Otruba, Novotný Lasers basics principles 1 Vítězslav Otruba, Karel Novotný Klepnutím lze upravit styly předlohy textu. Druhá úroveň Třetí úroveň Čtvrtá úroveň Pátá úroveň Simplest configuration? High energetic lasers - PALS Prague Asterix Laser System The vacuum chambers at the PALS laboratory in Prague, where a 1 kJ pulse creates plasma for Xray generation Lasers – Light Amplification by Stimulated Emission of Radiation  Spectral range 1 mm – 50 nm, (experimentally) X ray range up to 1 nm, extreme experiments up to 0,01 nm – radiation generators especially (XASER) sub millimeter wave range MASERS (Microwave Amplification by Stimulated Emission of Radiation) - mainly as low noise radio signal amplifiers 4  For 4 Commercially available – VUV – VIS – MID IR Properties of laser radiation  Emissions of elementary oscillators(atoms, molecules…) narrow beam– spatial energy concentration can be very small– spectral concentration of energy operation of elementary oscillators– time concentration of energy length up to tens (in vacuum up to thousands) kilometers 6 6  Δλ  Synchronous  Coherence Types of lasers by: • emission wavelengths • time mode of operation - continuous (cw) or pulse • type of excitation – optical excited lasers, electric discharge, chemical, mechanical (particle collisions), injection of charge carriers, … • type of active medium - solid, liquid (dye), gas, ion, excimer, semiconductor (diode),… • pulse duration (nanosecond, picosecond, femtosecond, ...) - the shorter pulse duration means higher 7 the Peak power at the same Average Power 7 Types of lasers Properties of Active laser medium (gain medium, lasing medium) Excitation of atoms up to metastable state By collisions between two kinds of atoms (He-Ne, CO2) Optical excitation – pumping (ruby, neodymium glass) Excitation in the chemical reaction (eximers) By electric current (semiconductors,GaAs) and other ways Light output of lasers: 1. 2. Continuous laser up to tens of mW Pulse laser with an average power of 10 mW can have parameters: • pulse duration = 1 ns, • 8 pulse energy = 1 mJ, • pulse power = 1 MW • repetition rate = 10 Hz Radiation Processes E1 Strong transitions : E1 (electric dipole) A~108 s-1 for neutrals hν = E1-E0 E0 spontaneous emission absorption stimulated emission Weak transitions: M1 (magnetic dipole), E2 (electric quadrupole), some E1 A ~1-100 s-1 for neutrals A ~ ΔE2 ~ λ-2 (transition probability) Radiation intensity : I(ν)=Nu·A·hν Radiative Processes cont’d O I lines: 3P1-1D2 3P2-1D2 1D2-1S0 M1 630 nm E2 mean lifetime exc. state 110 s 557,7 nm mean lifetime exc. state 0,7 s spontaneous emissions  Probability of photon absorption : w01=n0ρ(ν)B01  Probability of spontaneous emissions : w10=n1A10 ρ(ν) – spectral density of radiation with frequency ν B01 – Einstein coefficient of absorption A10 – Einstein coefficient of spontaneous emission Stimulated emission  Probability of stimulated 1 emission : w10=n1ρ(ν)B10 B10 – – Einstein coefficient of stimulated emission  Process of interaction with radiation : n0ρ(ν)B01= n1ρ(ν)B10 +n1A10 0 Interaction with radiation Two-level model in thermodynamic equilibrium : n0 ρ (ν ) B01 = n1 ρ (ν ) B10 + n1 A10 From the equation we express ρ(ν): n1 A10 A10 ρ (ν ) = = n0 B01 − n1 B10 n0 B − B 01 10 n1 Boltzmann distribution in TD equilibrium (exponential decrease in level occupation with increasing energy): n0  E1 − E0   hν  = exp   = exp   n1  kT   kT  [1] Relation between Einstein coefficients Substituting the Boltzmann distribution [1] into the previous equation for volume density of radiation we get: A10 1 ρ (ν ) = B10 B01  hν  exp   −1 B10  kT  For the spectral density of radiation we can use Planck relationship: 4 hν 3 ρ (ν ) = 3 c 1  hν  exp   −1  kT  By combining the equations, it is possible to find the relationship between the Einstein coefficients: B10 = B01 = B a 4 hν 3 A10 = 3 B10 c What is the relative number of acts of stimulated and spontaneous emission per unit of time? R= wavelength The number of stimulated emissions per second The number of spontaneous emissions per second wavenumber (cm-1) frequency (Hz) Inverse population  The Einstein coefficients for stimulated emission and absorption are equal: B01=B10=B For absorption: dΦA=hνn0Bρ(ν)dt For stimulated emission: dΦE=hνn1Bρ(ν)dt Total radiant flux change: dΦ/dt=hν(n1-n0)B Condition for amplification of radiation:     n1- n0 >0, tj. inverse population Inverse population  The normal population distribution is shown in Figure a). In order to create an active environment, it is necessary to intervene in the system in order to change the distribution of the energy level occupation in the way shown in Figure b). The process is usually referred to as laser excitation or pumping. The basic method is optical excitation.   Three-level system  Application: ruby laser 1 relaxation  Level 2 is metastable 2  The disadvantage is low efficiency - for reach the inverse population at least 50% of the particles have to be brought to level 2 0 pumping stimulated emission Energy diagram of a ruby laser Three-level system  Modified three - level system with excitation to metastable level 1. pumping 1 stimulated emission 2 relaxation 0 Four-level system  Example  High  An 1 Fast decay 2 - laser Nd: YAG efficiency Pump Transition Laser Transition inverse population must only be reached between levels 2 and 3 3 Fast decay 0 21 21 Radiation amplification - quantum amplifier  Active environment amplifies the incoming radiation: Φ0 Φ=Φ0exp[-l(α+β)] α - absorption coefficient (α‹0) β - losses (β›0) l - length of amplifying medium α Φ Generation of radiation  By introducing positive feedback from the output to the input of the amplifier we get an oscillator whose frequency is given by the amplifier and the feedback circuit, usually realized by a Fabry-Perot resonator + F.-P. Laser radiation generation  Feedback is usually realized by a Fabry-Perot resonator. For short pulse generation, the amplifier frequency bandwidth must be at least: Δf ≅ 1/(2τ)   where τ is the pulse width (polychromaticity of short pulses) Fourier decomposing functions Anharmonic waves are sums of sinusoids. 1 f (t ) = π ∑ m =0 ∞ 1 Fm cos( mt ) + π ∑ m =0 ∞ ' Fm sin( mt ) Conditions for radiation generation  The reflectance of the mirrors shall be chosen with regard to the amplification of the active environment so that the losses do not exceed the amplification of the active environment G: pumping  R1R2exp[-2l(α+β)]≥1 Optical resonator The length of resonator L is M multiple of half-wave (M is an integer). The length L corresponds to given resonator frequencies νM (longitudinal laser modes). Inside the resonator is a standing wave of electric field E with frequency νM = c/λM Fabry-Perot etalon  Quality of resonator Q (QFP~108-109) ω0 Em 2πν 0 Em Q= = Pz Pz Em- energy of the given mode Pz- power dissipation ω0- angular frequency of oscillator dEm Pz = − dt ω0 = 2πν0 =2π/T0 [s-1] Spectral line width and laser modes generation threshold Doppler line width Δλ~1 pm – 10 nm VIS, gas - semiconductor The figure shows the individual resonances basic longitudinal mode. Resonant modes and bandwidth gain of the active medium Optical resonators Volume of the optical (electric) field in resonator Planparallel : r1 = r2 = ∞ r1 r2 Concentric : r1 = r2 = L/2 F2 F1 S1=S2 focus center of curvature r S2 F1=F2 r1 S1 Confocal : r1 = r2 = r = L/4 Hemispherical : r1 = L, r2 ∞ = Coupled resonators L – length of open resonator l1,l2 – distance of interior mirrors a) open resonator modes Z1-Z3 b) internal resonator modes Z2-Z3 c) resulting spectrum of frequencies Single mode laser  Combination of resonant modes and internal FP standard generation threshold  or Lyot filter (narrowband polarization filter) internal etalon and the gain bandwidth generates only one longitudinal mode Open optical resonator glass support dielectric layer Open resonator modes Longitudinal modes: distribution of light radiation in the longitudinal direction Transverse modes: distribution of light radiation in the transverse direction Transverse modes of the resonator Transverse Electromagnetic Mode - TEM  Transverse modes are characterized by a pair of numbers m and n. These numbers represent the number of nodes of the standing wave on the axes (x, y) perpendicular to the optical axis.  The number of nodes of the standing wave in the optical axis L is high and is not given.  The basic mode is TEM00, in which the radiation intensity profile has a Gaussian profile. Transverse modes of the resonator Gaussian beam (profile) mode TEM00 f ( x) = exp( − x / w ) 2 2 s ws = distance from the resonator axis, where the radiation intensity decrease to 1/e axis intensity Profile of the focused laser beam in its focus Coherence of radiation coherence length lc- related to how long a continuous electromagnetic wave (sinusoidal wave) is emitted. lc = c ⋅ τ Heisenberg uncertainty principle : δE ⋅ δt ≈ h ⁄ 2π hδν= δE ⇒ hδν⋅ δt ≈ h ⁄ 2π ⇒δν ≈ 1 ⁄ 2π δt coherence time– τ ∆ whereν 1 ∆ν = τ is the width of the spectral interval In general, coherence can be understood as the ability of radiation to interfere with relative time shifts of the emitted radiation Brewster’s angle Exit windows separating the low pressure area from the atmosphere they are inclined at Brewster's angle to form a lossless optical feedthrough, which, as a by-product, causes the output radiation to be linearly polarized, a feature useful for a variety of applications. For the size of the Brewster angle, it can be deduced from the Fresnel equations (indicating the intensity of the reflected and refracted light) that: tg( α B ) = n Where αB is the value of the Brewster angle and n relative refractive index between input and output medium. +  B výbojová trubice s aktivním prostředím discharge tube with active medium polarizace polarization He – Ne and CO2 laser α Β 1. Energy scheme of excitation (so-called three-level system) 1. If the exit windows are inclined 2. 3. hν = E2 – at Brewster angle, the laser E1 E3 E2 E photon beam is linearly polarized 2. Glass discharge tube filled with He (pressure about 100 Pa) and Ne (pressure about 10 Pa). E3 3. For CO2 laser: nitrogen takes He Ne Ne over the function of He and molecule of CO2 takes over the function of neon 1. He atom is excited to E1 by the discharge Typical continuous lasers. 2. By collisions He and Ne atoms - Ne atom is excited to a λ(He-Ne) = 632.8 nm metastable state λ(CO2) = 10.6 µm 3. In the presence of an electric field with a frequency νM the Ne emits stimulated photon, otherwise spontaneous Semiconductor laser Mirrored modified front surface of crystal AlxGa1-xAs, n-typ GaAs, p-typ AlxGa1-xAs, p-typ + hole flow emission of stimulated photons radiative recombination electron flow 1. 2. 3. The external voltage of this polarity causes a large number of electrons and holes (with a sufficiently long lifetime) to accumulate simultaneously in the optically active layer of GaAs, which can only recombine together by radiative transitions. The mirrored crystal surface forms a plan-parallel optical resonator of about 1 mm in length. This ensures that stimulated photon emission occurs when electrons and holes recombining.Vlnová délka emitovaného světla je z intervalu 700 až 900 nm podle obsahu Al. Luminescent photodiodes (LEDs) work on a similar principle. They do not have a resonator and the electrons and holes in the active environment recombine almost immediately. Summary  laser radiation has a much smaller line width than the emission line of the active medium the laser emits radiation corresponding to the longitudinal (or transverse) modes, depending on the resonator configuration the laser emits only in those modes whose gain is greater than the threshold laser radiation has a high coherence if the optical system includes an element supporting a particular polarization orientation, the output radiation is polarized.     Literature  G.M. Hieftje, J.C. Travis, F. E. Lytle. Lasers in Chemical Analysis, The HUMANA Press. Inc. 1981  D. L. Andrews, Lasers in chemistry, Springer – Verlag, Third edition, 1997  N. Omenetto, Analytical Laser Spectroscopy, John Wiley & Sons, 18. 1. 1979