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Lasertheorie Vorlesung 3233 L 541 – SS12 Lasertheorie Kathy Lüdge, EW 741 Was ist ein Laser? LASER = Light Amplification by Stimulated Emission of Radiation Lichtverstärkung durch induzierte Emission von Strahlung R R1 2 Licht Aktives Medium Spiegel Hohlraum-Resonator Energiezufuhr (Pumpen) Eigenschaften des Lichtes? offenes Vielteilchensystem System im thermischen Nicht Gleichgewicht Eigenschaften von Laserlicht (1) Monochromasie 15 Frequenzunschärfe f 1 Hz, ff / 10 für sichtbares Licht (Laserlicht: reiner Ton Glühlampe: Rauschen) (2) Kohärenz langer Wellenzug, typisch 300000km (gewöhnliche Lampen: ca.5m) (3) Hohe Intensität Dauerbetrieb 100kW, 12 Gepulst von Gigawatt bis zu 10 W (Bsp. CO2-Laser) (4) Geringer Öffnungswinkel (5) Kurze intensive Lichtpulse Femtosekunden-Attosekunden Pulse möglich Photonenstatistik in Laser und Glühlampe Sieht man Licht an, ob es vom Laser oder von einer Glühlampe +Spektralfilter+strahlkorrigierende Optik kommt? Antwort: Ja Photonenstatistik ist verschieden Poisson-Verteilung Thermische Verteilung Quantenmechnischer Im Gleichgewicht gilt Charakter des Laserlichtes Bose Einstein Statistik Modell Hierachie Bilanzgleichungen Schwierigkeitsgrad Mittlere Photonenzahl und Besetzungszahlen Intensitätsverteilung, Einschaltdynamik,Modenwettbewerb Semiklassische Gleichungen Verstärker, Pulsdynamik, Modenkopplung Quantenmechnische Beschreibung Licht und Atome durch Schrödingergleichung beschieben Photonenstatistik, Linienbreite Logische Logische Herangehensweise Inhalt 1. Einführung i. Historisches ii. Lasertypen iii. Schwarzer Strahler 2. Bilanzgleichungen (Ratengleichungen) i. Ein-Moden-Laser • Spiking • Relaxationsoszillationen ii. Halbleiterlaser iii. Vielmodenlaser • Lochbrennen + Modenwettbewerb Inhalt 3. Semiklassische Lasergleichungen i. Wellengleichung für das elektrische Feld ii. Zeitabhängige Lösung und Modenkopplung iii. Ultrakurze Pulse 4. Vollquantenmechanische Beschreibung i. Spontane Emission ii. Photonenstatistik 5. Laserinstabilitäten i. Laser mit optischer Rückkopplung ii. Asymptotische Methoden Literatur • H. Haken, Licht und Materie Vol. I , Elemente der Quantenoptik • H. Haken, Licht und Materie Vol. II , Laser, North Holland 1985 • T. Erneux, P. Glorieux, Laser Dynamics, Cambridge Univ. Press, 2010 • L.A. Coldren, S.W. Corzine, Diode Lasers and Photonic Integrated Circuits Wiley & Sons, 1995 • A. Yariv, Optical Electronics in Modern Communications, Oxford Univ. Press, 1997 • W.W. Chow, S.W. Koch, M. Sargent III, Semiconductor Laser Physics, Springer Verlag 1994 1.2. Historisches Quelle: Physik Journal, Juli 2010 Notable Nobel Prizes for Lasers 1964: American Charles Townes shared the Nobel Prize in Physics with Russian scientists Nicolay Basov and Aleksandr Prokhorov for the 1958 invention of the maser. 1981: Americans Nicolaas Bloembergen and Arthur Schawlow shared the Physics Prize for development of laser spectroscopy. 1997: French scientist Claude Cohen-Tannoudji shared the Physics Prize with Americans Steven Chu and William Phillips for development of methods to cool and trap atoms with laser 1999: Ahmed Zewail of CalTech won the Chemistry Prize for showing that it is possible with rapid laser technique to see how atoms in a molecule move during a chemical reaction. 2000: Russian Zhores Alferov and American Herbert Kroemer shared half the Physics Prize for developing semiconductor heterostructures used in high-speed and opto-electronics and permitting room-temperature, continuous-wave semiconductor diode lasers. 2001: Americans Eric Cornell, Wolfgang Ketterle, and Carl E. Wieman shared the Physics Prize for the achievement of Bose-Einstein condensation in dilute gases of alkali atoms, and for early fundamental studies of the properties of the condensates. 2005: Germany’s Theodor Hansch shared the Physics Prize with American John Hall for development of laser-based precision spectroscopy, including the optical frequency comb technique. Induzierte Emission (postuliert von Einstein 1917) 2 Einsteins Ziel: Herleitung der Planckschen 8h Strahlungsformel. () dd ce3 h 1 Energiedichte des Strahlungsfeldes langwelliger Teil: gute Übereinstimmung mit klassischen Gleichverteilungssatz Spektrale Energiedichte Spektrale Energiedichte – Rayleigh Jeans Gesetz Wellenlänge kurzwelliger Teil: Ultraviolettkatastrophe Microwave Amplification by Stimulated Emission of Radiation • Angeregte NH3-Moleküle eingeschlossen im Hohlraumresonator (l=12,7 mm) (Selektion über inhomogene Felder die unterschiedlich auf die Dipolmoment der Moleküle wirken) • elektromagnetische Welle wird durch induzierte Emission verstärkt Stehende Welle im Resonator mit leitender Wand • geeignete Dimensionierung nur eine Mode im Resonator 1954: erster Ammoniak MASER von Charles Townes, J. P. Gordon (im Bild), und H. J. Zeiger 1964: Nobelpreis an Nikolay Basov, Aleksandr Prokhorov und Charles Townes Der erste Laser (1960) Aufbau eines Rubinlasers Vorgeschlagen von Schalow und Townes 1958) Gepulste optische Anregung durch Blitzlampe T.H. Mainman mit dem ersten Laser (1960) Dauerstrichbetrieb: Nelson and Boyle (1962) Historische- Entwicklung Datenübertragung mit Laserstrahl: 1961 Lichtleitung in Glasfasern: 1966 Dauerstrich Laserdiode: 1970 1961 A. Javan (rechts) bei der Justage eines HeNe Transatlantikkabel TAT1 (4 Mbit/s) 1956 Lasers TAT14 (6410 Gbit/s) 2001 Main One Cable System (2 Tbit/s) 2010 Erste GaAs Laserdiode, 1962 gepulster Betrieb in flüssigem He Dauerstrich Laserdiode (BellLabs) 1970 1.3. Lasertypen Festkörperlaser (1) Rubin-Laser 3-Niveau System 3+ Cr -Dotierungsatome in Al2O3-Kristall Festkörperlaser (2) Nd:YAG-Laser 4-Niveau System (Neodym-Yttrium-Aluminium-Granat-Laser) Atome sind als Störstellen in den Festkörper eingebaut Titan Saphir Laser: vibronischer Laser 0,79µm thermische Schwingungen des Kristallgitters führt zu starker Verbreiterung 670 bis 1070 nm Faserlaser • spezielle Form des Festkörperlasers: dotierte Glasfaser • robusten Aufbau, • hohe Strahlqualität und Effizienz – 50 kW (Multimode, ) und 3 kW (Singlemode) Gaslaser: Laseraktive Atome bilden ein Gas He-Ne-Laser • Pumpen durch Stoßanregung der Heliumatome mittels energiereicher Elektronen (Gasentladung) Übergänge von Elektronen in Molekülen •Excimer-Laser •2-atomige Moleküle aus einem Atom im Grundzustand und einem Atom im angeregten Zustand •relaxiert das angeregte Atom, so zerfällt das Molekül (N1=0) •Anregung durch hochenergetische Elektronenstrahlen •Emision im UV (Xe2, Kr2, Ar2, XeBr, ...) •Chemische Laser * •Elektronenanregung durch chemische Reaktion z.B. F+H2HF +H •Farbstofflaser •organische Farbstoffe, z.B. Rodamin6G (1966 von Schäfer erfunden) •durch unterschiedliche Farbstoffe leicht durchstimmbar •CO2-Laser - Übergänge zwischen Molekülschwingungszuständen •Hoher Wirkungsgrad (30%) •1964 von Patel entwickelt; l=10,6µm Röntgenlaser- Freie Elektronenlaser • Elektronenstrahl im Vakuum passiert räumlich moduliertes Magnetfeld • Ablenkung der Elektronen führt zur Ausstrahlung einer elektromagnetischen Welle • Abstimmbarkeit durch kontinuierliche Variation des Magnetfeldes •Neuer XFEL bei DESY im Bau Elektronische Übergänge in Halbleitern - Halbleiterlaser Vorteile: direkt elektrisch gepumpt Hohe Effizienz 50% (1% bei Gaslaser) gezielte Steuerung kleine Größe sehr zuverlässig, lange Lebensdauer 100 Jahre (1000 h bei anderen) Nachteile: großer Öffnungswinkel (korrigierende Optik nötig) geringe Intensität (zu lösen mit vielen Lasern) vielmodig (zu lösen mit Bragg Gitter) Stand der Technik Hochleistungslaser Herkules (Ti-Saphir Laser) University of Michigan Puls-Laserleistung: 300TW Pulsdauer: 30 fs Pulsabstand: 10s Strahldurchmesser: 1,3µm Diodenlaser, 635nm CW Laserleistung 7W Iris OPO (340 to 2500 nm) Leistung: >1W bei 340-520nm >400mW bei 490-750nm. Pulslängen 80 to 350fs Laseranwendungen 2008 sonstige Laser 45% Halbleiterlaser 55% LASER MARKETPLACE 2008 www.laserfocusworld.com Lasertheorie Generic Rate Equation Model N e-density dneej n e GRRR V ne dtgeneration recombination e st sp e dnphn ph photon dens. / ph … carrier/photon lifetime RRst sp R / R ... stimulated/spontaneous dt ph st sp emission rate V e … electron photon overlap Vph “Confinement factor” Below threshold Above threshold no laser emission nph0 laser emission j j th ne th ne 30 / 28 Bifurcation diagram Generic Laser Carrier density Laser characteristic ne nph th ne nph() j j th with Rsp j j threshold jth current jth unstable solution Carrier density clamped at threshold value (necessary to ensure steady state) Light output proportional to pump current I 2nd order Phase transition with Rsp : 1st order transition 31 / 28 Optical Gain Light amplification in resonator Pump n nn ph Gain g ph ph gz with z v t Light per unit Light nph n ph n ph e g length gz small z e1 g z z dn vg=c/n…group velocity ph g nph g() n e v g o … differential gain dt g ne g( ne ) g0 ln th ne gth Approx: Gain g depends on number of carriers th Linear approximation around threshold g()() ne g0 n e n e th ne ne 32 / 28 Stimulated emission Rind Rind Induced emission rate per unit volume between filled initial and empty final state R12W12 1(1 2 ) 2 (1-2) E 2 R21W12 2 (1 1 ) R 21 R12 RRRind ()()21 12 W12 21 1 … dipole matrix element E 1 … laser frequency W…Einstein coefficient Fermi’s Golden Rule yields W ; transition 2 3 1-2 rate per unit volume for 0D System: W n Wn 12 ph ph 3 0 vg Quantum Dot system: 111 h 2 1 e h W Rind W ( e h 1) n ph Gain: g vg 33 / 28 Spontaneous emission Rsp 0D Quantum Dots: WW 2 3 Rsp 12(1 ) e h VV W 1 3 0 vg W R n n spN QD e h 22k 2D Wetting Layer with parabolic bands: e Ee 2m 0.8 E =2.3 eV 2 end 3 W 2 2 eh -2 f(w )= w e 0.2 e WEEk43 k k nm 3 0 vg -1 s 8 0.4 Fermi-functions / 10 E =1.5eV end ke 1 spon R W f()() f2d k k W w 2 R sp k e h e 0 0.0 0 5 10 15 w /1012cm-2 e 34 / 28 .
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