Lecture 13: Laser-Induced Fluorescence: Two-Level Model
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Lecture 13: Laser-Induced Fluorescence: Two-Level Model 1. Introduction and background Laser-Induced Fluorescence 2. Typical experimental setup 3. Signal level (steady & pulsed) Possible collisional change 4. Two-level model 2 LIF 5. Detection limits (pulsed laser) hν (spont. emission) 6. Characteristic times Laser absorption 7. Modifications to two-level model 1 1. Introduction What is Laser-Induced Fluorescence (LIF)? Laser-induced spontaneous emission Multi-step process: absorption followed by emission (fluorescence) Possible collisional change This is the laser- 2 induced fluorescence hν (spont. Emission) = LIF signal Laser absorption (pulsed or CW laser) 1 Notes . May occur from multiple states . Not instantaneous 2 1. Introduction Why is LIF of interest? o The LIF signal can be monitored at 90 to the exciting laser beam, thereby gives spatial resolution to the absorption measurement The signal rides on a dark background, rather than being based on signal differences as in absorption Species specific, and much stronger than Raman scattering Volume element = A·L (~1mm3) L Waist LIF Trans. Int. Ω l Collection optics d λexc • Signal for scanned- LIF 3 1. Introduction LIF can be used to monitor multiple gas properties including ni (n,v,J) number density of species i in a state described by n, v, and J T temperature (from the Boltzmann fraction) χi species concentration P pressure (from line broadening) v velocity (from the Doppler shift of the absorption frequency) And species including Radicals: OH, C2, CN, NH, … Stable diatoms: O2, NO, CO, I2, … Polyatomics: NO2, NCO, CO2, Acetone (CH3COCH3), Biacetyl ((CH3CO)2), Toluene (C7H8), and other carbonyls and aromatic compounds As well as many atoms…. 4 1. Introduction Absorption LIF Possible collisional 2 change 2 LIF Laser absorption hν (spont. emission) 1 Laser absorption 1 NOT instantaneous Instantaneous Multi-step process: absorption followed Single-step process after some delay by spontaneous emission Line-of-sight Typically 90o to the excitation laser beam Based on incident/transmitted Rides on a dark background signal difference Absorption and LIF can be performed with either CW or pulsed lasers 5 1. Introduction History & Some Key Accomplishments Flash-lamp pumped dye laser (Schafer, 1966) Tunable CW dye laser (1970) CW-doubled ring dye laser (1980) Nd-YAG and excimer-pumped dye lasers (1980) CW -scanned LIF (1980s) First PLIF imaging in laminar combustion (1982), turbulent (1984) Single-laser-pulse PLIF imaging of NO, T, and velocity (1989) OH PLIF in Identification of ketone tracers for PLIF imaging (1991) laminar flame M>1 Combustion: NO, T imaging (1993), OH imaging (1996) Extension of PLIF to high pressure/temperature (1993-2005) PLIF with vibrational transitions (IR-PLIF) (2000) Pulse-burst PLIF (2000) UV- PLIF of CO (2004) 2 OH PLIF in High-speed PLIF (2005) spray flame CW PLIF (2009) 6 2. Typical Experimental Setup Typical experimental setup for LIF systems Volume element Experiment (e.g. flame, flow, plasma) Excitation λex (~1mm3) Laser Trap or powermeter Ω l Collection optics d PMT with spectral filter to record emission at λex or at λdet (≠ λex), or grating monochromator Recording modes to disperse the spectrum 1. Emission intensity at a fixed detection wavelength 2. Fluorescence spectrum (spectrometer) I 3. Excitation spectrum (scanned laser) Pulsed laser 4. Can be extended to 2-d with CCD LIF (decay rate array detector (PLIF) contains info on “quenching rate” 5. Can also measure temporal behavior 7 2. Typical Experimental Setup Measurement volume Volume element 3 = A·L (~1mm ) L Waist Area = A Ω l Collection optics d . Pathlength: L ≈ 0.5 – 5mm lens area . Solid angle of collection: Note: 2 l At f # = 2.5, Ω/4π = 0.01, d 2 / 4 1 or 1%. Collection process is l 2 f # 2 relatively inefficient, even for l fast lenses. f # of collection: f # d 8 3. Signal Level Spontaneous emission corresponds to a decay in energy 2 Spontaneous Emission A21 1 Steady conditions S 21# photons/sec N A n V A F 2 21 4 2 21 4 N2 = # molecules in the measurement volume in state 2 n2 = number density of molecules (#/cc) in state 2 V = volume (cc) A21 = probability/sec of emission from state 2 to state 1 Ω/4π = collection fraction 21 SF power collected SF # photons/sech S21 F ∴ The LIF signal depends on constants and n2. Hence, the challenge of LIF is to find a way of specifying n2 quantitatively 9 3. Signal Level Spontaneous emission corresponds to a decay in energy 2 Spontaneous Emission A21 1 Pulsed conditions For unsteady conditions (e.g., short times or pulsed excitation): 21 SF # photons n2 t dtV A21 0 4 n2(t) depends on the laser and the collision process (further explained later) 10 4. Two-level Model Entry-level model for LIF (two levels) Induced Induced Collisional Collisional Fluorescence Absorption Emission Excitation De-Excitation 2 Energy n1W12 n2W21 n1Q12 n2Q21 n2A21 1 negligible “quenching” B12 I d Einstein theory prob/sec12 B12 d d 1 I / c Let B12 B12 / c 11 4. Two-level Model Entry-level model for LIF (two levels) -1 Iν Laser (~0.5cm FWHM) for typical pulses Most pulsed lasers are spectrally broad compared ν0 ν with absorption lines Iν ≈ constant over abs. line Absorption line (~0.1cm-1 at STP) Rate12 n1 B12 I d n1B12 I n1W12 Probability per second of line absorption per unit spectral Rate (s-1) that individual molecules in intensity: state 1 undergo the transition to state 2 B12 B12 / c Rate analysis n2 n1I B12 n2 I B21 Q21 A21 S.S. W12 n2 SS n1 n1W12 n2 W21 Q21 A21 W21 Q21 A21 n2 0 So now we have a solution for n ! 2 12 4. Two-level Model Entry level model for LIF (two levels) W12 n2 SS n1 W21 Q21 A21 Two limits emerge from the steady-state analysis for n2: Weak excitation (“linear LIF”) Strong excitation (“saturated LIF”) Weak excitation limit: Induced emission from level 2 much weaker than the sum of collisional and spontaneous decay processes g1B12 g2 B21 W B I A Q 21 21 21 21 g1W12 g2W21 0 0 0 0 Then n 2 n 1 , andn1 n1 (usually n 1 n where n is the conserved total 0 number density,n n1 n2 ) 0 W12 n2 n1 A21 Q21 13 4. Two-level Model Weak excitation limit Fluorescence signal SF n2 V A21 photons/s in weak excitation limit 4 A 0 21 n1V W12 B12 I A21 Q21 4 photons absorbed/sec "fluor. yield" fraction collected Notes: 0 1. To find n 1, need to know Q21 (rate of the electronic quenching, a collisional process), A21, Iν, and 0 2. SF n1 ni fv,J T LIF is directly proportional to the population density in the lower quantum level LIF is typically viewed as a species diagnostic 3. Alternative view: # of absorptions/sec # molec in 1prob/s of abs 0 n1V B12 I 14 4. Two-level Model Consider the saturation limit Induced emission rate >> collisional and spontaneous emission rates W21 A21 Q21 . Recall: g1B12 g2 B21 W12 B12 g2 n2 n1 n1 n1 W B g so g1W12 g2W21 Notes: 21 21 1 1. If g2 = g1, then n2 = n1, when the transition is “saturated” 0 0 0 n1 n1 2. n1 total n1 n2 n2 when g2 g1 1 g1 / g2 2 Fluorescence signal 0 g S n 2 V A photons/s in saturation limit F 1 21 g1 g2 4 Virtue: does not depend on Q21, laser intensity Complication: may be difficult to reach the saturation limit in all parts of the laser beam If intensity not sufficiently high, may reach intermediate situation between weak excitation and saturation 15 4. Two-level Model Intermediate result W 12 1 n2 SS n1 0 B Q A W21 Q21 A21 12 21 21 n2 n1 1 0 B12 B21 B12 B21 I with n1 n2 n1 g1B12 g2 B21 B12 /B12 B21 g2 / g1 g2 S n 1 F 2 S n Q A F ,sat 2,sat 1 21 21 B12 B21 I 16 4. Two-level Model Typical values for A and Q in electronic transitions 5 8 -1 6 -1 8 -1 1. A21 ≈ 10 ~ 10 s (10 s for NO, OH; 10 s for Na) Q Zcollision frequency OH 2. 21 Note: A21 / Q21 P1atm,comb. T 2 n c 8kT / ~ 106 s1 /1010 s1 2 P / T ~ 104 9 10 1 A small number! Q21 10 10 s at STP 3. Fluorescence yield = A21/(A21+Q21) << 1 except at low P LIF is an inefficient process! 4. Spontaneous emission for IR is much weaker (smaller A21) than UV LIF is weaker in the IR, unless Q21 is small (as may be the case!) A21,IR / A21,UV 1 Q / Q ? 21,IR 21,UV 17 4. Two-level Model Typical values for A and Q in electronic transitions 5. What is Iν for B21Iν >>A21+Q21? Call this (Iν)sat . For low Q21, Iν,sat >>A21/B21 I P / T 1/ B . For high Q21, Iν,sat >>Q21/B21 so that ,sat 21 3 3 I B . B A /8h B B 21 A 21 21 21 21 c 21 8hc 2 @ λ = 500nm, B21 25A21cm /erg s 4 10 -1 6 -1 . Assume Q21 ≈ 10 A21 (e.g., Q21 = 10 s , A21 = 10 s ) 4 I ,sat 10 A21 / 25A21 erg/s 400 ergs/cm2 cm2 Hz 0.4 J/m2 18 4. Two-level Model Typical values for A and Q in electronic transitions - continued 5. What is Iν for B21Iν >>A21+Q21? Call this (Iν)sat Power -1 10 -1 .