L22-1LASERSRepresentative applications:Amplifiers: Broad-band communications (avoid down-conversion)Oscillators: Frequency/distance reference, local oscillators, illuminators, transmitters, CD/DVD players, sensorsBlasting: Laser machining, labeling, weapons, laser fusion (pellet compression). Peak > 1015W, average > 1kw; high intensity because I ∝ |∑⎯E |ii2Energy States:+ionization, free electronground state0 e.v-13.6 e.v.1420 MHzHydrogen atom++-HHOStates:electronic (visible, UV)vibrational (visible)bending (IR)rotational (microwave)Water vapor H2OChromium atoms in lattice (e.g. ruby), Erbium atoms in glassL22-2Rate Equation:Then: dn2/dt = -An2- B(n2–n1) [m-1s-1] (collisionless system)Assume: Two-level system, E2> E1, and ni= atoms m-1in state iSpontaneous emission Induced emissionStimulated emission and absorption:Photon flux density F:B coefficient: Bij=Fσij∝ Fgij(f) Aij/ω3Line shape gij(f): (Lorentzian)ij∞−∞=g (f)df 1∫gij(f)ΔffofSpontaneous emission, states i to j:Aij= ω3|Dij|2 (2/3hεc3) [s-1] (Decay time τA= A-1)Dij[C m] = quantum dipole moment (electric or magnetic)Note: τA∝ω-3⇒ very brief “visible” τ’s, long microwave τ’sn2n1An2n1BSTIMULATED EMISSION AND ABSORPTION2-2 -1oE1F [photons m s ]2hf=ηij2o221g(f) f(f f )14(f)=πΔ−+ΔL22-3Level Populations—Kinetic Temperature Tk:Thermal equilibrium ⇒ Boltzmann distribution:()ijEE kTijnen−−=Ei[J]State energyn2 ∝ e-E/kTn1⇒ ni→ njif Trad→∞, n2> n1if Trad< 0T = kinetic temperature if collisions dominateT = radiation temperature if radiation dominates fijElectron energy E in semiconductorΔE = hfkConduction bandValence bandEnergy band curvature broadens the linewidthLinewidth Broadening Mechanisms:ENERGY LEVEL POPULATION AND WIDTHCollisions ⇒ phase changes, Fourier transform ⇒ΔfΔffofIsolated atomsL22-4Amplification Process:inputamplification, exponential growth[Each is a separate atom or molecule;need n2 > n1for amplification]amplification linear growthPump (repopulates level 2)n2replacement-rate limited amplificationOptical fiber⇒21hfhf2hf4hf⇒6hf⇒BASIC LASER AMPLIFIER PHYSICSIntensity-limited amplificationAmplification frequency f [Hz]:E2–E1= hf [J], h = 6.625 × 10-34[Js]P(z) ≅ Pine(g-α)zexponential growthlinearzP(z)(g is gain, α is attenuation)L22-5PUMPING OF LASERSThree-Level Lasers:Pumping the 1-3 transition yields n1≅ n3Large A32populates L2 so n2>> n1≅ n3≅ 0More levels can utilize transitions with larger A’sLarge A23fills L2, and large A41empties L4Two-Level Lasers:Radiation pumping alone never yields n2> n1(some 2-level lasers spatially isolate n2group)fpump>foPump21Lasing?Pump321lasingLarge A32Pumplasing3214A32A411Laser Power Efficiency (Pout/Pin ):Intrinsic efficiency: ηi=fL/fp(P ∝ nhf [W]) < 1B/A efficiency @ 2: ηB= B21/(A21+B21) < 1A/A efficiency @ 3: ηA= A32/(A31+A32) < 1Total efficiency: η = ηiηBηAPump photons s-1∝ B >> A ∝ω3, so x-ray lasers need pump power ∝ hfB ∝ hfA ∝ω4dn2/dt = - An2- B(n2–n1)PumpA31A21321A32B =Fσ21L22-6LASER OSCILLATORSLaser Oscillation:LTAmplifierP+Lossy: Round-trip gain must exceed round-trip loss (threshold condition); gain ∝ pump power Pp, so need Pp>PthreshMirrors: Exit mirror has power transmission coefficient T > 0At threshold, Gain ≅ Loss, so: P+(1 – T)e2(g-α)L≥ P+⇒ round-trip gain = e2(g-α)L≥ 1/(1 – T) for oscillationPoutPthreshPpumpQ-switching: Set mirror reflectivity low ⇒round-trip gain < threshold. When laser is fully pumped, increase mirror reflectivity over threshold, yielding very large “Q-switched pulse”Lossless: With perfect mirrors at both ends a losslessamplifier must oscillate and saturateL22-7Resonances≅ 108Hz (100 MHz) for 1-meter fiber;≅ 50 GHz line spacing for 0.5-mm diodesLASER RESONANCESOscillator Resonant Frequencies f:Laser Output Spectrum:CavityresonancesLaser line shape, width = ΔfLine narrowingIf every atom can amplify at all frequencies, then the strongest round-trip gain wins ⇒ line narrowing (homogeneous line broadening)If atoms can amplify only a portion of the band, then all lines over threshold can yield output (inhomogeneous line broadening)mmmi+1 imL (mirrors short circuits)22L cm, f (N = refractive index)m2LNcff2LNλ=≈λ= =−=L22-8EXAMPLES OF LASERSElectrically Pumped Solid-State Lasers:Forward-biased GaAs p-n junction injects carriers into conduction bandCompact (grain of sand)~50 percent efficiency>100 W/cm2for arrays1 mW/micron2for diodes1-1000 mW typicalAstrophysical Masers:Stellar Pumping: UV-IR pumped: H2O, OH, CO, etc.Interstellar collisions: OH, etc.holesp-typeEFn-typeelectronsEActive regionzEFMirrors at both endsValence bandConduction band++++----Chemical lasers:Weapons (high energy, fast)starMIT OpenCourseWare http://ocw.mit.edu 6.013 Electromagnetics and Applications Spring 2009 For information about citing these materials or our Terms of Use, visit:
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