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Accueil > A propos du LPP > Communication > Actualités archivées > 2021 > Electric Field-Induced Second Harmonic (E-FISH) Generation : Towards a robust method for electric field measurements in plasmas

Electric Field-Induced Second Harmonic (E-FISH) Generation : Towards a robust method for electric field measurements in plasmas

The importance of the electric field for plasma characterization requires no overstating. It controls the distribution of energy within a plasma, and in nanosecond discharges for instance, is the main reason why the chemistry is dominated by reactions such as electronic excitation, ionization and molecular dissociation. In essence, the ability to measure the electric field is synonymous with an understanding of the plasma reactivity.

Yet electric field measurement techniques for non-equilibrium plasmas, which typically require excellent temporal (sub-ns) and spatial resolution (sub-mm), at conditions of moderate to ambient pressures, are generally sparse. State-of-the-art methods such as Stark shift measurements, laser induced fluorescence dip spectroscopy and coherent four-wave mixing perhaps offer the most promise going forward.

Over the past few years, electric field-induced second harmonic generation, or E-FISH, is another candidate that has shown significant potential. This laser-based method relies on quantifying the optical second harmonic response to an externally applied electric field. As shown in figure 1, the presence of an electric field induces a coherent optical signal (at the second harmonic wavelength), which is otherwise absent without a plasma. Key advantages of this technique include its simplicity and exemplary detection sensitivity – a field strength of about 450 V/cm has been measured in a nanosecond discharge at 100 Torr. The signal production is governed by the duration of the laser excitation, and in principle permits sub-psec temporal resolution with ultrashort laser pulses. Finally, the non-resonant mechanism of the second harmonic generation implies that E-FISH may be applied in virtually any gas, without constraints on the gas composition.

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Figure 1
Schéma illustrant les principes de fonctionnement d’E-FISH.

Recent work in collaboration with our colleagues at LOB has led to an improved understanding of the spatial behaviour and origin of the signal generation, given that the path-integrated nature of the E-FISH method has long been a source of inquiry. A theoretical and experimental investigation involving focused laser beams reveals that the E-FISH signal, in addition to parameters such as the externally applied electric field, is also strongly dependent on the entire length (and shape) of this electric field profile [5]. Figure 2 shows evidence of this observation confirmed by both theory and experiment for a parallel plate electrode geometry. The reason for this behaviour can be explained by the intrinsic phase variation (the Gouy phase shift) present in a focused beam, and has also been observed in biological applications involving second harmonic generation. This spatially varying phase component results in a spatially dependent phase difference between the fundamental and second harmonic waves as they propagate forward. The consequent interaction means that changes along the signal buildup path, beyond the focal region of the laser (where the laser intensity is highest), can also alter the eventual signal.

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Figure 2
a) Effet de la longueur des électrodes sur le signal E-FISH pour trois gammes de Rayleigh différentes, zR (correspondant à trois longueurs focales de lentilles différentes), comme prédit par (i) la théorie et (ii) les expériences. b) Schéma de la géométrie des électrodes à plaques parallèles.

While this counter-intuitive finding does not affect the time resolution of the measurement, it raises complications in arriving at quantitative data, since electric field profiles present during calibration and in the plasma have to be strictly matched, to maintain accuracy. A few recommendations have been put forward as a result of this study, and are currently being pursued at LPP through several collaborations. These suggestions include the crossing of two laser beams to localize the interaction volume to the beam intersection region, as well as to make use of numerical simulations to provide inputs for correcting the experimental data.

These studies are expected to yield a robust electric field measurement technique that is well-tailored for non-equilibrium plasmas.


  1. Chng, T.L., Orel, I.S., Starikovskaia, S.M. and Adamovich, I.V., 2019. Electric field induced second harmonic (E-FISH) generation for characterization of fast ionization wave discharges at moderate and low pressures. Plasma Sources Science and Technology, 28(4), p.045004.
  2. Chng, T.L., Brisset, A., Jeanney, P., Starikovskaia, S.M., Adamovich, I.V. and Tardiveau, P., 2019. Electric field evolution in a diffuse ionization wave nanosecond pulse discharge in atmospheric pressure air. Plasma Sources Science and Technology, 28(9), 09LT02
  3. Chng, T. L., Ding, Ch., Naphade, M., Goldberg, B. M., Adamovich, I. V., & Starikovskaia, S. M. (2020). Characterization of an optical pulse slicer for gas-phase electric field measurements using field-induced second harmonic generation, Journal of Instrumentation, 15(03), p.C03005.
  4. Chng, T. L., Naphade, M., Goldberg, B. M., Adamovich, I. V., & Starikovskaia, S. M. (2020). Electric field vector measurements via nanosecond electric field induced second harmonic generation, Optics Letters, 45(7), pp.1942-1945.
  5. Chng, T. L., Starikovskaia, S. M., & Schanne-Klein M.-C. (2020) Electric field measurements in plasmas : how focusing strongly distorts the E-FISH signal, Plasma Sources Science and Technology, 29, 125002 (14pp).

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