Standing Wave Effect Research Articles

Experimental investigation of standing wave effect in dual-frequency capacitively coupled argon discharges: role of a low-frequency source

It is well known that the plasma non-uniformity caused by the standing wave effect has brought about great challenges for plasma material processing. To improve the plasma uniformity, a low-frequency (LF) power source is introduced into a 100 MHz very-high-frequency (VHF) capacitively coupled argon plasma reactor. The effect of the LF parameters (LF voltage amplitude ϕL and LF source fL) on the radial profile of plasma density has been investigated by utilizing a hairpin probe. The result at a low pressure (1 Pa) is compared to the one obtained by a 2D fluid-analytical capacitively coupled plasma model, showing good agreement in the plasma density radial profile. The experimental results show that the plasma density profile exhibits different dependences on ϕL and fL at different gas pressures/electrode driven types (i.e., the two rf sources are applied on one electrode (case I) and separate electrodes (case II)). At low pressures (e.g., 8 Pa), the pronounced standing wave effect revealed in a VHF discharge can be suppressed at a relatively high ϕL or a low fL in case I, because the HF sheath heating is largely weakened due to strong modulation by the LF source. By contrast, ϕL and fL play insignificant roles in suppressing the standing wave effect in case II. At high pressures (e.g., 20 Pa), the opposite is true. The plasma density radial profile is more sensitive to ϕL and fL in case II than in case I. In case II, the standing wave effect is surprisingly enhanced with increasing ϕL at higher pressures; however, the center-high density profile caused by the standing wave effect can be compensated by increasing fL due to the enhanced electrostatic edge effect dominated by the LF source. In contrast, the density radial profile shows a much weaker dependence on ϕL and fL in case I at higher pressures. To understand the different roles of ϕL and fL, the electron excitation dynamics in each case are analyzed based on the measured spatio-temporal distributions of the electron-impact excitation rate by phase resolved optical emission spectroscopy.

The electric field standing wave effect in infrared transflection spectroscopy

We show that an electric field standing wave effect is responsible for the oscillations and the non-linear dependence of the absorbance on the layer thickness in thin layers on a reflective surface. This effect is connected to the occurrence of interference inside these layers. Consequently, the absorptance undergoes a maximum electric field intensity enhancement at spectral positions close to those where corresponding non-absorbing layers on a metal show minima in the reflectance. The effect leads to changes of peak maxima ratios with layer thickness and shows the same periodicity as oscillations in the peak positions. These peculiarities are fully based on and described by Maxwell's equations but cannot be understood and described if the strongly simplifying model centered on reflectance absorbance is employed.

Electric field standing wave effects in internal reflection and ATR spectroscopy

We investigate electric field standing wave effects in the system semiinfinite incidence medium with high index of refraction/layer/vacuum, the latter being the semiinfinite exit medium. If the layer has a lower index of refraction than the incidence medium, then very strong resonances occur between the two critical angles of the system defined by the systems incidence medium/layer and incidence medium/vacuum, as the layer is then a cavity. In particular close to the lower critical angles, the evanescent fields extend strongly into the exit medium. Based on this effect we suggest two new spectroscopic modalities, namely interference-enhanced internal reflection Raman spectroscopy and interference-enhanced attenuated total reflection infrared spectroscopy.

The Electric Field Standing Wave Effect in Infrared Transmission Spectroscopy.

When band ratios in infrared absorbance spectra of films are compared (which had been converted from transmittance spectra), it can be noted that even after background correction and removal of interference fringes these band ratios change with the thickness of the films. The main goal of this work is to show that this effect is a consequence of an electric field standing wave based on the coherent superposition of light waves in the film. We further investigate how transmittance and reflectance, as well as absorbance and the (from absorbance) regained index of absorption, depend on the thickness of the film and how these parameters influence the positions of bands. We compare the results with those for the incoherent case and the case where a single pass of light through the film without reflection loss is assumed.

Broadband microwave absorption and standing wave effect in helium capacitively coupled plasma

The broadband microwave absorption of a large volume helium plasma, which is generated by two parallel rectangular plates based on the principle of capacitively coupled plasma (CCP) is developed in this paper. The transmission attenuation is simulated by the combination of the time-dependent fluid model and dispersion equation, and measured by a high dynamic range measurement system in a frequency range of 1–12 GHz. The results show that the plasma can absorb microwave energy efficiently, especially in the frequency range of 1–5 GHz, where the transmission attenuation is more than −5 dB. The attenuation increases with gas pressures and applied voltages. Besides, the standing wave effect in plasma can increase the microwave absorption effectively. The numerical and experimental results have a qualitative agreement, and these characteristics suggest that the helium CCP has tremendous potential to be applied in plasma stealth.

A nonlinear electromagnetics model of an asymmetrically-driven, low pressure capacitive discharge

It is well-known that standing waves having radially center-high voltage profiles exist in high frequency driven capacitive discharges. Capacitive sheaths can also nonlinearly excite driving frequency harmonics near the series resonance that can be spatially near-resonant, and therefore enhance the on-axis power deposition. The powered-electrode/plasma/grounded-electrode sandwich structure of an asymmetrically excited cylindrical discharge forms a three electrode system in which both z-symmetric and z-antisymmetric radially propagating wave modes can exist. We develop a nonlinear electromagnetics model for this system with radially- and time-varying sheath widths, incorporating both symmetric and antisymmetric modes, and the plasma skin effect. Waves generated in the electrostatic wave limit are also treated. The discharge is modeled as a uniform density bulk plasma with either homogeneous or Child law sheaths at the electrodes, incorporating their nonlinear voltage versus charge relations. The model includes a finite power source resistance and a self-consistent calculation of the dc bias voltages. The resulting set of nonlinear partial differential equations is solved numerically to determine the symmetric and antisymmetric mode amplitudes and the nonlinearly-excited radially-varying harmonics. Two examples driven at lower frequency (30 MHz) or at higher frequency (60 MHz) are examined. The first case displays the excited dominant ninth harmonic near the series resonance frequency with the fundamental frequency having a weak standing wave. The higher frequency case shows a more obvious standing wave effect, enhanced by the nonlinear harmonics. The symmetric and antisymmetric modes are of similar amplitudes over the driving electrode, summing to give a larger bottom sheath.

Standing wave effect and fractal structure in dislocation evolution

Theoretical model required for the evolution of regular dislocation pattern should simultaneously take into account both static distribution and dynamic evolution of dislocation pattern. In principle, there exists a stable uniformly moving dislocation with both core and far field advancing at the same constant velocity, which suggests the existence of the traveling waves representing moving dislocation. Therefore, one new term “dislocation wave” is defined by simultaneously consisting of both an elastic wave and a dislocation in each wavefront. According to the standing wave effect, the edge dislocation segments capture mutually to form the periodic ladder structures at the nodes. These persistent slip band (PSB) ladders are not only self-organized but also self-similar dislocation patterns. The fractal dimension further reveals the intrinsic nature of crack initiation and propagation along slip bands and deformation bands.

On the non-existence of the so-called “electric field standing wave effect” in transflection FTIR spectra

The so-called Electric Field Standing Wave (EFSW) Effect has been used by several groups to explain the experimental observation that relative absorbance in FTIR spectra varies with thickness of biomedical samples mounted on a reflective slide. Here, by involving both electric and magnetic fields of an electromagnetic wave, we establish, by classical optical analysis, that there is no such effect. Furthermore, application of multi-interface Fresnel-like simulations to three different systems shows that reflections, transmission and consequent interferences at the “vacuum”/sample interface are solely responsible for the dependence of relative band heights on sample thickness.

Suppressing excitation effects in microwave induced thermoacoustic tomography by multi-view Hilbert transformation

Microwave induced thermoacoustic tomography (TAT) images usually suffer from distortions arising from the microwave polarization effect and standing wave effect. The microwave polarization effect, resulting from linearly polarized microwave illumination, splits the image of the object along the polarization direction, while the standing wave effect, when the object size is larger than the microwave wavelength within the object, modulates the image of the object. Both effects cause non-uniform energy distribution in a uniformly absorbing object and create artifacts in the reconstructed images. To address these problems in TAT, we propose an image reconstruction method that combines multi-view Hilbert transformation with the back-projection algorithm. We experimentally validate this method by imaging breast and brain tumor phantoms, showing that the aforementioned distortions are significantly suppressed. We anticipate that this method will contribute to clinical tumor diagnosis.

Low-Noise Single-Frequency 1.5- $\mu$ m Fiber Laser With a Complex Optical-Feedback Loop

A low-noise narrow-linewidth distributed Bragg reflector (DBR) single frequency 1.5- $\mu \text{m}$ fiber laser with a complex optical-feedback loop (COFL) is demonstrated. The COFL is used to reduce the relative intensity noise (RIN) and narrow the linewidth, which is composed of an erbium-doped fiber amplifier (EDFA), an unpumped Er80 fiber and a sagnac loop mirror. The COFL combines the nonlinear amplification effect of saturated optical amplifiers, the standing-wave saturation effects of saturable absorber (SA), and the self-injection locking technology at the same time. The effects of self-injection locking give a sufficient proof, which the RIN is reduced and the resonance peak shifts to lower frequency. The RIN of low frequency is greatly reduced by the EDFA. In addition, the SA narrows the linewidth. After the COFL suppression, the RIN of relaxation oscillation is reduced by 24.5 dB from 80.3 dB/Hz at 219 kHz to 104.8 dB/Hz at 87 kHz. Furthermore, the linewidth narrows from 7.47 kHz to 720 Hz. Even after two-stage fiber amplification, the RIN does not increase significantly, and a spectral linewidth well below 1.8 kHz is also achieved at the output power of 11.1 W.

Experimental investigations of the plasma radial uniformity in single and dual frequency capacitively coupled argon discharges

In the current work, the radial plasma density has been measured by utilizing a floating double probe in single and dual frequency capacitively coupled argon discharges operated in a cylindrical reactor, aiming at a better understanding of electromagnetic effects and exploring a method of improving the radial uniformity. The experimental results indicate that for single-frequency plasma sustained at low pressure, the plasma density radial profile exhibits a parabolic distribution at 90 MHz, whereas at 180 MHz, the profile evolves into a bimodal distribution, and both cases indicate poor uniformities. With increasing the pressure, the plasma radial uniformity becomes better for both driving frequency cases. By contrast, when discharges are excited by two frequencies (i.e., 90 + 180 MHz), the plasma radial profile is simultaneously influenced by both sources. It is found that by adjusting the low-frequency to high-frequency voltage amplitude ratio β, the radial profile of plasma density could be controlled and optimized for a wide pressure range. To gain a better plasma uniformity, it is necessary to consider the balance between the standing wave effect, which leads to a maximum plasma density at the reactor center, and the edge field effect, which is responsible for a maximum density near the radial electrode edge. This balance can be controlled either by selecting a proper gas pressure or by adjusting the ratio β.

ЛОКАЛЬНО-НЕРАВНОВЕСНОЕ ВОЗДЕЙСТВИЕ СТОЯЧЕЙ ВОЛНЫ НА ДВ УХМЕРНЫЕ ПЕРИОДИЧЕСКИЕ ТЕПЛОВЫЕ СТРУКТУРЫ

ЛОКАЛЬНО-НЕРАВНОВЕСНОЕ ВОЗДЕЙСТВИЕ СТОЯЧЕЙ ВОЛНЫ НА ДВ УХМЕРНЫЕ ПЕРИОДИЧЕСКИЕ ТЕПЛОВЫЕ СТРУКТУРЫ

Practical considerations of terahertz communications for short distance applications

This paper describes two practical issues of terahertz (THz) communications for short-distance applications. One is the effect of standing waves formed between transmitter and receiver antennas in close-proximity or near-field communications. We discuss and propose new approaches to decreasing or eliminating the standing-wave effect by carrier signal modulation and by using array antenna structures. The other issue is the effect of beam misalignment between transmitter and receiver on the transmission characteristics in indoor communications at a link distance of a few meters. Theoretical and experimental comparison is made between THz communications and free-space optics (FSO) using infrared light waves.

Strong and large area field enhancement outside a microcavity due to propagating surface plasmons and standing wave effect

We investigated the optical property of periodic inverted pyramidal microcavities and observed large area field enhancement outside a cavity when the incident wavelength and structure parameters match certain relations. The mechanism of this phenomenon has been studied. Propagating surface plasmons and the standing wave effect both contribute to the field enhancement outside the cavity. The relations between the incident wavelength and structure parameters have been clarified. Based on the relations, one can control the field enhancement outside the cavity for a specific laser wavelength.

Stacked‐Disk Nanotower Arrays for Use as Omniphobic Surface‐Enhanced Raman Scattering Substrates

Herein, a simple interference lithographic technique to design omniphobic surface‐enhanced Raman scattering active surfaces composed of stacked‐disk nanotower arrays is reported. To create the nanotower arrays in a highly reproducible fashion, the authors use a single laser exposure onto the photoresist‐on‐dielectric mirror using a phase mask. The interference by the phase shift produces a nanotower array with a submicrometer periodicity, whereas the standing wave effect by reflection from the mirror defines the stacked‐disk structure at each nanotower at sub‐100 nm periodicity. The stacked‐disk nanotowers with silver outer‐coating provide a strong electric field localization at the vertically integrated nanogaps on the side wall. At the same time, the series of reentrant geometry on the side walls can efficiently pin the liquid–air interface for a variety of liquids, including water and toluene, thereby providing omniphobic surface property. The molecules dissolved in either water or toluene at low concentration can be enriched in the drop on the surface in a course of evaporation, which are finally deposited onto a tiny spot. Raman spectra of the molecules are further amplified by the strong electric field at the nanogaps on the side walls of the nanotowers. Therefore, the surfaces provide high sensitivity of Raman analysis for both polar and nonpolar molecules.

Energetic, spatial, and momentum character of the electronic structure at a buried interface: The two-dimensional electron gas between two metal oxides

The interfaces between two condensed phases often exhibit emergent physical properties that can lead to new physics and novel device applications, and are the subject of intense study in many disciplines. We here apply novel experimental and theoretical techniques to the characterization of one such interesting interface system: the two-dimensional electron gas (2DEG) formed in multilayers consisting of SrTiO$_3$ (STO) and GdTiO$_3$ (GTO). This system has been the subject of multiple studies recently and shown to exhibit very high carrier charge densities and ferromagnetic effects, among other intriguing properties. We have studied a 2DEG-forming multilayer of the form [6 unit cells STO/3 unit cells of GTO]$_{20}$ using a unique array of photoemission techniques including soft and hard x-ray excitation, soft x-ray angle-resolved photoemission, core-level spectroscopy, resonant excitation, and standing-wave effects, as well as theoretical calculations of the electronic structure at several levels and of the actual photoemission process. Standing-wave measurements below and above a strong resonance have been introduced as a powerful method for studying the 2DEG depth distribution. We have thus characterized the spatial and momentum properties of this 2DEG with unprecedented detail, determining via depth-distribution measurements that it is spread throughout the 6 u.c. layer of STO, and measuring the momentum dispersion of its states. The experimental results are supported in several ways by theory, leading to a much more complete picture of the nature of this 2DEG, and suggesting that oxygen vacancies are not the origin of it. Similar multi-technique photoemission studies of such states at buried interfaces, combined with comparable theory, will be a very fruitful future approach for exploring and modifying the fascinating world of buried-interface physics and chemistry.

MEMS Based Broadband Piezoelectric Ultrasonic Energy Harvester (PUEH) for Enabling Self-Powered Implantable Biomedical Devices.

Acoustic energy transfer is a promising energy harvesting technology candidate for implantable biomedical devices. However, it does not show competitive strength for enabling self-powered implantable biomedical devices due to two issues – large size of bulk piezoelectric ultrasound transducers and output power fluctuation with transferred distance due to standing wave. Here we report a microelectromechanical systems (MEMS) based broadband piezoelectric ultrasonic energy harvester (PUEH) to enable self-powered implantable biomedical devices. The PUEH is a microfabricated lead zirconate titanate (PZT) diaphragm array and has wide operation bandwidth. By adjusting frequency of the input ultrasound wave within the operation bandwidth, standing wave effect can be minimized for any given distances. For example, at 1 cm distance, power density can be increased from 0.59 μW/cm2 to 3.75 μW/cm2 at input ultrasound intensity of 1 mW/cm2 when frequency changes from 250 to 240 kHz. Due to the difference of human body and manual surgical process, distance fluctuation for implantable biomedical devices is unavoidable and it strongly affects the coupling efficiency. This issue can be overcome by performing frequency adjustment of the PUEH. The proposed PUEH shows great potential to be integrated on an implanted biomedical device chip as power source for various applications.

Improving discharge uniformity of industrial-scale very high frequency plasma sources by launching a traveling wave

Very high frequency (VHF) PECVD has been demonstrated to be able to significantly increase the deposition rate without compromising the film quality for the manufacture of silicon heterojunction and silicon thin film solar cells. To further reduce the production costs by enhancing the throughput, larger electrode and higher frequency are often required at the same time. Nevertheless, raising frequency in large-area PECVD results in non-uniform discharge caused by the standing wave effect and deteriorates the processing uniformity. In this study, a technique that generates a traveling wave via superposing two specific standing waves launched simultaneously is proposed to resolve this issue. An industrial-scale linear plasma reactor with length and width of 125 and 10 cm, respectively, is adopted for experimental tests and two 80 MHz power supplies are utilized to separately control the standing waves. The experimental results show that the discharge gap is only partially covered by plasma discharge when only one standing wave is applied. However, as both standing waves are launched, the non-uniformity of plasma discharge can be effectively reduced to <±5%. In addition, numerical simulation is also conducted in this study to clarify whether the proposed technique can be applied to large-area rectangular PECVD (substrate size: 1.4 m × 1.1 m). By arranging multiple feeding points on opposite sides of the powered electrode, the simulation results indicate the non-uniformity of electric field can be maintained within ±10%.

Measurement of spatial and temporal evolution of electromagnetic fields in a 100 MHz plasma source using B dot and double dipole probes

Very high frequency plasma sources are often accompanied by plasma density nonuniformities associated with a standing-wave effect. Electron density measurements using a plasma absorption probe show density nonuniformities that can be larger than predicted by a standing wave model. These structures have been associated with harmonics of the electric fields in the plasma. The authors present the first time and phase-resolved measurements of the spatial structure of the electromagnetic waves in a 100 MHz plasma source using argon at 40 mTorr employing a B dot probe. The authors show that the harmonic structure is related to a current reversal and subsequent circulation that appears when the sheath collapses during the radio frequency cycle. The circulation is driven by inward traveling waves that are electromagnetic in nature, not plasma waves traveling at the electron thermal velocity. Double dipole probe measurements were used to validate the B dot probe electric field measurements derived from the time derivative of Βθ which is derived from the B dot probe signal.

Design and performance analysis of microcavity-enhanced graphene photodetector

There is an increasing interest in grapheme photodetector for its applications, because graphene has rich optical and electronic properties, including zero band gap, high mobility and special optical absorption properties. A design of microcavity-enhanced photodetector based on ultra-thin graphene is proposed in this paper: detector absorption can be effectively improved by confining the light field in the microcavity. Through studying the light field resonant condition in the microcavity and enhanced mechanism of detector responsivity under resonant mode, the light absorption model of a microcavity-enhanced graphene photodetector under standing wave effect is established; it is analyzed that the influences of microcavity mirror reflectivity and length on detector performance are increased by light field. Further the optimal structure parameters and performance evaluations of microcavity-enhanced graphene photodetector at different incident wavelengths are demonstrated. Theoretical analysis shows that under the standing wave effect the effective absorption coefficient of monolayer graphene at the antinode is one multiple enlargement compared with no cavity; the microcavity length and topbottom mirror reflectivity directly affect the optical total phase during light folding back at one time in the microcavity, and the shift of the total optical phase changes the full width at half maximum (FWHM) of the responsivity of the microcavity-enhanced graphene photodetector. Through coordinating the relations among the microcavity length and reflectivities of two mirrors and the incident wavelength, it can be realized that the photodetector has a good characteristic of wavelength selectivity. At a nominal operating wavelength of 850 nm, the presented microcavity-enhanced graphene photodetector can reach a responsivity of 0.5 A/W, 32-fold increase compared with monolayer graphene photodetector with no cavity and FWHM can reach 10 nm, indicating that the designed photodetector has a high responsivity and a good charactoristic of narrowband. As for the application in the practical engineering, through adopting bias on the two sides of graphene in the cavity to speed up the migration velocity of the photon-generated carrier, more photon-generated carriers are produced to increase the photodetector responsivity. However, the increased level of photodetector responsivity will be impeded acctually on account of the high contact resistance between graphene and electrode, and the measured value will not equal the theoretical value, so the quantitative analysis on the value of the bias should be carried out. Through combining the microcavity with graphene the incident light can be confined to reflect multiple times between two mirrors in the microcavity to improve the graphene absorption, and then make the microcavity-enhanced graphene photodetector responsivity improved. Our approach can be used to improve the optical response of graphene photodetector, and provides a way to solve the trade-off between photodetector responsivity and response speed.