! Laser Physics
Who we are Lectures - Fabien Bretenaker (LAC) - Marc Hanna (LCF) - Thierry Ruchon (LIDyL) Exercice classes - Frédéric Druon (LCF) - Sophie Kazamias (LPGP) - Dimitris Papadopoulos (LULI) Lecture notes wrimen by Fabien Bretenaker. Slides are based mainly on the notes 22
Who you are Students from three different academic backgrounds: - M2 Laser OpUque MaUère - M2 Grands Instruments - M1 General Physics Three exercice class groups: - M2 LOM (English, DP) - M2 LOM (French, FD) - M2 GI + M1 GP (English, SK) 33
Wednesdays 14h 15h30 and 15h45 17h15 Schedule Part 1: All students Part 2: M2 LOM only 16/09 L1 L2 23/09 L3 EC1 30/09 L4 EC2 07/10 L5 EC3 14/10 L6 EC4 21/10 L7 EC5 04/11 Midterm Exam (1h30) 04/11 L8 Midterm Exam 18/11 L9 EC6 25/11 L10 EC7 02/12 L11 EC8 09/12 L12 EC9 16/12 Final Exam (3h) 44
! Laser Physics 1 Introduction and laser matter interaction Fabien Bretenaker Fabien.Bretenaker@u-psud.fr Laboratoire Aimé Cotton Orsay - France
Fabien Bretenaker Fabien.Bretenaker@u-psud.fr Laser Physics Quantum Optics!!! Laboratoire Aimé Cotton Orsay (Bat. 505) Nonlinear Optics Microwave Photonics
Course objec3ves Understand physical principles that allow laser operauon in various regimes Prerequisites : basic quantum mechanics and electromagneusm Not covered : laser technology and applicauons 77
Course objec3ves PLEASE INTERRUPT AND ASK QUESTIONS!!! 88
Outline IntroducUon Light- MaMer interacuon EquaUons of the single frequency laser Single frequency laser in the steady state regime Transient operauon Inhomogeneous broadening Laser noise SpaUal aspects : OpUcal resonators InjecUon locking and mode compeuuon PropagaUon and characterizauon of ultrashort pulses Mode locking 99
A. Einstein (1921): photoelectric effect Laser- related Nobel prizes C. H. Townes, N. G. Basov, A. M. Prokhorov (1964): laser A. Kastler (1966): spectroscopy N. Bloembergen, L. Schawlow (1981): spectroscopy C. Cohen- Tannoudji, S. Chu, W. Phillips (1997): laser cooling A. H. Zewail (Chemistry 1999): femtochemistry Z. Alferov, H. Kroemer (2000): semiconductor heterostructures E. Cornell, W. KeMerle, C. Wieman (2001): Bose- Einstein condensates R. J. Glauber, J. L. Hall, T. W. Hänsch (2005): frequency combs C. K. Kao (2009): opucal fibers S. Haroche and D. Wineland (2012): manipulaung individual quantum systems I. Akasaki, H. Amano, S. Nakamura (2014): blue LEDs E. Betzig, S. W. Hell, W. E. Moerner (2014): super- resolved microscopy 10 10
Minimal laser history 1917 A. Einstein, sumulated emission 1949 A. Kastler, J. Brossel, opucal pumping and populauon inversion 1950 A Schawlow, C. Townes, N. Basov, A. Prokhorov, maser proposal 1955 J. Gordon, H. Zeiger, C. Townes, ammonia maser (λ=1.25 cm) 1958 A Schawlow, C. Townes, opucal maser proposal 1960 T. Maiman, first laser (ruby, pulsed, λ=694.3 nm) 1960 A. Javan, first CW laser (He- Ne, λ=1.15 µm) 1961 P. Franken, SHG of a ruby laser in quartz (birth of nonlinear opucs) 1962 Semiconductor laser 1963 CO 2 laser 1964 Nd:YAG laser 1966 Dye laser 1977 Free electron laser 1993 fs Ti:Sa laser 1994 quantum cascade laser 2003 isolated amosecond pulse generauon 2010 MJ laser at NIF 11 11
What is a laser? Ac3ve medium: atoms, molecules, ions, electrons in gas, liquid, solid, plasma medium Excita3on scheme (pumping): provides energy to the acuve medium to turn it into an amplifier Op3cal resonator (cavity): resonant oscillator (Fabry- Perot, Ring) Output coupler: Extracts the radiaton stored in the cavity 12 12
Some terminology Energy E [J] (energy of a laser pulse) Fluence E surf [J.m 2 ]: energy per beam secuon area, E surf = de/ds Power P [W] (power of a light beam, pulse peak power): energy crossing the beam secuon by Ume unit, P = de/dt Intensity I [W.m 2 ]: power density per surface area unit, power per beam secuon area, average value of the modulus of the PoynUng vector, I = dp/ds Photon flux Φ [m 2.s 1 ] : number of photons of frequency ν crossing a unit area surface per second, Φ = I/hν Energy density u [J.m 3] : energy of the electromagneuc wave per unit volume 13 13
Rela3ons between energe3c quan33es For a plane traveling wave, the intensity, energy density, electric field, and electric field complex envelope are related by 14 14
Energy conversion between atoms and radia3on 15 15
4- level model, Statz and de Mars equauons Heuris3c equa3ons of the laser N: number of atoms in level 2 F: number of photons R p : Pumping rate τ cav : photon lifeume τ: level 2 populauon lifeume κ: atom/field coupling coefficient 16 16
Sezng dx/dt=0 leads to Steady- state regime: satura3on and threshold 17 17
Derivation of the laser equations Now let s start to be (more) rigorous! 18 18
Electric- dipole interac3on two- level system described by Schrödinger s equauon ElectromagneUc field and interacuon hamiltonian EvoluUon of the atom in the 1,2> basis 19 19
Rabi oscilla3ons Rabi angular frequency Detuning OscillaUon of P 2 at the nutauon frequency Ω 1 δ = 0 P 2 (t) 0.5 δ 0 0 Time 20 20
Density matrix: Bloch equa3ons Problem: Introduce the relaxauons. Couple the system to the outside world density matrix Two- level atom + quasi resonant approximauon + rotaung frame defined by Electric dipole interacuon leads to Bloch equauons for a two- level system 21 21
Homogeneous broadening Natural linewidth E 2 ω = ( E 1)/! 0 2 E E 1 ΔE! ΔE! = Δω =1 τ 2 2 / = Δω = 1 τ 1 1 / 1 2 1 Δν = Δω + 1 Δ 2π ω 2 1/2 ν 0 ν 22 22
Collisional homogeneous broadening φ' φ φ t 0 t 0 +T Time Δν = Δν + Δν total natural collisions, phonons, etc Lineshape not necessarily Lorentzian 23 23
Relaxa3on Pumping HeurisUcally take into account - finite lifeumes of populauon and coherences - Pumping Three different relaxauon rates Coherences are more fragile than populauon (e.g. collisions and phase) 24 24
Steady- state regime Without the laser field: To get populauon inversion: γ1 > A Λ2γ1 > Λ1γ 2 With the laser field: These soluuons allow us to introduce the suscepubility of the acuve atoms and the concept of saturauon 25 25
Satura3on SaturaUon intensity defined as Leading to When I >> I sat, the system becomes transparent and does no longer interact with the field When detuning increases, the interacuon is less efficient I sat (δ) 0 δ 26 26
Suscep3bility Macroscopic polarizauon Leads to 1 χ'' χ''( ν 0 ) 1/2 χ' χ'( ν 0 ) 1/2 ν ν 0 Δν 27 27
Satura3on broadening I sat depends on δ, leading to saturauon broadening '' χ ( ν ) I increases ν 28 28
Influence of the suscepubility on the propagauon: Gain Dispersion PropagaUon equauon: Leads to Dispersion Gain Gain coefficient We see that a posi3ve gain is equivalent to popula3on inversion 29 29
Laser cross- sec3on Laser cross secuon defined as Where the populauon inversion per unit volume is The saturauon intensity and gain can now be wrimen (response Ume of the system in the 4- level approximauon) Separates the transiuon characterisucs from the status of populauons 30 30
Why cross- secuon? 1 I di dz Power incident on surface S: Can be rewrimen σ is the secuon area of the atom for the absorpuon process = α = σ Δn P = IS Absorp3on cross- sec3on = σ n 1 dp dz = σn σ dp = 1 1 S P 1 P ( n Sdz) P = I( n Sdzσ ) Number of atoms in the considered volume dz Equivalent absorpuon surface 31 31
Generaliza3on to arbitrary profile Lorentzian profile: Normalized Lorentzian profile Normalized arbitrary profile 32 32