Martina Mrkvičková 20. 12. 2023 Martina Mrkvičková Lase r-induced fluorescence 20. 12. 2023 1 /29 Motivation: methods for detection of reactive particles in plasma optical emission spectroscopy (incl. actinometry) absorption spectroscopy (incl. cavity ring-down spectroscopy) mass spectrometry Martina Mrkvickovä Laser-induced fluorescence 20. 12. 2023 2/29 unit °ye laser Lense< H2+Ar+ hydrjde p~ Oiffusi power meter Nd:Y/\Q pumping laser °n flame atom izer 'CCD camera Excitation schemes 6s26p7s(V2, V2),J = 1 HYDROGEN Laser-induced fluorescence 20. 12. 2023 4/29 Laser-induced fluorescence Connection between the fluorescence signal and the concentration of excited state is easy: oo f Cr) = J A32 A73(r, ř)dř o But what is the connection between n3 and En? Martina Mrkvickovä Laser-induced fluorescence 20. 12. 2023 5/29 Laser-particle interactions (not only) • absorption of laser photon • two-photon absorption • spontaneous emission • stimulated emission • collisional quenching • amplified spontaneous emission • atomisation by laser • ionisation by laser Martina Mrkvickovä Laser-induced fluorescence Spontaneous emission solution: dn3\ dt J sp. emission "3 = "3(0) e To 1 to = 3/ A - Einstein coefficient of emission (you can find on NIST) t0 - radiative lifetime Martina Mrkvickovä Laser-induced fluorescence 20. 12. 2023 7/29 Absorption of laser photon dn3\ = k —— / A?1 dt C / absorption • S13 - Einstein coefficient of absorption (S13 ~ /A31) • /- laser intensity • k - spectral overlap of laser l(v) and absorption line g{v) 0.5 r 0.4 ■ H—' 0.3 ■ CD H—i 0.2 ■ C 0.1 ■ 283.295 283.3 wavelength [nm] 283.305 Martina Mrkvickovä Lase r-induced fluorescence 20. 12. 2023 8/29 Stimulated emission ^ stim.emission c d jqu! q ____-----" — Martina Mrkvičková Lase r-induced fluorescence 20. 12. 2023 Collisional quenching dn2 = -(Q31 + Q32) "3 quenching m • q - effective quenching rate • nm - concentration of collisional partner m • qm - quenching coefficient for collisions with m Lifetime of excited state r: 1 Martina Mrkvickovä Laser-induced fluorescence 20. 12. 2023 10/29 • used in method Two-photon absorption laser-induced fluorescence (TALIF) • (j(2) - two-photon absorption cross section • G(2) - two-photon statistical factor Martina Mrkvickovä Laser-induced fluorescence 20. 12. 2023 11/29 Atomisation, ionisation, ... by laser processes leading to gain or loss of particles in the fluorescence process due to laser example for gain: laser causes dissociation of 03 to 02 + O example for loss: laser causes ionization of O to 0+ Martina Mrkvickovä Laser-induced fluorescence 20. 12. 2023 12/29 Rate equations - simple three-level model d/7-i dn2 ~~dT dn3 dt ln3 + = -k — In-i +k — c c (A31 + Q31) "3 + (4>1 + O21) n2 = (A32 + Q32) n3 - (/A21 + Q21) n2 k —— / /7-| - k^ln3- c c (4*1 + 432 + 0*1 +032)^3 Measured fluorescence signal: 6s26p7s(V2, V2),J 405.8 nm 00 f(7) = J A32n3{7, t)dt 6s26p2(3/2, V2)J=2 0 We want to find relation between ŕ and En. Pb i 283.3 nm 6s26p2(V2, V2),J=0 Martina Mrkvičková Lase r-induced fluorescence 20. 12. 2023 Solution: low-intensity approximation - "Linear regime" assumptions: • a71 > a72,a73 • n-| « konst. • no stimulated emission solution: k _ . dn3 a73(f)= (-Sl3/"l-^f )t oo f = A '32 0 f{7)=A32TK^-ni L(7) oo /_(?) - temporal integral of laser intensity, /_(?) = J 1(7, t)dt o r - lifetime of the excited state, r = A ,A }n ,n Martina Mrkvickovä Laser-induced fluorescence 20.12.2023 14/29 Note for the lifetime What is hapenning to the excited state after the laser pulse? dn3 dr solution: = -(431 + 4s2 + Q3I + Q32) "3 T = "3 = n3(0)e" 1 A31 + 432 + O31 + Q32 t - "reaľlifetime of the excited state Martina Mrkvickovä Laser-induced fluorescence 20. 12. 2023 15/29 A bit more laser intensity? • the dependence of signal on energy stops to be linear • reason: stimulated emission and depletion of the ground state A bit more laser intensity? • the dependence of signal on energy stops to be linear • reason: stimulated emission and depletion of the ground state Saturation of LI F dni (Q dř dn2(t) dř dnajt) dř = Jj^lB,3n, (ř) + ^lB31n3(ř) + (A31 + Q3)n3(t) + +(A>1 +Q2)n2(ř) = ^32^3(0-^21+02)^2(0 = %(0 ß13A7l (0 - %^ß3i n3(0 - (Asi + A32 + Q3)n3(0 •00 /r= / A32n3(t)dt Jo 20 30 cas [ns] 50 Energie laseru [J/m ] Martina Mrkvičková Laser-induced fluorescence 20. 12. 2023 Saturation of LI F dni (Q dř dn2(t) dř dnajt) dř = Jj^lB,3n, (ř) + ^lB31n3(ř) + (A31 + Q3)n3(t) + +(A>1 +Q2)n2(ř) = ^32^3(0-^21+02)^2(0 = %(0 ß13A7l (0 - %^ß3i n3(0 - (Asi + A32 + Q3)n3(0 •00 /r= / A32n3(t)dt Jo 20 30 cas [ns] 50 Energie laseru [J/m ] Martina Mrkvičková Laser-induced fluorescence 20. 12. 2023 Saturation: conclusion Thanks to some modelling, we are able to find "correction factors" which quantificate how many excited species were lost in comparison with ideal linear regime. 2500 2000 - 1500 ■ 1000 500 ■ % experimental ---F=aE2/(1 +/3E2) 0 0.5 1 1.5 2 2.5 3 3.5 4 e[ [J2] x 10" Martina Mrkvickovä Laser-induced fluorescence 20. 12. 2023 18/29 How much fluorescence is really detected? • signal M is integrated from some definite volume V, not only point in space 7 • fluorescence is emitted to all angles, only small part ^ goes to the camera • wavelength filters have some transmitivity T, camera has some sensitivity C, ... Martina Mrkvičková Lase r-induced fluorescence 20. 12. 2023 19/29 Calibration How to obtain ? • Let's measure some another signal caused by the exactly same shape of the laser beam, but we know exactly how much signal we should get from it. Rayleigh scattering of the laser fluorescence of noble gases with known concentration Than compare the theoretical signal and really obtained signal. Martina Mrkvickovä Laser-induced fluorescence 20. 12. 2023 20/29 Formula for absolute concentration n — ^ c _J__0 Mc, theoretical ~ EL T C rA32B^3k Mc n - concentration of measured species M - measured fluorescence signal EL - laser pulse energy , EL = J J 1(7, t) dSdt s,t g - correction factor describing the saturation of signal T - wavelength filter transmisivity C - camera sensitivity (depends on wavelength) c- speed of light r - lifetime of the excited state A32 - Einstein coefficient of the fluorescence transition &i3 - Einstein coefficient of absorption of laser photon k - spectral overlap of laser and absorption line ^^theoretical - theoretical amount of calibration signal M^^reaWy detected calibration signa^^^^^^^^^^^^^^^^ Martina Mrkvičková Laser-induced fluorescence 20.12.2023 21/29 Measurement • prepare optical path (...) • set the correct wavelength and find the first fluorescence signal • check parasitic effects, signal saturation ► does the signal disappear when the laser wavelength is detuned? ► does the signal have linear dependence on the laser energy? • measure the shape of the absorption line (->> k) • measure the timeshape of the fluorescence (->> r) • nice pictures of the whole fluorescence signal (—>> M) • calibration (->> Mc) • do not forget to get darkframes and monitor the energy EL for all the measurements Martina Mrkvickovä Laser-induced fluorescence 20. 12. 2023 22/29 L,F equipment Frequency conversi 'on unit °ye laser H2+Ar + hydr/de p~ Oiffusi 0n flame atom Nd'^G oumoing /aser Our LI F laboratory Martina Mrkvičková Lase r-induced fluorescence 20. 12. 2023 • Nd:YAG pumping laser + dye laser + frequency conversion unit • pulsed - 10 ns, 30 Hz • tunable wavelength (1064 nm fundamental; higher harmonics; cca 200 - 900 nm from dye laser and FCU) • peak power: kW (in UV) - GW (in IR) ► comparison: laser pointer 20 mW, ELI 10PW Laser-induced fluorescence Dye laser beam splitter reversing ipre_amp) unit beam pump beam