Frequency Splitting Research Articles

Strain-Induced Frequency Splitting in PT Symmetric Coupled Silicon Resonators.

When two resonators of coupled silicon resonators are identical and the gain on one side is equal to the loss on the other side, a parity-time (PT) symmetric-coupled silicon resonator is formed. As non-Hermitian systems, the PT-symmetric systems have exhibited many special properties and interesting phenomena. This paper proposes the strain-induced frequency splitting in PT symmetry-coupled silicon resonators. The frequency splitting of the PT system caused by strain perturbations is derived and simulated. Theory and simulation both indicate that the PT system is more sensitive to strain perturbation near the exceptional point (EP) point. Then, a feedback circuit is designed to achieve the negative damping required for PT symmetry. Based on a simple silicon-on-insulator (SOI) process, the silicon resonator chip is successfully fabricated. After that, the PT-symmetric-coupled silicon resonators are successfully constructed, and the frequency splitting phenomenon caused by strain is observed experimentally.

Synthesis, nanocrystalline morphology, lattice dynamics and nonlinear optics of mesoporous SiO2&LiNbO3 nanocomposite

We demonstrate a hybrid nanocomposite combining mesoporous silica, pSiO2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hbox {SiO}_2$$\\end{document}, as a host medium and guest lithium niobate LiNbO3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hbox {LiNbO}_3$$\\end{document} nanocrystals embedded into tubular silica nanochannels by calcination of the precursor mixed solution of lithium and niobium salts. High-resolution transmission electron microscopy, X-ray diffraction and Raman scattering techniques reveal trigonal LiNbO3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hbox {LiNbO}_3$$\\end{document} nanocrystals within the pSiO2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hbox {SiO}_2$$\\end{document} nanochannels, indicating their random texture morphology. Annealing at high temperatures ( 950∘\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{\\circ }$$\\end{document}C) during calcination also leads to partial crystallization of the pSiO2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hbox {SiO}_2$$\\end{document} matrix with the formation of trigonal α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha$$\\end{document}-SiO2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hbox {SiO}_2$$\\end{document} nanocrystals. The Raman microscopy analysis of the pSiO2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hbox {SiO}_2$$\\end{document}:LiNbO3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hbox {LiNbO}_3$$\\end{document} nanocomposite reveals three structural crystalline phases, α-SiO2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha -\\hbox {SiO}_2$$\\end{document}, LiNbO3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hbox {LiNbO}_3$$\\end{document} and a mixed phase which involves the α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha$$\\end{document}-SiO2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hbox {SiO}_2$$\\end{document} phase of host membrane and LiNbO3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hbox {LiNbO}_3$$\\end{document} nanocrystals embedded into the membrane. The finite size of the LiNbO3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hbox {LiNbO}_3$$\\end{document} nanocrystals results in specific features of the LO-TO phonon frequency splitting, which are investigated by Raman microscopy. In the transmission geometry, the second harmonic generation emission exhibits no Maker fringes and is characterized by a broad angular diagram of diffusely scattered light. The second harmonic generation response is independent of the polarization direction of the incident pump light, thus indicating a spatial isotropy of the nonlinear optical conversion in the pSiO2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hbox {SiO}_2$$\\end{document}:LiNbO3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hbox {LiNbO}_3$$\\end{document} composite, consistent with the randomly oriented textural morphology of the deposited LiNbO3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hbox {LiNbO}_3$$\\end{document} nanocrystals. The contribution of the guest LiNbO3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hbox {LiNbO}_3$$\\end{document} nanocrystals to the second harmonic generation effect was found to be strongly dominant compared to the partially crystallized host pSiO2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hbox {SiO}_2$$\\end{document} matrix. The nanocomposite pSiO2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hbox {SiO}_2$$\\end{document}:LiNbO3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hbox {LiNbO}_3$$\\end{document} membrane, set in the 90∘\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^\\circ$$\\end{document} nonlinear optical geometry, shows unusually high diffusely transmitted second harmonic generation light (back-reflected emission), apparently supported by internal light reflection from the tubular nanochannel network. Despite the fundamental interest, the revealed anomalous back-reflected second harmonic generation emission from pSiO2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hbox {SiO}_2$$\\end{document}:LiNbO3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hbox {LiNbO}_3$$\\end{document} nanocomposite membranes expands the prospects for their photonic and nonlinear optical applications.

Fixed frequency wireless power transfer using series-connected variable inductors for mitigation of frequency splitting

Fixed frequency wireless power transfer using series-connected variable inductors for mitigation of frequency splitting

Observation at radio frequencies of the hydroxyl (OH) absorption line in filaments and prominences above active regions of the Sun

When observing the Sun with RATAN-600 radio telescope using a spectropolarimetric complex in the range 1–3 GHz, as well as when observing coronal rain, absorption in the radio emission was discovered in the spectral region 1.5–1.65 GHz in active solar regions located under a cold filament or on the limb under a prominence. The observed line structure corresponds to the hyperfine splitting frequencies in the ground state of X2Π3/2 hydroxyl (OH) 1612–1720 MHz. When the observed active region passes through the knife-shaped beam pattern of the telescope antenna, the absorption band shifts in frequency due to a shift in the energy levels of the OH molecule in a magnetic field, which changes along the filament.

Наблюдение в радиодиапазоне линии поглощения гидроксила (ОН) в волокнах и протуберанцах над активными областями Солнца

When observing the Sun with RATAN-600 radio telescope using a spectropolarimetric complex in the range 1–3 GHz, as well as when observing coronal rain, absorption in the radio emission was discovered in the spectral region 1.5–1.65 GHz in active solar regions located under a cold filament or on the limb under a prominence. The observed line structure corresponds to the hyperfine splitting frequencies in the ground state of X2Π3/2 hydroxyl (OH) 1612–1720 MHz. When the observed active region passes through the knife-shaped beam pattern of the telescope antenna, the absorption band shifts in frequency due to a shift in the energy levels of the OH molecule in a magnetic field, which changes along the filament.

Tunable spin splitting of reflected vortex-beam of Weyl semimetal metasurface with stronger optical activity

This work investigated the spin splitting of a reflected beam with a vortex beam irradiating on a metasurface. This metasurface structure is the periodically rectangular-groove array of ionic crystal, where the array is a sub-wavelength grating with its periodical direction situated in the surface plane. In the grating structure, we embedded magnetic Weyl semimetals. Consequently, a stronger optical activity can be found, which originates from the unique electronic structure of Weyl semimetals and the orientation of the grating arrangement. By controlling the separation of Weyl points and grating orientation, we observe notable asymmetric spin splitting in different frequency ranges with distinctly unique distributions. Significant spin splitting was observed to be correlated with substantial Kerr rotation angles and reflectance differences, indicating strong optical activity. Additionally, with the increasing topological charges, the spin splitting increases significantly. Our results are useful for the manipulation of infrared radiations and infrared optical detection.

Measurement of transition frequencies and hyperfine constants of molecular iodine at 520.2 nm

We measured the transition frequencies of the hyperfine components in the four lines (P(34) 39-0, R(36) 39-0, P(33) 39-0, and R(35) 39-0) of the B-X transitions of molecular iodine at 520.2 nm. The 520.2 nm laser was generated by wavelength-converting the output of a 1560.6 nm external-cavity diode laser using a dual-pitch periodically poled lithium niobate (PPLN) waveguide. The frequencies were measured by counting the heterodyne beats between the laser stabilized at the frequencies of the hyperfine components and a frequency comb synchronized with a hydrogen maser. We determined the transition frequencies of the a1 components with relative uncertainties of 1×10−11; the uncertainty was limited by the impurity of the molecular iodine in the cell. From the measured hyperfine splitting frequencies, we calculated the hyperfine constants of these four transitions to obtain the rotational dependence of the excited-state hyperfine constants.

Full-Wave Simulation of a Helmholtz Radiofrequency Coil for Magnetic Resonance Applications

Magnetic resonance imaging (MRI) is a non-invasive diagnostic technique able to provide information about the anatomical, structural, and functional properties of different organs. A magnetic resonance (MR) scanner employs radiofrequency (RF) coils to generate a magnetic field to excite the nuclei in the sample (transmit coil) and pick up the signals emitted by the nuclei (receive coil). To avoid trial-and-error approaches and optimize the RF coil performance for a given application, accurate design and simulation processes must be performed. We describe the full-wave simulation of a Helmholtz coil for high-field MRI performed with the finite-difference time-domain (FDTD) method, investigating magnetic field pattern differences between loaded and unloaded conditions. Moreover, the self-inductance of the single loops constituting the Helmholtz coil was estimated, as well as the frequency splitting between loops due to inductive coupling and the sample-induced resistance. The result accuracy was verified with data acquired with a Helmholtz prototype for small phantom experiments with a 3T MR clinical scanner. Finally, the magnetic field variations and coil detuning after the insertion of the RF shield were evaluated.

Monolithically integrated EP-based optical isolator

Exceptional points (EPs) display peculiar degeneracies, where complex eigenvalues and associated eigenvectors coalesce simultaneously, resulting in a defective Hamiltonian. Meanwhile, the negative imaginary part of the energy eigenvalues related to a finite spectral linewidth at the resonant energy, which could provide a solution to tackle the isolation bandwidth limitation of MRR-based optical isolators without sacrificing the insertion loss. Here, a second-order EP2 system constructed by SiN-based cascaded racetrack resonators is proposed, while the metal strip operating as an integrated electromagnet provides magnetic fields required for non-reciprocal phase shifting (NRPS). Owing to the existence of the NRPS perturbation, the system is pushed away from EP and consequently triggers complex frequency splitting, resulting in the isolation bandwidth proportional to the square-root perturbation instead. The results show that the isolation bandwidth of the EP isolator is increased by 163% and 22% compared to single-racetrack and cascaded-racetrack isolators with 2.85 dB insertion loss and 34.3 dB isolation ratio, respectively. The presented EP-based optical isolator shows tremendous potential for high-density monolithic integration and packaging.

Intensification and Changing Spatial Extent of Heavy Rainfall in Urban Areas

AbstractUrban areas have been shown to impact rainfall by altering both its intensity and spatial structure at sub‐hourly and sub‐kilometer scales. However, there is currently no clear understanding of the precise pattern of change and the mechanisms that drive these changes. Since the hydrological response in urban areas is highly sensitive to such rainfall properties, understanding these changes is critical to improving our ability to assess urban flood risk. We use 7 years of high‐resolution weather radar data (4‐ or 5‐min and 1 km) to analyze changes in patterns of rainfall intensity, spatial structure, and storm evolution across eight urban areas within Europe and the United States. The use of the same methodology across the different cities enables a consistent comparison among them. We track convective rainfall events using a storm tracking algorithm and assess changes in rainfall properties in the upwind, center, and downwind regions of each city. We also investigate changes in the frequency of storm initiations, terminations, splitting, and merging. Our results show that urban areas act to intensify rainfall—mostly over them, but sometimes on their peripheries. Overall, larger cities tend to show the largest rainfall enhancements. Our findings highlight that rainfall spatial structure is altered over the urban core; usually resulting in more spatially concentrated rainfall. We also observe increased storm initiations over most cities and increased storm splitting over one. Given that demographic projections show that future urban population will increase, our results point toward an increased future flood risk in growing cities.

AC Zeeman effect in microfabricated surface traps.

Quantum processors and atomic clocks based on trapped ions often utilize an ion's hyperfine transition as the qubit state or frequency reference, respectively. These states are a good choice because they are insensitive in first order to magnetic field fluctuations, leading to long coherence times and stable frequency splittings. In trapped ions, however, these states are still subject to the second order AC Zeeman effect due to the necessary presence of an oscillating magnetic field used to confine the ions in a Paul trap configuration. Here, we measure the frequency shift of the 2S1/2 hyperfine transition of a 171Yb+ ion caused by the radio frequency (RF) electromagnetic field used to create confinement in several microfabricated surface trap designs. By comparing different trap designs, we show that two key design modifications significantly reduce the AC Zeeman effect experienced by the ion: (1) an RF ground layer routed directly below the entire RF electrode, and (2) a symmetric RF electrode. Both of these changes lead to better cancellation of the AC magnetic field and, thus, overall reduced frequency shifts due to the AC Zeeman effect and reduced variation across the device. These improvements enable a more homogeneous environment for quantum computing and can reduce errors for precision applications such as atomic clocks.

Suppression of Azimuthal Combustion Instability Using Perforated Liner Under Symmetry Breaking

Symmetry breaking occurring in annular combustors shows different stability patterns due to the formation of nondegenerate modes with different frequencies. This also brings about more profound complexity for control methodology. This paper presents a three-dimensional analytical model to investigate how to control nondegenerate azimuthal modes by modifying the wall boundary conditions of a multiburner annular combustor. The stability of the system can be evaluated by solving the eigenvalue of the dispersion relation equation derived in this study. Results show that changes in the parameters of the perforated liner cause different performance in nondegenerate modes due to frequency splitting. Meanwhile, the asymmetric perforated liner alters the original asymmetry of the annular combustor, inducing a shift in the nature of nondegenerate modes when significant symmetry breaking exists. Furthermore, variations of pressure amplitude in the backing cavity lead to diverse acoustic energy dissipation and even distinct stability patterns under two types of azimuthally nonuniformly perforated liner. Overall, this paper presents a new methodology for suppressing nondegenerate azimuthal modes under symmetry breaking by utilizing a perforated liner in an annular combustor. Additionally, a clear understanding of the evolution behavior of nondegenerate modes is also provided by studying their stability behavior and energy dissipation.

Low-Damage Trimming of Micro Hemispherical Resonators by Chemical Etching.

To enhance the performance of micro-hemispherical gyroscopes, achieving low-damage and high-surface-quality trimming is essential. This enables greater stability and reliability for the gyroscopes. Current methods for reducing frequency split often come with drawbacks such as high cost, adverse effects on the Q-factor, or surface damage. In this paper, a chemical etching trimming method is proposed to reduce frequency split in micro-hemispherical resonators. This method allows for trimming with minimal damage, while also being cost-effective and easy to implement. The theoretical basis of this method was analyzed, followed by a simulation to determine the optimal trimming range and location on the resonator. The simulated Q-factor analysis before and after trimming preliminarily validated the method's low-damage characteristics. Ultimately, the frequency split of the resonator was reduced to below 1 Hz. Additionally, test results of the Q-factor and surface quality before and after trimming further confirmed that chemical etching offers effective low-damage trimming capabilities. The proposed method holds significant potential for improving the performance of micro-hemispherical resonator gyroscopes.

Unified theory of alpha, mu, and tau rhythms via eigenmodes of brain activity.

A compact description of the frequency structure and topography of human alpha-band rhythms is obtained by use of the first four brain activity eigenmodes previously derived from corticothalamic neural field theory. Just two eigenmodes that overlap in frequency are found to reproduce the observed topography of the classical alpha rhythm for subjects with a single, occipitally concentrated alpha peak in their electroencephalograms. Alpha frequency splitting and relative amplitudes of double alpha peaks are explored analytically and numerically within this four-mode framework using eigenfunction expansion and perturbation methods. These effects are found to result primarily from the different eigenvalues and corticothalamic gains corresponding to the eigenmodes. Three modes with two non-overlapping frequencies suffice to reproduce the observed topography for subjects with a double alpha peak, where the appearance of a distinct second alpha peak requires an increase of the corticothalamic gain of higher eigenmodes relative to the first. Conversely, alpha blocking is inferred to be linked to a relatively small attention-dependent reduction of the gain of the relevant eigenmodes, whose effect is enhanced by the near-critical state of the brain and whose sign is consistent with inferences from neural field theory. The topographies and blocking of the mu and tau rhythms within the alpha-band are explained analogously via eigenmodes. Moreover, the observation of three rhythms in the alpha band is due to there being exactly three members of the first family of spatially nonuniform modes. These results thus provide a simple, unified description of alpha band rhythms and enable experimental observations of spectral structure and topography to be linked directly to theory and underlying physiology.

Exceptional point enhanced nanoparticle detection in deformed Reuleaux-triangle microcavity

In this paper, we propose a deformed Reuleaux-triangle resonator (RTR) to form exceptional point (EP) which results in the detection sensitivity enhancement of nanoparticle. After introducing single nanoparticle to the deformed RTR at EP, frequency splitting obtains an enhancement of more than 6 times compared with non-deformed RTR. In addition, EP induced a result that the far field pattern of chiral mode responses significantly to external perturbation, corresponding to the change in internal chirality. Therefore, single nanoparticle with far distance of more than 4000 nm can be detected by measuring the variation of far field directional emission. Compared to traditional frequency splitting, the far field pattern produced in deformed RTR provides a cost-effective and convenient path to detect single nanoparticle at a long distance, without using tunable laser and external coupler. Our structure indicates great potential in high sensitivity sensor and label-free detector.Graphical

Achieving Sub-5-mHz Frequency Split Trimming of Micro Hemispherical Resonator Gyroscope With Method of Mass–Stiffness Decoupling

Achieving Sub-5-mHz Frequency Split Trimming of Micro Hemispherical Resonator Gyroscope With Method of Mass–Stiffness Decoupling

Efficient determination of Born-effective charges, LO-TO splitting, and Raman tensors of solids with a real-space atom-centered deep learning approach

We introduce a deep neural network (DNN) framework called the Real-space Atomic Decomposition NETwork (radnet), which is capable of making accurate predictions of polarization and of electronic dielectric permittivity tensors in solids and aims to address limitations of previously available machine learning models for Raman predictions in periodic systems. This framework builds on previous, atom-centered approaches while utilizing deep convolutional neural networks. We report excellent accuracies on direct predictions for two prototypical examples: GaAs and BN. We then use automatic differentiation to efficiently calculate the Born-effective charges, longitudinal optical-transverse optical (LO-TO) splitting frequencies, and Raman tensors of these materials. We compute the Raman spectra, and find agreement with ab initio results. Lastly, we explore ways to generalize the predictions of polarization while taking into account periodic boundary conditions and symmetries.

Enhanced detection limit in an exceptional surface-based fiber resonator by manipulating Fano interference.

An exceptional surface (ES) has advantages in improving sensing robustness and enhancing frequency splitting. Typically, the eigenvalue splitting must exceed the mode linewidth in order to be clearly visible in the spectrum, which limits the precision of the ES-based sensing structure. In this paper, a strategy for manipulating spectral line shape in an ES-based structure is experimentally realized. In addition, the limit of the minimum detectable displacement can be further reduced by monitoring the peak intensity of the Fano interference line shape. The demonstration of Fano interference in an ES-based system opens the way for a new class of ultrasensitive optical sensors.

Detectability of Axisymmetric Magnetic Fields from the Core to the Surface of Oscillating Post-main-sequence Stars

Magnetic fields in the stellar interiors are key candidates to explain observed core rotation rates inside solar-like stars along their evolution. Recently, asteroseismic estimates of radial magnetic field amplitudes near the hydrogen-burning shell (H-shell) inside about 24 red giants (RGs) have been obtained by measuring frequency splittings from their power spectra. Using general Lorentz-stress (magnetic) kernels, we investigated the potential for detectability of near-surface magnetism in a 1.3 M ⊙ star of supersolar metallicity as it evolves from a mid subgiant to a late subgiant into an RG. Based on these sensitivity kernels, we decompose an RG into three zones—deep core, H-shell, and near-surface. The subgiants instead required decomposition into an inner core, an outer core, and a near-surface layer. Additionally, we find that for a low-frequency g-dominated dipolar mode in the presence of a typical stable magnetic field, ∼25% of the frequency shift comes from the H-shell and the remaining from deeper layers. The ratio of the subsurface tangential field to the radial field in the H-burning shell decides if subsurface fields may be potentially detectable. For p-dominated dipole modes close to νmax , this ratio is around two orders of magnitude smaller in subgiant phases than the corresponding RG. Further, with the availability of magnetic kernels, we propose lower limits of field strengths in crucial layers in our stellar model during its evolutionary phases. The theoretical prescription outlined here provides the first formal way to devise inverse problems for stellar magnetism and can be seamlessly employed for slow rotators.

Identification and trimming of the eccentric mass in shell resonators

This paper presents a novel method to identify and suppress the undesired spurious mode caused by the 1st and 3rd harmonics of eccentric mass defects in shell resonators. This approach eliminates the need for pre-trimming of frequency split, simplifying the identification and trimming process, with the advantages of high efficiency and minimal structural damage. Firstly, the influence of the mass defects on the dynamics of resonators is analyzed using the mass ring model. The shear force caused by the 1st and 3rd harmonics of the eccentric mass, as well as the axial force caused by the 2nd harmonic, result in forced bending vibration and axial vibration of resonators. These two types of vibrations are superimposed as spurious modes with the operating mode. The bending vibration caused by eccentric mass is decoupled from the mixed vibration signal by analyzing the dynamic characteristics. An analytic scheme is proposed to identify the 1st and 3rd harmonics without eliminating frequency split. To validate the proposed scheme, the identification and trimming process for eccentric mass is simulated by the finite element method based on the geometric model with preset first four harmonics. Finally, experimental identification and trimming of the eccentric mass for the hemispherical resonator are performed based on the laser Doppler vibrometer and ion beam etching process. After multiple iterations, the 1st and 3rd harmonics are reduced by 87.2% and 49.8%, and the quality factors of the operating modes increase by 26.7% and 40.7%, respectively, demonstrating the effectiveness of the proposed method.