Electrostrictive Forces Research Articles

Low threshold quantum correlations via synthetic magnetism in Brillouin optomechanical system

We propose a scheme to generate low driving threshold quantum correlations in Brillouin optomechanical system based on synthetic magnetism. Our proposal consists of a mechanical (acoustic) resonator coupled to two optical modes through the standard optomechanical radiation pressure (an electrostrictive force). The electrostrictive force that couples the acoustic mode to the optical ones striggers Backward Stimulated Brillouin Scattering (BSBS) process in the system. Moreover, the mechanical and acoustic resonators are mechanically coupled through the coupling rate Jm, which is θ-phase modulated. Without a mechanical coupling, the generated quantum correlations, i.e., between optical and mechanical modes, require strong optomechanical and acoustic couplings. By accounting phonon hopping coupling, the synthetic magnetism is induced and the quantum correlations are generated for low coupling strengths. The generated quantum correlations display sudden death and revival phenonmena, and are robust against thermal noise. Our results suggest a way for low threshold quantum correlations generation, and are useful for quantum communications, quantum sensors, and quantum computational tasks.

A two-dimensional numerical characterization on the droplet dynamics in the electric field by VOSET method

A coupled volume-of-fluid and level set (VOSET) model is extended to the simulation of electro-hydrodynamic (EHD) flow. The good accuracy of proposed model is validated by comparing with previous results. Although the electrostrictive force might be greater than the Coulomb and dielectric forces under certain conditions, it has no influence on droplet dynamic behaviors except the pressure distribution. The electro-coalescence of droplet pair is systematically investigated. In addition to the coalescence and repulsion, two droplets might neither coalesce nor repulse with the repulsive hydrodynamic force and attractive electric force strike a balance. The electro-coalescence of two droplets always happens as long as the electric conductivity ratio is smaller than the permittivity ratio. The critical permittivity ratio separating the coalescence and repulsion of droplets increases as the increase of electric conductivity ratio. The electro-coalescence time of two droplets decreases as the permittivity ratio and electric capillary number increase. Nevertheless, the electro-coalescence time shows different variation tendency as the increase of electric conductivity ratio with different permittivity ratios and electric capillary numbers.

Process Development of Aluminum Electroplating from an Ionic Liquid on 150 mm Wafer Level.

This paper focuses on the development of electroplating on 150 mm wafer level for microsystem technology applications from 1-Ethyl-3-methylimidazolium chloride (EMImCl) with Aluminumtrichloride (AlCl3). The deposition was carried out on 150 mm wafers with Au or Al seed layers deposited by physical vapor deposition (PVD). The electrodeposition was carried out using pattern plating. On the Au seed layer, bipolar pulse plating was applied. Compared to the Au seed layer, the electrodeposition on the Al seed layer was favorable, with lower current densities and pulsing frequencies. Utilizing the recurrent galvanic pulses and avoiding ionic liquid convection, inhomogeneities lower than 15% were achieved with a laboratory plating cell. One major aspect of this study was the removal of the native Al oxide prior to deposition. It was investigated on the chip and wafer levels using either current- or potential-controlled removal pulses. This process step was affected by the plasma treatment of the wafer, thus the surface free energy, prior to plating. It turned out that a higher surface free energy hindered proper oxide removal at a potential of 3 V. The theory of oxide breakdown based on electrostriction force via the electrical field was applied to discuss the findings and to derive conclusions for future plating experiments.

Experimental study of cavitation development in liquid in pulsed non-uniform electric field under the action of ponderomotive forces

In this paper, the Rayleigh scattering method is used to study the formation of cavitation in water in a pulsed inhomogeneous electric field when a nanosecond high voltage pulse is applied to a needlelike electrode. The observational results confirm the theoretical picture of cavitation development under the action of electrostrictive ponderomotive forces. The values of the negative pressure, the average size of the cavitation nanovoids, and their concentration were obtained from these measurements, which are in agreement with theoretical estimates.

Towards high-sensitivity and high-accuracy forward Brillouin scattering-based optomechanical temperature sensing in thin-diameter fibers.

We numerically and experimentally demonstrated a high-sensitivity and high-accuracy temperature sensor based on guided acoustic radial modes of forward stimulated Brillouin scattering (FSBS)-based optomechanics in thin-diameter fibers (TDF). The dependence of the FSBS-involved electrostrictive force on the fiber diameter is systematically investigated. As the diameters of the fiber core and cladding decrease, the intrinsic frequency of each activated acoustic mode and corresponding FSBS gain are expected to be accordingly increased, which benefits the significant enhancement of its temperature sensitivity as well as the optimization of the measurement accuracy. In validations, by utilizing TDFs with fiber diameters of 80 µm and 60 µm, the proof-of-concept experiments proved that sensitivities of the TDF-based FSBS temperature sensor with radial modes from R0,4 to R0,15 increased from 35.23 kHz/°C to 130.38kHz/°C with an interval of 8.74 kHz/°C. The minimum measurement error (i.e., 0.15 °C) of the temperature sensor with the 60 µm-TDF is 2.5 times lower than that of the 125 µm-SSMF (i.e., 0.39 °C). The experimental and simulated results are consistent with theoretical predictions. It is believed that the proposed approach with high sensitivity and accuracy could find potential in a wide range of applications such as environmental monitoring, chemical engineering, and cancer detection in human beings.

Study on the Dynamic Evolution of Bubbles in Oil/Pressboard Insulation

Power transformer may generate bubbles in the transformer oil due to various factors such as internal insulation winding vibration and pressure change. Bubbles distort the spatial electric field, which makes the discharge breakdown along the gas channel, accelerate the discharge breakdown of insulating medium. Therefore, in order to prevent the arc discharge induced by micro bubbles inside the transformer from increasing the risk of transformer combustion damage, it is necessary to conduct in-depth research on the dynamic law of suspended bubbles before insulation breakdown from the source by combining experiments and simulations. In this paper, the bubble dynamic model of needle plate electrode under the multi coupling physical field of transformer is established in terms of the migration and deformation of suspended bubbles in liquid phase. By comparing the migration trajectories of single suspended bubbles obtained from experiments and simulations, the reliability of the model is verified. The variation of velocity component of voltage amplitude and the change of shape stretching of single suspended bubble in power frequency period are simulated, and the fluctuation law of pressure formed by electrostriction force inside and outside the bubble during migration is analyzed. The capacity absorption process of multi bubbles in the strong field region near the needle electrode was simulated. The changes of the surrounding liquid pressure and the spatial electric field distribution during the formation of the gas channel were analyzed, and the internal relationship between the gas channel and the formation of the discharge breakdown was revealed.

Numerical investigation on nucleate bubble departure by electrowetting-on-dielectric in battery cooling plates

A thermal management system is necessary to control battery operating temperature in electric vehicles (EV). Typically, the most common way to dissipate heat from the battery pack is to use the cooling plate. The cooling medium in the cooling plate removes the excess heat from the battery pack through boiling heat transfer. This paper proposes an electrowetting-on-dielectric (EWOD) method to enhance the bubble departure in nucleate boiling heat transfer in a cooling plate. In order to investigate the bubble splitting due to the EWOD effect, theoretical models are developed to solve for the electrophoretic force, dielectrophoretic force, and electrostrictive force. The theoretical model coupled a phase field method with an electric conservation model, where the body force acts as an external force due to the electric field. Our preliminary simulation results demonstrated that the EWOD effect can change the apparent contact angle when applied to a certain electric field. The free charge density displays at the dielectric layer interface with water and at the bubble’s interface near the triple contact point. Then two types of simulation case were investigated to apply the voltage in the battery cooling plates. In the first case, a pair of parallel discs are used as the electrodes at the bottom and top of the region. In the second case, the voltage is applied at the top of the nucleate bubble in a rod electrode. The various behavior of bubble dynamics were compared and discussed to indicate the optimized case for enhancing the nucleate bubble departure in the EV battery cooling plates.

Time-dependent theory of optical electro- and magnetostriction

Electrostriction, the deformation of dielectric materials under the influence of an electric field, is of continuous interest in optics. The classic experiment by Hakim and Higham [Proc. Phys. Soc. 80, 190 (1962)] for a stationary field supports a different formula of the electrostrictive force density than the recent experiment by Astrath et al. [Light Sci. Appl. 11, 103 (2022)] for an optical field. In this work, we study the origin of this difference by developing a time-dependent covariant theory of optical force densities in photonic materials. When a light pulse propagates in a bulk dielectric, the field-induced force density consists of two parts: (i) The optical wave momentum force density ${\mathbf{f}}_{\mathrm{owm}}$ carries the wave momentum of light and drives forward a mass density wave of the covariant coupled field-material state of light. (ii) The optostrictive force density ${\mathbf{f}}_{\mathrm{ost}}$ arises from the atomic density dependence of the electric and magnetic field energy densities. It represents an optical Lorentz-force-law-based generalization of the electro- and magnetostrictive force densities well known for static electromagnetic fields and derived from the principle of virtual work. Since the work done by ${\mathbf{f}}_{\mathrm{ost}}$ is not equal to the change of the field energy density during the contraction of the material, we have to describe this difference with optostriction-related dissipation terms to fulfill the energy conservation. The detailed physical model of the dissipation is left for further work. The optostrictive force density can be understood in terms of field-induced pair interactions inside the material. Because of the related action and reaction effects, this force density cannot contribute to the net momentum transfer of the optical field. The theory is used to simulate the propagation of a Gaussian light pulse through a dielectric material. We calculate the electric and magnetic fields of the Gaussian light pulse from Maxwell's equations and simultaneously solve Newton's equation of motion of atoms to find how the velocity and displacement fields of atoms develop as a function of time under the influence of the field-induced force density.

Characteristic of acoustic waves generated in dielectrics under divergent electric fields

Space charge measurement under divergent electric fields can provide crucial insight into various insulating phenomena, and the space charge reconstruction relies on the relation between the measured acoustic wave and the space charge distribution if the pulsed electroacoustic method is used. However, the relation is still unclear. In this work, the characteristic of acoustic waves generated by a divergent electric field is studied. Three components of electrostatic force leading to acoustic waves, which are surface force, internal Coulomb force, and electrostrictive force, are considered. The relation between the acoustic wave and these three components is provided, and the acoustic wave characteristic is, therefore, investigated. The results show that the acoustic wave exhibits two opposite peaks for each component due to the local distribution of the force, which is different from that with a uniform electric field, and the combined waveform is greatly influenced by the contribution of electrostrictive force, making it challenging to extract space charge information.

Implementation of the electrohydrodynamics’ perfect dielectric model in OpenFOAM

The electrohydrodynamics’ (EHD) perfect dielectric model was added into computational fluid dynamics (CFD) software OpenFOAM in order to improve its usability for the EHD field and specifically for the mentioned model. Based on the investigated literature, it can be said that this is the most complete implementatiton of the said model. Two sets of numerical simulations with two different fluids are presented and analyzed. One set is one-dimensional. The other set is with a drop of one fluid surrounded by other fluid. Oscillations can be observed with certain expressions or calculation strategies for the electrostrictive force, and used for disregarding them. Results that are closer to analytical predictions can be obtained by using appropriate expression for the dielectric force. The electrostrictive force was implemented not only for nonpolar, but also for polar fluids, and it is shown that it might significantly influence the drop deformation. Calculated and analytically predicted drop deformations were close or comparable even up to around 0.25, what is significantly higher and different from a previous study made by other authors. Different expressions for the electric permittivity and usage of limiters for volume fractions were investigated. Conclusions from this paper can be transferred to more complicated models.

Analysis of secondary emission mechanism in electron avalanches propagating in cylindrical nanoruptures in liquid water

Recently, a bouncing-like mechanism for electron multiplication inside long nano-ruptures during the early stages of nanosecond discharge in liquid water has been proposed in (Bonaventura 2021 Plasma Sources Sci. Technol. 30 065023). This mechanism leads to the formation of electron avalanches within nano-ruptures caused by strong electrostrictive forces. The avalanche propagation is a self-sustaining process: the electrons emitted from the water surface to the cavity support the propagation of the avalanche and the avalanche itself is a source of the parent electrons impinging on the surface of the nano-rupture and causing secondary emission. We analyze the process of the electron secondary emission directly from the simulation results of the electron avalanche propagation. This allow us to perform an in situ study of the secondary emission and related physical processes. We present the results of an extensive parametric study performed using the state-of-the-art simulation toolkit Geant4-DNA for modeling electron-liquid water interactions. It is shown that the typical lifetime of an electron in an avalanche is about 0.1 to 0.2 picoseconds and that the electron experiences about 4 bounces before ending up in liquid water. In addition, it is shown that the secondary electrons are formed in a layer adjacent to the nano-rupture surface that is only a few nanometres thin. The secondary electron velocity distribution at the moment of the electron birth, the velocity space of electrons (re-)emitted from the water, and the velocity space of electrons at the moment of their impact to the cavity surface are analyzed in detail. Electron bouncing and secondary electron generation efficiency are quantified using the secondary emission coefficient, the secondary emission efficiency, and the effective energy consumed to produce new electrons.

Experimental investigation of the angular symmetry of optical force in a solid dielectric

The textbook-accepted formulation of electromagnetic force was proposed by Lorentz in the 19th century, but its validity has been challenged due to incompatibility with the special relativity and momentum conservation. The Einstein–Laub formulation, which can reconcile those conflicts, was suggested as an alternative to the Lorentz formulation. However, intense debates on the exact force are still going on due to lack of experimental evidence. Here, we report the first experimental investigation of angular symmetry of optical force inside a solid dielectric, aiming to distinguish the two formulations. The experiments surprisingly show that the optical force exerted by a Gaussian beam has components with the angular mode numbers of both 2 and 0, which cannot be explained solely by the Lorentz or the Einstein–Laub formulation. Instead, we found that a modified Helmholtz theory by combining the Lorentz force with additional electrostrictive force can explain our experimental results. Our results represent a fundamental leap forward in determining the correct force formulation and will update the working principles of many applications involving electromagnetic forces.

High spatiotemporal resolution optoacoustic sensing with photothermally induced acoustic vibrations in optical fibres

Optoacoustic vibrations in optical fibres have enabled spatially resolved sensing, but the weak electrostrictive force hinders their application. Here, we introduce photothermally induced acoustic vibrations (PTAVs) to realize high-performance fibre-based optoacoustic sensing. Strong acoustic vibrations with a wide range of axial wavenumbers kz are photothermally actuated by using a focused pulsed laser. The local transverse resonant frequency and loss coefficient can be optically measured by an intra-core acoustic sensor via spectral analysis. Spatially resolved sensing is further achieved by mechanically scanning the laser spot. The experimental results show that the PTAVs can be used to resolve the acoustic impedance of the surrounding fluid at a spatial resolution of approximately 10 μm and a frame rate of 50 Hz. As a result, PTAV-based optoacoustic sensing can provide label-free visualization of the diffusion dynamics in microfluidics at a higher spatiotemporal resolution.

Electron generation and multiplication at the initial stage of nanosecond breakdown in water

Electrical breakdown of liquid dielectrics under nanosecond pulsed high voltage has been investigated extensively in the last decade. Prior studies have focused on either experimental characterization of the breakdown process and discharge plasma or formulation/verification of the electrostrictive cavitation mechanism of the breakdown initiation. There remain knowledge gaps toward a clear physical picture of how the first plasma is generated in a region saturated by nanoscale cavities created by electrostrictive forces in inhomogeneous fields at the nanosecond timescale. Initial plasma results from the multiplication of primary electrons that gain energy collisionlessly in the cavities to cause collisional ionization of water molecules on the cavity walls. This paper quantitatively discusses the possible sources of primary electrons that seed the plasma discharge. Electron detachment from hydroxide is shown to be the most probable and sustainable electron source. Using numerical modeling, this study demonstrates the plausibility of an electron multiplication mechanism involving two neighboring cavities. The drift of hydrated electrons from one cavity to the next is the rate-limiting step and sets the minimum electric field requirement. This work will inform subsequent experimental studies and have implications in various applications such as plasma sources in biomedical applications, cavitation study, and insulation of pulsed power equipment.

Development of High Dielectric Electrostrictive PVDF Terpolymer Blends for Enhanced Electromechanical Properties.

Electroactive polymers with high dielectric constants and low moduli can offer fast responses and large electromechanical strain under a relatively low electric field with regard to theoretical driving forces of electrostriction and electrostatic force. However, the conventional electroactive polymers, including silicone rubbers and acrylic polymers, have shown low dielectric constants (ca. < 4) because of their intrinsic limitation, although they have lower moduli (ca. < 1 MPa) than inorganics. To this end, we proposed the high dielectric PVDF terpolymer blends (PVTC-PTM) including poly(vinylidene fluoride-trifluoroethylene-chlorofluoro-ethylene) (P(VDF-TrFE-CFE), PVTC) as a matrix and micelle structured poly(3-hexylthiophene)-b-poly(methyl methacrylate) (P3HT-b-PMMA, PTM) as a conducting filler. The dielectric constant of PVTC-PTM dramatically increased up to 116.8 at 100 Hz despite adding only 2 wt% of the polymer-type filler (PTM). The compatibility and crystalline properties of the PVTC-PTM blends were examined by microscopic, thermal, and X-ray studies. The PVTC-PTM showed more compatible blends than those of the P3HT homopolymer filler (PT) and led to higher crystallinity and smaller crystal grain size relative to those of neat PVTC and PVTC with the PT filler (PVTC-PT). Those by the PVTC-PTM blends can beneficially affect the high-performance electromechanical properties compared to those by the neat PVTC and the PVTC-PT blend. The electromechanical strain of the PVTC-PTM with 2 wt% PTM (PVTC-PTM2) showed ca. 2-fold enhancement (0.44% transverse strain at 30 Vpp μm−1) relative to that of PVTC. We found that the more significant electromechanical performance of the PVTC-PTM blend than the PVTC was predominantly due to the electrostrictive force rather than electrostatic force. We believe that the acquired PVTC-PTM blends are great candidates to achieve the high-performance electromechanical strain and take all benefits derived from the all-organic system, including high electrical breakdown strength, processibility, dielectrics, and large strain, which are largely different from the organic–inorganic hybrid nanocomposite systems.

Tuning rigidity and negative electrostriction of multi-walled carbon nanotube filled poly(lactic acid)

Multi-walled carbon nanotubes (MWCNTs) were utilized as an effective filler and dibutyl phthalate (DBP) as a plasticizer in the electro-responsive poly (lactic acid) matrix. Under on and off electric field, the MWCNT/PLA/DBP composites showed electromechanical recoverability with typical fast response times less than 1 min. The 0.1%v/v MWCNT-1200/PLA/DBP possessed the highest positive storage modulus sensitivity value of 1.95 at the electric field strength of 1.5 kV/mm. The storage modulus response with a value close to zero was observed at a MWCNT content between 0.8 and 0.9 %v/v. At high MWCNT concentrations, the storage modulus response became negative definite at high electric field strengths. This negative electrostriction behavior was in contrast to the positive definite electrostrictive responses of other materials. In the bending experiments, the 0.1%v/v MWCNT-2100/PLA/DBP produced relatively higher bending responses and dielectrophoresis forces at electric field strengths below 300 V/mm. At higher electric field strengths and higher MWCNTs contents, the dipole moment interaction was screened resulting in the decreases in the electrostriction, bending response and dielectrophoresis force. Thus, it has been demonstrated here that the MWCNTs induced the negative electrostriction in the plasticized PLA, possibly through the physical screening and free volume.

Multiphysics simulation of the initial stage of plasma discharge formation in liquids

Plasma initiation simulations in homogenous liquids in response to ∼3.0–5.0 ns voltage pulse is conducted. An in-house numerical framework consisting of a compressible fluid solver together with charged species conservation and Poisson’s equation solver is employed for the simulations. The simulations are conducted for a needle-like powered electrode with two different voltage profiles—linear and exponential increase. The model predictions show that under the influence of nanosecond voltage rise the liquid experiences the formation of negative pressure region near the vicinity of the powered electrode and surpasses the cavitation threshold pressure. The cavitation locations initiate as sub-micron regions and then extends up to a few microns. The electrical forces which is a combination of electrostatic, polarization and electrostrictive ponderomotive forces contributes significantly in cavitating the medium and forming low-density region. The ponderomotive forces have the highest impact followed by the polarization forces. The effect of electrostatic forces only become significant when sufficient free charges are formed. Despite the formation of low-density region, the ionization process is still predominantly driven by field dependent ionization—Zener tunneling; as the electric field across the sub-micron to micron scale low-density regions are not sufficient for electron impact ionization to be significant. A parametric study on maximum driving voltage and voltage profile is conducted. The results indicate that at higher voltage both the exponential and linear voltage profile form a compression wave and an associated high-density region in the medium. The magnitude of the compressive waves is not representative of shock waves. The bulk liquid velocity can reach hundreds of meters per second but maintains subsonic conditions when the maximum driving voltage is increased by a factor of 2.5–15 kV suggesting shock like conditions will be formed under higher electric field conditions.

Dynamics of bubbles in liquid dielectrics under the action of an electric field: lattice Boltzmann method

The initial stage of deformation of bubbles before partial discharges under the action of the electric field is studied. The bubbles are placed on the surface of the electrode. The lattice Boltzmann method is used for 3D computer simulations of dielectric liquid dynamics. The electrostatic forces acting on a dielectric fluid in an electric field are taken into account as complete Helmholtz formula that includes the electrostriction forces. After the application of the electric field, the bubbles begin to elongate in the field direction. Above the critical value of the electrical Bond number, the bubbles can detach from the surface of the electrode and float.

Design of a hybrid on-chip waveguide with giant backward stimulated Brillouin scattering.

On-chip waveguides on insulator with high stimulated Brillouin gain have wide potential application prospects in the field of nanophotonic structures. We propose a new on-chip hybrid silicon-chalcogenide slot waveguide structure consisting of a chalcogenide As2S3 rectangle core with an air slot and a wrapping layer of silicon. In the new hybrid waveguide, the high radiation pressure and electrostriction force, determined by pump and Stokes optical waves, and the acoustic displacement, determined by acoustic wave, can be achieved by adjusting the dimensions of rectangle core, the thickness of wrapping layers and the width of air slot. Therefore, a strong optomechanical coupling between high radiation pressure and transverse acoustic displacement will be generated. In such a way, a nonlinear gain for backward stimulated Brillouin scattering can be theoretically achieved with a high gain coefficient of 2.88×104 W-1m-1. The enhanced gain coefficient in the proposed waveguide is around 2.4 times as that in an on-chip silicon-chalcogenide hybrid slot waveguide on insulator without the wrapping layer. The Stokes amplification reaches 85.7 dB with the waveguide length of 2.5 cm. Therefore, this method provides a new idea to design nanophotonic waveguides for giant backward stimulated Brillouin scattering.

Strong optomechanical coupling of light and highly confined acoustic phonons in slot dual-beam phoxonic crystal cavities

In this study, strong optomechanical (OM) coupling is proposed through the introduction of a slot in a dual-beam phoxonic crystal cavity structure. The structure can support a confined optical slot mode and localized phononic cavity modes to interact effectively through the slot surfaces. In addition to using conventional OM coupling rates for evaluating the coupling strength of photonic and phononic modes, we consider the optical forces induced by the optical slot mode to discuss the coupling between different mode pairs and the underlying mechanisms of the strong OM coupling. The optical field can induce radiation pressure and electrostrictive forces in the structure. We demonstrate that the radiation pressure dominates the coupling enhancement of photonic and phononic modes because of the slot, whereas the electrostrictive surface pressure plays a minor role and the electrostrictive body force has a negligible contribution. On the basis of the optical forces, we can then calculate the acoustic phonon spectrum through optical excitation. The spectrum indicates the appearance of strong OM coupling in the additional phononic cavity modes. The results suggest that the slot dual-beam cavity structure can be a promising choice for tailoring effective optical forces in micro- and nano-optomechanical systems for enhancing OM coupling.