Download Laser Fundamentals PDF

Laser Fundamentals
Name: Laser Fundamentals
Author: edited by alison fiander
Pages: 263
Year: 2005
Language: English
File Size: 2.65 MB
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ISSN 1619 4802 (Advanced Materials and Technologies ISBN 10 3 540 44379 7 Springer Berlin Heidelberg New York ISBN 13 978 3 540 44379 7 Springer Berlin Heidelberg New York Library of Congress Cataloging in Publication Data: Landolt B rnstein: Numerical Data and Functional Relationships in Science and Technology, New Series. Editor in Chief: W. Martienssen. Group VIII, Volume 1: Laser Physics and Applications. Subvolume A: Laser Fundamentals. Part 1. Edited by H. Weber, G. Herziger, R. Poprawe. Springer Verlag, Berlin, Heidelberg, New York 2004. Includes bibliographies. 1. Physics Tables. 2. Chemistry Tables. 3. Engineering Tables. I. B rnstein, Richard (1852 1913 Landolt, Hans (1831 1910 QC 61.23 502".12 62 53136 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in other ways, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer Verlag. Violations are liable for prosecution act under German Copyright Law. Springer is a part of Springer Science+Business Media. springeronline.com Springer Verlag Berlin Heidelberg 2005 Printed in Germany The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Product Liability: The data and other information in this handbook have been carefully extracted and evaluated by experts from the original literature. Furthermore, they have been checked for correctness by authors and the editorial staff before printing. Nevertheless, the publisher can give no guarantee for the correctness of the data and information provided. In any individual case of application, the respective user must check the correctness by consulting other relevant sources of information. Cover layout: Erich Kirchner, Heidelberg Typesetting: Authors and Redaktion Landolt B rnstein, Darmstadt Printing and Binding: AZ Druck, Kempten (Allg u) SPIN: 1050 7868 63/3020 5 4 3 2 1 0 Printed on acid free paper


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Editors Weber, Horst Technische Universit at Berlin, Optisches Institut, Berlin, Germany Herziger,Gerd Rheinisch Westf alische Technische Hochschule, Aachen, Germany Poprawe, Reinhart Fraunhofer Institut f ur Lasertechnik (ILT), Aachen, Germany Authors Eichler, Hans Joachim Technische Universit at Berlin, Optisches Institut, Berlin, Germany Eppich,Bernd Technische Universit at Berlin, Optisches Institut, Berlin, Germany Fischer, Joachim Physikalisch Technische Bundesanstalt, Abteilung Temperatur und Synchrotronstrahlung, Berlin, Germany G uther,Reiner Ferdinand Braun Institut f ur H ochstfrequenztechnik, Berlin, Germany Gurzadyan, Gagik Technische Universit at M unchen, Institut f ur Physikalische und Theoretische Chemie, Garching, Germany Hermerschmidt, Andreas Technische Universit at Berlin, Optisches Institut, Berlin, Germany Laubereau,Alfred Technische Universit at M unchen, Physik Department E11, M unchen, Germany Lopota, Vitalyi A., member of Russian Academy of Sciences Central R & D Institute of Robotics and Technical Cybernetics, Saint Petersburg, Russian Feder ation Mehl, Oliver Technische Universit at Berlin, Optisches Institut, Berlin, Germany Vidal,CarlRudolf Max Planck Institut f ur Extraterrestrische Physik, Garching, Germany Weber, Horst Technische Universit at Berlin, Optisches Institut, Berlin, Germany Wende, Burkhard Physikalisch Technische Bundesanstalt, Abteilung Temperatur und Synchrotronstrahlung, Berlin, Germany


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Preface The three volumes VIII/1A, B, C document the state of the art of "Laser Physics and Applica tions". Scientific trends and related technological aspects are considered by compiling results and conclusions from phenomenology, observation and experience. Reliable data, physical fundamentals and detailed references are presented. In the recent decades the laser source matured to a universal tool common to scientific research as well as to industrial use. Today a technical goal is the generation of optical power towards shorter wavelengths, shorter pulses and higher power for application in science and industry. Tailoring the optical energy in wavelength, space and time is a requirement for the investigation of laser induced processes, i.e. excitation, non linear amplification, storage of optical energy, etc. According to the actual trends in laser research and development, Vol. VIII/1 is split into three parts: Vol. VIII/1A with its two subvolumes 1A1 and 1A2 covers laser fundamentals, Vol. VIII/1B deals with laser systems and Vol. VIII/1C gives an overview on laser applications. In Vol. VIII/1A1 the following topics are treated in detail: Part 1: Fundamentals of light matter interaction This part compiles the basic elements of classical electromagnetic wave theory, non relativistic quantum mechanics of the two level system and its interaction with the non quantized radiation field. The relevant relations with their approximations and range of validity are discussed. It starts with Maxwell"s equations, wave equation and SVE approximations, presents the Schr odinger equations, the field/atom interaction including the Einstein coe1cients and cross sections. The main parameters characterizing the two level system with typical numbers are given in several tables. Finally, the coherent interaction is briefly discussed. This semiclassical approach is su1cient for most applications in laser technology. The fully quantized theory is o2ered in Vol. VIII/1A2, Chap. 5. Part 2: Radiometry In the first section the definitions of the radiometric quantities and their measurement are sum marized. In the second part the main elements of laser beam characterization are compiled with a detailed discussion of the theoretical background. The experimental determination of the essential quantities according to the ISO normalizations is given. Part 3: Linear optics The design of optical resonators and beam handling requires a broad knowledge in optics. In this part the fundamentals of beam propagation, Gaussian beams, di2raction, refraction, lens design and crystal optics are presented. The extensive references give access to detailed information.


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Contents Part 1 Fundamentals of light matter interaction 1.1 Fundamentals of the semiclassical laser theory V.A. Lopota, H. Weber...............................................3 1.1.1 The laser oscillator...................................................... 3 1.1.2 Theelectromagneticfield................................................. 5 1.1.2.1 Maxwell"s equations..................................................... 5 1.1.2.2 Homogeneous,isotropic,lineardielectrics................................... 6 1.1.2.2.1 Theplanewave ......................................................... 7 1.1.2.2.2 Thesphericalwave ...................................................... 8 1.1.2.2.3 Theslowlyvaryingenvelope(SVE)approximation........................... 9 1.1.2.2.4 TheSVE approximationfordi2raction..................................... 9 1.1.2.3 Propagation in doped media.............................................. 10 1.1.3 Interactionwithtwo levelsystems......................................... 11 1.1.3.1 Thetwo levelsystem .................................................... 11 1.1.3.2 Thedipoleapproximation ................................................ 12 1.1.3.2.1 Inversiondensityandpolarization ......................................... 12 1.1.3.2.2 Theinteractionwithamonochromaticfield................................. 14 1.1.3.3 TheMaxwell Blochequations............................................. 15 1.1.3.3.1 Decay timeT 1 oftheupperlevel(energyrelaxation)......................... 15 1.1.3.3.1.1 Spontaneousemission.................................................... 15 1.1.3.3.1.2 Interactionwiththehostmaterial......................................... 15 1.1.3.3.1.3 Pumping process........................................................ 16 1.1.3.3.2 Decay timeT 2 ofthepolarization(entropyrelaxation) ....................... 16 1.1.4 Steady state solutions.................................................... 17 1.1.4.1 Inversiondensityandpolarization ......................................... 17 1.1.4.2 Small signalsolutions.................................................... 19 1.1.4.3 Strong signalsolutions................................................... 19 1.1.5 Adiabaticequations ..................................................... 20 1.1.5.1 Rate equations.......................................................... 20 1.1.5.2 Thermodynamicconsiderations............................................ 21 1.1.5.3 Pumpingschemesandcompleterateequations.............................. 22 1.1.5.3.1 Thethree levelsystem ................................................... 23 1.1.5.3.2 Thefour levelsystem.................................................... 24 1.1.5.4 Adiabaticpulseamplification ............................................. 25 1.1.5.5 Rate equations for steady state laser oscillators.............................. 26 1.1.6 Lineshapeandlinebroadening ........................................... 26 1.1.6.1 Normalized shape functions............................................... 27 1.1.6.1.1 Lorentzianlineshape .................................................... 27 1.1.6.1.2 Gaussianlineshape...................................................... 27


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X Contents 1.1.6.1.3 Normalizationoflineshapes.............................................. 27 1.1.6.2 Mechanismsoflinebroadening............................................ 28 1.1.6.2.1 Spontaneousemission.................................................... 28 1.1.6.2.2 Dopplerbroadening...................................................... 28 1.1.6.2.3 Collision or pressure broadening........................................... 28 1.1.6.2.4 Saturationbroadening ................................................... 29 1.1.6.3 Typesofbroadening..................................................... 29 1.1.6.3.1 Homogeneousbroadening................................................. 29 1.1.6.3.2 Inhomogeneousbroadening ............................................... 30 1.1.6.4 Timeconstants ......................................................... 31 1.1.7 Coherentinteraction..................................................... 31 1.1.7.1 The Feynman representation of interaction................................. 32 1.1.7.2 Constantlocalelectricfield............................................... 33 1.1.7.3 Propagation of resonant coherent pulses.................................... 34 1.1.7.3.1 Steady state propagation ofn1 pulses...................................... 35 1.1.7.3.1.1 21 pulseinaloss freemedium ............................................ 35 1.1.7.3.1.21 pulseinanamplifyingmedium.......................................... 36 1.1.7.3.2 Superradiance .......................................................... 37 1.1.8 Notations.............................................................. 37 Referencesfor1.1 ....................................................... 40 Part 2 Radiometry 2.1 De nition and measurement of radiometric quantities B. Wende, J. Fischer.................................................45 2.1.1 Introduction............................................................ 45 2.1.2 Definitionofradiometricquantities........................................ 45 2.1.3 Radiometricstandards................................................... 47 2.1.3.1 Primarystandards....................................................... 47 2.1.3.2 Secondarystandards..................................................... 48 2.1.4 Outlook State of the art and trends...................................... 50 Referencesfor2.1 ....................................................... 51 2.2 Beam characterization B. Eppich.............................................................53 2.2.1 Introduction............................................................ 53 2.2.2 TheWignerdistribution ................................................. 53 2.2.3 The second order moments of the Wigner distribution........................ 55 2.2.4 The second order moments and related physical properties.................... 56 2.2.4.1 Nearfield .............................................................. 56 2.2.4.2 Farfield................................................................ 58 2.2.4.3 Phaseparaboloidandtwist............................................... 59 2.2.4.4 Invariants .............................................................. 60 2.2.4.5 Propagation of beam widths and beam propagation ratios.................... 60 2.2.5 Beamclassification ...................................................... 61 2.2.5.1 Stigmaticbeams ........................................................ 62 2.2.5.2 Simpleastigmaticbeams ................................................. 63


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Contents XI 2.2.5.3 Generalastigmaticbeams ................................................ 64 2.2.5.4 Pseudo symmetricbeams................................................. 64 2.2.5.5 Intrinsicastigmatismandbeamconversion ................................. 65 2.2.6 Measurementprocedures ................................................. 66 2.2.7 Beam positional stability................................................. 67 2.2.7.1 Absolutefluctuations .................................................... 67 2.2.7.2 Relativefluctuations..................................................... 69 2.2.7.3 E2ectivelong termbeamwidths .......................................... 69 Referencesfor2.2 ....................................................... 70 Part 3 Linear optics 3.1 Linear optics R. G uther............................................................73 3.1.1 Waveequations ......................................................... 73 3.1.2 Polarization ............................................................ 75 3.1.3 Solutionsofthewaveequationinfreespace................................. 78 3.1.3.1 Waveequation.......................................................... 78 3.1.3.1.1 Monochromaticplanewave............................................... 78 3.1.3.1.2 Cylindricalvectorwave .................................................. 78 3.1.3.1.3 Spherical vector wave.................................................... 78 3.1.3.2 Helmholtzequation...................................................... 79 3.1.3.2.1 Planewave............................................................. 79 3.1.3.2.2 Cylindricalwave ........................................................ 79 3.1.3.2.3 Spherical wave.......................................................... 79 3.1.3.2.4 Di2raction freebeams.................................................... 79 3.1.3.2.4.1 Di2raction free Bessel beams.............................................. 79 3.1.3.2.4.2 Real Bessel beams....................................................... 80 3.1.3.2.4.3 Vectorial Bessel beams................................................... 80 3.1.3.3 Solutionsoftheslowlyvaryingenvelopeequation............................ 80 3.1.3.3.1 Gauss Hermitebeams(rectangularsymmetry) .............................. 81 3.1.3.3.2 Gauss Laguerre beams (circular symmetry)................................. 83 3.1.3.3.3 Cross sectional shapes of the Gaussian modes............................... 83 3.1.4 Di2raction.............................................................. 84 3.1.4.1 Vectortheoryofdi2raction............................................... 85 3.1.4.2 Scalardi2ractiontheory.................................................. 85 3.1.4.3 Time dependentdi2ractiontheory......................................... 89 3.1.4.4 Fraunhofer di2raction patterns............................................ 89 3.1.4.4.1 Rectangular aperture with dimensions 2a 2b.............................. 89 3.1.4.4.2 Circular aperture with radiusa........................................... 90 3.1.4.4.2.1 Applications............................................................ 92 3.1.4.4.3 Gratings ............................................................... 92 3.1.4.5 Fresnel"sdi2ractionfigures ............................................... 93 3.1.4.5.1 Fresnel"sdi2ractiononaslit.............................................. 93 3.1.4.5.2 Fresnel"sdi2ractionthroughlenssystems(paraxialdi2raction)................ 94 3.1.4.6 Fourieropticsanddi2ractiveoptics........................................ 94 3.1.5 Opticalmaterials........................................................ 95 3.1.5.1 Dielectricmedia......................................................... 96 3.1.5.2 Optical glasses.......................................................... 97


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XII Contents 3.1.5.3 Dispersion characteristics for short pulse propagation........................ 97 3.1.5.4 Optics of metals and semiconductors....................................... 98 3.1.5.5 Fresnel"sformulae ....................................................... 98 3.1.5.6 Specialcasesofrefraction ................................................101 3.1.5.6.1 Two dielectric isotropic homogeneous media (32nand 32n 1 arereal)...............101 3.1.5.6.2 Variationoftheangleofincidence.........................................101 3.1.5.6.2.1 External reflection (n<n 1 )...............................................101 3.1.5.6.2.2 Internal reflection (n>n 1 ) ...............................................101 3.1.5.6.3 Reflection at media with complex refractive index (Case 32n=1and32n 1 =n 1 +ik 1 ) ...........................................103 3.1.5.7 Crystaloptics...........................................................104 3.1.5.7.1 Classification ...........................................................104 3.1.5.7.2 Birefringence(example:uniaxialcrystals)...................................106 3.1.5.8 Photonic crystals........................................................107 3.1.5.9 Negative refractive index materials........................................108 3.1.5.10 Referencestodataoflinearoptics.........................................108 3.1.6 Geometricaloptics.......................................................108 3.1.6.1 Gaussianimaging(paraxialrange).........................................108 3.1.6.1.1 Singlesphericalinterface .................................................109 3.1.6.1.2 Imagingwithathicklens.................................................110 3.1.6.2 Gaussian matrix (ABCD matrix, ray transfer matrix) formalism for paraxial optics..................................................................111 3.1.6.2.1 Simple interfaces and optical elements with rotational symmetry..............112 3.1.6.2.2 Non symmetricalopticalsystems..........................................112 3.1.6.2.3 Propertiesofasystem ...................................................112 3.1.6.2.4 General parabolic systems without rotational symmetry......................112 3.1.6.2.5 Generalastigmaticsystem................................................116 3.1.6.2.6 Symplecticopticalsystem ................................................116 3.1.6.2.7 Misalignments ..........................................................116 3.1.6.3 Lensaberrations ........................................................117 3.1.7 Beam propagation in optical systems......................................120 3.1.7.1 Beamclassification ......................................................120 3.1.7.2 Gaussian beam: complexq parameter and itsABCD transformation............120 3.1.7.2.1 Stigmaticandsimpleastigmaticbeams.....................................120 3.1.7.2.1.1 Fundamental Mode......................................................120 3.1.7.2.1.2 Higher orderHermite Gaussianbeamsinsimpleastigmaticbeams.............123 3.1.7.2.2 Generalastigmaticbeam.................................................123 3.1.7.3 Waisttransformation ....................................................124 3.1.7.3.1 General system (fundamental mode).......................................124 3.1.7.3.2 Thin lens (fundamental mode)............................................124 3.1.7.4 Collins integral..........................................................126 3.1.7.4.1 Two dimensional propagation.............................................126 3.1.7.4.2 Three dimensional propagation............................................127 3.1.7.5 Gaussian beams in optical systems with stops, aberrations, and waveguide coupling................................................................127 3.1.7.5.1 Field distributions in the waist region of Gaussian beams including stops and waveaberrationsbyopticalsystem ........................................127 3.1.7.5.2 Modematchingforbeamcouplingintowaveguides ..........................128 3.1.7.5.3 Free spacecouplingofGaussianmodes.....................................128 3.1.7.5.4 Laserfibercoupling......................................................129 Referencesfor3.1 .......................................................131


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