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Die TIB übernimmt keine Verantwortung für etwaige Fehler, Auslassungen oder Folgen, die aus der Nutzung dieser Datei resultieren. xml_created 28-08-2026 dc.identifier.uri https://doi.org/10.1088/1361-6595/adad13 dc.rights.license CC BY 4.0 Unported dc.relation.doi https://doi.org/10.34657/41313 Optical inline interferometer for enhanced low-field detection via electric-field induced second harmonic generation 29 01 2025 Optical inline interferometer for enhanced low-field detection via electric-field induced second harmonic generation, Billeau, Jean-BaptisteCusson, PatrickSeletskiy, DenisReuter, Stephan, , (2025-01-29). Nonlinear optical methods, such as Electric-Field Induced Second Harmonic (E-FISH) generation, have emerged as powerful tools for diagnosing electric fields in plasma environments. The E-FISH technique depends quadratically on the electric field under study, which results in complete insensitivity to its polarity and diminished sensitivity to its low amplitudes. Both of these challenges have been recently resolved in a Local Oscillator Electric-Field Induced Second Harmonic (LOE-FISH) technique, introducing coherent homodyne amplification of a weak E-FISH signal using of an optical local oscillator field. Early LOE-FISH demonstrations relied on a delay line, resulting in decreased accuracy due to the higher sensitivity of the interferometer to environmental noise. In this work, we introduce an ‘inline’ design of the interferometer with maximally shared common paths and a balanced photodetection system, thus greatly reducing sensitivity to environmental noise and laser technical noise and hence improving the robustness of the technique. To this end, we achieve a factor of 143 increase in signal-to-noise ratio (SNR) when LOE-FISH is compared to E-FISH. Furthermore, we successfully measured an electric field as low as 32 V cm⁻¹ with an SNR of 7.4 during 0.15 s measurement time, estimating an unprecedented detection limit of 1.7 V ( cm ⋅ Hz )⁻¹. Our work represents a significant step toward real-time, high-precision diagnostics of electric fields in complex plasma environments, electric field amplitude fluctuations can influence reactive species’ generation and overall process efficiency. IntroductionThe rapidly evolving temporal and spatial electrical characteristics of plasma sources are essential for producing highly reactive species. Precise measurement and control of the reduced electric field (E/N)-the electric field normalized by the neutral species density-can significantly enhance the tailoring of plasma processes, ensuring more efficient and targeted outcomes. This precise control promises to enable a more efficient generation of highly reactive species (Richards et al 2022), which play a key role in driving specific plasma reactions. Tailoring the electric field can influence energy transfer mechanisms, reaction rates, and chemical pathways within the plasma. This is particularly important in application fields such as plasma medicine (Fridman et al 2008, von Woedtke et al 2013, Ulmer et al 2014, Laroussi 2020), where optimizing interactions between reactive species and biological tissues is critical, as well as in plasma-based environmental technologies (Guo et al 2018, Lewis et al 2020, Li et al 2023), agricultural processes (Puac ˇet al 2017, Guo et al 2021), and chemical synthesis (Asadollahi et al 2020, Panchal et al 2024, Tian et al 2024). As the demand for real-time, adaptive plasma treatments grows, achieving accurate and reliable control over the reduced electric field becomes critical for advancing plasma technologies across these domains.Recently, a nonresonant and non-invasive optical technique called Electric-Field Induced Second Harmonic (E-FISH) has been developed to temporally and spatially probe the reduced electric field E, independent of the gas composition (Dogariu et al 2017). By exploiting the hyperpolarizability of a medium to induce nonlinear optical effects through the application of an electric field, this method has demonstrated the ability to diagnose electric fields in plasma sources across a wide temporal range, from the femtosecond to nanosecond regimes (Dogariu et al 2017, Goldberg et al 2018, 2019, Adamovich et al 2020). In a third-order nonlinear optical process, a second-harmonic field E E-FISH can be produced in the x-direction by a co-polarized external DC field E x when the medium is illuminated by an input field at frequency ω:I 2ω x ∝ |E E-FISH,x | 2 ∝ ( χ (3) xx E x I ω x ) 2 L 2 , (1)where χ(3) xx (−2ω; 0, ω, ω) is the nonlinear susceptibility of third-order proportional to the gas density, I ωx is the intensity of the beam at frequency ω and polarized along the x direction, and L is the length of the interaction region in the direction of propagation.Due to its quadratic dependence on the applied field E x , the E-FISH technique has two main limitations: (1) low sensitivity to weak electric fields and (2) the inability to detect polarity changes of the field due to the E 2 dependence. To address the first limitation, E-FISH signals are typically captured using high-energy pulsed (femtosecond to nanosecond) laser systems in the mJ range, along with intensified imaging devices such as photomultiplier tubes (PMTs) and intensified CCDs (ICCDs) (Dogariu et al 2017, Goldberg et al 2019). Low repetition rates of such lasers coupled with low I 2ω signal levels and possibly slow acquisition speeds impose technological limits on the applicability of the E-FISH technique for tracking real-time processes.Improvement of the first limitation and lifting of the second one has been recently demonstrated through a homodyne amplification of the E-FISH signal by mixing it with an optical local oscillator (LO) beam (Hogue et al 2023, Billeau et al 2024):S LOE−FISH ∝ E 2 LO + E 2 E−FISH + 2E LO E E−FISH cos (ϕ) . (2)The signal S originates from the superposition of the electric field E LO with the E-FISH field (both at the 2ω carrier frequency), and ϕ is the phase angle between the two fields. The interference term gives access to the linear dependence on the applied field and its multiplication by a strong LO field (E LO ≫ E E-FISH ). Furthermore, ϕ dependence enables the detection of the polarity of the signal, referenced to the LO field. In practice, the LO field is produced by second-harmonic generation (SHG) of the fundamental wave. The phase (polarity) of the applied electric field can be extracted from the interference component of the total signal. The existence of the interference term can in turn be proven through a scan of the phase angle ϕ between the LO and the E-FISH signal, through a controlled insertion of the thin glass wedges (see figure 1). In doing so, the interference term can be scanned in the range from ±2E LO E E-FISH when ϕ is scanned from ±π. First implementation of the Local Oscillator Electric-Field Induced Second Harmonic (LOE-FISH) technique in a plasma characterization context has demonstrated enhancement up to a factor of 7 in the signal-to-noise ratio (SNR) when compared to the E-FISH signal (Hogue et al 2023). Furthermore, the Amplified Crossed-beam E-FISH (ACE-FISH) technique (Billeau et al 2024), which employs interferometry in a crossed-beam configuration, has demonstrated enhanced spatial resolution by achieving beam angles up to 3.6 • while providing critical insights into the electric field directionality in plasma jets. However, both systems rely on an optical delay line between the interferometer arms, which introduces optomechanical variations and heightens sensitivity to environmental conditions (Brandi and Gizzi 2019). These factors are ultimately linked to environmental disturbance of the interferometer's relative path length difference which, through ϕ, reduces the SNR.In this work, we propose an improved interferometer design to overcome these challenges and enhance the SNR between classical E-FISH and amplified E-FISH techniques. Based on second-harmonic interferometry utilizing 'single-arm' systems (referring to interferometers with maximally shared common path between its arms) (Hopf and Cervantes 1982), our 'inline' design multiplexes orthogonal polarizations of the E-FISH and LO signals as two interferometer arms, employing one SHG crystal and a polarizing beam splitter as two beamsplitters of a general interferometer layout. Using a second harmonic crystal and balanced detection, a minimum sensitivity value of 1.7 V (cm• √ Hz) −1 has been demonstrated. During writing, we found out about a parallel investigation, which proposed a similar 'inline' geometry, achieving the LOE-FISH concept with the LO beam served by a second harmonic generation on interface surfaces of the E-FISH optics (LaCombe et al 2024). MethodologyFigure 1 presents a schematic of our inline LOE-FISH system. For this demonstration we chose a PHAROS Yb:KGW regenerative amplifier (Light Conversion) operated at a 3.3 kHz repetition rate and a wavelength of 1030 nm. The system delivers pulses with a duration of 260 fs and an energy of 20 µJ. In this configuration, the polarization of the beam is parallel to the table.The key component of the interferometer is the BBO crystal, whose optical axis is rotated 45 • relative to the polarization of the laser beam at a frequency ω. This generates LO in two collinear beams of vertical and horizontal polarization and equal intensity. After the BBO, the laser beam is focused between square electrodes (15 mm in length, with rounded edges) where a high-voltage DC power supply (Speelman, USA) generates the electric field. The applied voltage is measured using a CT4028 voltage probe (Cal Test Electronics, USA). A pair of glass wedge prisms is used to fine-tune the temporal overlap between the fundamental and second harmonic beams, ultimately providing control over the ϕ phase of the LOE-FISH interferometer and a way for optimizing the interference fringe for maximum signal gain. After the interaction region between the two electrodes, the beams are sent onto a Wollaston prism, which sends beams of orthogonal polarizations in different directions. Those beams are then sent toward input ports of a balanced photodetector (PDB, PDB450A, Thorlabs, USA), which detects a photon number difference between the two polarization channels. E E-FISH signal inline-generated by the intense ω beam (equation (1)) will then interfere with one (co-polarized) LO component, thus upsetting an otherwise balanced photon number difference readout. As such, the signal proportional to the interference term (and hence E E-FISH ) in equation ( 2) is detected as a positive (or negative) voltage output of the PDB, depending on the polarity of the field under study. This scheme allows suppression of technical laser noise (common-noise rejection), once the interferometer readout is balanced when the external field is not applied. A half-wave plate on the ω beam before the SHG crystal can be used to fine-tune this balancing. Finally, the optical filtering system consists of two reflective short-pass filters, a Wollaston prism and a collimating plano-convex lens (f = 300 mm). The differential signal between the photodiodes is recorded using an SDS1104X-U digital storage oscilloscope (Siglent, USA), with a 500 kHz low-pass electrical filter (EF506, Thorlabs, USA) in order to suppress unwanted frequency noise contributions. ResultsTo first compare the E-FISH signal to the LOE-FISH, a calibration curve set at known electric field values was made (see figure 2). Both signals were obtained using the same experimental setup, with the only difference being the presence of the BBO crystal in the LOE-FISH configuration. It should be noted that SH conversion efficiency is less than 0.1%, validating the comparison procedure. Furthermore, post-processing was identical for both signals; the prominence of 45 signal pulses was averaged, with the uncertainty represented by the standard deviation across all signals. Each individual signal represents an average of 512 measurements. To ensure consistency, the origin was set to zero by subtracting the signal value measured in an environment without an electric field.Accounting for the behavior of both regimes-linear for LOE-FISH and quadratic for E-FISH-a fit of the ratio of their SNRs is shown in figure 3 to highlight the signal improvement achieved with our new technique. The reference fit is plotted according to equation (3)S SNR Ratio ∝ S LOE-FISH S E-FISH ∝ a + bx c + dx 2 . (3)The ratio was plotted with error bars calculated using differential uncertainty propagation based on the data from figure 2.To highlight the ability to detect low electric fields, an additional calibration curve using a set of known, small electric field values is presented in figure 4. As with previous results, the data in figure 4 is based on an average of 45 signals, each consisting of an accumulation of 512 pulses. The y-axis represents the mean prominence of all the signals, with the error bars indicating the standard deviation. DiscussionOur work has the following unique results: the first is a substantial improvement in the SNR compared to previous iterations of the LOE-FISH technique. With an SNR gain of approximately 143 over conventional E-FISH methods, we demonstrate a 20-fold enhancement relative to earlier versions. This improvement not only enables more precise and reliable measurements but also facilitates the use of more costeffective equipment. It also allows access to lower laser power systems with a higher repetition rate and balanced readout systems. Furthermore, this improvement creates the possibility of using single-shot diagnostics on plasma sources. The second major result is the ability to detect very low electric fields. As shown in figure 4, the system successfully measured an electric field of 32 V cm −1 with an SNR of 7.4 in 0.15 s, equating to a sensitivity of 1.7 V (cm• √ Hz) −1 . This capability represents a major advancement in low-field sensitivity, particularly in complex plasma environments where fluctuations in electric field strength can significantly impact reaction pathways and overall efficiency. The third result addresses practical improvements. By employing an inline design, rather than the traditional two-arm system with a delay line, we reduce the complexity of the experimental setup. This simplifies both manipulation and alignment procedures. Moreover, the compact nature of the inline interferometer design makes it more easily integrated into existing E-FISH setups, further enhancing its practicality and ease of use in various research environments. ConclusionIn this paper, we have demonstrated significant advancements in electric field detection using the LOE-FISH technique. The use of the BBO crystal, balanced photodetector and refined optical alignment strategies has played a crucial role in optimizing signal amplification while minimizing phase shifts between the fundamental and second harmonic signals. This comprehensive approach to system refinement has led to measurable improvements in both performance and ease of use, making it a promising development for future research and applications in high-precision electric field measurements. With an SNR gain of approximately 143 and the capability to detect very low electric fields, down to an estimated current limit of 1.7 V (cm• √ Hz) −1 , we believe these advancements are pivotal for the development of real-time electric field diagnostics in the plasma science domain. Figure 1 . Figure 1. Top view of the experimental setup of the inline local oscillator E-FISH system. Figure 2 . Figure 2. Comparison between the E-FISH signal and the LOE-FISH signal. Figure 3 . Figure 3. Gain in the SNR of the LOE-FISH technique over the E-FISH technique. Figure 4 . Figure 4. Low electric-field characterization. Panchal D, Lu Q, Sakaushi K and Zhang X 2024 Advanced cold plasma-assisted technology for green and sustainable ammonia synthesis Chem. Eng. J. 498 154920 Puac ˇN, Škoro N, Spasić K, Živković S, Milutinović M, Malović G and Petrović Z L 2017 Activity of catalase enzyme in Paulownia tomentosa seeds during the process of germination after treatments with low pressure plasma and plasma activated water Plasma Process. Polym. 15 1700082 Richards C, Jans E, Gulko I, Orr K and Adamovich I V 2022 N 2 vibrational excitation in atmospheric pressure ns pulse and RF plasma jets Plasma Sources Sci. Technol. 31 034001 Tian Q, Bi L, Lin S, Gao J and He Y 2024 A review of cold plasma for catalyst synthesis and modification Clean Energy Sci. Technol. 2 131 Ulmer M, Lademann J, Patzelt A, Knorr F, Kramer A, Koburger T, Assadian O, Daeschlein G and Lange-Asschenfeldt B 2014 New strategies for preoperative skin antisepsis Skin Pharmacol. Physiol. 27 283-92 von Woedtke T, Reuter S, Masur K and Weltmann K D 2013 Plasmas for medicine Phys. Rep. 530 291-320 Data availability statementThe data that support the findings of this study are openly available at the following URL/DOI: https://doi.org/10.6084/ m9.figshare.28236323. FundingFinancial support from the Natural Sciences and Engineering Research Council of Canada (including Grant RGPIN-06820), New Frontiers in Research Fund, and the TransMedTech Institute through its main financial partner, the Apogee Canada First Research Excellence Fund is acknowledged. This work has been partially funded by the European Union's Horizon Europe Research and Innovation Programme under Agreement 101070700 (Project MIRAQLS), cofunded by NSERC. ORCID iDsJean-Baptiste Billeau  https://orcid.org/0009-0002-3957-061X Stephan Reuter  https://orcid.org/0000-0002-4858-1081 Nanosecond second harmonic generation for electric field measurements with temporal resolution shorter than laser pulse duration, Adamovich, IButterworth, TOrriere, TPai, D ZLacoste, DCha, M SJ. Phys. D: Appl. Phys, 53, 145201 (2020). 10.1088/1361-6463/ab6790 Multi-pass deposition of organosilicon-based superhydrophobic coatings in atmospheric pressure plasma jets, Asadollahi, SProfili, JFarzaneh, MStafford, LThin Solid Films, 714, 138369 (2020). 10.1016/j.tsf.2020.138369 Coherent homodyne detection for amplified cross-beam electric-field induced second harmonic, Billeau, JCusson, PDogariu, AMorozov, ASeletskiy, DReuter, SAppl. Opt, 63, 5203 (2024). 10.1364/AO.527243 Optical diagnostics for density measurement in high-quality laser-plasma electron accelerators, Gizzi, Brandi, L AHigh Power Laser Sci. Eng, 7, e26 (2019). 10.1017/hpl.2019.11 Species-independent femtosecond localized electric field measurement, Dogariu, AGoldberg, B MByrne, O'Miles, S, R BPhys. Rev. Appl, 7, 24024 (2017). 10.1103/PhysRevApplied.7.024024 , Fridman, GFriedman, GGutsol, AShekhter, AVasilets, VFridman, AApplied plasma medicine Plasma Process. Polym, 5, (2008). 10.1002/ppap.200700154 Electric field measurements in a near atmospheric pressure nanosecond pulse discharge with picosecond electric field induced second harmonic generation, Goldberg, MChng, TMiles, Dogariu, R BAppl. Phys. Lett, 112, 64102 (2018). 10.1063/1.5019173 1D time evolving electric field profile measurements with sub-ns resolution using the E-FISH method, Goldberg, MReuter, SMiles, Dogariu, R BOpt. Lett, 44, 3853 (2019). 10.1364/OL.44.003853 Plasma-activated water production and its application in agriculture, Guo, DLiu, HZhou, LXie, JHe, CJ. Sci. Food Agric, 101, (2021). 10.1002/jsfa.11258 , Synergistic degradation of bisphenol A by pulsed discharge plasma with granular activated carbon: effect of operating parameters, synergistic mechanism and possible degradation pathway Vacuum, 156, (2018). Sensitive detection of electric field-induced second harmonic signals, Hogue, JCusson, PMeunier, MSeletskiy, DReuter, SOpt. Lett, 48, 4601 (2023). 10.1364/OL.492443 , Hopf, FCervantes, MNonlinear optical interferometer Appl. Opt, 21, 668 (1982). 10.1364/AO.21.000668 , Sub-1 V/cm E-FISH-based picosecond electric field measurements in atmospheric pressure air, , (2024). , Cold plasma in medicine and healthcare: the new frontier in low temperature plasma applications Front, , (2020). Rapid degradation of PFAS in aqueous solutions by reverse vortex flow gliding arc plasma, Lewis, AEnviron. Sci.: Water Res. Technol, 6, (2020). 10.1039/C9EW01050E PFAS-CTAB complexation and its role on the removal of PFAS from a lab-prepared water and a reverse osmosis reject water using a plasma reactor, Li, RIsowamwen, ORoss, K CHolsen, TThagard, S MEnviron. Sci. Technol, 57, (2023). 10.1021/acs.est.3c03679