Order Resonance Research Articles

The Hydrogen Atom Fundamental Resonance States

In the 1920’s, Louis de Broglie’s observation that the integer sequence that could be related to the interference patterns produced by the various electromagnetic energy quanta emitted by hydrogen atoms was identical to those of very well known classical resonance processes, made him conclude that electrons were captive in resonance states within atoms. This led Schr?dinger to propose a wave function to represent these resonance states that still have not been reconciled with the electromagnetic properties of electrons. This article is meant to identify and discuss the electromagnetic harmonic oscillation properties that the electron must possess as a resonator in order to explain the resonance volume described by the wave function, as well as the electromagnetic interactions between the elementary charged particles making up atomic structures that could explain electronic and nucleonic orbitals stability. An unexpected benefit of the expanded space geometry required to establish these properties and interactions is that the fundamental symmetry requirement is respected by structure for all aspects of the distribution of energy within electromagnetic quanta.

Nonlinear resonances in the ABC-flow.

In this paper, we study resonances of the ABC-flow in the near integrable case ( C≪1). This is an interesting example of a Hamiltonian system with 3/2 degrees of freedom in which simultaneous existence of two resonances of the same order is possible. Analytical conditions of the resonance existence are received. It is shown numerically that the largest n:1 (n = 1, 2, 3) resonances exist, and their energies are equal to theoretical energies in the near integrable case. We provide analytical and numerical evidences for existence of two branches of the two largest n:1 (n = 1, 2) resonances in the region of finite motion.

Моделирование резонансов диэлектрических сфер в терагерцевом диапазоне

AbstractWe have studied the resonance properties of dielectric spheres with subwavelength dimensions in the optical and terahertz frequency range. Distribution of the electric field vector in a sphere irradiated by a plane polarized wave has been numerically simulated using the finite element method. The obtained results clearly demonstrate that it is in principle possible to use resonances of various orders in dielectric spheres for the amplification of current in a conducting antenna with dimensions several times smaller than the radiation wavelength. In the case of resonances within short spectral intervals, it is possible to provide a current density gain up to 25–30 dB as compared to that in the absence of a dielectric sphere surrounding the antenna.

Temperature dependence of the nonlinear optical response of smectic liquid crystals containing gold nanorods.

The present study is devoted to the investigation of the nonlinear optical properties of a smectic liquid crystal doped with gold nanorods. Using the Z-scan technique, we investigate the changes in the optical birefringence of a homeotropic sample upon laser exposure, considering the configurations of normal and oblique incidence. Our results reveal that the birefringence variations may be governed by distinct physical mechanisms, depending on the relative angle between the far-field director and the wave vector of the excitation laser beam. In particular, we observe that the position dependence of the far-field transmittance exhibits different behaviors as the incidence angle is changed, indicating that distortions in the beam wavefront may be associated with the thermal lens phenomenon or an optically induced reorientation of the nematic director. The temperature dependence of the nonlinear refractive and absorptive coefficients is investigated close to the smectic-A-nematic phase transition. A detailed analysis of the interplay between smectic order and plasmon resonance is performed, thus unveiling the capability of plasmonic liquid crystal to be used in optical devices.

Limit cycle oscillations at resonances

This paper deals with limit cycles in one degree of freedom systems. The van der Pol equation is an example of an equation describing systems with clear limit cycles in the phase space (displacement-velocity 2 dimensional plane). In this paper, it is shown that a system with nonlinear loading, representing the drag load acting on structures in an oscillatory flow (the drag term of the Morison equation), will in fact exhibit limit cycles at resonance and at higher order resonances. These limit cycles are stable, and model self-excited oscillations. As the damping in the systems is linear and constant, the drag loading will to some degree work as negative damping. The consequences of the existence of these limit cycles are that systems starting at lesser amplitudes in the phase plane will exhibit increased amplitudes until the limit cycle is obtained.

The TRAPPIST-1 system: orbital evolution, tidal dissipation, formation and habitability

We study the dynamical evolution of the TRAPPIST-1 system under the influence of orbital circularization through tidal interaction with the central star. We find that systems with parameters close to the observed one evolve into a state where consecutive planets are linked by first order resonances and consecutive triples, apart from planets c, d and e, by connected three body Laplace resonances. The system expands with period ratios increasing and mean eccentricities decreasing with time. This evolution is largely driven by tides acting on the innermost planets which then influence the outer ones. In order that deviations from commensurability become significant only on $Gy$ time scales or longer, we require that the tidal parameter associated with the planets has to be such that $Q' > \sim 10^{2-3}.$ At the same time, if we start with two subsystems, with the inner three planets comprising the inner one, $Q'$ associated with the planets has to be on the order (and not significantly exceeding) $10^{2-3}$ for the two subsystems to interact and end up in the observed configuration. This scenario is also supported by modelling of the evolution through disk migration which indicates that the whole system cannot have migrated inwards together. Also in order to avoid large departures from commensurabilities, the system cannot have stalled at a disk inner edge for significant time periods. We discuss the habitability consequences of the tidal dissipation implied by our modelling, concluding that planets d, e and f are potentially in habitable zones.

Unambiguous nuclear spin detection using an engineered quantum sensing sequence

Sensing, localising and identifying individual nuclear spins or frequency components of a signal in the presence of a noisy environments requires the development of robust and selective methods of dynamical decoupling. An important challenge that remains to be addressed in this context are spurious higher order resonances in current dynamical decoupling sequences as they can lead to the misidentification of nuclei or of different frequency components of external signals. Here we overcome this challenge with engineered quantum sensing sequences that achieve both, enhanced robustness and the simultaneous suppression of higher order harmonic resonances. We demonstrate experimentally the principle using a single nitrogen-vacancy center spin sensor which we apply to the unambiguous detection of external protons.

Effects of an external electric field on the nonlinear optical absorption of smectic liquid crystals containing gold nanorods

ABSTRACTThe present manuscript is devoted to the study of the nonlinear optical absorption of a smectic liquid crystal doped with gold nanorods in the presence of an external electric field. By using Z-scan technique in the configuration of fully open aperture and normal incidence, we analyze the changes in the absorption coefficient of a homeotropic sample upon laser exposure. Our results reveal that the electric field may suppress the nonlinear absorption of the samples well bellow to smectic-A-nematic transition temperature. The effects of the external electric field on the interplay between smectic order and plasmon resonance are analyzed.

Compact Low-Power Consumption Single-Mode Coupled Cavity Lasers

Ultra-compact, widely-tunable and low-power InP­based four-section coupled-cavity lasers are designed and analyzed. Two Fabry–Perot cavities of unequal lengths, each containing an amplifier and a phase­tuning section, are coupled together through low-loss Bragg grating. The theoretical analysis of such multisection lasers starts with calculating the poles of a linear transfer function of the entire resonator in order to obtain resonant wavelengths and wavelength-dependent threshold gains. The differential quantum efficiency and the power-current characteristics are then calculated to evaluate the laser performance. The effectiveness of the design procedure is verified by the experimental and proof­of-principle demonstration using simplified three-section lasers. Devices exhibit single-mode operation with a side-mode suppression ratio of over 24 dB and tuning range of 11.2 nm. These telecom-suitable lasers can be used as on-chip local oscillators in low-power integrated optical coherent receivers.

Microfluidically Reconfigurable Microstrip Line Combline Filters With Wide Frequency Tuning Capabilities

Microfluidically repositionable selectively metallized plates (SMPs) are utilized for the first time to design and realize microstrip line combline filters with wide frequency tuning and high power-handling capability. A continuous frequency tuning range of 2.7:1 is achieved by utilizing tight coupling between the SMP and open-ended microstrip line resonators in order to change their length for tuning from 2.5 to 4 GHz and capacitively load one of their open ends for tuning from 1.5 to 2.5 GHz. The unloaded quality factor (Q <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">u</sub> ) of the resonators is maintained relatively constant (210-190) across the entire tuning range allowing for the low insertion loss (IL) and high power-handling capability. Specifically, a ~5% constant fractional bandwidth fourth-order filter design is discussed and experimentally verified. The filter exhibits less than 3-dB IL across the 2.7:1 tuning range. It is shown that the filter's power handling capability can reach up to 15 W under constant average power excitation.

Generalized Magnetic Mirrors.

We propose generalized magnetic mirrors that can be achieved by excitations of sole electric resonances. Conventional approaches to obtain magnetic mirrors rely heavily on exciting the fundamental magnetic dipoles, whereas here we reveal that, besides magnetic resonances, electric resonances of higher orders can be also employed to obtain highly efficient magnetic mirrors. Based on the electromagnetic duality, it is also shown that electric mirrors can be achieved by exciting magnetic resonances. We provide direct demonstrations of the generalized mirrors proposed in a simple system of a one-dimensional periodic array of all-dielectric wires, which may shed new light on many advanced fields of photonics related to resonant multipolar excitations and interferences.

Linearization of Hénon Maps with Resonant Eigenvalues at an Attracting Fixed Point

We study holomorphic linearization of Henon maps in $$\mathbb {C}^2$$ at an attracting fixed point. The natural obstacle to linearization is a resonance between the eigenvalues at the fixed point. However, it had not been known whether the presence of resonances is always an obstruction to linearization of Henon maps. We will show that this depends on the degree $$d\ge 2$$ of the Henon map and the order $$k \ge 2$$ of the resonance. In particular, we give examples of Henon maps of arbitrary degree $$d\ge 3$$ which are linearizable despite having resonances of order $$k\ge 2$$ . Among Henon maps of degree $$d=2$$ , on the other hand, a resonance of order $$k=2,3,4,5,6$$ always prevents linearization, whereas there are examples of linearizable maps for $$k\ge 7$$ .

A compact metamaterial loaded monopole antenna with offset-fed microstrip line for wireless applications

A compact metamaterial loaded monopole antenna with offset-fed microstrip line is proposed for Universal Mobile Telecommunication System (UMTS), Worldwide interoperability for Microwave Access (WiMAX), and Wireless Local Area Network (WLAN) wireless applications. The proposed antenna is printed on a 19.18×22.64×1.6mm3 FR-4 substrate having a dielectric constant (εr) of 4.4. The antenna radiating element consists of split ring structure and CSRR for generating multiband characteristics, which is fed by offset microstrip line. A split in the outer vertical arm creates a lower order resonance at 2.1GHz and the Complementary Split Ring Resonator (CSRR) in the monopole antenna is used to generate a new resonance frequency of 3.45GHz. The precise equivalent circuit design equations are used to analyze the CSRR resonance frequency. Also, the band characteristics of a split ring structure and CSRR are enlightened in detail to verify the metamaterial property. Simulated results are verified with measured results. The measured azimuthal plane (H-Plane) exhibits omnidirectional radiation pattern and elevation plane (E-plane) represents a bidirectional radiation pattern.

Design of two-stage fish spear-shaped UWB bandpass filter with sharp selectivity and good out-of-band performances

In this paper, a novel two-stage fish spear-shaped multimode resonator (MMR)-based ultra wideband (UWB) bandpass filter (BPF) is presented. The fish spear-shaped MMR is loaded with stepped impedance resonator in order to improve the out-of-band performance of the proposed filter. The proposed UWB BPF filter has fractional bandwidth better than 110%. In order to validate the present design approach, the filter is fabricated on RT/Duroid 5880 having dielectric constant 2.2, thickness 0.787 mm and loss tangent of 0.0009. The measured passband bandwidth of the filter is from 3.3 to 11.85 GHz, with insertion loss of 1.5 dB and return loss better than 12 dB in the passband. The proposed filter has sharp selectivity and upper stopband with 20 dB attenuation from 12 to 24 GHz.

UWB Metamaterial-based miniaturized planar monopole antennas

In this paper, ultra wide band (UWB) metamterial based compact planar antennas have been designed and experimentally verified. Four novel unit cells have been realized and each unit cell dispersion characteristics are numerically calculated which follows CRLH-TL properties. These four CRLH-TL unit cells are loaded into monopole antennas which result, four open-ended MTM antennas respectively. Further, a novel via free version of CRLH-TL unit cells have been designed, which increases the fabrication flexibility. The compactness has been achieved by realizing ZOR (zeroth order resonance) mode and its bandwidth is increased by realizing small shunt capacitance and large shunt inductance. Further, by optimizing CRLH-TL unit cells, two closely spaced zeroth-order and first-order resonance modes are merged into a single pass band, which gives wide bandwidth. The each proposed antenna has a compact dimension of 0.27 λ0×0.19 λ0×0.02 λ0 (22×15×1.6mm3), where λ0 is a free space wavelength at 3.8GHz. The four proposed antennas have S11<−10dB impedance bandwidths of 8.4GHz, 8.5GHz, 8.2GHz and 8.3GHz respectively. The optimum gain, good efficiency, desired radiation characteristics in frequency domain analysis and less distortion of waves in time domain analysis have been achieved for proposed antennas, which are most suitable for UWB applications. The CST-MWS has been used for the parametric study of the proposed antennas. A good agreement has been observed between simulated and experimental results.

Coupled UHF Micromechanical Ring Resonators With Schottky Transducers

In this letter, we present ultra-high frequency coupled ring resonators realized in a suspended AlGaN/GaN heterostructure. The piezoelectric transducers consist of back-to-back nickel (Ni) Schottky diodes deposited on a 20-nm-thick AlGaN layer and a floating 2-D electron gas (2-DEG) sheet at the AlGaN/GaN interface. The dispersion characteristics of symmetric and anti-symmetric Lamb waves in ring resonators are characterized. Higher order resonance harmonics are targeted with very high mechanical quality factors ( $Q\text{s}$ ) through optimized design of the coupling beam. Such a scheme minimizes the acoustic energy leakage to the substrate, and thus increases anchor $Q$ . We report on a high-order breathing resonance mode at 900.7 MHz with very high mechanical $Q$ of 8350 measured at room temperature and ambient pressure, achieving a record high frequency $\times Q$ value of $7.5\times 10^{12}$ . [2017-0064]

Features of light scattering by particles with a high absorption coefficient

This paper presents a brief review of resonance scattering of light by subwavelength particles with a large refraction index and small dissipation. It shows that each partial mode can be represented outside the particles as a superposition of infinite cascades of Fano resonances. The nature of these resonances is explained. Simple relationships are given that directly express the parameters of an asymmetric Fano line in terms of the particle size, the wave number of the incident radiation, and the complex refractive index. The resonances are characterized inside the particles by a traditional Lorentzian line shape; however, the amplitude of the resonances can be very large, while resonances of various orders can substantially overlap. This creates conditions for giant (by orders of magnitude) amplification of the field inside such a particle, as well as for controlling the contrast of this field. The indicated properties open up new possibilities for creating nonlinear heterogeneous nanostructures and other metamaterials.

The Trapezoid Counterweight Method in Dynamic Balance of Symmetric Flexible Rotor

Steam turbine generator unit, water pump and other high speed revolution symmetric flexible rotor were regarded as research objects in this paper. According to variation characteristic of rotor shaft in rigid and flexible working mode, nine-reel high pressure water pump rotor was analyzed. The former four-order intrinsic frequency of flexible rotor was obtained by modal analysis and harmonic response analysis. The methods of reaction force response and unbalance response were been studied after first order and second order resonance region eliminating in different modes of simple harmonic exciting force. Based on above theoretical research results, trapezoid counterweight method was proposed for dynamic balance of flexible rotor. This method solved problem that rigid dynamic balance of low speed rotor was destroyed after first order and second order resonance region counter weight in dynamic balance of flexible rotor. The dynamic balancing techniques of flexible rotor could be improved the qualities of rotor and its relative products by this method, eliminating the vibration of unbalance mass of products radically.

Via-less CRLH-TL unit cells loaded compact and bandwidth-enhanced metamaterial based antennas

The via-less composite right hand left hand (CRLH)-TL unit cells loaded compact and bandwidth-enhanced metamaterial (MTM) antennas have been designed and experimentally investigated. Four novel unit cells are designed and its dispersion characteristics of the proposed unit cells are numerically calculated which follows CRLH-TL properties. Further, the conventional metallic vias of CRLH-TL have been eliminated to increase the fabrication flexibility. The four CRLH-TL unit cells are loaded into monopole antennas which result, four via-less open-ended MTM antennas respectively. Its ZOR (zeroth order resonance) bandwidth is increased by realizing small shunt capacitance and large shunt inductance. Further, to increase overall antenna bandwidth, merging of ZOR mode to the higher and lower order modes into a single pass band has been done by realizing proper CRLH-TL unit cells. The each proposed antenna has a dimension of 0.13λ0×0.08λ0×0.0085λ0, where the free space wavelength λ0 at 1.6GHz. The four proposed antennas have S11<−10dB fractional bandwidths (FBW) 173% (1–13.6GHz), 169% (1.2–14.5GHz), 158% (1.6–13.5GHz) and 158% (1.6–13.5GHz) respectively. The optimum gain and desired radiation characteristics have been obtained for all proposed antennas, which can be suitable for UWB applications. The CST-MWS has been used for the parametric study of the proposed antennas. A good agreement has been observed between simulated and experimental results.

High figure of merit hydrogen sensor using multipolar plasmon resonance modes

Fabrication of long Au nanorods (AuNRs) has resulted in the appearance of higher order plasmon resonance modes, or multipoles, in the absorbance spectrum that can be monitored as a function of time and gas exposure. Due to the proximity of the multipolar mode to the transverse dipole mode of the AuNRs, both modes were monitored as the sample was exposed to hydrogen in an air background. These results were also compared to a shorter AuNR sample where the longitudinal dipole peak position matched the multipolar peak position. Polarization dependence of the higher order resonance as well as boundary element method (BEM) simulations confirm that the mode order is n=3. Due to the 36% decrease in linewidth of the multipolar peak compared to the dipole, the figure of merit (FoM) of the multipolar resonance is calculated to be 22% higher than the longitudinal dipole resonance for the shown gas sensing results and is promising for high temperature gas sensing applications.