Standing-wave Resonator Research Articles

Bulk-driven acoustic streaming at resonance in closed microcavities.

Bulk-driven acoustic (Eckart) streaming is the steady flow resulting from the time-averaged acoustic energy flux density in the bulk of a viscous fluid. In simple cases, like the one-dimensional single standing-wave resonance, this energy flux is negligible, and therefore the bulk-driven streaming is often ignored relative to the boundary-driven (Rayleigh) streaming in the analysis of resonating acoustofluidic devices with length scales comparable to the acoustic wavelength. However, in closed acoustic microcavities with viscous dissipation, two overlapping resonances may be excited at the same frequency as a double mode. In contrast to single modes, the double modes can support a steady rotating acoustic energy flux density and thus a corresponding rotating bulk-driven acoustic streaming. We derive analytical solutions for the double modes in a rectangular-box-shaped cavity including the viscous boundary layers, and use them to map out possible rotating patterns of bulk-driven acoustic streaming. Remarkably, the rotating bulk-driven streaming may be excited by a nonrotating actuation, and we determine the optimal geometry that maximizes this excitation. In the optimal geometry, we finally simulate a horizontal 2×2, 4×4, and 6×6 streaming-roll pattern in a shallow square cavity. We find that the high-frequency 6×6 streaming-roll pattern is dominated by the bulk-driven streaming as opposed to the low-frequency 2×2 streaming pattern, which is dominated by the boundary-driven streaming.

Periodic self-modulation of an electrodynamically driven heated wire near resonance.

A thin nichrome wire driven near resonance by the Lorentz force and heated by an alternating electrical current is a popular lecture demonstration. Due to the convective cooling of the portions of the wire moving with the greatest amplitude, only glowing regions near a velocity node will be visible in a darkened room. Nonlinear effects and the thermal expansion coefficient of the wire displace the wire's tensioning mass. By adiabatic invariance, the work done on or by the vibrating wire, due to the changes in the mass's elevation, causes the natural frequency of the standing wave resonance to be shifted. Competition between the thermal inertia of the wire and the convective heat transfer coefficient introduces an exponential thermal relaxation time so that the amplitude of vibration is dependent on the ratio of the drive frequency to the changing resonance frequency at an earlier (retarded) time. These thermal and kinetic effects are incorporated into three coupled nonlinear ordinary differential equations that are separated by the method of multiple time scales and are solved numerically, reproducing both the spontaneous appearance of stable periodic amplitude modulation and the hysteretic behavior observed with increasing or decreasing of the drive frequency.

Thermoacoustic energy conversion in a square duct

The present study aims to demonstrate the thermoacoustic energy conversion phenomenon in a standing wave resonator driven by a commercial loudspeaker with a stack made of plastic straws and atmospheric air as the working fluid. The system is driven at resonance frequency of 70 Hz with the stack kept in the middle section of the resonator and a temperature difference of 14.1℃ was produced between the ends of the stack at a drive ratio of 3.57 %. The hot end reached a temperature of 36.5℃ and the cold end reached a temperature of 22.4℃ at the highest drive ratio. Moving the stack towards the end of the resonator reduces the temperature difference produced showing the influence of stack position. Thermoacoustic devices offer an environment-friendly solution to utilize waste heat or renewable energy sources, to upgrade low grade heat or generate cooling or produce electricity using acoustic-electric transducers. This study is done as a pre-cursor, to develop a relatively inexpensive prototype for studying non-linear effects at high drive ratios seen in thermoacoustic devices, which are known to reduce their performance.

Theoretical analysis of entanglement enhancement with two cascaded optical cavities

Entanglement source with high entanglement degree is the guarantee for accomplishing the quantum information transmission and process with higher fidelity. Continuous variable Einstein-Podolsky-Rosen (EPR) entangled optical field with quantum correlation of amplitude and phase quadrature is a basic and important quantum resource in the quantum information science area, which can be obtained by a non-degenerate optical parametric amplifier (NOPA) operated below the threshold pump power. Because of the limitation of the imperfect performance of optical components in optical cavity, we should find efficient methods of implementing quantum manipulation to improve the entanglement degree of the entangled state of light. Connecting NOPA1 and NOPA2 in series, the entangled state of light output from the NOPA1 can be manipulated by NOPA2, and the entanglement degree can be enhanced under certain conditions. To improve the entanglement degree to a greater extent, the structure of the NOPA1 is chosen as a half-monolithic standing-wave optical resonator with the triple resonance of the pump and two subharmonic modes. The NOPA1 is able to output the entangled optical fields with an entanglement degree of 8.4 dB, which is the highest entanglement generated by a single device so far. The structure of the NOPA2 can be chosen as a standing-wave optical cavity or a four-mirror ring optical cavity. According to the different structures of the NOPA2, we theoretically design two kinds of optical systems with two cascaded cavities and compare the effects of the two optical systems on the continuous variable EPR entanglement cascaded enhancement in detail. Based on the above contrastive analysis, when the entanglement degree of the input optical fields is 8.4 dB and the transmissivity of the output coupler is lower, the structure of a four-mirror ring optical cavity for NOPA2 cannot enhance the entanglement degree, so the optical system including NOPA2 with standing wave cavity structure and the optical isolator with high transmission efficiency is appropriate. When the transmissivity of the output coupler and transmission efficiency of the optical isolator are higher, the structure of the NOPA2 should be chosen as a standing-wave optical cavity, otherwise the structure of the NOPA2 should be chosen as a four-mirror ring optical cavity. We also theoretically analyze the dependence of the correlation degree of output optical fields on physical parameters. The results show that under the conditions of higher input and output coupling efficiency, higher transmission efficiency and lower intro-cavity loss, the entangled state of light with higher entanglement degree can be obtained experimentally. This provides the reference for obtaining entangled optical fields with higher entanglement degree in the future.

Degenerate four-wave mixing in nonlinear resonators comprising two-dimensional materials: A coupled-mode theory approach

Two-dimensional (2D) or sheet materials have been recently recognized as fascinating materials for nonlinear photonics. Here, we develop a rigorous mathematical framework based on perturbation theory and temporal coupled-mode theory capable of analyzing third-order, ${\ensuremath{\chi}}^{(3)}$, multichannel nonlinear processes in resonant systems comprising 2D materials. The framework is applied to model degenerate four-wave mixing in a guided-wave graphene plasmon-polariton resonant structure, consisting of a standing-wave resonator directly coupled to access waveguides. The results obtained with the proposed framework are compared with full-wave finite-element simulations revealing excellent agreement. Aside from being accurate and efficient, our framework allows for selectively incorporating different nonlinear phenomena, identifying their unique impact on the nonlinear response and providing valuable physical insight. We are, thus, able to specify the optimal operating point leading to maximum conversion efficiency for the generated wave in a multiparameter space. In addition, we identify unstable operating regimes exhibiting optical bistability or limit cycles, thoroughly characterizing the component performance. Our framework enables the study of diverse multichannel phenomena (frequency generation, frequency mixing, and parametric amplification) in the thriving field of 2D material photonics, thus allowing for assessing the potential of these exciting materials for practical nonlinear applications.

Counter-propagating modes in a Fabry-Perot-type resonator.

The longitudinal optical modes of a Fabry-Perot resonator are investigated. We consider (1)the three- and one-dimensional spectral mode density in free space and in standing-wave resonators, (2)the infinite sum of mode profiles, resulting in the Airy distribution, (3)comparison between a two-mirror resonator and an infinite periodic lensguide, and (4)comparison between a two-mirror resonator and a ring resonator. It is consistently deduced that the two counter-propagating waves with wave vectors ±|kq| at the same resonance frequency νq and polarization constitute independent optical modes with mode indices ±|q|.

Traveling-wave meets standing-wave: A simulation study using pair-of-transverse-dipole-ring (PTDR) coils for adjustable longitudinal coverage in ultra-high field MRI.

1.At ultrahigh fields (B 0 ≥7T), it is challenging to cover a large field of view using single-row conventional RF coils (standing wave resonators) due to the limited physical dimensions. In contrast, traveling wave approaches can excite large fields of view even using a relatively simple hardware setup, but suffer from poor efficiency and high local specific absorption rate in non-imaged regions. In this study, we propose and numerically analyze a new coil which combines the concept of traveling wave and standing wave. The new coil consists of a Pair of Transverse Dipole Rings (PTDR) whose separation is adjusted according to the desired imaging coverage. The PTDR coil was validated using electromagnetic (EM) simulations in phantoms and human leg models, which showed that coverage can be as long as 60 cm. When the coverage of the PTDR coil was shortened to 20 cm to cover the knees only, it's transmit and SAR efficiencies were 84% and 37% higher than those of the 50 cm coverage, respectively.

Precision feedback control of a normal conducting standing wave resonator cavity

Precision feedback control of a normal conducting standing wave resonator cavity

Influence of tube geometry on the performance of standing-wave acoustic resonators.

A general and simple calculation method is presented to investigate the effects of tube shape on the resonant frequency and performance of a resonator. First, the resonant frequency of a variable cross-section resonator is modeled using a transfer matrix. Then, the amplification ratio of the pressure amplitude (ARPA), defined as the ratio of the pressure amplitude at the small end to that at the large end of the resonator, is used to evaluate its performance. The ARPA value for a variable cross-section resonator can be directly calculated from its resonant frequency. It is shown that the ARPA value is closely related to the compression ratio. However, its value is only determined by the resonator itself and is independent of the working conditions. Therefore, the ARPA index is potentially a more convenient tool for evaluating the performance of resonators compared with other indexes. Additionally, the presented method is validated by a comparison with analytical results and experimental data. Moreover, the harmonic frequencies for cylindrical, exponential, conical, half-cosine, 3/4 cosine, and Horn-Cone shape tubes are numerically investigated, in addition to the influence of the resonator shape on the resonance frequency and ARPA. Finally, optimal shape parameters for several types of resonators are suggested.

Reconfigurable optical-microwave filter banks using thermo-optically tuned Bragg Mach-Zehnder devices.

A new reconfigurable, tunable on-chip optical filter bank is proposed and analyzed for the silicon-on-insulator platform at the ~1550 nm wavelength. The waveguided bank is a cascade connection of 2 x 2 Mach-Zehnder interferometer (MZI) filters. An identical standing-wave resonator is situated in each MZI "arm." Using the thermo-optic (TO) effect to perturb this waveguide's index, the TO heater stripes provide continuous tuning of the filter by shifting the resonance smoothly along the wavelength axis. To reconfigure and program the cascade array, a broadband 2 x 2 MZI-related switch is inserted between adjacent filters. The novel TO switch, described here, can provide either single or double interconnection of 2 x 2 filters. The filter resonator is a new in-guide array of N closely coupled phase-shifted Bragg-grating resonators that provide one resonant spectral profile with 5 to 100 GHz bandwidth. The length of each grating cavity in the N group is chosen according to the Butterworth filter technique, and this gives high peak transmission for the composite. The predicted spectral profiles of a three-stage cascade show two-or-three peaks, or two-or-three notches with movable wavelength-locations as well as tunable wavelength-separations between those features. A tunable notch within a wider movable passband is also feasible. Potential applications include microwave photonics, wavelength-selective systems, optical spectroscopy and optical sensing.

Probing dynamics of micro-magnets with multi-mode superconducting resonator

In this work, we propose and explore a sensitive technique for investigation of ferromagnetic resonance and corresponding magnetic properties of individual micro-scaled and/or weak ferromagnetic samples. The technique is based on coupling the investigated sample to a high-Q transmission line superconducting resonator, where the response of the sample is studied at eigen frequencies of the resonator. The high quality factor of the resonator enables sensitive detection of weak absorption losses at multiple frequencies of the ferromagnetic resonance. Studying the microwave response of individual micro-scaled permalloy rectangles, we have confirmed the superiority of fluxometric demagnetizing factor over the commonly accepted magnetometric one and have depicted the demagnetization of the sample, as well as magnetostatic standing wave resonance.

Advanced photonic filters based on cascaded Sagnac loop reflector resonators in silicon-on-insulator nanowires

We demonstrate advanced integrated photonic filters in silicon-on-insulator (SOI) nanowires implemented by cascaded Sagnac loop reflector (CSLR) resonators. We investigate mode splitting in these standing-wave (SW) resonators and demonstrate its use for engineering the spectral profile of on-chip photonic filters. By changing the reflectivity of the Sagnac loop reflectors (SLRs) and the phase shifts along the connecting waveguides, we tailor mode splitting in the CSLR resonators to achieve a wide range of filter shapes for diverse applications including enhanced light trapping, flat-top filtering, Q factor enhancement, and signal reshaping. We present the theoretical designs and compare the CSLR resonators with three, four, and eight SLRs fabricated in SOI. We achieve versatile filter shapes in the measured transmission spectra via diverse mode splitting that agree well with theory. This work confirms the effectiveness of using CSLR resonators as integrated multi-functional SW filters for flexible spectral engineering.

Plasmon resonances, anomalous transparency, and reflectionless absorption in overdense plasmas

The structure of the surface and standing wave resonances and their coupling in the configuration of the overdense plasma slab with a single diffraction grating are studied, using impedance matching techniques. Analytical criteria and exact expressions are obtained for plasma and diffraction grating parameters which define resonance conditions for absolute transparency in the ideal plasma and reflectionless absorption in a plasma with dissipation.

Electromagnetically Induced Transparency in a Silicon Self-Coupled Optical Waveguide

We investigate the resonance property of a self-coupled optical waveguide (SCOW) with four coupling points. Under a special condition that the two outer couplers are in weak coupling and the two inner couplers are in strong coupling, an implicit standing-wave resonance mode is formed inside the SCOW structure. As the resonance is feedback coupled via an S-shape bus waveguide, electromagnetically induced transparency (EIT)-like resonance features are observed in the output transmission spectrum. The SCOW resonator is analyzed using the coupled mode theory and finite-difference time-domain simulation. The device is experimentally demonstrated on the silicon-on-insulator platform. The measurement results overall agree well with the theoretical calculation. The EIT-like peak can be tuned by a thermo-optic phase shifter made of a NIN-type silicon resistor integrated in the feedback waveguide. The results point to new ways of creating on-chip optical analog of the EIT phenomenon that can be utilized for various optical signal processing applications.

Tutorial: Integrated-photonic switching structures

Recent developments in waveguided 2 × 2 and N × M photonic switches are reviewed, including both broadband and narrowband resonant devices for the Si, InP, and AlN platforms. Practical actuation of switches by electro-optical and thermo-optical techniques is discussed. Present datacom-and-computing applications are reviewed, and potential applications are proposed for chip-scale photonic and optoelectronic integrated switching networks. Potential is found in the reconfigurable, programmable “mesh” switches that enable a promising group of applications in new areas beyond those in data centers and cloud servers. Many important matrix switches use gated semiconductor optical amplifiers. The family of broadband, directional-coupler 2 × 2 switches featuring two or three side-coupled waveguides deserves future experimentation, including devices that employ phase-change materials. The newer 2 × 2 resonant switches include standing-wave resonators, different from the micro-ring traveling-wave resonators. The resonant devices comprise nanobeam interferometers, complex-Bragg interferometers, and asymmetric contra-directional couplers. Although the fast, resonant devices offer ultralow switching energy, ∼1 fJ/bit, they have limitations. They require several trade-offs when deployed, but they do have practical application.

Simulating energy cascade of shock wave formation process in a resonator by gas kinetic scheme

The temporal-spatial evolution of gas oscillation was simulated by gas kinetic scheme (GKS) in a cylindrical resonator, driven by a piston at one end and rigidly closed at the other end. Periodic shock waves propagating back and forth were observed in the resonator under finite amplitude of gas oscillation. The studied results demonstrated that the acoustic pressure is a saw-tooth waveform and the oscillatory velocity is a square waveform at the central position of the resonant tube. Moreover, it was found by harmonic analysis that there was no presence of obvious feature for pressure node in such a typical standing wave resonator, and the distribution of acoustic fields displayed a one-dimensional feature for the acoustic pressure while a quasi-one-dimensional form for oscillatory velocity, which demonstrated the nonlinear effects. The simulation results for axial distribution of acoustic intensity showed a good consistency with the published experimental data in the open literature domain, which provides a verification for the effectiveness of the GKS model proposed. The influence of displacement amplitude of the driving piston on the formation of shock wave was numerically investigated, and the simulated results revealed the cascade process of harmonic wave energy from the fundamental wave to higher harmonics. In addition, this study found that the acoustic intensity at the driving end of the resonant tube would increase linearly with the displacement amplitude of the piston due to nonlinear effects, rather than the exponential variation by linear theory. This research demonstrates that the GKS model is strongly capable of simulating nonlinear acoustic problems.

\u201cOptical and Surface Enhanced Raman Scattering properties of Ag modified silicon double nanocone array\u201d

Surface enhanced Raman scattering (SERS) systems with large number of active sites exhibit superior capability in detection of low concentration analytes. In this paper, we present theoretical as well as experimental studies on the optical properties of a unique hybrid nanostructure, Ag NPs decorated silicon double nanocones (Si-DNCs) array, which provide high density of hot spots. The Si-DNC array is fabricated by employing electron beam lithography together with plasma etching process. Multipole analysis of the scattering spectra, based on the multipole expansion theory, confirms that the toroidal dipole moment dominates over other electric and magnetic multipole moments in the Si-DNCs array. This response occurs as a result of generating current densities flowing in opposite directions and consequently generating H-field vortexes inside the nanocones. Moreover, SERS applicability of this type of nanostructure is examined. For this purpose, the Si-DNCs array is decorated with Ag nanoparticles (NPs) by means of electroless deposition method. Simulation results indicate that combination of multiple resonances, including LSPR resonance of Ag NPs, longitudinal standing wave resonance of Ag layer and inter-particle interaction in the gap region, result in a significant SERS enhancement. Our experimental results demonstrate that Si-DNC/Ag NPs array substrate provides excellent reproducibility and ultrahigh sensitivity.

Development of High Voltage and High Current Test Bed for Transmission Line Components

A test bed for testing of MW level transmission line components, based on the concept of standing wave resonator is being developed at ITER-India, Ion Cyclotron Heating and Current Drive (ICH&CD) lab. This test bed can be configured and operated for various lengths of the resonator for optimum requirement. Estimated 32 kV peak voltage and 650 A peak current can be achieved inside the resonator during operation with an input power level of ∼ 20 kW. In this paper, detailed design and simulation results of test bed using high frequency simulator Microwave Studio (MWS) is presented. A brief description on implementation plan is described as well.

An extending broadband near-infrared absorption of Si-based deep-trench microstructures

We design and investigate numerically a Si-based deep-trench microstructure covered with continuous thin gold (Au) films. It breaks through the absorption limitation of Si material and greatly extends the near-infrared (NIR) absorption range to 1500nm. By the simulated distributions of electric-field intensity, we observe clearly the excitation of surface plasmon polaritons and the standing wave resonance of plasmon cavity formed inside the deep trench, by which we explain the extending broadband NIR absorption well. We further discuss the influence of trench depth on the cavity mode and NIR absorption in detail. By combination of the proposed microstructures, it is a promising approach to realize an extending broadband and high NIR photoresponse in Si-based detectors.

Three-dimensional cavity nanoantennas with resonant-enhanced surface plasmons as dynamic color-tuning reflectors.

As plasmonic antennas for surface-plasmon-assisted control of optical fields at specific frequencies, metallic nanostructures have recently emerged as crucial optical components for fascinating plasmonic color engineering. Particularly, plasmonic resonant nanocavities can concentrate lightwave energy to strongly enhance light-matter interactions, making them ideal candidates as optical elements for fine-tuning color displays. Inspired by the color mixing effect found on butterfly wings, a new type of plasmonic, multiresonant, narrow-band (the minimum is about 45 nm), high-reflectance (the maximum is about 95%), and dynamic color-tuning reflector is developed. This is achieved from periodic patterns of plasmonic resonant nanocavities in free-standing capped-pillar nanostructure arrays. Such cavity-coupling structures exhibit multiple narrow-band selective and continuously tunable reflections via plasmon standing-wave resonances. Consequently, they can produce a variety of dark-field vibrant reflective colors with good quality, strong color signal and fine tonal variation at the optical diffraction limit. This proposed multicolor scheme provides an elegant strategy for realizing personalized and customized applications in ultracompact photonic data storage and steganography, colorimetric sensing, 3D holograms and other plasmon-assisted photonic devices.