogen containing compounds Milosˇ Burgera,∗,Jorg¨ Hermannb aUniversity of Belgrade, Faculty of Physics, POB 44, 11000 Belgrade, Serbia bLP3, CNRS - Aix-Marseille University, 13008 Marseille, France Abstract We present a method for the measurement of Stark broadening parameters of atomic and ionic spectral lines based on laser ablation of hydrogen containing compounds. Therefore, plume emission spectra, recorded with an echelle spectrometer coupled to a gated detector, were compared to the spectral radiance of a plasma in local thermal equi- librium.
    [Show full text]
  • UFS Lecture 13: Passive Modelocking
    UFS Lecture 13: Passive Modelocking 6 Passive Mode Locking 6.2 Fast Saturable Absorber Mode Locking (cont.) (6.3 Soliton Mode Locking) 6.4 Dispersion Managed Soliton Formation 7 Mode-Locking using Artificial Fast Sat. Absorbers 7.1 Kerr-Lens Mode-Locking 7.1.1 Review of Paraxial Optics and Laser Resonator Design 7.1.2 Two-Mirror Resonators 7.1.3 Four-Mirror Resonators 7.1.4 The Kerr Lensing Effects (7.2 Additive Pulse Mode-Locking) 1 6.2.2 Fast SA mode locking with GDD and SPM Steady-state solution is chirped sech-shaped pulse with 4 free parameters: Pulse amplitude: A0 or Energy: W 2 = 2 A0 t Pulse width: t Chirp parameter : b Carrier-Envelope phase shift : y 2 Pulse width Chirp parameter Net gain after and Before pulse CE-phase shift Fig. 6.6: Modelocking 3 6.4 Dispersion Managed Soliton Formation in Fiber Lasers ~100 fold energy Fig. 6.12: Stretched pulse or dispersion managed soliton mode locking 4 Fig. 6.13: (a) Kerr-lens mode-locked Ti:sapphire laser. (b) Correspondence with dispersion-managed fiber transmission. 5 Today’s BroadBand, Prismless Ti:sapphire Lasers 1mm BaF2 Laser crystal: f = 10o OC 2mm Ti:Al2O3 DCM 2 PUMP DCM 2 DCM 1 DCM 1 DCM 2 DCM 1 BaF2 - wedges DCM 6 Fig. 6.14: Dispersion managed soliton including saturable absorption and gain filtering 7 Fig. 6.15: Steady state profile if only dispersion and GDD is involved: Dispersion Managed Soliton 8 Fig. 6.16: Pulse shortening due to dispersion managed soliton formation 9 7.
    [Show full text]
  • Lab 10: Spatial Profile of a Laser Beam
    Lab 10: Spatial Pro¯le of a Laser Beam 2 Background We will deal with a special class of Gaussian beams for which the transverse electric ¯eld can be written as, r2 1 Introduction ¡ 2 E(r) = Eoe w (1) Equation 1 is expressed in plane polar coordinates Refer to Appendix D for photos of the appara- where r is the radial distance from the center of the 2 2 2 tus beam (recall r = x +y ) and w is a parameter which is called the spot size of the Gaussian beam (it is also A laser beam can be characterized by measuring its referred to as the Gaussian beam radius). It is as- spatial intensity pro¯le at points perpendicular to sumed that the transverse direction is the x-y plane, its direction of propagation. The spatial intensity pro- perpendicular to the direction of propagation (z) of ¯le is the variation of intensity as a function of dis- the beam. tance from the center of the beam, in a plane per- pendicular to its direction of propagation. It is often Since we typically measure the intensity of a beam convenient to think of a light wave as being an in¯nite rather than the electric ¯eld, it is more useful to recast plane electromagnetic wave. Such a wave propagating equation 1. The intensity I of the beam is related to along (say) the z-axis will have its electric ¯eld uni- E by the following equation, formly distributed in the x-y plane. This implies that " cE2 I = o (2) the spatial intensity pro¯le of such a light source will 2 be uniform as well.
    [Show full text]
  • Performance Evaluation of a Thz Pulsed Imaging System: Point Spread Function, Broadband Thz Beam Visualization and Image Reconstruction
    applied sciences Article Performance Evaluation of a THz Pulsed Imaging System: Point Spread Function, Broadband THz Beam Visualization and Image Reconstruction Marta Di Fabrizio 1,* , Annalisa D’Arco 2,* , Sen Mou 2, Luigi Palumbo 3, Massimo Petrarca 2,3 and Stefano Lupi 1,4 1 Physics Department, University of Rome ‘La Sapienza’, P.le Aldo Moro 5, 00185 Rome, Italy; [email protected] 2 INFN-Section of Rome ‘La Sapienza’, P.le Aldo Moro 2, 00185 Rome, Italy; [email protected] (S.M.); [email protected] (M.P.) 3 SBAI-Department of Basic and Applied Sciences for Engineering, Physics, University of Rome ‘La Sapienza’, Via Scarpa 16, 00161 Rome, Italy; [email protected] 4 INFN-LNF, Via E. Fermi 40, 00044 Frascati, Italy * Correspondence: [email protected] (M.D.F.); [email protected] (A.D.) Abstract: Terahertz (THz) technology is a promising research field for various applications in basic science and technology. In particular, THz imaging is a new field in imaging science, where theories, mathematical models and techniques for describing and assessing THz images have not completely matured yet. In this work, we investigate the performances of a broadband pulsed THz imaging system (0.2–2.5 THz). We characterize our broadband THz beam, emitted from a photoconductive antenna (PCA), and estimate its point spread function (PSF) and the corresponding spatial resolution. We provide the first, to our knowledge, 3D beam profile of THz radiation emitted from a PCA, along its propagation axis, without the using of THz cameras or profilers, showing the beam spatial Citation: Di Fabrizio, M.; D’Arco, A.; intensity distribution.
    [Show full text]
  • Gaussian Beams • Diffraction at Cavity Mirrors Creates Gaussian Spherical
    Gaussian Beams • Diffraction at cavity mirrors creates Gaussian Spherical Waves • Recall E field for Gaussian U ⎛ ⎡ x2 + y2 ⎤⎞ 0 ⎜ ( ) ⎟ u( x,y,R,t ) = exp⎜i⎢ω t − Kr − ⎥⎟ R ⎝ ⎣ 2R ⎦⎠ • R becomes the radius of curvature of the wave front • These are really TEM00 mode emissions from laser • Creates a Gaussian shaped beam intensity ⎛ − 2r 2 ⎞ 2P ⎛ − 2r 2 ⎞ I( r ) I exp⎜ ⎟ exp⎜ ⎟ = 0 ⎜ 2 ⎟ = 2 ⎜ 2 ⎟ ⎝ w ⎠ π w ⎝ w ⎠ Where P = total power in the beam w = 1/e2 beam radius • w changes with distance z along the beam ie. w(z) Measurements of Spotsize • For Gaussian beam important factor is the “spotsize” • Beam spotsize is measured in 3 possible ways • 1/e radius of beam • 1/e2 radius = w(z) of the radiance (light intensity) most common laser specification value 13% of peak power point point where emag field down by 1/e • Full Width Half Maximum (FWHM) point where the laser power falls to half its initial value good for many interactions with materials • useful relationship FWHM = 1.665r1 e FWHM = 1.177w = 1.177r 1 e2 w = r 1 = 0.849 FWHM e2 Gaussian Beam Changes with Distance • The Gaussian beam radius of curvature with distance 2 ⎡ ⎛π w2 ⎞ ⎤ R( z ) = z⎢1 + ⎜ 0 ⎟ ⎥ ⎜ λz ⎟ ⎣⎢ ⎝ ⎠ ⎦⎥ • Gaussian spot size with distance 1 2 2 ⎡ ⎛ λ z ⎞ ⎤ w( z ) = w ⎢1 + ⎜ ⎟ ⎥ 0 ⎜π w2 ⎟ ⎣⎢ ⎝ 0 ⎠ ⎦⎥ • Note: for lens systems lens diameter must be 3w0.= 99% of power • Note: some books define w0 as the full width rather than half width • As z becomes large relative to the beam asymptotically approaches ⎛ λ z ⎞ λ z w(z) ≈ w ⎜ ⎟ = 0 ⎜ 2 ⎟ ⎝π w0 ⎠ π w0 • Asymptotically light
    [Show full text]
  • Optics of Gaussian Beams 16
    CHAPTER SIXTEEN Optics of Gaussian Beams 16 Optics of Gaussian Beams 16.1 Introduction In this chapter we shall look from a wave standpoint at how narrow beams of light travel through optical systems. We shall see that special solutions to the electromagnetic wave equation exist that take the form of narrow beams – called Gaussian beams. These beams of light have a characteristic radial intensity profile whose width varies along the beam. Because these Gaussian beams behave somewhat like spherical waves, we can match them to the curvature of the mirror of an optical resonator to find exactly what form of beam will result from a particular resonator geometry. 16.2 Beam-Like Solutions of the Wave Equation We expect intuitively that the transverse modes of a laser system will take the form of narrow beams of light which propagate between the mirrors of the laser resonator and maintain a field distribution which remains distributed around and near the axis of the system. We shall therefore need to find solutions of the wave equation which take the form of narrow beams and then see how we can make these solutions compatible with a given laser cavity. Now, the wave equation is, for any field or potential component U0 of Beam-Like Solutions of the Wave Equation 517 an electromagnetic wave ∂2U ∇2U − µ 0 =0 (16.1) 0 r 0 ∂t2 where r is the dielectric constant, which may be a function of position. The non-plane wave solutions that we are looking for are of the form i(ωt−k(r)·r) U0 = U(x, y, z)e (16.2) We allow the wave vector k(r) to be a function of r to include situations where the medium has a non-uniform refractive index.
    [Show full text]
  • Arxiv:1510.07708V2
    1 Abstract We study the fidelity of single qubit quantum gates performed with two-frequency laser fields that have a Gaussian or super Gaussian spatial mode. Numerical simulations are used to account for imperfections arising from atomic motion in an optical trap, spatially varying Stark shifts of the trapping and control beams, and transverse and axial misalignment of the control beams. Numerical results that account for the three dimensional distribution of control light show that a super Gaussian mode with intensity − n I ∼ e 2(r/w0) provides reduced sensitivity to atomic motion and beam misalignment. Choosing a super Gaussian with n = 6 the decay time of finite temperature Rabi oscillations can be increased by a factor of 60 compared to an n = 2 Gaussian beam, while reducing crosstalk to neighboring qubit sites. arXiv:1510.07708v2 [quant-ph] 31 Mar 2016 Noname manuscript No. (will be inserted by the editor) Comparison of Gaussian and super Gaussian laser beams for addressing atomic qubits Katharina Gillen-Christandl1, Glen D. Gillen1, M. J. Piotrowicz2,3, M. Saffman2 1 Physics Department, California Polytechnic State University, 1 Grand Avenue, San Luis Obispo, CA 93407, USA 2 Department of Physics, University of Wisconsin-Madison, 1150 University Av- enue, Madison, Wisconsin 53706, USA 3 Department of Physics, University of Michigan, Ann Arbor, MI 48109, USA April 4, 2016 1 Introduction Atomic qubits encoded in hyperfine ground states are one of several ap- proaches being developed for quantum computing experiments[1]. Single qubit rotations can be performed with microwave radiation or two-frequency laser light driving stimulated Raman transitions.
    [Show full text]
  • Chapter 7 Kerr-Lens and Additive Pulse Mode Locking
    Chapter 7 Kerr-Lens and Additive Pulse Mode Locking There are many ways to generate saturable absorber action. One can use real saturable absorbers, such as semiconductors or dyes and solid-state laser media. One can also exploit artificial saturable absorbers. The two most prominent artificial saturable absorber modelocking techniques are called Kerr-LensModeLocking(KLM)andAdditivePulseModeLocking(APM). APM is sometimes also called Coupled-Cavity Mode Locking (CCM). KLM was invented in the early 90’s [1][2][3][4][5][6][7], but was already predicted to occur much earlier [8][9][10] · 7.1 Kerr-Lens Mode Locking (KLM) The general principle behind Kerr-Lens Mode Locking is sketched in Fig. 7.1. A pulse that builds up in a laser cavity containing a gain medium and a Kerr medium experiences not only self-phase modulation but also self focussing, that is nonlinear lensing of the laser beam, due to the nonlinear refractive in- dex of the Kerr medium. A spatio-temporal laser pulse propagating through the Kerr medium has a time dependent mode size as higher intensities ac- quire stronger focussing. If a hard aperture is placed at the right position in the cavity, it strips of the wings of the pulse, leading to a shortening of the pulse. Such combined mechanism has the same effect as a saturable ab- sorber. If the electronic Kerr effect with response time of a few femtoseconds or less is used, a fast saturable absorber has been created. Instead of a sep- 257 258CHAPTER 7. KERR-LENS AND ADDITIVE PULSE MODE LOCKING soft aperture hard aperture Kerr gain Medium self - focusing beam waist intensity artifical fast saturable absorber Figure 7.1: Principle mechanism of KLM.
    [Show full text]
  • Frequency Generation (HD 2D SFG) Spectroscopy
    Adding a dimension to the infrared spectra of interfaces using heterodyne detected 2D sum- frequency generation (HD 2D SFG) spectroscopy Wei Xiong, Jennifer E. Laaser, Randy D. Mehlenbacher , and Martin T. Zanni1 Department of Chemistry, University of Wisconsin-Madison, Madison, WI 53706 Edited by Michael L. Klein, Temple University, Philadelphia, PA, and approved October 13, 2011 (received for review September 13, 2011) In the last ten years, two-dimensional infrared spectroscopy has of carbon monoxide on polycrystalline platinum. Pt-CO is studied become an important technique for studying molecular structures extensively to better understand electrochemical catalysis (13– and dynamics. We report the implementation of heterodyne de- 16). The linear SFG spectrum of Pt-CO has been measured many tected two-dimensional sum-frequency generation (HD 2D SFG) times previously. The spectrum is almost always fit to a Lorent- spectroscopy, which is the analog of 2D infrared (2D IR) spectro- zian line shape (14–16), from which one concludes that Pt-CO is scopy, but is selective to noncentrosymmetric systems such as vibrationally narrowed, meaning that the structural dynamics interfaces. We implement the technique using mid-IR pulse shap- of the CO and its surrounding environment are so fast that the ing, which enables rapid scanning, phase cycling, and automatic system is homogeneous. By resolving the 2D line shape of Pt-CO, phasing. Absorptive spectra are obtained, that have the highest we find that there is a significant inhomogeneous contribution, frequency resolution possible, from which we extract the rephas- which indicates that there is a slow component to the vibrational ing and nonrephasing signals that are sometimes preferred.
    [Show full text]