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## Vol. 69, No. 18 (2020)

##### Topics
###### ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID DYNAMICS
2020, 69 (18): 184101. doi: 10.7498/aps.69.20200415
Abstract +
Two kinds of two-dimensional photonic crystal with hexagonal honeycomb lattices are constructed in which the scatterer and the matrix materials are reversed. Due to the symmetry of special point group, the lattices have p and d orbitals in the center of Brillouin region, which are similar to those in the electronic system. With the structure reversal, the p and d orbitals are also directly inverted. Quantitative analysis shows that the orbital inversion is due to the inversion of air band and medium band because of the local resonance effect in the low frequency bands. Based on the parity properties of p and d orbitals, the pseudo spin states are constructed by analogy to the quantum spin Hall effect in electronic systems. The analysis of the effective Hamiltonian at Γ point shows that the topological phase transition caused by orbital inversion is revealed. The pseudo spin edge states construct an optimal structure. The electromagnetic wave simulations and energy flow vector analysis show that the structure edge takes on the properties of quantum spin Hall effect, namely, the propagation direction is locked by the spin direction and the propagation is topologically protected. The results also show that the quantum spin Hall effect can be realized without undergoing the closing of gap. The comparison among similar researches indicates that the realization of the pseudo spin states does not need the deformation of lattice, and the structure proposed in this work possesses the characteristics of simple design, wide band gap and strong edge localization.
2020, 69 (18): 184203. doi: 10.7498/aps.69.20200695
Abstract +
$(l)$, called the topological charge. By illuminating terahertz vortex beam on the metallic disk with periodic subwavelength grooves normally, we find that the terahertz dark multipole plasmons can be excited by the terahertz vortex beam carrying different OAM and SAM. We analyze the correspondence between the spin and orbital angular momentum of vortex beam and the excited dark multipolar plasmon modes. In the experiment, a terahertz stepped spiral phase plate (SPP) with high transmission and low dispersion based on the Tsurupica olefin polymer is developed and the stepped SPP can generate a terahertz vortex beam having a topological charge of 1. Then, we further study the excitation of dark multipolar Spoof-LSPs by utilizing the stepped SPP in combination with the near-field scanning terahertz microscopy. The collimated terahertz wave, which is radiated from a 100 fs (λ = 780 nm) laser pulse pumped photoconductive antenna emitter, is converted into terahertz circular polarized light (CPL) which can carry SAM by the combination of the quarter wave plate and the polarizer, and then terahertz CPL impinges on the stepped SPP, producing the terahertz vortex beam which can carry OAM. The spatial two-dimensional electric field distribution is collected in steps of 0.02 mm along the x-direction and y-direction by a commercial terahertz near-field probe which is located close (≈ 10 μm) to the one side of polyimide film by three-dimensional electric translation stage and a microscope (FORTUNE TECHPLOGY FT-FH1080). The experimental results are in good agreement with simulations. We believe that our method will open the way for detailed research on the terahertz physics, plasma and imaging fields.">We theoretically and experimentally investigate a method of exciting multipole plasmons, including terahertz dark spoof localized surface plasmon (Spoof-LSP) modes, by using normally incident terahertz vortex beam. The vortex beam with angular intensity profile and phase singularities, has well-defined angular momentum which can be decomposed into the polarization-state-related spin angular momentum (SAM) for characterizing the spin feature of photon, and the helical-wavefront-related orbital angular momentum (OAM) that is characterized by an integer $(l)$, called the topological charge. By illuminating terahertz vortex beam on the metallic disk with periodic subwavelength grooves normally, we find that the terahertz dark multipole plasmons can be excited by the terahertz vortex beam carrying different OAM and SAM. We analyze the correspondence between the spin and orbital angular momentum of vortex beam and the excited dark multipolar plasmon modes. In the experiment, a terahertz stepped spiral phase plate (SPP) with high transmission and low dispersion based on the Tsurupica olefin polymer is developed and the stepped SPP can generate a terahertz vortex beam having a topological charge of 1. Then, we further study the excitation of dark multipolar Spoof-LSPs by utilizing the stepped SPP in combination with the near-field scanning terahertz microscopy. The collimated terahertz wave, which is radiated from a 100 fs (λ = 780 nm) laser pulse pumped photoconductive antenna emitter, is converted into terahertz circular polarized light (CPL) which can carry SAM by the combination of the quarter wave plate and the polarizer, and then terahertz CPL impinges on the stepped SPP, producing the terahertz vortex beam which can carry OAM. The spatial two-dimensional electric field distribution is collected in steps of 0.02 mm along the x-direction and y-direction by a commercial terahertz near-field probe which is located close (≈ 10 μm) to the one side of polyimide film by three-dimensional electric translation stage and a microscope (FORTUNE TECHPLOGY FT-FH1080). The experimental results are in good agreement with simulations. We believe that our method will open the way for detailed research on the terahertz physics, plasma and imaging fields.
2020, 69 (18): 184204. doi: 10.7498/aps.69.20200589
Abstract +
${l_{{\rm{FC}}}}$ should satisfy ${\rm{189}}\;{\text{μm}} > {l_{{\rm{FC}}}} > {\rm{119}}\;{\text{μm}}$. This cavity length is too small to be measured with a ruler. To measure the cavity length, we introduce an optical method, in which Gouy phases of Hermite Gaussian transverse modes TEM00 and TEM10 are used. When the cavity length is scanned, resonant peaks and the corresponding scanning voltages are recorded. From theoretical derivation, the cavity length is related to the filter cavity piezo response to the scanning voltage ${\varPsi '_{\rm{G}}}$, the slope rate of piezo scanning voltage $U'$, and the time distance between TEM00 and TEM10 resonant peaks $\Delta t$. The finally measured cavity length is ${l_{{\rm{FC}}}} = ({\rm{141}} \pm 28)~{\text{μm}}$, which satisfies the design requirement. The measurement error mainly originates from inaccurate fitting of ${\varPsi '_{\rm{G}}}$ and $U'$, and readout error of $\Delta t$. It is shown that the error of ${\varPsi '_{\rm{G}}}$ is dominant since less data are used in the curve fitting. The measurement error is expected to be reduced if much more data of piezo response to scanning voltage are collected and used to fit ${\varPsi '_{\rm{G}}}$ with higher order polynomials. The proposed measurement method of short cavity length needs neither wide tuning laser nor any peculiar instrument, and does not depend on any dispersion property of the cavity, and hence it has a certain generality. It can be hopefully used in many other optical systems, such as cavity quantum electrodynamics, where ultrashort cavity plays a central role.">Optical Schrödinger cat state is not only one of the basic elements of quantum mechanics, but also a pivotal resource of continuous-variable quantum information. The non-Gaussian operation in its preparation can also be a key technology in distilling continuous-variable squeezing and entanglement. In the experimental preparation, a small part of a beam of vacuum squeezing is separated and detected as the trigger of appearance of Schrödinger cat state. Filter operation in the trigger optical path is important since it affects dark counts of single photon detector, frequency mode matching of trigger mode and signal mode, and preparing rate of the Schrödinger cat state, etc. In this paper, we describe the design of optical filter in the trigger path and the measurement of the filter cavity length. According to the design, filter cavity length ${l_{{\rm{FC}}}}$ should satisfy ${\rm{189}}\;{\text{μm}} > {l_{{\rm{FC}}}} > {\rm{119}}\;{\text{μm}}$. This cavity length is too small to be measured with a ruler. To measure the cavity length, we introduce an optical method, in which Gouy phases of Hermite Gaussian transverse modes TEM00 and TEM10 are used. When the cavity length is scanned, resonant peaks and the corresponding scanning voltages are recorded. From theoretical derivation, the cavity length is related to the filter cavity piezo response to the scanning voltage ${\varPsi '_{\rm{G}}}$, the slope rate of piezo scanning voltage $U'$, and the time distance between TEM00 and TEM10 resonant peaks $\Delta t$. The finally measured cavity length is ${l_{{\rm{FC}}}} = ({\rm{141}} \pm 28)~{\text{μm}}$, which satisfies the design requirement. The measurement error mainly originates from inaccurate fitting of ${\varPsi '_{\rm{G}}}$ and $U'$, and readout error of $\Delta t$. It is shown that the error of ${\varPsi '_{\rm{G}}}$ is dominant since less data are used in the curve fitting. The measurement error is expected to be reduced if much more data of piezo response to scanning voltage are collected and used to fit ${\varPsi '_{\rm{G}}}$ with higher order polynomials. The proposed measurement method of short cavity length needs neither wide tuning laser nor any peculiar instrument, and does not depend on any dispersion property of the cavity, and hence it has a certain generality. It can be hopefully used in many other optical systems, such as cavity quantum electrodynamics, where ultrashort cavity plays a central role.
2020, 69 (18): 184207. doi: 10.7498/aps.69.20200530
Abstract +
Different frequency detuning can excite different working mode in a dual coupled optical microcavities. Based on the nonlinear Schrödinger equations of dual coupled field, and by using the split-step Fourier method, the optical field evolution in the microcavities is analyzed under the condition of both positive and negative tuning, and various optical distributions are generated in the process of frequency tuning. Simulation results indicate that the field can develop into the bright soliton in the region of positive tuning. However, the region in which the bright soliton is maintained is small, and the field in the microcavities grows into direct current (DC) distribution because of the serious frequency detuning. In the region of negative tuning, the field of “turning pattern” with high power is generated. There is only chaos inside the microcavities without frequency detuning or the detuning parameters close to 0. In addition, under the condition of strong coupling, the bright soliton and the “turning pattern” cannot be excited. Even stronger coupling leads to optical field in the form of DC directly. After the bright soliton exciting in the microcavity, it can be preserved by selecting appropriate detuning parameters and pump power. Moreover, the bright soliton can be changed into “turning pattern” with low power by continuously changing the detuning parameter of the first microcavity. Theoretical analyses are significant for experimental research on the dual coupled microcavities.
2020, 69 (18): 184209. doi: 10.7498/aps.69.20200466
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In the past decades, thulium-doped fiber lasers (TDFLs) operating in an eye-safe range have attracted considerable attention, for they have extensive applications such as LIDAR, free space communication, medical diagnostics and pumping source for holmium-doped fiber laser or optical parameter oscillator. In this paper, we report a high power all-fiberized TDFL based on main-oscillator power-amplifier (MOPA) configuration. The preform is fabricated by the modified chemical vapor deposition method combined with solution doping technique and drawn into a core/clad size of 25/400 μm. The numerical aperture of the TDF is 0.1. The concentration of Tm2O3 and Al2O3 are 2.6 wt% and 1.01 wt%, respectively, measured by an electron probe micro-analyzer. The cladding absorption is 3 dB/m at 793 nm measured by cut-back method. The oscillator consists of 8 m 25/400 TDF mentioned above and a pair of fiber Bragg gratings. The oscillator yields maximum power of 91 W with pump power of 202 W and a 3 dB spectral bandwidth as narrow as 75 pm. In the amplifier stage, the bi-directional pumping scheme is employed. The narrow linewidth seed with output power of 57 W is scaled to 530 W through one-stage amplification, corresponding to a slope efficiency of 50%. The central wavelength of the Tm-doped MOPA is 1980.89 nm and the linewidth is broadened to 0.11 nm at 530 W. The measured M 2 factor at 100 W is less than 1.3. Neither obvious amplified spontaneous emission nor non-linear effect is observed, and the output power is only limited by pump power. To the best of our knowledge, this is the highest output power of TDF at present.
2020, 69 (18): 184213. doi: 10.7498/aps.69.20200575
Abstract +
The plasmon resonance effect is one of the effective ways to enhance the upconversion (UC) luminescence, which is realized by enhancing the electromagnetic field from incident light interacting with free electrons of AuNRs surface. In this work, a series of GVA@SiO2@NaYF4:Yb3+/Er3+ composite structures with different thickness values of SiO2 isolation layer is successfully built from self-assembled gold nanorods, steamed SiO2, and spin-coating rare-earth nanocrystals. The results of the SEM indicate that the size of gold-nanorods is approximately 22 nm in diameter and 65 nm in length. The X-ray diffraction and transmission electron microscope results demonstrate that the NaYF4:Yb3+/Er3+ nanocrystals possess hexagonal-phase structure with a size of about 20 nm. Under 980 nm near-infrared (NIR) excitation, the UC emission characteristics of GVA@SiO2@NaYF4:Yb3+/Er3+ composite structure are studied by using a confocal microscope spectroscopic test system, and regulated by changing the thickness of SiO2 isolation layer. The results indicate that the UC emission intensity of NaYF4:20%Yb3+/2%Er3+ nanocrystals is enhanced by about 8.8 times, and the enhancement factor of red UC emission intensity is about 16.2. In order to further prove the enhancement effect of the red UC emission, the GVA@SiO2@ NaYF4:40%Yb3+/20%Er3+ composite structure with red UC emission is constructed in the same way. It can be found that the UC emission intensity of NaYF4:40%Yb3+/20%Er3+ nanocrystals is enhanced by 8.7 times and the red UC emission intensity is raised by about 9.7 times under the 980 nm NIR excitation. The corresponding excitation enhancement mechanism is simulated according to the power excitation dependence. And it is found that the rate of UC emission decreases and the R/G ratio also decreases with the excitation pump power increasing. The analysis of the above results shows that the excitation enhancement plays a leading role and is accompanied by emission enhancement. Meanwhile, the study of Er3+ ion dynamic process indicates that the Er3+ ion transition rate is accelerated due to the coupling from UC emission peaks and gold nanorod absorption peaks in GVA@SiO2@NaYF4:40%Yb3+/20%Er3+ composite structure. The enhancement mechanism of UC emission is also simulated, which further proves that the excitation enhancement is dominant. This kind of composite structure can not only help us to further understand the physics mechanism of the plasmon-enhanced UC luminescence but also promote the applications of rare-earth materials in medical imaging and fingerprint recognition.
2020, 69 (18): 184214. doi: 10.7498/aps.69.20200538
Abstract +
Recently, quantum computing and information processing based on photons has become one research frontier, attracting significant attentions. The optical asymmetric transmission devices (OATD), having similar function to the diode in electric circuitry, will find important applications. In particular, the OATDs based on nanophotonic structures are preferred due to their potential applications in the on-chip integration with other photonic devices. Therefore, there have been numerous applications of OATDs based on different nanostructures, including composite grating structures, metasurfaces, surface plasmon polaritons, metamaterials, photonic crystals (PhCs). However, in general, those designs show relatively low forward transmittance (< 0.5) and narrow working bandwidth (< 100 nm), and they are able to work with only one polarization state. This makes the current OATDs unsuitable for many applications. To solve this challenge, here we design a two-dimensional (2D) PhC heterostructure based on the self-collimating effect and bandgap properties. The PhC heterostructure is composed of two square lattice 2D PhCs (PhC 1 and PhC 2) on a silicon substrate with different lattice shapes and lattice constants. The PhC 1 is composed of periodically arranged silicon cylinders in air. Meanwhile, the PhC 2 is an square air hole array embedding in silicon. The two PhCs are integrated with an inclined interface with an angle of 45° with respect to the direction of incident light. The plane wave expansion method is used to calculate the band diagrams and equal frequency contours (EFCs) of the two PhCs. As the propagation directions of light waves in PhCs are determined by the gradient direction of the EFCs, we are able to control the light propagation by controlling the EFCs of PhCs. By engineering the EFCs, the PhC 2 shows strong self-collimation effect in a broad wavelength range with a central wavelength of 1550 nm for both TE and TM polarization. By self-collimating the forward incident light from different incident angles to couple to the output waveguide, we are able to significantly increase the forward transmittance to > 0.5 for both TE and TM polarized light. Meanwhile, the backward transmittance can be effectively cut off by the unique dispersion properties of the PhC heterostructures. In this way, the heterostructure is able to achieve polarization independent asymmetric transmission of light waves in a broad wavelength range. To visualize the light propagation in the PhC heterostructure, we use the finite-difference-time-domain method to calculate the electric intensity distributions of the forward and backward propagation light of both TE and TM polarization at a wavelength of 1550 nm. Strong self-collimation effect of forward propagation light and the nearly complete blockage of backward propagation light can be identified unambiguously in the intensity plots, confirming the theoretical analysis. The calculation of transmittance and contrast ratio spectra show that the asymmetric transmission wavelength bandwidth can reach 532 nm with the forward transmittance and contrast ratio being 0.693 and 0.946 at an optical communication wavelength of 1550 nm for TE polarized light. On the other hand, for the TM polarized light, the asymmetric transmission wavelength bandwidth is 128 nm, the forward transmittance and contrast ratio are 0.513 and 0.972, respectively, at 1550 nm wavelength. Thus, it is confirmed that the PhC heterostructure achieves highly efficient, broadband and polarization independent asymmetric transmission. Finally, to further improve the forward transmittance of the TE polarized light, we modulate the radius of the front row of photonic lattice of PhC 1 at the interface. It shows that the forward transmittance can be further improved to a record high value of 0.832 with a bandwidth of 562 nm for TE polarized light. Our design opens up new possibilities for designing OATDs based on PhCs, and will find broad applications, for the design can be realized by current nanofabrication techniques.
2020, 69 (18): 184702. doi: 10.7498/aps.69.20200562
Abstract +
Atomization of droplets is ubiquitous in many natural and industrial processes, such as falling rain drops, inkjet printing, fuel injection in automotive and gas-turbine engines. Acoustic irradiation provides a very effective method of atomizing fluid. However, the acoustic atomization of acoustically levitated droplet is seldom studied. To assess the possibility of achieving ultrafine atomization, we, in this paper, systematically study the atomization of an acoustically levitated droplet placed in a hot gas of a flame. High speed camera is utilized to investigate the atomization characteristics of various droplets with diameters ranging from 0.5 mm to 3.5 mm. The experimental results show that the sound pressure of the resonance acoustic field has the ability to atomize the droplet when it is suddenly bathed in hot gas. Here the heating acts as a switch to convert the droplet surface from an acoustic isolator to conductor by heating the surface to strong evaporation. The presence of a high concentration of vapor molecules surrounding the droplet caused the acoustic field to change, thus, a much larger pressure gradient is established along the droplet surface, resulting in the atomization of droplet from the equator. Furthermore, Faraday wave stimulation and discretization on the film cause the droplet to further disintegrate when the droplet diameter is large enough. The atomization consists of three different styles, i.e. rim spray (RS), film disintegration (FD) and normal sputtering (NS). When exposed to hot gas, the droplets with equivalent diameter D0 < 2.8 mm are depleted with RS until the whole mass is atomization. A thin rim is extruded at the equator and then splashed in the equator plane, the spray speed is around 9.5 m/s. Larger droplets end with the sudden FD of liquid film of the residual mass after the the RS has been consumed up. When the thickness of the rim and buckled film decrease to half of wave length, Faraday wave emerges, resulting in the vertical droplet ejection and the disintegration of the thin films. And the droplets with D0 > 3.2 mm undergo further film buckling, forming a closed bubble due to the Helmholtz resonator effect and NS at the bottom. This sound driven atomization of droplets enriches the understanding of fluid mechanism in multi-physical fields, and may provide new ideas for relative application research.
2020, 69 (18): 184703. doi: 10.7498/aps.69.20200546
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Acoustically-excited bubble dynamics is the foundation of pipeline bubble detection based on acoustic technology. Due to the existence of multiple bubbles in pipeline flow, the Bjerknes forces among arbitrary bubbles under acoustic excitation may enforce bubble-bubble interaction and then change the features of bubble dynamics. Based on traditional free bubble’s Rayleigh-Plesset (R-P) model, this paper tries to establish bubble-bubble interaction model in consideration of the second Bjerknes force and bubble distribution in the pipeline axial direction. Meanwhile, the influence of finite wave speed in compressible fluid is considered. The proposed model is numerically calculated by the fourth-order Runge-Kutta method. Firstly, the differences in bubble feature between the free bubble’s R-P model and bubble-bubble interaction model are compared under excitation with different frequencies and amplitudes. Results show that the differences in bubble dynamics are minor when the bubble’s distance is large enough. When the bubble’s distance is fixed, the differences are significant on condition that the frequency of acoustic excitation is nearly the resonant frequency of bubbles. Secondly, through establishing compressible model and incompressible fluid model, we compare the differences between the two models. Numerical calculations show that the second Bjerknes force under the compressible assumption acts as an external force and forces the bubble to vibrate. On the other hand, the second Bjerknes force under the incompressible assumption changes the dynamics of bubble-bubble interaction as well as the resonant features. Finally, we study the effect of bubble-bubble distance and bubble’s axial position on bubble vibration characteristics. The bubble-bubble distance affects the second Bjerknes force and may lead the bubbles to vibrate nonlinearly. The bubble’s axial position changes the phase of external acoustic force and leads to the difference in initial vibration feature. When this difference is coupled with the second Bjerknes force, the bubble-bubble interaction may be changed even into nonlinear vibration, leading the bubble’s oscillation spectrum to differ from linear vibrations significantly. These results demonstrate that the resonant state of a small bubble may be converted into nonlinear vibration state if the second Bjerknes force is present. On the other hand, the resonant state of a large bubble can keep linear vibration when the second Bjerknes force is not obvious.
###### SPECIAL TOPIC—Nonlinear optics and devices of low-dimensional materials
2020, 69 (18): 184205. doi: 10.7498/aps.69.20200337
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As a new two-dimensional material, bismuth nanosheet is an effective modulator for realizing a mid-infrared pulsed laser, which benefits from its suitable band gap, higher carrier mobility and better room temperature stability, as well as its excellent electrical and optical properties. The mid-infrared single-crystal fiber is a preferable gain medium for high-power laser because of its advantages of both crystal and fiber. In this paper, a bismuth nanosheet saturable absorber is successfully prepared by the ultrasonic method and used for the first time in a diode-pumped Er:CaF2 single-crystal fiber mid-infrared passively Q-switching pulsed laser. A compact concave planar linear resonator is designed to study the Q-switching Er:CaF2 single-crystal fiber laser with bismuth nanosheets serving as saturable absorbers. The pump source is a fiber-coupled semiconductor laser with a core diameter of 105 μm, a numerical aperture of 0.22, and a central emission wavelength of 976 nm. The pump light is focused onto the front end of the gain medium through a coupled collimating system with a coupling ratio of 1∶2. The gain medium is a 4 at. % Er3+:CaF2 single-crystal fiber grown by the temperature gradient method, and this fiber has two polished but not coated ends, a diameter of 1.9 mm, and a length of 10 mm. To reduce the thermal effect, the single-crystal fiber is tightly wrapped with indium foil and mounted on a copper block with a constant temperature of 12 ℃. The input mirror has a high reflection coating at 2.7–2.95 μm and an antireflection coating at 974 nm, with a curvature radius of 100 mm. A group of partially transmitting plane mirrors are used as output couplers, respectively, with transmittances of 1%, 3%, and 5% at 2.7–2.95 μm. The total length of the resonant cavity is 26 mm. By inserting the bismuth nanosheet into the resonator and carefully adjusting its position and angle, a stable mid-infrared Q-switching laser is obtained. At the absorbed pump power of 1.52 W, a pulsed laser with an average output power of 190 mW is obtained for an output mirror with a transmittance of 3%. The shortest pulse width is 607 ns, the repetition frequency is 58.51 kHz, and the corresponding single pulse energy and peak power are 3.25 μJ and 5.35 W, respectively.
2020, 69 (18): 184218. doi: 10.7498/aps.69.20201305
Abstract +
In this paper, a dissipative soliton mode-locked fiber laser is established based on carbon nanotube in order to study the polarization dynamics of dissipative soliton by using a commercial polarimeter. Under the pump power of 160 mW, stable dissipatives soliton are observed to have a limited cycle polarization trajectory shown on Poincare sphere, indicating the periodic modulation of anisotropy in cavity. The stable dissipative soliton possesses a high signal noise ratio of 57.7 dB at fundamental frequency. Moreover, the fast oscillation of state of polarization leads to a lower degree of polarization (DOP). In addition, the polarization controllers are employed to compensate for the birefringence in the cavity to adjust the ratio between cavity length and birefringence length. As a result, we can observe the polarization evolving from the polarization locked attractor to the limited cycle attractor by adjusting polarization controllers. It is noted that this dynamic polarization trajectory can be manually controlled. By comparing polarization attractor with DOP, it is clear that the size of trajectory shown on Poincare sphere is inversely proportional to DOP. We expect our work to be conducible to studying the physics in lasers and creating a new type of polarization tunable laser.
###### PHYSICS OF GASES, PLASMAS, AND ELECTRIC DISCHARGES
2020, 69 (18): 185201. doi: 10.7498/aps.69.20200636
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$10.1 \times {10^{17}}\;{\rm{c}}{{\rm{m}}^{ - {\rm{3}}}}$). After that, the electron density drops rapidly within 200 ns because the recombination between electrons and ions decreases with delay time. Finally, it is proved that the SF6 plasma is in local thermal equilibrium based on the Mc Whirter criterion. The results are of great significance for studying the decomposition mechanism of SF6 and the on-line monitoring technique of high-voltage equipment.">SF6 is widely used in gas insulated switchgear due to its excellent insulating and arcing performance. SF6 arc plasma has been extensively studied, but time-resolved spectral characteristics of SF6 arc plasma have not been reported. In this paper, the optical filament generated from focused femtosecond laser is used to guide the high-voltage discharge for generating SF6 plasma in SF6 environment. The SF6 plasma spectrum is obtained in a wavelength range of 300–820 nm, and the identification and attribution of the spectral lines are investigated. The S and F lines are mainly in the 300–550 nm band and 600–800 nm band, respectively. The analysis shows that the S and F atoms are mainly directly or indirectly generated by the collision between SF6 and high-energy electrons during the SF6 decomposition caused by discharge. The S ions are generated by the collision of S atoms with high-energy electrons. The time-resolved spectrum of the SF6 plasma superimposed by the continuous spectrum and the line spectrum is given, and its intensity increases and then decreases. The continuous spectrum is mainly generated by the combined effect of bremsstrahlung and recombination radiation. The recombination radiation is mainly generated by the collision of electron with ions and the recombination between molecular and atoms after SF6 decomposition. The fluorescence lifetime of S ion at 409.91 nm is 57 ns, and the fluorescence lifetime of F atom at 685.60 nm is 341 ns. The evolution law of electron temperature and density with time are given. The electron temperature reaches 2047 K in the early stage of plasma formation. After that, the electron temperature quickly falls to about 1600 K within 300 ns due to the rapid expansion of the plasma and the increase in energy loss during electron movement. At the beginning of discharge, a large number of electrons are generated due to the rapid decomposition of SF6, and the electron density is highest ($10.1 \times {10^{17}}\;{\rm{c}}{{\rm{m}}^{ - {\rm{3}}}}$). After that, the electron density drops rapidly within 200 ns because the recombination between electrons and ions decreases with delay time. Finally, it is proved that the SF6 plasma is in local thermal equilibrium based on the Mc Whirter criterion. The results are of great significance for studying the decomposition mechanism of SF6 and the on-line monitoring technique of high-voltage equipment.
###### CONDENSED MATTER: ELECTRONIC STRUCTURE, ELECTRICAL, MAGNETIC, AND OPTICAL PROPERTIES
2020, 69 (18): 187701. doi: 10.7498/aps.69.20200544
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Relaxor ferroelectric single crystal piezoelectric materials have become the core components of new piezoelectric devices such as ultrasonic transducers used in high-end medical ultrasound diagnostic and therapeutic equipment. High-element density array technology and micro-electro-mechanical systems have developed rapidly. For the new generation of 20–80 MHz medical high-frequency ultrasound transducers, the thickness of high-frequency piezoelectric composite material is usually 20–60 μm, and the width of each piezoelectric column is about 5–15 μm. However, the kerf of traditional cutting-and-filling method is too wide, and it is difficult to reduce the size of the array element, which is not conducive to the density of the array element and the demand for higher frequency applications with higher resolution. In this work, a micromechanical fabrication method based on deep reactive ion etching is used to reduce the slit width and increase the array density. We study the fabrication technology of novel and high-performance relaxor ferroelectric single crystal Mn doped Pb(In1/2Nb1/2)O3-Pb(Mg1/3Nb2/3)O3-PbTiO3 (Mn-PIMNT) micro scale piezoelectric array. The influence of the parameters of lithography and deep reactive ion etching on the morphology of piezoelectric array are studied. We obtain the formation mechanisms of different kerfs, different shapes of piezoelectric array element and the relationship among etching rate of Mn-PIMNT single crystal with antenna power, bias power and etching gas ratio. Finally, the size of piezoelectric array element is less than 10 μm, the etching depth is more than 20 μm, the kerf width is less than 5 μm, the angle is controllable, and the maximum is more than 87°. The ferroelectric domain structure and the regulation of electric field effect of micro scale piezoelectric elements are studied by means of piezoelectric force microscope. The variation rules of piezoelectric properties and micro scale are obtained. This method can effectively bypass the shortcomings of the wide kerf and the destruction of the crystal orientation by the traditional cutting-and-filling method. It provides a new preparation technology for the development of high-frequency piezoelectric composites, high-density ultrasonic transducer arrays and new piezoelectric micro mechanical systems. This project presents the guidance and reference for the new micromachining technology of ferroelectric materials, and also lays the foundation for the high-frequency piezoelectric composite and high-frequency ultrasonic transducer.