Frequency Ω0 Research Articles

A universal description of stochastic oscillators

Many systems in physics, chemistry, and biology exhibit oscillations with a pronounced random component. Such stochastic oscillations can emerge via different mechanisms, for example, linear dynamics of a stable focus with fluctuations, limit-cycle systems perturbed by noise, or excitable systems in which random inputs lead to a train of pulses. Despite their diverse origins, the phenomenology of random oscillations can be strikingly similar. Here, we introduce a nonlinear transformation of stochastic oscillators to a complex-valued function [Formula: see text](x) that greatly simplifies and unifies the mathematical description of the oscillator's spontaneous activity, its response to an external time-dependent perturbation, and the correlation statistics of different oscillators that are weakly coupled. The function [Formula: see text] (x) is the eigenfunction of the Kolmogorov backward operator with the least negative (but nonvanishing) eigenvalue λ1 = μ1 + iω1. The resulting power spectrum of the complex-valued function is exactly given by a Lorentz spectrum with peak frequency ω1 and half-width μ1; its susceptibility with respect to a weak external forcing is given by a simple one-pole filter, centered around ω1; and the cross-spectrum between two coupled oscillators can be easily expressed by a combination of the spontaneous power spectra of the uncoupled systems and their susceptibilities. Our approach makes qualitatively different stochastic oscillators comparable, provides simple characteristics for the coherence of the random oscillation, and gives a framework for the description of weakly coupled oscillators.

Optical Spectra of Plasmon–Exciton Core–Shell Nanoparticles: A Heuristic Quantum Approach

Light–matter coupling in plasmonic nanocavities has been widely studied in the past years. Yet, for core–shell particles, popular electromagnetic models that use the classical Lorentz oscillator to describe the shell predict extinction spectra with three maxima, if the plasmon and the shell absorption are in resonance. In contrast, experiments exhibit only two peaks, as also expected from simple quantum models of hybrid states. In order to reconcile the convenient and widely used classical electromagnetic description with experimental data, we connect it to the quantum world by conceiving a heuristic quantum model. Our model is based on the permittivity of a two-level system in a classical electric field derived from the optical Bloch equations. The light–matter coupling is included via the collective vacuum Rabi frequency Ω0. Using our model, we obtain excellent agreement with a series of experimental extinction spectra of particles with various coupling strengths due to a systematic size variation. The suppression of the third maximum, which mainly stems from the absorption in the shell, can be interpreted as a vacuum induced power broadening, which may occur in lossy (plasmonic) cavities below the strong-coupling regime.

Terahertz generation by beat-wave mechanism of two Gaussian laser beams with corrugated noble-metal nanospheres in external magnetic field

An analytical model is presented that deals with THz generation by nonlinear mixing of two Gaussian laser beams with different frequencies ω1 and ω2 and wave vectors k1→ and k2→simultaneously propagating through an array of spatially corrugated noble-metal nanoparticles placed in the presence of a static magnetic field where ponderomotive nonlinearities are operative. The two co-propagating laser beams exert a nonlinear ponderomotive force on the plasma electrons, causing them to acquire nonlinear oscillatory velocity. This velocity leads to the generation of nonlinear macroscopic current density at the beat frequency ω (ω1-ω2) which further gives rise to strong terahertz radiation. The beat frequency lies in the THz region and density ripple provides the necessary phase-matching conditions. The externally applied magnetic field enhances the nonlinear coupling between the electric field of the lasers and causes resonant interaction of the laser beam with electrons of the NPs. THz radiations being non-invasive and biologically innocuous, play an important role in medical imaging, biomedical and pharmaceutical fields, and THz spectroscopy.

Excitation of third harmonic terahertz surface plasmon over a rippled graphene-free space interface

We examined the third harmonic (TH) terahertz (THz) surface plasmon waves (SPWs) generation over a graphene surface deposited on a rippled dielectric substrate (SiO2) by obliquely incidenting a p-polarized laser beam on a graphene surface with frequency ω0 and wave numbers k0x and k0z at an incident angle θ. Laser beam exerts ponderomotive force on free electrons of the graphene surface and produce nonlinear second harmonic (SH) oscillatory velocity v→2ω0 at frequency 2ω0. SH oscillatory velocity couples with perturbed ripple electron density to produce TH nonlinear current density J→3ω0nl at frequency 3ω0. Ripple wave number (q) provides an extra wave number to develop resonant TH THz SPWs at frequency 3ω0 and wave number kz=3k0z+q. The required ripple wave number for the excitation of THz TH SPWs is lower for the higher Fermi energy of the graphene sheet as compared to lower Fermi energy. Graphene sheet’s Fermi energy and angle of incidence laser beam significantly modify the amplitude of TH THz SPWs.

Determining the volume fraction in 2-phase composites and bodies using time varying applied fields

A body Θ containing two phases, which may form a periodic composite with microstructure much smaller that the body, or which may have structure on a length scale comparable to the body, is subjected to slowly time varying boundary conditions that would produce an approximate uniform field in Θ were it filled with homogeneous material. Here slowly time varying means that the wavelengths and attenuation lengths of waves at the frequencies associated with the time variation are much larger than the size of Θ, so that we can make a quasistatic approximation. At least one of the two phase does not have an instantaneous response but rather depends on fields at prior times. The fields may be those associated with electricity, magnetism, fluid flow in porous media, or antiplane elasticity. We find, subject to these approximations, that the time variation of the boundary conditions can be designed so boundary measurements at a specific time t=t0 exactly yield the volume fractions of the phases, independent of the detailed geometric configuration of the phases. Moreover, for specially tailored time variations, the volume fraction can be exactly determined from measurements at any time t, not just at the specific time t=t0. We also show how time varying boundary conditions, not oscillating at the single frequency ω0, can be designed to exactly retrieve the response at ω0.

Excitation of second harmonic terahertz surface magnetoplasmons over a rippled surface of n-InSb

We analyzed the excitation of second harmonic (SH) terahertz (THz) surface magnetoplasmons (SMPs) over a n-type semiconductor (n-InSb)-free space interface. P-polarized laser obliquely incidents on the magnetized rippled surface of semiconductor with frequency ω and wave number k0z and k0x and exerts a ponderomotive force on free electrons of semiconductor surface and imparts second harmonic oscillatory velocity v→2ω. Second harmonic oscillatory velocity v→2ω couples with modulated electron density nq of rippled surface to produce a second harmonic nonlinear current J→2ωnl, which resonantly derives SH THz SMPs with wave number k2z=2k0z+q and frequency 2ω. SH THz SMPs amplitude increases with applied external magnetic field as well as with incident angle and gets the maximum value then decreases further increase in the applied external magnetic field and incident angle. The conversion efficiency of SH THz SMPs amplitude is achieved up to 4.2%.

Generation of second harmonic terahertz surface plasmon wave over a rippled graphene surface

Abstract We propose a mechanism for the generation of second harmonic terahertz surface plasmon waves by incident terahertz electromagnetic radiation (ω, k 0) over a graphene surface deposited on the rippled dielectric substrate (SiO2). A p-polarized THz radiation incident obliquely on the graphene surface exerts a nonlinear ponderomotive force on free electrons in the rippled regime. This nonlinear ponderomotive force imparts oscillatory velocity to the electrons at frequency 2ω. Second harmonic oscillatory velocity couples with the modulated electron density and generates a nonlinear current density that drives second harmonic terahertz surface plasmon waves. Rippled surface provides an extra wave number for the phase matching condition to produce resonantly second harmonic at frequency 2ω and wavenumber (2k 0z + q). We examine the tunable response of second harmonic terahertz surface plasmon waves with respect to change in Fermi energy of graphene and laser incident angle. Second harmonic amplitude gets higher values by lowering the Fermi energy (E F) and increasing incident angle.

Negative refraction in hyperbolic hetero-bicrystals.

We visualized negative refraction of phonon polaritons, which occurs at the interface between two natural crystals. The polaritons-hybrids of infrared photons and lattice vibrations-form collimated rays that display negative refraction when passing through a planar interface between the two hyperbolic van der Waals materials: molybdenum oxide (MoO3) and isotopically pure hexagonal boron nitride (h11BN). At a special frequency ω0, these rays can circulate along closed diamond-shaped trajectories. We have shown that polariton eigenmodes display regions of both positive and negative dispersion interrupted by multiple gaps that result from polaritonic-level repulsion and strong coupling.

Thermoelastic micro-stretch solid immersed in an infinite inviscid fluid and subject to a rotation under two theories

This work is interested with a thermoelastic response in a micro-stretch half-space submerged in an unlimited non-viscous fluid under rotation, the medium is studied using the theory of Green-Naghdi (G-N III) and the model of three-phase-lag (3PHL). The governing equations are formulated in the context of G-N theory and the 3PHL model. Analytical solution to the problem is acquired by utilizing the normal mode method. The magnesium crystal element is utilized as an application to compare the predictions induced by rotation on microstretch thermoelastic immersed in an infinite fluid of G–N theory with those for the 3PHL model. Rotation has been noticed to have a major effect on all physical quantities. Comparisons were also made for three values of wave number b and three values of the real part frequency ω0.

Exact Solution of a Time-Dependent Quantum Harmonic Oscillator with Two Frequency Jumps via the Lewis-Riesenfeld Dynamical Invariant Method.

Harmonic oscillators with multiple abrupt jumps in their frequencies have been investigated by several authors during the last decades. We investigate the dynamics of a quantum harmonic oscillator with initial frequency ω0, which undergoes a sudden jump to a frequency ω1 and, after a certain time interval, suddenly returns to its initial frequency. Using the Lewis−Riesenfeld method of dynamical invariants, we present expressions for the mean energy value, the mean number of excitations, and the transition probabilities, considering the initial state different from the fundamental. We show that the mean energy of the oscillator, after the jumps, is equal or greater than the one before the jumps, even when ω1<ω0. We also show that, for particular values of the time interval between the jumps, the oscillator returns to the same initial state.

Electron Bernstein wave aided cosh-Gaussian laser beam absorption in plasma

In this paper, we investigate the electron Bernstein wave aided cosh-Gaussian laser beam absorption in a plasma with static magnetic field. The cosh-Gaussian laser beam has potential to couple with pre-existed electron Bernstein wave and the coupled wave has frequency ω1=ω0+ω and wave number k1=k0+k where ω0 and ω are the laser and electron Bernstein wave frequencies respectively and k0 and k are the wave numbers of laser and electron Bernstein wave respectively. The oscillatory velocity due to laser couples with the density perturbation due to electron Bernstein waves to produce nonlinear current density driving the electromagnetic sideband wave. An expression of absorption coefficient is analytically derived when the nonlinear current density is in phase with cosh-Gaussian laser field. The graphical discussion promises the more absorption in plasma by varying laser beam decentered parameter, beam width, laser frequency, electron cyclotron frequency, parameter b, and electron Bernstein wave frequency. The laser beam decentered parameter behaves as a very sensitive parameter. The absorption process is found to be very robust even for very small change in electron Bernstein wave frequency as compared with laser frequency. This tunable and efficient absorption theory might be applicable in heating of plasma.

Coherent Control of the Nonlinear Emission of Single Plasmonic Nanoantennas by Dual‐Beam Pumping (Advanced Optical Materials 20/2022)

An asymmetric plasmonic nanoantenna mediates the nonlinear mixing between ultrashort infrared laser pulses at frequency ω and 2ω. The third harmonic at ω + ω + ω and the sum frequency at ω + 2ω are coherent and degenerate at the visible frequency 3ω. Consequently, a relative time delay between the ω and 2ω pumps brings a strong modulation of the power at 3ω due to interference. This phase-dependent modulation, as presented in article number 2200757 by Michele Celebrano and co-workers, realizes an ultrafast coherent control scheme of nonlinear emission.

The development a fully-balanced current-tunable first-order low-pass filter with Caprio technique

This paper presents the development and design of a fully-balanced current-tunable first-order low-pass filter with Caprio technique, which could include the design and implementation of a first-order low-pass filter circuits. The filter consists of six bipolar junction transistor (BJT) and a single capacitor. The filter construction uses a bipolar junction transistor (BJT) as the main device and a single capacitor. A fully-balanced current-tunable first-order low-pass filter with Caprio technique developed. The architecture of the circuit is quite simple and proportional, symmetrical with signs of difference. Circuits developed into integrated circuits act like basic circuits for frequency filter circuits, current modes with Caprio techniques, obtained by improving the first-order low-pass filter for signal differences with incoming impedances. Adjusting the parameters of the circuit with the caprio technique achieves the optimal parameter value for correcting the total harmonic distortion value.&#x0D; The results of testing the operation of the circuit, a fully-balanced current-tunable first-order low-pass filter with Caprio technique developed and designed using the PSpice program. The simulation results showed good results in line with predicted theoretical analysis. The sensitivity of the device to the center frequency (ω0) response is low and independent of variables, the angular frequency is linear with wide current adjustment throughout the sweeping range of a wide frequency range, with a wide range of over tree orders of magnitude. Therefore, fully-balanced current-tunable first-order low-pass filter developed is very suitable to apply various applications regarding low frequency signal filtration, for example in biomedical systems, for example.

Observed Near-Inertial Waves Trapped in a Propagating Anticyclonic Eddy

Abstract Near-inertial waves (NIWs) trapped in a propagating anticyclonic eddy (AE) are investigated along the eddy path at three areas spanning 660 km by using two mooring arrays and a cruise transect. In the upstream area, the reconstructed three-dimensional structure reveals that NIWs are concentrated within the eddy core with wave current amplitudes exceeding 0.2 m s−1; vertically, due to the critical layer effect caused by eddy baroclinicity, NIWs are trapped at depths around 200 and 315 m with frequencies estimated to be ω1 ≈ 0.918f and ω2 ≈ 0.985f, respectively. After the AE propagates southwestward for hundreds of kilometers, the NIWs of frequency ω1 are still detectable inside the AE, while NIWs of frequency ω2 are absent because of the equatorward migration of the AE on a beta plane. Meanwhile, the wave kinetic energy downstream is trapped closer to the eddy center in radial direction, with the wave amplitude decaying roughly in a Gaussian form along the eddy radius, and becomes more homogeneous in the azimuthal direction, showing a more regular trapping form in the three-dimensional view. Investigation on wind shows that trapped NIWs are likely to be generated by a typhoon but less affected by the wind during the eddy passage time. By an energy analysis, we find that enhanced wave dissipation near the critical layer is roughly balanced by the energy transfer from mean flows, and therefore the trapped wave kinetic energy is largely conserved during the long-distance migration.

Application of high-resolution processing in seismic data based on an improved synchrosqueezing transform

This study proposes a high-resolution processing technique for seismic data based on the improved synchrosqueezing transform (SST). The SST rearranges the complex spectrum of the wavelet transform along the frequency axis. However, the energy is not concentrated in the position with the faster frequency change rate. To overcome these problems, the proposed method first transformed the seismic signal into an analytical one via Hilbert transformation and then determined the phase correction value (x0(t)) before and after the transformation. This was achieved using the instantaneous frequency attribute (ω(t)) of the analytical signal and a specific frequency (ω0) selected as the dominant frequency of the input data to adjust the change rate of the signal frequency before the SST falls close to zero, which can improve the time–frequency resolution after compression transformation. The essence of this method only adjusts the phase of the signal before and after transformation, without affecting the inverse expression of the SST. The one- and two-dimensional model data results show that the proposed method can better identify the time–frequency distribution characteristics of seismic signals and improve their resolution and the focusing effect in the time–frequency domain. The proposed method shows good prospects for application in gas reservoir detection and identification.

High-frequency limit of spectroscopy.

We consider an arbitrary quantum mechanical system, initially in its ground-state, exposed to a time-dependent electromagnetic pulse with a carrier frequency ω0 and a slowly varying envelope of finite duration. By working out a solution to the time-dependent Schrödinger equation in the high-ω0 limit, we find that, to the leading order in ω0 -1, a perfect self-cancellation of the system's linear response occurs as the pulse switches off. Surprisingly, the system's observables are, nonetheless, describable in terms of a combination of its linear density response function and nonlinear functions of the electric field. An analysis of a jellium slab and jellium sphere models reveals a very high surface sensitivity of the considered setup, producing a richer excitation spectrum than accessible within the conventional linear response regime. On this basis, we propose a new spectroscopic technique, which we provisionally name the Nonlinear High-Frequency Pulsed Spectroscopy (NLHFPS). Combining the advantages of the extraordinary surface sensitivity, the absence of constraints by the traditional dipole selection rules, and the clarity of theoretical interpretation utilizing the linear response time-dependent density functional theory, NLHFPS has a potential to evolve into a powerful characterization method for nanoscience and nanotechnology.

Structural design and dynamics optimization for heald frame made by carbon fiber reinforced composites

For improving the performance defects of traditional heald frame, the carbon fiber reinforced composites was applied to technical upgrading of the heald frame. On the basis of the theory analysis of composites laminates, the symmetrical ply scheme suitable for manufacturing of the heald frame in overall laminated was constructed, and a type of parametric program for finite element modeling was developed by ANSYS Parametric Design Language (APDL). The optimal mathematical model of the composites heald frame was proposed, and then the thickness parameter ( t) and direction parameters (α, θ) of fiber layer were dynamic optimized by using of Sub-problem method. The work increased the fundamental frequency (ω1) of the heald frame by 10.38%. Besides, the harmonic response frequency was also increased from 48.41 Hz to 53.77 Hz, which conductive to further improve dynamics properties of the composites heald frame. This paper provides technical guidance for innovative design of new heald frame, and is helpful to solve the problem of speed matching between heald frame and high-speed loom.

Excitation of terahertz surface magnetoplasmons by nonlinear mixing of two lasers on a rippled surface of magnetized n-InSb

We investigated the generation of terahertz (THz) surface magnetoplasmons (SMPs) over a rippled surface of magnetized n-type semiconductor (n-InSb) by using the nonlinear mixing of two p-polarized lasers with frequencies ω1, ω2 and wave numbers k1z, k2z, respectively. Incident obliquely from free space on the semiconductor surface with ripple wave number q exerts a nonlinear ponderomotive force on the free electrons at the frequency difference, ω=ω1−ω2. Ponderomotive force induces the nonlinear current that drives resonant terahertz surface magnetoplasmons at beat frequency with suitable wave number, kz=k1z−k2z+q. The amplitude of THz SMPs increases with the increase in applied external magnetic field. It also increases with increase the incidence angle of lasers and attains a maximum, and then drops to zero with further increase in the angle of incidence.

Efficient high-order harmonics generation from overdense plasma irradiated by a two-color co-rotating circularly polarized laser pulse.

High-order harmonics generated from the interaction between a two-color circularly polarized laser and overdense plasma is proposed analytically and investigated numerically. By mixing two circularly polarized lasers rotating in the same direction with different frequencies (ω0, 2ω0), the laser envelope is modulated to oscillate at the laser fundamental frequency while the peak intensity of each cycle becomes greater than that of the monochromatic light. This feature makes the plasma oscillate more violently and frequently under the striking of the two-color laser than the monochromatic one, thereby generating stronger harmonics and attosecond pulses. In addition, the incorporation of the 2ω0 light greatly expands the spectral width of harmonics, which facilitates the production of shorter attosecond pulses. Particle-in-cell simulations prove that under the same condition, the harmonic radiation efficiency in the two-color laser case can be improved by orders of magnitude, and isolated attosecond pulses can be even generated as a bonus in some cases.

CFOA‐based simple mixed‐mode first‐order universal filter configurations

AbstractThis brief communication presents two current feedback op‐amp (CFOA)‐based simple first‐order mixed‐mode universal filter topologies—one of them providing first‐order low‐pass (LP), high pass (HP), and all pass (AP)—all the three filters in voltage‐mode (VM)/trans‐admittance‐mode (TAM) while the other one realizing the quoted three functions in current‐mode (CM)/trans‐impedance‐mode (TIM). Except the all pass filter realization from the first configuration which needs a second CFOA also as gain‐of‐two amplifier, in all the remaining cases of both the configurations, only a single CFOA is needed. The other notable features of the circuits are employment of only three resistors and a grounded capacitor (as preferred for IC implementation) and the availability of independent tunability of the gain (H0) and cut‐off frequency/pole frequency (ω0) of all the three filters, in both the cases. In spite of not offering ideally infinite input impedance in VM/TAM mode and ideally zero input impedance in CM/TIM mode, the circuits still possess easy cascadability due to providing a voltage output from a low‐output impedance terminal W while the current output from the high output impedance terminal Z. Non‐ideal and sensitivity analyses have also been carried out. The workability of the proposed circuits has been demonstrated through PSPICE simulations and experimental results using the commercially available AD844‐type IC CFOA.