DOCSLIB.ORG

Multielectron Effects in Strong Field Processes in Molecules

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Multielectron Effects in Strong Field Processes in Molecules Multielectron effects in strong field processes in molecules by Yuqing Xia B.A., University of Science and Technology of China, 2010 M.S., University of Colorado at Boulder, 2013 A thesis submitted to the Faculty of the Graduate School of the University of Colorado in partial fulfillment of the requirements for the degree of Doctor of Philosophy Department of Physics 2016 This thesis entitled: Multielectron effects in strong field processes in molecules written by Yuqing Xia has been approved for the Department of Physics Prof. Agnieszka Jaro´n-Becker Prof. Andreas Becker Date The final copy of this thesis has been examined by the signatories, and we find that both the content and the form meet acceptable presentation standards of scholarly work in the above mentioned discipline. iii Xia, Yuqing (University of Colorado at Boulder) Multielectron effects in strong field processes in molecules Thesis directed by Prof. Agnieszka Jaro´n-Becker Laser technology has experienced a rapid evolution in available intensities, frequencies, and pulse durations over the last three decades. Many new laser induced phenomena in atoms have been discovered, such as multiphoton ionization, above-threshold ionization, high-order harmonic generation etc. For the interaction with atoms, usually only one electron in the outermost shell is assumed to be active (called single-active-electron approximation) while all other electrons are considered to remain frozen in their initial states. Due to the extra degrees of freedom (vibration and rotation) and the more complex structures, the interaction of molecules with intense laser pulses reveals many new features. Recent experiments have indicated that electrons from inner valence orbitals of molecules can have significant contributions to ionization and high harmonic generation. Theoretical analysis of these processes in molecules faces the challenge to extend previous theories developed for the atomic case by including the multielectron character of the molecular target. In this thesis we systematically investigate multielectron effects in the interaction of molecules with intense laser light. To this end, we apply time-dependent density-functional theory to solve the multielectron Schr¨odingerequation and analyze highly nonlinear processes such as high harmonic generation, laser-induced ionization and nonadiabatic electron localization. Based on the results of our numerical simulations we predict a new feature in the harmonic spectra of molecules, namely the occurrence of fractional harmonics in the form of Mollow sidebands. Such additional peaks in the spectra appear due to a field-induced resonant coupling of an inner valence orbital with the outermost orbital in a molecule. Furthermore, we show that the theoretical explanation of recent experimental data for the ellipticity of high harmonics in N2 and CO2 require the systematic con- sideration of all inner valence shells as well as the proper alignment distribution in the experiment. We also show that the coupling of molecular orbitals in the field can lead to an enhancement of iv (inner-shell) ionization, potentially leading to a population inversion in the ion, as well as nonadia- batic electron dynamics, where the electron can be trapped at one side of the molecule over several field cycles. Finally, we present the development of a new intense-field theory based on the Floquet theorem with complex Gaussian basis sets and show results of first applications for ionization of simple systems. Dedication To my love and family vi Acknowledgements Firstly, I would like to express my sincere gratitude to my advisor Prof. Agnieszka Jaro´n- Becker for her excellent guidance, caring, patience, and providing me with an excellent atmosphere during my Ph.D study and research. She taught me a lot how to question thoughts and express ideas. Her patience and broad knowledge in Chemistry and Physics helped me to overcome many crisis situation in our project and finish this dissertation. She is also very warmhearted and always be ready to help us no matter what problem we met in both research and daily life. Next, I would like to thank Prof. Andreas Becker, who is like a co-advisor for me in the group. He is a very nice and easygoing person but with rigorous attitude towards science. I am deeply grateful to him for the discussion and always get new ideas because of his keen intuition in Physics. I would also like to thank my previous and current group members: Dr. Carlos Hernandez- Garcia, Daniel Weflen, Hongcheng Ni, Jing Su, Andrew Spott, Michelle Miller, Cory Goldsmith, Benjamin Miller, Ran Reiff, Erez Shani, Quynh Nguyen, as well as Felipe Cajiao. We not only share our ideas on projects but also any interesting things in life. They helped create a pleasant working environment and make the research full of fun. The Janus supercomputer and the clusters at JILA have given me continuous computational support during these years. Without these computation resources, I would not be able to finish my research. So I am grateful to all the people working for the Janus supercomputer and the staff members of JILA computing group. vii Finally, and most importantly, I would also like to thank my family and my friends for the support they provided me. In particular, I must acknowledge my wife. Thanks for her encourage- ment when I was frustrated and thanks to her to let me have a such lovely son. All in all, without their love, encouragement I would not have accomplished this thesis. viii Contents Chapter 1 Introduction 1 2 Time-dependent density-functional theory 6 2.1 Multielectron system . 7 2.2 The Hohenberg-Kohn theorem . 9 2.3 Kohn-Sham equation . 10 2.4 Time-dependent density-functional theory . 13 2.5 Exchange correlation functionals . 15 2.5.1 LDA and LB94 functionals . 17 2.6 The pseudopotential approximation . 19 2.7 Implementation of TDDFT . 20 2.7.1 Comparison of exchange-correlation functionals . 22 3 Multielectron effects in high-order harmonic generation from molecules 25 3.1 Classical and semi-classical description of HHG . 26 3.1.1 Three-step model . 26 3.1.2 Strong field approximation (SFA) . 28 3.1.3 Saddle point approximation . 31 3.2 High-order harmonic generation from molecules . 32 3.3 Fractional harmonics . 36 ix 3.3.1 Open shell molecules . 36 3.4 Ellipticity of high-order harmonics . 54 + 3.4.1 Ellipticity from one-electron system H2 ..................... 56 3.4.2 Complex ellipticity pattern due to two-electron effects . 58 3.4.3 Alignment angle average . 59 3.4.4 Comparison with experimental data for N2 ................... 60 3.4.5 Inner shell contributions to ellipticity of harmonics . 66 3.4.6 Ellipticity of harmonics from CO2 ........................ 69 3.5 Summary . 73 4 Multielectron effects in strong-field ionization from molecules 75 4.1 Role of ionization potential and orbital symmetry . 76 4.2 Resonance enhanced ionization of open-shell molecules . 78 4.3 Multiorbital contributions and enhanced ionization from inner-shell orbitals of N2 . 80 4.3.1 Total ionization . 89 4.3.2 Ionization of N2 in filamentation experiments . 90 4.4 Ionization from other molecules . 92 4.5 Summary . 95 5 Nonadiabatic electron localization 96 5.1 Coupling induced nonadiabatic electron dynamics . 98 5.2 Dependence of nonadiabatic behavior on laser intensity . 101 5.3 Nonadiabatic localization in two-color laser field . 102 5.4 Electron localization in other molecules . 104 5.5 Summary . 105 6 Complex Gaussian basis for non-Hermitian Floquet formalism 108 6.1 Floquet theorem . 109 x 6.2 Complex basis sets . 111 6.3 Gaussian basis integral . 113 6.3.1 Fundamental integral . 113 6.3.2 Recursion relation for general primitive Gaussian basis integrals . 117 6.4 Technical details . 120 6.5 Optimization for complex Gaussian basis . 122 6.5.1 Optimization algorithm . 123 6.6 Results and discussion . 126 6.6.1 One photon ionization of H atom . 126 6.6.2 Two photon ionization from H atom . 130 + 6.6.3 Two photon ionization from H2 . 131 6.7 Summary . 133 7 Summary 134 Bibliography 136 xi Tables Table + 3.1 Orbital energies (eigenvalue) of N2 ............................ 47 6.1 Results for one-photon ionization cross sections compared to those from the litera- ture. F is root mean square of laser electric field in atomic units. All the calculations above are performed for n = 0; 1 except for F = 0:05, in which n is −1; 0; 1; 2 due to the strong coupling at high intensity. The superscripts of the reference values: (a) stand for [243] and (b) for [233] . 128 6.2 The exponents of complex Gaussian basis sets for different laser frequencies. These basis sets are tested for the range of laser intensity from 7 × 108 W/cm to 1:8 × 1014 W/cm2. ........................................129 6.3 Complex Gaussian exponents for two photon ionization . 133 xii Figures Figure 2.1 Density plots for H atom in a 800 nm laser field at intensity of 1 × 1014 W/cm2 with mask function (left) and imaginary absorbing potential (right). 21 2.2 Comparison of population from valence orbitals of N2 between LB94 (left) and LDA (right) functionals. Laser field is at wavelength of 400 nm and intensity of 5 × 1013 W/cm2. Only the relevant KS orbitals which possess an important response to the laser field are shown with their labels. 22 2.3 Comparison of high harmonic spectra of N2 for LDA and LB94 functionals. Laser field is at wavelength of 400 nm and intensity of 1 × 1014 W/cm2 with polarization parallel to the molecular axis. 23 2.4 Projection between coupled orbitals of N2 in a 400 nm laser field at intensity of 1 × 1014 W/cm2 for LDA and LB94 functionals. 23 3.1 Three step model for high-order harmonic generation (left) and typical harmonic spectra from noble gas atom (right), adapted from [144].
Load more

Recommended publications
  • An Application of the Theory of Laser to Nitrogen Laser Pumped Dye Laser
    SD9900039 AN APPLICATION OF THE THEORY OF LASER TO NITROGEN LASER PUMPED DYE LASER FATIMA AHMED OSMAN A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science in Physics. UNIVERSITY OF KHARTOUM FACULTY OF SCIENCE DEPARTMENT OF PHYSICS MARCH 1998 \ 3 0-44 In this thesis we gave a general discussion on lasers, reviewing some of are properties, types and applications. We also conducted an experiment where we obtained a dye laser pumped by nitrogen laser with a wave length of 337.1 nm and a power of 5 Mw. It was noticed that the produced radiation possesses ^ characteristic^ different from those of other types of laser. This' characteristics determine^ the tunability i.e. the possibility of choosing the appropriately required wave-length of radiation for various applications. DEDICATION TO MY BELOVED PARENTS AND MY SISTER NADI A ACKNOWLEDGEMENTS I would like to express my deep gratitude to my supervisor Dr. AH El Tahir Sharaf El-Din, for his continuous support and guidance. I am also grateful to Dr. Maui Hammed Shaded, for encouragement, and advice in using the computer. Thanks also go to Ustaz Akram Yousif Ibrahim for helping me while conducting the experimental part of the thesis, and to Ustaz Abaker Ali Abdalla, for advising me in several respects. I also thank my teachers in the Physics Department, of the Faculty of Science, University of Khartoum and my colleagues and co- workers at laser laboratory whose support and encouragement me created the right atmosphere of research for me. Finally I would like to thank my brother Salah Ahmed Osman, Mr.
    [Show full text]
  • Population Inversion X-Ray Laser Oscillator
    Population inversion X-ray laser oscillator Aliaksei Halavanaua, Andrei Benediktovitchb, Alberto A. Lutmanc , Daniel DePonted, Daniele Coccoe , Nina Rohringerb,f, Uwe Bergmanng , and Claudio Pellegrinia,1 aAccelerator Research Division, SLAC National Accelerator Laboratory, Menlo Park, CA 94025; bCenter for Free Electron Laser Science, Deutsches Elektronen-Synchrotron, Hamburg 22607, Germany; cLinac & FEL division, SLAC National Accelerator Laboratory, Menlo Park, CA 94025; dLinac Coherent Light Source, SLAC National Accelerator Laboratory, Menlo Park, CA 94025; eLawrence Berkeley National Laboratory, Berkeley, CA 94720; fDepartment of Physics, Universitat¨ Hamburg, Hamburg 20355, Germany; and gStanford PULSE Institute, SLAC National Accelerator Laboratory, Menlo Park, CA 94025 Contributed by Claudio Pellegrini, May 13, 2020 (sent for review March 23, 2020; reviewed by Roger Falcone and Szymon Suckewer) Oscillators are at the heart of optical lasers, providing stable, X-ray free-electron lasers (XFELs), first proposed in 1992 transform-limited pulses. Until now, laser oscillators have been (8, 9) and developed from the late 1990s to today (10), are a rev- available only in the infrared to visible and near-ultraviolet (UV) olutionary tool to explore matter at the atomic length and time spectral region. In this paper, we present a study of an oscilla- scale, with high peak power, transverse coherence, femtosecond tor operating in the 5- to 12-keV photon-energy range. We show pulse duration, and nanometer to angstrom wavelength range, that, using the Kα1 line of transition metal compounds as the but with limited longitudinal coherence and a photon energy gain medium, an X-ray free-electron laser as a periodic pump, and spread of the order of 0.1% (11).
    [Show full text]
  • What Is the Shape of the Helium Trimer? a Comparison with the Neon and Argon Trimers Dario Bressanini* and Gabriele Morosi
    ARTICLE pubs.acs.org/JPCA What Is the Shape of the Helium Trimer? A Comparison with the Neon and Argon Trimers Dario Bressanini* and Gabriele Morosi Dipartimento di Scienze Chimiche e Ambientali, Universita' dell'Insubria, Via Lucini 3, 22100 Como, Italy ABSTRACT: Despite its apparent simplicity and extensive theoretical investiga- tions, the issue of what is the shape of the helium trimer is still debated in the literature. After reviewing previous conflicting interpretations of computational studies, we introduce the angleÀangle distribution function as a tool to discuss in a simple way the shape of any trimer. We compute this function along with many different geometrical distributions using variational and diffusion Monte Carlo methods. We compare them with the corresponding ones for the neon and argon fl trimers. Our analysis shows that while Ne3 and Ar3 uctuate around an 4 equilibrium structure that is an equilateral triangle, He3 shows an extremely broad angleÀangle distribution function, and all kinds of three-atom configura- 4 tions must be taken into account in its description. Classifying He3 as either equilateral or linear or any other particular shape, as was done in the past, is not sensible, because in this case the intuitive notion of equilibrium structure is ill defined. Our results could help the interpretation of future experiments aimed at measuring the geometrical properties of the helium trimer. ’ INTRODUCTION candidate for the Efimov effect, first discussed in nuclear physics. 1 Weakly bound van der Waals noble gases clusters in the last The recent paper of Kolganova et al. provides a nice review of the literature of this field of research.
    [Show full text]
  • Rate Equations
    Ultrafast Optical Physics II (SoSe 2019) Lecture 4, May 3, 2019 (1) Laser rate equations (2) Laser CW operation: stability and relaxation oscillation (3) Q-switching: active and passive 1 Possible laser cavity configurations The laser (oscillator) concept explained using a circuit model. 2 Self-consistent in steady state V.A. Lopota and H. Weber, fundamentals of the semiclassical laser theory 3 Laser rate equations Interaction cross section: [Unit: cm2] !") ") Spontaneous = −*") = − !$ τ21 emission § Interaction cross section is the probability that an interaction will occur between EM !" field and the atomic system. # = −'" ( !$ # § Interaction cross section only depends Absorption on the dipole matrix element and the linewidth of the transition !" ) Stimulated = −'")( !$ emission 4 How to achieve population inversion? relaxation relaxation rate relaxation Induced transitions Pumping rate relaxation Pumping by rate absorption relaxation relaxation rate Four-level gain medium 5 Laser rate equations for three-level laser medium If the relaxation rate is much faster than and the number of possible stimulated emission events that can occur , we can set N1 = 0 and obtain only a rate equation for the upper laser level: This equation is identical to the equation for the inversion of the two-level system: upper level lifetime equilibrium upper due to radiative and level population w/o non-radiative photons present processes 6 More on laser rate equations Laser gain material V:= Aeff L Mode volume fL: laser frequency I: Intensity vg: group velocity
    [Show full text]
  • Terahertz Sources
    Terahertz sources Pavel Shumyatsky Robert R. Alfano Downloaded from SPIE Digital Library on 22 Mar 2011 to 128.59.62.83. Terms of Use: http://spiedl.org/terms Journal of Biomedical Optics 16(3), 033001 (March 2011) Terahertz sources Pavel Shumyatsky and Robert R. Alfano City College of New York, Institute for Ultrafast Spectroscopy and Lasers, Physics Department, MR419, 160 Convent Avenue, New York, New York 10031 Abstract. We present an overview and history of terahertz (THz) sources for readers of the biomedical and optical community for applications in physics, biology, chemistry, medicine, imaging, and spectroscopy. THz low-frequency vibrational modes are involved in many biological, chemical, and solid state physical processes. C 2011 Society of Photo-Optical Instrumentation Engineers (SPIE). [DOI: 10.1117/1.3554742] Keywords: terahertz sources; time domain terahertz spectroscopy; pumps; probes. Paper 10449VRR received Aug. 10, 2010; revised manuscript received Jan. 19, 2011; accepted for publication Jan. 25, 2011; published online Mar. 22, 2011. 1 Introduction Yajima et al.4 first reported on tunable far-infrared radiation by One of the most exciting areas today to explore scientific and optical difference-frequency mixing in nonlinear crystals. These engineering phenomena lies in the terahertz (THz) spectral re- works have laid the foundation and were used for a decade and gion. THz radiation are electromagnetic waves situated between initiated the difference-frequency generation (DFG), parametric the infrared and microwave regions of the spectrum. The THz amplification, and optical rectification methods. frequency range is defined as the region from 0.1 to 30 THz. The The THz region became more attractive for investigation active investigations of the terahertz spectral region did not start owing to the appearance of new methods for generating T-rays until two decades ago with the advent of ultrafast femtosecond based on picosecond and femtosecond laser pulses.
    [Show full text]
  • A Fundamental Approach to Phase Noise Reduction in Hybrid Si/III-V Lasers
    A fundamental approach to phase noise reduction in hybrid Si/III-V lasers Thesis by Scott Tiedeman Steger In Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy California Institute of Technology Pasadena, California 2014 (Defended May 14, 2014) ii © 2014 Scott Tiedeman Steger All Rights Reserved iii Contents Acknowledgements ix Abstract xi 1 Introduction1 1.1 Narrow-linewidth laser sources in coherent communication......1 1.2 Low phase noise Si/III-V lasers.....................4 2 Phase noise in laser fields7 2.1 Optical cavities..............................8 2.1.1 Loss................................8 2.1.2 Gain................................9 2.1.3 Quality factor........................... 10 2.1.4 Threshold condition....................... 11 2.2 Interaction of carriers with cavity modes................ 11 2.2.1 Spontaneous transitions into the lasing mode.......... 12 2.2.2 Spontaneous transitions into all modes............. 17 2.2.3 The spontaneous emission coupling factor........... 19 2.2.4 Stimulated transitions...................... 19 2.3 A phenomenological calculation of spontaneous emission into a lasing mode above threshold........................... 21 2.3.1 Number of carriers........................ 21 2.3.2 Total spontaneous emission rate................. 21 2.4 Phasor description of phase noise in a laser............... 23 iv 2.4.1 Spontaneous photon generation................. 25 2.4.2 Photon storage.......................... 27 2.4.3 Spectral linewidth of the optical field.............. 29 2.4.4 Phase noise power spectral density............... 30 2.4.5 Linewidth enhancement factor.................. 32 2.4.6 Total linewidth.......................... 34 3 Phase noise in hybrid Si/III-V lasers 35 3.1 The advantages of hybrid Si/III-V...................
    [Show full text]
  • Arxiv:1410.6667V2 [Physics.Optics]
    Self-starting stable coherent mode-locking in a two-section laser R. M. Arkhipova, M. V. Arkhipovb, I. Babushkinc,d a ITMO University, Kronverkskiy prospekt, 49, 197101 St. Petersburg, Russia, b Faculty of Physics, St. Petersburg State University, Ulyanovskaya 1, Petrodvoretz, St. Petersburg 198504, Russia c Institute of Quantum Optics, Leibniz University Hannover, Welfengarten 1 30167, Hannover, Germany d Max Born Institute, Max Born Str. 2a, 12489 Berlin, Germany Coherent mode-locking (CML) uses self-induced transparency (SIT) soliton formation to achieve, in contrast to conventional schemes based on absorption saturation, the pulse durations below the limit allowed by the gain line width. Despite of the great promise it is difficult to realize it experimentally because a complicated setup is required. In all previous theoretical considerations CML is believed to be non-self-starting. In this article we show that if the cavity length is selected properly, a very stable (CML) regime can be realized in an elementary two-section ring-cavity geometry, and this regime is self-developing from the non-lasing state. The stability of the pulsed regime is the result of a dynamical stabilization mechanism arising due to finite-cavity-size effects. I. INTRODUCTION Development of ultrashort laser pulse sources with high repetition rates and peak power is an area of principal in- terest in optics. Such lasers have applications in a high- bit-rate optical communications, real time-monitoring of ultrafast processes in matter etc. A well-known method for generating high power ultrashort optical pulses is a passive mode-locking (PML) [1–6]. In order to achieve PML, a nonlinear saturable absorbing medium is placed into the laser cavity.
    [Show full text]
  • Chapter 6. Laser: Theory and Applications
    Chapter 6. Laser: Theory and Applications Reading: Sigman, Chapter 6, 7, and 26 Bransden & Joachain, Chapter 15 Laser Basics Light Amplification by Stimulated Emission of Radiation hν = E − E E1 1 0 Stimulated emission hν E0 Population inversion (N1 > N0) ⇒ laser, maser 2 2 4π ⎛ e ⎞ I(ω ) 2 Transition rate W = ⎜ ⎟ 01 M (ω ) ∝ I(ω ) for stimulated emission 01 2 ⎜ ⎟ 2 01 01 01 m c ⎝ 4πε0 ⎠ ω01 Incident light intensity Pumping (optical, electrical, etc.) for population inversion Gain medium High reflector Out coupler Optical cavity Longitudinal Modes in an Optical Cavity EM wave in a cavity Boundary condition: λ cτ πc L = m = m = m m = 1, 2, 3, … 2 2 ω 2L c π c ⇒ λ = ,ν = m, ω = m m 2L L 2L Round-trip time of flight: T = = mτ c Typical laser cavity: L = 1.5 m, λ = 0.75 µm 2L 3 m : T = = =10−8 sec =10 nsec : c 3×108 m / sec 1 ⇒ ν = =108 Hz =100 MHz R T 2L 3 m L m = = = 4×106 = 4 milion !! λ 0.75×10−6 m Single mode 2 2 I(t) = cosω0t = cost Spectrum Intensity 1 Frequency Intensity -100 -50 0 50 100 Time Cavity Quality Factors, Qc End mirror L Out coupler R ≈ 1 T = 1 ~ 5 % Energy loss by reflection, transmission, etc. ∞ −δct /T −iω0t E(ω) = E0e e dt ∫0 E e−δct /T e−iω0t 0 E = 0 i(ω −ω0 ) +δc /T t E(ω) 2 Lorentzian Emission spectrum 2 2 E δ c ω E(ω) = 0 ~ = 2 2 2 T Q (ω −ω ) +δ /T c 0 c ω ω0 Energy of circulating EM wave, Icirc(t) ⎡ t ⎤ 2L T = Icirc (t) = Icirc (0)×exp⎢−δ c ⎥, : round-trip time of flight ⎣ T ⎦ c Number of round trips in t ⎡ ω ⎤ ⇒ Icirc (t) = Icirc (0)×exp⎢− t⎥ ⎣ Qc ⎦ Q-factor of a RLC circuit ωT 4π L 1 ω ωL Q = = Q = = where
    [Show full text]
  • Step-Pulse Modulation of Gain-Switched Semiconductor Pulsed Laser
    applied sciences Article Step-Pulse Modulation of Gain-Switched Semiconductor Pulsed Laser Bin Li , Changyan Sun, Yun Ling *, Heng Zhou and Kun Qiu School of Information and Communication Engineering, University of Electronic Science and Technology of China, Chengdu 611731, China; [email protected] (B.L.); [email protected] (C.S.); [email protected] (H.Z.); [email protected] (K.Q.) * Correspondence: [email protected] Received: 12 December 2018; Accepted: 8 February 2019; Published: 12 February 2019 Featured Application: The proposed novel approach presented in this paper offers a highly effective modulated method for a gain-switched semiconductor laser. As a result, we can acquire the output pulse with a higher peak power (the limit can be reached) and shorter width and can be incorporated as a practical and cost-effective approach for many fields which need high extinction ratio short pulse, such as the optical time domain reflectometry. Abstract: To improve the peak power and extinction ratio and produce ultra-short pulses, a novel approach is presented in this paper offers a highly effective modulated method for a gain-switched semiconductor laser by using step-pulse signal modulation. For the purpose of single pulse output, then the effects on the output from the gain-switched semiconductor laser are studied by simulating single mode rate equation when changing the amplitude and width of the modulated signal. The results show that the proposed method can effectively accelerate the accumulation speed of the population inversion and we can acquire the output pulse with higher peak power and shorter width. Compared with the traditional rectangular wave modulation, this method is advantageous to obtain a high gain switching effect by increasing the second modulation current and reduce the pulse width to saturation at the best working point.
    [Show full text]
  • 23. Lasers II Four-Level Systems Are the Best for Lasers
    23. Lasers II Four-level systems are the best for lasers Steady-state conditions: - threshold - longitudinal modes Some laser examples “The teleforce ray will send concentrated beams of particles through the free air, of such tremendous energy that they will bring down a fleet of 10,000 enemy airplanes at a distance of 250 miles from the defending nation's border and will cause armies of millions to drop dead in their tracks.” - Nikolai Tesla, 1937 Two-, three-, and four-level systems Two-level Three-level Four-level system system system Fast decay Fast decay Pump Pump Laser Transition Laser Transition Transition Transition Laser Pump Transition Transition Fast decay At best, you get If you hit it hard, equal populations. Lasing is easy! you get lasing. No lasing. II/ sat always NN negative 1/ I Isat Gain must exceed loss Having a population inversion (N < 0) isn’t enough. Additional losses in intensity occur, due to absorption, scattering, and reflections. Also there is an output beam… L I1 I0 output I2 a laser medium with gain, I3 G = exp(gL) Mirror with Mirror with R < 100% R = 100% The laser will lase if the beam maintains Gain = Loss its intensity after one round trip, that is, if: This means: I3 = I0. Here, it means a condition on I3: II30 exp(gLR ) exp(gLI ) 0 In this expression, we are ignoring sources of loss other than the mirror reflectivity R. This is an approximation, because there are always other sources of loss. N < 0 is necessary, but not sufficient. Solving for g, we find: 1 gRln(1/ ) 2L There is a minimum value of the gain which is required in order to turn on a laser.
    [Show full text]
  • Fantasy Versus Reality in Fragment-Based Quantum Chemistry
    The Journal PERSPECTIVE of Chemical Physics scitation.org/journal/jcp Fantasy versus reality in fragment-based quantum chemistry Cite as: J. Chem. Phys. 151, 170901 (2019); doi: 10.1063/1.5126216 Submitted: 31 August 2019 • Accepted: 6 October 2019 • Published Online: 4 November 2019 John M. Herberta) AFFILIATIONS Department of Chemistry and Biochemistry, The Ohio State University, Columbus, Ohio 43210, USA a)[email protected] ABSTRACT Since the introduction of the fragment molecular orbital method 20 years ago, fragment-based approaches have occupied a small but growing niche in quantum chemistry. These methods decompose a large molecular system into subsystems small enough to be amenable to electronic structure calculations, following which the subsystem information is reassembled in order to approximate an otherwise intractable supersys- tem calculation. Fragmentation sidesteps the steep rise (with respect to system size) in the cost of ab initio calculations, replacing it with a distributed cost across numerous computer processors. Such methods are attractive, in part, because they are easily parallelizable and there- fore readily amenable to exascale computing. As such, there has been hope that distributed computing might offer the proverbial “free lunch” in quantum chemistry, with the entrée being high-level calculations on very large systems. While fragment-based quantum chemistry can count many success stories, there also exists a seedy underbelly of rarely acknowledged problems. As these methods begin to mature, it is time to have a serious conversation about what they can and cannot be expected to accomplish in the near future. Both successes and challenges are highlighted in this Perspective.
    [Show full text]
  • Amplified Spontaneous Emission at 5.23 Μm in Two-Photon Excited Rb Vapour
    Amplified spontaneous emission at 5.23 μm in two-photon excited Rb vapour A.M. Akulshin1, N. Rahaman1, S.A. Suslov2 and R.J. McLean1 1Centre for Quantum and Optical Science, Swinburne University of Technology, PO Box 218, Melbourne 3122, Australia 2Department of Mathematics, Faculty of Science, Engineering and Technology, Swinburne University of Technology, Melbourne 3122, Australia Abstract. Population inversion on the 5D5/2-6P3/2 transition in Rb atoms produced by cw laser excitation at different wavelengths has been analysed by comparing the generated mid-IR radiation at 5.23 μm originating from amplified spontaneous emission (ASE) and isotropic blue fluorescence at 420 nm. Using a novel method for detection of two photon excitation via ASE, we have observed directional co- and counter-propagating emission at 5.23 μm. Evidence of a threshold-like characteristic is found in the ASE dependences on laser detuning and Rb number density. We find that the power dependences of the backward- and forward- directed emission can be very similar and demonstrate a pronounced saturation characteristic, however their spectral dependences are not identical. The presented observations could be useful for enhancing efficiency of frequency mixing processes and new field generation in atomic media. 1. Introduction The interest in frequency conversion of resonant light and laser-like new field generation in atomic media specially prepared by resonant laser light is driven by a number of possible applications [1, 2, 3, 4]. The transfer of population to excited levels, particularly to create population inversion on strong transitions in the optical domain, is an essential part of the nonlinear process of frequency up- and down-conversion [5, 6, 7].
    [Show full text]