Electric field induced second harmonic generation (EFISH) PrF:FB501 Plasma Diagnostics and Simulations Martina Mrkvickovä autumn 2023 Martina Mrkvickovä EFISH autumn 2023 1/21 Motivation Electric field determines, which plasmochemical processes take place in the plasma. It determines how the coupled energy is distributed. 100 c g w -in CO lu E? c LU MW& GA .... i , ...... DBD ........i / _ ■ -Rotational excit. ---Vibrational excit. < ......Electronic excit. ----Dissociation \ / / -----Ionization ; \ / i 1 1 i / - \ t r . * \ r ! A \ I \ t \ i \. f / ''' \ / / \ X. J ' 1 1 1 1 1-'-'-■ ■ ■ ■ l' ' 10 100 Reduced electric field (Td) 1000 [A Bogaerts et al, ACS Energy Lett. 3 1013-27, 2018]: Fraction of electron energy transferred to different channels of excitation, as well as ionization and dissociation of N2, as a function of the reduced electric field. Martina Mrkvickovä EFISH autumn 2023 2/21 Motivation Ex.: conversion C02 —>> C + 02: MW plasma has better energy efficiency than DBD • MW: vibrational excitation + "leather climbing", dis. en. 5.5 eV o DBD: electron excitation to repulsive state - 7-10 eV coc1!*) + o^s) COCZ+) + OOD) coCz+) + o(3p) O-CO distance [R Snoecks, A, Bogaerts, Chem. Soc. Rev., 2017,46, 5805-5863] Martina Mrkvičková EFISH autumn 2023 3/21 'Electric field" vs. "Reduced electric field" • Electric field: E, [V • rrr1] • Reduced electric field: E//V, [Td = 10"21 V -m2] ► connected with the amount of energy gained by charged particle in the el. field between two collisions: // 1 r- Q E £ = q ■ U = q ■ A ■ E = - ■ — a N ► A [m] - mean free path between two collisions, A = ^ ► a [m2] - collisional cross section ► N [rrr3] - concentration of particles Martina Mrkvickovä EFISH autumn 2023 4/21 Diagnostic methods exhibition electrical probes: ► equivalent circuit ► capacitive probes ► Pockels-effect-sensitive crystals optical emission spectroscopy: ► Townsend coefficient ► line intensity ratio (FNS/SPS) ► Stark broadening, Stark polarization emission spectroscopy ► bremsstrahlung (Z. Navrátil) laser-based methods: ► CARS (Coherent anti-Stokes Raman scattering) ► laser-induced fluorescence dip spectroscopy ► EFISH Martina Mrkvičková EFISH autumn 2023 5/21 Diagnostic methods exhibition Zajímá mě prostorové rozložení? Martina Mrkvičková EFISH autumn 2023 Electric field induced second harmonic generation (EFISH) Electric field in a gas -> polarisation of the gas -> optical anisotrophy second harmonics generation powermeter 2a DBD reactor lb 4 photodiode Nd:YAG laser 2b^ 3 4. 5. photomultiplier Signal is week, coherent, line-integrated EFISH autumn 2023 7/21 A trip to the nonlinear optics • nonlinear polarization: P, = eQ (41} Ej + xf EjEk + xf, EjEkE, + ► Pj - induced polarisation of the material ► Ej - electric field intensity ► ~ the n-th order nonlinear susceptibility tensor • wave equation: _o_ 1 d2E d2P ) V E~ 2 a ,2 C2 dt2 second harmonics generation: dt2 Ej = Ek = Eocos(o;f) e0xfkEjEk eoxfkEo cos2 (cvt) = UoxfkEfi + ^eoxfk]E$ cos(2cvt) X W = 0 in a centrosymmetric media Martina Mrkvickovä autumn 2023 8/21 A trip to the nonlinear optics - EFISH EFISH: Ej = Ek = E^cos(tot), E, = Eext • induced polarization at the second harmonic frequency: ^)-|4'/)(-2o;,0,a;^)EeXt(EM)2 • signal intensity scales with the square of the induced polarization /(2o0 „ U3)Eext/M l2 Martina Mrkvickovä EFISH autumn 2023 9/21 EFISH equations for homogeneous field Laser in EFISH in homogeneous el. field E = ^: /(2a;) OL (3).A/./M-E Sin(A/C/-} i 2 ■ext A/c ► /(2a;) - EFISH signal intensity ► #(3) - third order nonlinear hyperpolarizability of the gas ► N- gas number density ► - intensity of the primary laser beam ► Eext - external el. field (that's what we measure) ► A/c = (2/^ - k2w) - wave vector mismatch ► L - interaction length ■1061 nm S32nm Martina Mrkvickovä EFISH autumn 2023 10/21 EFISH for inhomogeneous field EFISH autumn 2023 11/21 And that's how we do it! If the gas composition, shape of the laser beam nor the spatial distribution of the external field Eex^ do not change during the whole measurement and calibration: /(2*0 =4.(/("))2.E* We find the calibration constant A by measurement of signal dependency on the known el. field (Laplacian field, sub-breakdown conditions) The desired el. field is determined from Eo= X/(«) Martina Mrkvickovä EFISH autumn 2023 12/21 EFISH strengths • high spatial and temporal resolution (~ laser pulse duration and shape) • it works for most of gases • nonresonant method, any laser wavelength • sensitivity ~ 1 kV/cm • only one laser beam - simple alignment • polarisation of the signal || Eext 1.0 ■ c i LLj 0.5 1 Carbon dioxide • Nitrogen v Methane □ o Argon Air 1000 2000 3000 Electric field (V/cm) 4000 [Dogariu et al, Phys. Rev. Applied 7, 024024 (2017)] Martina Mrkvičková EFISH autumn 2023 13/21 EFISH limitations • line-integrated signal ->> uncertainty in signal origin; the signal can also originate surprisingly far from the focusal point • unintuitive dependancy on /_, difficult calibration if the shape of the field is unknown • signal is dependent on the gas composition - forex. (3) on (3) for three different z.h and AJt — —0.5 cm-' (note the logarithmic scale on the vertical axis), (b) Spatial (z)evolution of the E-FESH signal (given by equation [5)) in a constant external field, fori — 6.4 cm. and z.r ~ 3.39 mm. Gray and blue vertical dashed lines correspond to z = ±Zr and ±5zr respectively. [T L Chng et al Plasma Sources Sei. Technol. 29 (2020) 125002] EFISH successful results 2500 2000 1500 1000 500 P = 20 mbar, V = 1,6 cm/ns P = 40 mbar, V = 1.2 cm/ns P = 70 mbar, V = 0.6 cm/ns P ■ 100 mbar, V ■ 0.4 cm/ns 78 80 62 84 Time, ns 1-1- 86 88 90 Figure 7. Reduced electric field measured in the front of a fast ionization wave discharge in nitrogen at/3 = 20—100 mbar, plotted on the same scale. [T L Chng et al 2019 Plasma Sources Sci. Technol. 28 045004] 6 8 10 12 Time (ns) Figure 4, Longitudinal electric field temporal profile at 500 jtm from tlie cathode obtained using the EFISH technique (Iine-|-symbol line} compared with the electric field profile calculated as a voltage over gap length ratio (dashed line). HeiN? = 5:1 miMuiv til inhtii". r.-^nLiv-j- p:il:■ iiI\ LLi-d'.uiiV. L Iv L-IL-i-denote the boundaries of the regions with different field behavior; see test. [N D Lepikhin et al 2021 J. Phys. D: Appl. Phys. 54 055201] Martina Mrkvickovä EFISH autumn 2023 17/21 EFISH successfull results I 01 CT (0 4-J o > 40 60 time [ßs] 40 60 time [ps] 200 150 100 40 60 time [ßs] 40 60 time [ps] 12 L. C g> Vi JZ IS) 4— 0J -10 ■ 1 kV - 5 kV ■ 2 kV 6 kV 3 kV ...........6.5 kV ■ 4 kV ...........7 kV 7.5 kV 8 kV -5 0 voltage [kV] [M Mrkvickovä et al 2023 Plasma Sources Sei. Technol. 32 065009] A *' i v • : _ V v n \\ f M r • . p-i i * k.-r M1 Je * A* ■ * * * .* / / .* /// \ .w\\\w\j t ? / \ s\\\8B 10 Martina Mrkvickovä EFISH autumn 2023 18/21 EFISH successful! results 12 „ 10 L. c JZ 4— (U 1 kV -5 kV 2 kV 6 kV 3 kV ...........6.5 kV 4 kV ...........7 kV 7.5 kV 8 kV ft. ■ _ *, V H 7*F LS •a i <-W v _LÄÜ J-f? J/i> f / / ? ■ - * U \ W \V 5fc \ \ »» «V v t j* '/Hiii. 7/ f / » 1 r r m jh j j j *** -10 0 voltage [kV] 10 -2 0 voltage [kV] Martina Mrkvickovä EFISH autumn 2023 19/21 EFISH successful! results Experimental part powermeter DBD atomizer photodiode Nd:YAG laser 5b I iL^photomultiplier Tasks: • align the optical setup • find the EFISH signal • measure the dependency on the voltage amplitude or the discharge phase Martina Mrkvickovä autumn 2023 21/21