Electric Field Induced Second Harmonic Research Articles

Optical Second‐ and Third‐Order Nonlinearities in Plasma‐Enhanced Chemical Vapor Deposition‐Grown Silicon Oxides and Silicon Nitrides

Optical second‐ and third‐order nonlinearities ( and ) in nonstoichiometric silicon oxides and silicon nitrides grown by plasma‐enhanced chemical vapor deposition are investigated by second‐harmonic generation (SHG) and electric field‐induced second‐harmonic (EFISH) measurements. The free‐space SHG measurements with a fundamental wavelength of 1030 nm allow us to determine the bulk values of both material platforms for various material compositions. It is demonstrated that the bulk values can be strongly enhanced by increasing the silicon content, reaching maximum values of the main tensor component of for silicon‐rich nitrides and for silicon‐rich oxides. EFISH measurements demonstrate that the values can be pushed even further by adding a static electric field to the materials. Similar to the values, the values are strongly enhanced by increasing the silicon content, leading to a maximum value of m2 V−2 for the silicon‐rich nitrides and m2 V−2 for the silicon‐rich oxides.

Coherent homodyne detection for amplified cross-beam electric-field induced second harmonic

The electric-field induced second harmonic (E-FISH) signal sensing is commonly used as a nonlinear optical technique to probe electric fields inside a plasma region. Cross-beam E-FISH is being investigated to improve spatial resolution by defining the interaction volume via a controlled geometry of two overlapping noncolinear optical beams. This drastic reduction in interaction length of the electric field and laser region results in a significant signal reduction. To overcome this signal reduction, we introduce coherent amplification of the cross-beam E-FISH signal by mixing the low E-FISH signal with a phase-locked bright local oscillator. We demonstrate enhancement of the signal. By introducing a local oscillator we can now derive the polarity of the measured electric field through the phase of the homodyne signal. To illustrate the technique, we, for the first time, to the best of our knowledge, measure the magnitude and the direction of the electric field in a cold atmospheric pressure plasma jet, which dynamically follows the profile of the applied bias current.

Electric field induced second harmonic generation in arsenic sulfide deposited by thermal evaporation.

Electric field induced second harmonic (EFISH) measurements are performed on thin films of arsenic sulfide deposited on chromium coated fused silica substrates by thermal evaporation of amorphous As2S3 bulk material. EFISH allows to widely tune the second-order optical susceptibility (χ(2)). An observed shift of the minimum of the second harmonic generation (SHG) intensity away from 0 V reveals a non-EFISH bulk χ(2), which is unexpected for amorphous materials. Additional SHG measurements on as-deposited films for investigation of the non-EFISH bulk χ(2) show Maker fringe patterns. Analyzing them and calibrating the SHG response against beta barium borate (BBO) crystal allows us to extract the components of the χ(2) tensor. The main component of this non-EFISH bulk χ(2) has a value of ∼0.22 pm/V. By increasing the χ(2) by applying the dc electric field a maximum value of 3.8 pm/V was achieved in EFISH measurements. This value is comparable to the χ(2) of traditional nonlinear crystals, e.g., BBO, which makes arsenic sulfide an interesting candidate for nonlinear hybrid structures.

Time-resolved investigations of a glow mode impulse dielectric barrier discharge in pure ammonia gas by means of E-FISH diagnostic

Time-resolved electric field strength measurements have been performed, using an electric-field induced second harmonic (E-FISH) diagnostic, in a nanosecond glow discharge of an impulse dielectric barrier discharge, in an ammonia gas environment. A temporal resolution of 2 ns and a spatial resolution estimated at 70 µm (given by laser waist) have been achieved. The comparative study of E-FISH measurements with and without a plasma discharge, operated at 4 kHz, reveal the presence of a persistent counter electric field, which is assumed to be caused by charge accumulation in between the AlN dielectrics used. Furthermore, by studying the influence of the applied voltage, the pressure, and the inter-dielectric distance, measurements seem to indicate the presence of charges remaining also in the post-discharge volume from the previous discharge to the next one.

DC Voltage Induces Quadratic Optical Nonlinearity in Ion-Exchanged Glasses at Room Temperature

We demonstrate that applying DC voltage at room temperature to an ion-exchanged glass induces quadratic optical nonlinearity in a subsurface region of the glass. We associate this with the EFISH (Electric-Field-Induced Second Harmonic) effect due to the Maxwell–Wagner charge accumulation in the subsurface region of the glass, in which a conductivity gradient forms as a result of the ion exchange processing. The second harmonic (SH) signal from the soda–lime glass subjected to potassium-for-sodium ion exchange is comparable with one from the same glass after thermal poling. The signal linearly increases with the duration of the ion exchange. The lower mobility of the potassium ions results in a higher SH signal from the potassium-for-sodium exchanged glass than that from the silver-for-sodium ion-exchanged one. This phenomenon is resistant to thermal annealing: only a 500 °C anneal caused noticeable degradation of the SH signal after “charging” the specimen. The phenomenon found is of interest for characterizing graded conductivity regions and providing and controlling second-order optical nonlinearity in transparent isotropic media.

Polarization properties of E-FISH signals and optimization of simultaneous measurement of electric field vectors

Electric field measurements based on the electric field induced second harmonic (E-FISH) method have been employed in a wide range of studies. Most studies typically measure two components of the electric field separately. Although there have been proposals for the simultaneous measurement of electric field vectors, the imbalance of the two corresponding E-FISH signals has limited its application. Furthermore, the relationship between the polarization of the E-FISH signal and the direction of external electric field remains unclear. In this paper, the general expressions for the polarization and power of both components of E-FISH signals are derived, assuming arbitrary probe beam polarization and external electric field direction. The theoretical results indicate that the polarization of E-FISH signals varies along the interaction length. The final signal’s polarization is elliptically polarized for arbitrary electric field distribution and is correlated with the polarization of the probe beam, which deviates from what is commonly assumed to be consistent with the external electric field. If the polarization of the probe beam is not parallel to the axes, the power of each signal component is determined by both components of the external electric field, which lays the foundation for the simultaneous measurement of electric field vectors. This theoretical prediction is subsequently validated by experimental results. Finally, the power maps suggest that the optimal polarization angle of the probe beam is 45° or 135° to achieve a balanced signal power when measuring an unknown electric field vector. Both components of the electric field can be simultaneously obtained according to the theoretical relationship.

Spatio-temporal electric field distributions in an atmospheric plasma jet impinging on a microchannel array surface

The electric field distribution in the ionization waves (IWs) propagating over a microchannel array dielectric surface, with the channels either empty or filled with distilled water, is measured by ps electric field induced second harmonic generation. The surface IW is initiated by the atmospheric pressure N2–Ar plasma jet impinging on the surface vertically and powered by ns pulse discharge bursts. The results show that the electric field inside the microchannels, specifically its horizontal component, is enhanced by up to a factor of 2. The field enhancement region is localized within the channels. The vertical electric field inside the channels lags in time compared to the field measured at the ridges, indicating the transient reversal of the IW propagation direction across the channels (toward the jet). This is consistent with the phase-locked plasma emission images and confirmed by the kinetic modeling predictions, which show that the IW ‘jumps’ over the empty channels and propagates into the channels only after the jump between the adjacent ridges. When the channels are filled with water, the wave speed increases by up to 50%, due to the higher effective dielectric constant of the surface. No evidence of a significant electric field enhancement near the dielectric surface (ceramic or water) has been detected, within the spatial resolution of the present diagnostic, ∼100 μm.

Nonlinear optical properties of natural hydroxyanthraquinones studied using density functional theory (DFT) technique

The present study reports the theoretical investigation of nonlinear optical (NLO) properties of natural hydroxyanthraquinones using the Density Functional Theory (DFT) method. The results show that all eleven compounds have appreciable NLO properties. The reported experimental results are supported by computational method. The optimized geometry, linear optical absorption, HOMO-LUMO energy gap, molecular electrostatic potential (MEP), and dipole moments were computed by employing the B3LYP/6-311++G(d,p) level of theory. The static and dynamic linear polarizability (α), first hyperpolarizability (β), and second hyperpolarizability (γ) components were calculated. At the working wavelength of the device, 1064 nm, the Nd:YAG laser's wavelength, and the doubling wavelength of 532 nm, which is also used to detect electric field induced second harmonic (EFISH), the nonlinear response of the molecules was evaluated.

Breakdown development in a nanosecond pulsed dielectric barrier discharge in humid air in plane-to-plane geometry

We used the ns electric field induced second harmonic (EFISH) generation diagnostic to measure the electric field evolution in a 200 ns pulse, dielectric barrier, plane-to-plane discharge in humid air, on the time scale shorter than the laser pulse duration. Plasma imaging by an ICCD camera detected a uniform evolution of the discharge emission during the breakdown. Spectroscopic measurements tracked the N2 second positive and first negative systems to infer the reduced electric field (E/N) evolution. EFISH measurements showed the electric field persistent during the entire HV pulse, with the residual field between pulses and the field inversion at the start and end of the HV pulse. The experimental data are consistent with the simulations, with the electron attachment and negative ion kinetics incorporated. The modeling predictions indicate that the rapid electron density decay due to attachment and recombination is the dominant factor sustaining the electric field in the plasma after breakdown. Spectroscopic E/N determination showed the time evolution at variance with the EFISH measurements, which may be due to the electron attachment and non-locality of the EEDF. Possible explanations are discussed.

Experimental and numerical investigation of surface streamers in a nanosecond pulsed packed bed reactor

Packed bed reactor (PBR) is the commonly used configuration in plasma catalysis, and its plasma characteristics have been extensively investigated. The filled catalysts in PBR make it challenging to carry out in-situ measurements of electric fields, and limited experimental data have been obtained. We investigated the surface streamer propagation and electric field distribution in a simplified PBR through simulations and experiments. The simplified PBR in the experiments is comprised of a blade-plate electrode structure filled with an Al2O3 column (ϵr = 9) in the discharge gap. An ICCD camera and an electric field diagnosis method called EFISH (electric field induced second harmonic generation) were employed, and a two-dimensional fluid model was established for the simulation. Four discharge types in the PBR were identified based on ICCD images and simulation results, including polar discharge at the contact areas, surface streamer along the dielectric column, expansion of surface discharge along the dielectric column, and surface ionization waves along the dielectric plate. Surface streamers with opposite propagation directions were found in the model, namely the forward streamer during the pulse rising time and the reverse streamer during the pulse falling time. Notably, the reverse streamer exhibits a significantly lower velocity compared to the forward streamer. Both experimental measurements and simulation were conducted to investigate the spatiotemporal electric field near the surface of the packing material. The results of both E exp and E sim showed peaks with opposite polarities, and exhibited similar trends. In the simulation, the forward streamer head showed a higher electric field compared to the reverse streamer head. Moreover, during the rest pulse time, the surface electric field was more intense at the contact areas than in other regions. The findings of this work provide valuable insights into the discharge mechanism and electric field on the catalytic material surface within the PBR.

Suppression of coherent interference to electric-field-induced second-harmonic (E-FISH) signals for the measurement of electric field in mesoscale confined geometries.

We present spatially enhanced electric-field-induced second-harmonic (SEEFISH) generation with a chirped femtosecond beam for measurements of electric field in mesoscale confined geometries subject to destructive spurious second-harmonic generation (SHG). Spurious SHG is shown to interfere with the measured E-FISH signal coherently, and thus simple background subtraction is not sufficient for single-beam E-FISH approaches, especially in a confined system with a large surface-to-volume ratio. The results show that a chirped femtosecond beam is effective in preventing higher-order mixing and white light generation in windows near the beam focal point which further contaminates the SEEFISH signal. The successful measurements of electric field of a nanosecond dielectric barrier discharge in a test cell demonstrated that spurious SHG detected with a congruent traditional E-FISH approach can be eliminated using the SEEFISH approach.

Temporal electric field of a helium plasma jet by electric field induced second harmonic (E-FISH) method

Electric field is an important parameter of plasma, which is related to electron temperature, electron density, excited species density, and so on. In this work, the electric field of an atmospheric pressure plasma jet is diagnosed by the electric field induced second harmonic (E-FISH) method, and the time-resolved electric field under different conditions is investigated. When positive pulse voltage is applied, the electric field has a peak of about 25 kV cm−1 at the rising edge of the voltage pulse. A dark channel is left behind the plasma bullet and the electric field in the dark channel is about 5 kV cm−1. On the other hand, when negative pulse voltage is applied, the electric field has a peak of −16 kV cm−1 when the negative voltage is increased to −8 kV. A relatively bright channel is left behind the plasma head and the electric field in this relatively bright channel is about −6 kV cm−1. When the pulse rising time increases from 60 to 200 ns, the peak electric field at both the rising edge and the falling edge of the voltage decreases significantly. When 0.5% of oxygen is added to the main working gas helium, the peak electric field at the rising edge is only about 15 kV cm−1. On the other hand, when 0.5% nitrogen is added, the peak electric field increases especially at the falling edge of the voltage pulse, where it increases reversely from −12 to −16 kV cm−1 (the minus sign only represents the direction of electric field).

Electric field measurements of DC-driven positive streamer coronas using the E-FISH method

This paper reports on electric field measurements, using the electric field-induced second harmonic (E-FISH) method, sampling the spatial structure and temporal development of DC-driven positive streamer coronas in atmospheric-pressure air at relevant timescales to examine the self-pulsating behavior of the discharge. The discharge is triggered from a point-to-plate geometry and consists of transient coronas, which bridge the inter-electrode gap and pulsate at about 3 kHz, superimposed with a persisting glow corona. The measurements presented challenge the phenomenological explanation for the pulsations based on field recovery at the anode driven by the evacuation of positive ions by electric drift effects and hint at a propagating wave-like feature from the plate-cathode to the tip-anode.

Spatially enhanced electric field induced second harmonic (SEEFISH) generation for measurements of electric field distributions in high-pressure plasmas

The spatial resolution of the ps electric field induced second harmonic (EFISH) generation has been enhanced by using non-collinear pump laser beam arrangements. The pump laser beam (1064 nm, nominal pulse duration 150 ps, pulse energy 20–40 mJ) is separated into two coaxial or crossing beams, overlapping only near the focal point. The spatially enhanced EFISH (SEEFISH) signal is generated over a shorter beam overlap region compared to the collinear beam arrangement. Blocking of either of the two beams results in a complete suppression of the signal. The signal is spatially isolated from the ‘conventional’ EFISH signal and measured by a photomultiplier detector. Measurements of a known Laplacian field generated between two parallel cylinder electrodes in ambient air shows that SEEFISH improves the spatial resolution of the measurements by up to a factor of 2, such that the measurement results agree with the Laplacian field distribution. The spatial resolution is improved further by reducing the focal distance of the lens. The magnitude of the SEEFISH signal is significantly lower compared to that of the single-beam EFISH and decreases rapidly as the beam crossing angle is increased, due to the phase mismatch. This approach has a significant potential for measurements of electric field distributions in high-pressure plasmas, with an additional benefit of removing the stray second harmonic signal from the optical access windows.

Spatiotemporally resolved measurements of electric field around a piezoelectric transformer using electric-field induced second harmonic (E-FISH) generation

When a piezoelectric transformer (PT) is actuated at its second harmonic frequency by a low input voltage, the generated electric field at the distal end can be sufficient to breakdown the surrounding gas, making them attractive power sources for non-equilibrium plasma generation. Understanding the potential and electric field produced in the surrounding medium by the PT is important for effectively designing and using PT plasma devices. In this work, the spatiotemporally resolved characteristics of the electric field generated by a PT operating in open air have been investigated using the femtosecond electric field-induced second harmonic generation (E-FISH) method. Electric field components were determined by simultaneously conducting E-FISH measurements with the incident laser polarized in two orthogonal directions relative to the PT crystal. Results of this work demonstrate the spatial distribution of electric field around the PT’s output distal end and how it evolves as a function of time. Notably, the strongest electric field appears on the face of the PT’s distal surface, near the top and bottom edges and decreases by approximately 70% over 3 mm. The time delay between the PT’s input voltage and measured electric field indicates that there is an about 0.45π phase difference between the PT’s input voltage and output signal.

Non-premixed counterflow methane flames in DC/AC/NS electric fields

The response of counterflow diffusion flames to sub-breakdown DC and AC electric fields, as well as their superposition with ns pulse discharge waveforms, is studied in the plane-to-plane electrode geometry. Sub-breakdown DC and low-frequency AC electric fields cause the flame displacement toward the grounded electrode, in the direction of the applied field, indicating that the body force on the positive ions exceeds that on the electrons and negative ions. As the AC frequency increases, the flame response becomes less pronounced, due to the reduction of the electrohydrodynamic (EHD) body force impulse over the AC half-period. The electric field in the electrode gap is determined by ps Electric Field Induced Second Harmonic (E-FISH) generation, with absolute calibration using sub-breakdown ns pulses overlapped with the measured electric field waveform. The results show that the electric field distribution across the flame in the current saturation regime follows the Laplacian field. This indicates that the space charge density in the gap is too low to distort the applied DC or AC field, consistent with the kinetic modeling predictions. Combining a nanosecond pulse discharge with a sub-breakdown DC field generates a diffuse plasma across the entire gap. Time-resolved and spatially resolved measurements of the electric field in the discharge indicate the ionization wave propagation between the electrodes. The present results do not exhibit a detectable flame displacement enhancement by ns discharge pulses combined with a sub-breakdown field, observed previously. Kinetic modeling calculations show that the absence of this effect in the plane-to-plane geometry is due to the rapid plasma self-shielding. This indicates that alternative electrode geometries limiting the self-shielding would be more effective for the plasma / electric field enhanced flameholding and flame stabilization applications.

Terahertz phase slips in striped La2−xBaxCuO4

Interlayer transport in high-$T_C$ cuprates is mediated by superconducting tunneling across the CuO$_2$ planes. For this reason, the terahertz frequency optical response is dominated by one or more Josephson plasma resonances and becomes highly nonlinear at fields for which the tunneling supercurrents approach their critical value, $I_C$. These large terahertz nonlinearities are in fact a hallmark of superconducting transport. Surprisingly, however, they have been documented in La$_{2-x}$Ba$_x$CuO$_4$ also above $T_C$ for doping values near $x=1/8$, and interpreted as an indication of superfluidity in the stripe phase. Here, Electric Field Induced Second Harmonic (EFISH) is used to study the dynamics of time-dependent interlayer voltages when La$_{2-x}$Ba$_x$CuO$_4$ is driven with large-amplitude terahertz pulses, in search of other characteristic signatures of Josephson tunnelling in the normal state. We show that this method is sensitive to the voltage anomalies associated with 2$\pi$ Josephson phase slips, which near $x=1/8$ are observed both below and above $T_C$. These results document a new regime of nonlinear transport that shares features of fluctuating stripes and superconducting phase dynamics.

Effect of the electric field profile on the accuracy of E-FISH measurements in ionization waves

Electric field induced second harmonic (E-FISH) generation has emerged as a versatile tool for measuring absolute electric field strengths in time-varying, non-equilibrium plasmas and gas discharges. Yet recent work has demonstrated that the E-FISH signal, when produced with tightly focused laser beams, exhibits a strong dependence on both the length and shape of the applied electric field profile (along the axis of laser beam propagation). In this paper, we examine the effect of this dependence more meaningfully, by predicting what an E-FISH experiment would measure in a plasma, using 2D axisymmetric numerical fluid simulations as the true value. A pin-plane nanosecond discharge at atmospheric pressure is adopted as the test configuration, and the electric field evolution during the propagation of the ionization wave (IW) is specifically analysed. We find that the various phases of this evolution (before and up to the front arrival, immediately behind the front and after the connection to the grounded plane) are quite accurately described by three unique electric field profile shapes, each of which produces a different response in the E-FISH signal. As a result, the accuracy of an E-FISH measurement is generally predicted to be comparable in the first and third phases of the IW evolution, and significantly poorer in the second (intermediate) phase. Fortunately, even though the absolute error in the field strength at certain time instants could be large, the overall shape of the field evolution curve is relatively well captured by E-FISH. Guided by the simulation results, we propose a procedure for estimating the error in the initial phase of the IW development, based on the presumption that the starting field profile mirrors that of its corresponding Laplacian conditions before evolving further. We expect that this approach may be readily generalized and applicable to other IW problems or phenomena, thus extending the utility of the E-FISH diagnostic.

Simulation of ionization-wave discharges: a direct comparison between the fluid model and E-FISH measurements

For a long period, there was a resolution gap between numerical modeling and experimental measurements, making it hard to conduct a direct comparison between them, but they are now developing in parallel. In this work, we numerically study diffusive ionization wave and fast ionization wave discharge experiments using recently published electric-field-induced second-harmonic (E-FISH) data together with a classical fluid model. We propose a pressure-E/N range for the drift diffusion approximation and a pressure-grid range for the local field/mean energy approximation of the fluid model. The three-term Helmholtz photoionization model is generalized using parameters given for N2, O2, CO2, and air. The capabilities of the classical fluid method for modeling the inception, propagation, and channel breakdown stages are studied. The calculated electric field evolution of the ionization is compared with E-FISH measurements in the discharge development and gap-closing stages. The influence of electrode shape and predefined electron density on the streamer morphology and the long-standing inception problem of the ionization waves are discussed in detail. Within the application range of the classical fluid model, good agreement can be achieved between calculation and measurement.

Formation and propagation of ionization waves during ns pulse breakdown in plane-to-plane geometry

Ionization wave development during ns pulse breakdown in nitrogen between two parallel plate, dielectric-covered electrodes is studied by ps electric field induced second harmonic (EFISH) generation and kinetic modeling. The results indicate formation of two well-defined ionization waves in the discharge gap, which requires a relatively high initial electron density. The first, anode-directed, wave is produced by ‘sweeping’ the initial electrons by the applied voltage pulse. The second wave originates between the cathode and the first wave front, due to the field enhancement in this region, generating two wave fronts propagating in opposite directions and observed in plasma emission images. Only the anode-directed front of the second wave is detected by the EFISH measurements, most likely due to the proximity of the cathode-directed front to the wall. Both the measurements and the modeling predictions exhibit a transient electric field overshoot in the center of the gap, caused by the anode-directed front of the second wave. The boundary between the plasma domains formed ahead of the first wave and behind the second wave, observed in the plasma emission images, is detected by the EFISH measurements and predicted by the modeling calculations. The electron density and coupled energy distributions predicted by the model at the end of the discharge pulse are nearly uniform, except near the cathode-adjacent wall, where the applicability of the present model is uncertain and which is not accessible to the EFISH measurements.