Order Resonance Research Articles

Multiband Ultrathin Polarization-Insensitive Terahertz Perfect Absorbers With Complementary Metamaterial and Resonator Based on High-Order Electric and Magnetic Resonances

Terahertz perfect metamaterial absorbers (PMA) based on higher order resonances have exhibited important applications in detecting, sensing, and imaging. However, most of them suffer from polarization and incident-angle dependence due to their asymmetrical structure. Here, we numerically investigate a kind of ultrathin triple-band PMA with polarization stability and wide angle of incidence. Numerical results reveal that three resonance peaks with nearly 100% absorptivity are obtained at 1.605, 4.425, and 4.946 THz under different polarization angles. It is interestingly found that the absorptance of two higher order resonances is inversely increased when the size of the middle dielectric spacer is smaller. The three resonance peaks in transverse electric and transverse magnetic modes nearly maintain fixed for oblique incidence up to 60°. Importantly, another four-band and dual-band perfect absorptions are easily achieved by a complementary method without doing iterative numerical simulation. The complementary metamaterial based absorber reaches more than 98% absorptance at four resonance frequencies. The metamaterial absorber based on complementary resonator also obtains two absorption peaks at 2.65 and 5.84 THz.

Nonlinear Holographic All-Dielectric Metasurfaces.

Nonlinear holographic metasurfaces have been intensively studied due to their potentials in practical applications. So far, nonlinear holographic metasurfaces have only been realized with plasmonic nanoantennas, suffering from high absorption loss and low damage threshold. Herein we propose and experimentally demonstrate a novel mechanism for nonlinear holographic metasurfaces. In contrast with conventional studies, the all-dielectric metasurface is composed of C-shaped Si nanoantennas. The incident laser is enhanced by their fundamental resonance, whereas the generated third-harmonic generation (THG) signals are redistributed to the air gap region via the higher order resonance, significantly reducing the absorption loss at short wavelength and resulting in an enhancement factor as high as 230. After introducing abrupt phase changes from 0 to 2π to the C elements, high-efficiency cyan and blue THG holograms have been experimentally generated with the Si metasurface for the very first time. This research shall shed light on the advances of nonlinear all-dielectric metasurfaces.

Excitation of plasmonic resonances within UV-Vis wavelength range using low-purity aluminum nanoconcave arrays

Size-controllable aluminum nanoconcave arrays were synthesized by electrochemical anodization of high and low-purity aluminum foils using oxalic, phosphoric, and citric acids. The plasmonic properties of the nanoconcave arrays in the two types of Al were investigated based on the specular reflectance in the 190–1400 nm wavelength range. We found that their optical reflectance was dramatically reduced as compared with unstructured Al. At the same time, pronounced reflectivity dips were detectable in the 280–1250 nm wavelength range for the case of high-purity aluminum, while for low-purity aluminum, they were within 260–580 nm, which were ascribed to plasmonic resonances of first and second orders. As a proof of principle of an application, we placed graphene on top of the nanoconcave arrays and observed a Surface Enhanced Raman Scattering (SERS) effect that resulted in an intensity increase in the characteristic G and 2D bands of graphene induced by the plasmonic properties of Al nanoconcave arrays. The maximum increase was achieved when the plasmonic resonance almost matched with the wavelength of the excitation laser probe of the Raman system. This study is important since we used low purity aluminum at a low cost to design and fabricate SERS substrates which can be used in practical applications.

The perturbed photogravitational restricted three-body problem: Analysis of resonant periodic orbits

In the framework of the perturbed photo-gravitational restricted three-body problem, the first order exterior resonant orbits and the first, third and fifth order interior resonant periodic orbits are analyzed. The location, eccentricity and period of the first order exterior and interior resonant orbits are investigated in the unperturbed and perturbed cases for a specified value of Jacobi constant C.It is observed that as the number of loops increases successively from one loop to five loops, the period of infinitesimal body increases in such a way that the successive difference of periods is either 6 or 7 units. It is further observed that for the exterior resonance, as the number of loops increases, the location of the periodic orbit moves towards the Sun whereas for the interior resonance as the number of loops increases, location of the periodic orbit moves away from the Sun. Thereby we demonstrate that the location of resonant orbits of the given order moves away from the Sun when perturbation is included.The evolution of interior first order resonant orbit with three loops is studied for different values of Jacobi constant C. It is observed that when the value of C increases, the size of the loop decreases and degenerates finally into a circle, the eccentricity of periodic orbit decreases and location of the periodic orbit moves towards the second primary body.

Folded monopole antenna with CSRRS for tri-band applications

In this paper, a miniaturize folded monopole antenna with complementary split ring resonator (CSRR) is proposed for tri-band applications. In the design procedure of the antenna, first a single band monopole antenna is designed for 2.88 GHz. For design a single band to dual band, the both arms of the radiating element (i.e. Monopole) is folded then it is resonated at 2.68GHz and 5.15GHz resonance frequencies, the resonance of the lower frequency is based on length of the monopole and higher order resonance is excited due to its folding effect. In order to extend its resonances for tri-band operation, the two identical size CSRRs (one on the left and another on the right from the feed line) are placed on the ground plane of the edge of the folded monopole, thus the entire structure is resonated at 2.47 GHz, 3.46GHz and 4.36 GHz frequencies. A simplified equivalent circuit model is developed for understanding its electrical behavior. Therefore, the proposed antenna has been suitable for WLAN, WiMAX and C-band applica- tions.

Multi-functional RF coils for ultra-high field MRI based on 1D/2D electromagnetic metamaterials

Electromagnetic metamaterials have already proven very valuable for the enhancement and molding of RF magnetic fields within ultra-high field MRI scanners at 7T. We report on our development of coil elements based on composite right-/left-handed (CRLH) 1D electromagnetic (EM) metamaterial transmission lines (metalines) operating in the zeroth order resonance (ZOR) to foster uniform RF magnetic field distributions along the scanner axis. Tailored EM metalines supporting full-wave or quarter-wave resonances are used either as metamaterial ring antenna or as dual-band coil elements for simultaneous 1H/23Na imaging. The EM metalines are key to the MetaBore, which is a fully adaptive RF field control scheme based on a periodic axial arrangement of conformal metamaterial ring antennas in the framework of high-field traveling-wave MRI. With the 2D EM metamaterials (metasurfaces) we realized high-impedance surfaces (HIS) in order to enhance the uniformity and directivity of the RF magnetic field from e.g. overlaid (elongated) dipole elements towards the probe volume. The designs include simulation studies of the overall multichannel coil systems, which are carried out with our home-made, open source electromagnetic 3D EC-FDTD solver openEMS supporting conformal cylindrical inhomogeneous meshing. Experimental verifications of our coils have been carried out within 7T MRI scanners (Siemens Magnetom).

Resonance identification studies at the CERN PS

In view of the LHC Injectors Upgrade (LIU) and the challenging high brightness target beam parameters, a broad range of possible working points for the Proton Synchrotron (PS) is being investigated. High order resonances have been identified, both structural resonances driven by space charge due to the lattice harmonics of the PS, and resonances excited by multipolar components in the machine. This paper provides a summary of the performed tune scan studies, covering both experimental and simulation results. Furthermore, non-linear analysis techniques have been used to characterize the resonances and their effect on the beam in presence of space charge.

Very-Low-Profile, Triband, Two-Antenna System for WLAN Notebook Computers

A very-low-profile, two-antenna system formed by combining two identical monopole antennas with a decoupling inductor is presented. The two-monopole design was capable of operating in the 2.4 GHz (2400–2484 MHz), 5.2 GHz (5150–5350 MHz), and 5.8 GHz (5725–5825 MHz) wireless local area network bands and yet merely occupied a small size of 5 mm × 42 mm (about 0.04λ × 0.33λ at 2.4 GHz). The two antennas symmetrically facing each other were closely packed with 1 mm spacing and required almost no separation distance. An inductor connecting the open ends of the two monopoles was employed to reduce the mutual coupling in the 2.4 GHz band. Over the 5.2/5.8 GHz bands was good isolation achieved by the devised arrangement of the antenna current nulls of higher order resonance. Owing to its low height of 5 mm, the two antennas can fit in the current narrow bezel of the notebook display.

Instability of equilibrium solutions of Hamiltonian systems with n-degrees of freedom under the existence of a single resonance and an invariant ray

In this paper we prove the instability of one equilibrium point in an autonomous Hamiltonian system with n-degrees of freedom under two assumptions: the first is the existence of a single resonance of order s (without resonance of lower order, but it could exist resonance of greater order); and the second is the existence of an invariant ray solution of the truncated Hamiltonian system up to order s. Application of our main result to the satellite problem is considered.

A Criterion for the Onset of Chaos in Systems of Two Eccentric Planets

Abstract We derive a criterion for the onset of chaos in systems consisting of two massive, eccentric, coplanar planets. Given the planets’ masses and separation, the criterion predicts the critical eccentricity above which chaos is triggered. Chaos occurs where mean motion resonances overlap, as in Wisdom's pioneering work. But whereas Wisdom considered the overlap of first-order resonances only, limiting the applicability of his criterion to nearly circular planets, we extend his results to arbitrarily eccentric planets (up to crossing orbits) by examining resonances of all orders. We thereby arrive at a simple expression for the critical eccentricity. We do this first for a test particle in the presence of a planet and then generalize to the case of two massive planets, based on a new approximation to the Hamiltonian. We then confirm our results with detailed numerical simulations. Finally, we explore the extent to which chaotic two-planet systems eventually result in planetary collisions.

Betatron phase and nonlinear lattice correction

Betatron phase measured from excited oscillation can be used to correct the beta function and the nonlinear lattice. With an improved algorithm the measurement precision has achieved 1 mrad (rms), or equivalently, 0.3% of beta beat at NSLS-II. The beta beating can be corrected to 1% in less than half an hour. This precise technique can be applied to the nonlinear lattice correction as well. The betatron phase probed by an off-axis beam provides information on the sextupole strength. In comparison with the model the nominal strength can be restored. It was shown that the proposed scheme treated all the leading order resonance driving terms generated by sextupoles, as well as the detuning terms and the nonlinear chromaticity. At NSLS-II a half percent sextupole correction led to a 15% increase of the dynamic aperture.

The effect of UV irradiation duty cycle on the 2nd harmonic coupling efficiency in optical fiber long period gratings

Long period gratings (LPGs) as a sensing platform have the potential for multi-parameter measurement through the utilization of 2nd order coupling resonance bands. Although the current literature has produced LPGs with 2nd order resonance bands, the fabrication parameters required to generate these features have not been elucidated. Here, using UV irradiation via the point-by-point method, it is shown that by varying the duty cycle it is possible to fabricate LPGs that exhibit 2nd, 3rd, and 4th order coupling resonance bands. Fabrication of LPGs with a 25% or 75% duty cycle produces distinct 2nd order resonance bands, which are not observed when a 50% duty cycle is adopted.

Novel dual band patch antenna With Gap coupled composite right/left-handed transmission line

AbstractA novel low profile dual band patch antenna is presented. It consists of a composite right/left-handed transmission line (CRLH TL) unit cell gap coupled with the radiating edge of a rectangular patch antenna. The dual band behavior is achieved by coupling the zeroth order resonance mode of CRLH TL and TM10 mode of the patch antenna. It is shown that frequency ratio can be changed by varying the gap between the patch and CRLH TL unit cell. The proposed configuration enables frequency reconfigurability by changing the CRLH TL unit cell using a switch. A prototype of the antenna having frequency ratio f2/f1 = 1.08 is designed and fabricated. The proposed antenna shows measured S11 ≤ −10 dB bandwidth of 100 and 50 MHz at resonance frequencies of f1 = 4.84 and f2 = 5.22 GHz, respectively. A 2 × 2 dual band CRLH TL coupled patch array is also presented, showing more than 12.7 dBi gain at both resonance frequencies.

Design and Fabrication of the Novel Miniaturized Microstrip Coupler 3dB Using Stepped Impedance Resonators for the ISM Applications

In this work, a novel miniaturized compact coupler using the shunt-stubs artificial transimission lines with high and low impedances is presented. Design of the proposed coupler is accomplished by modifying the length and impedance of the branch lines in the conventional structure with the planar resonators in order to achieve branch line coupler with compact size and improvement of the performances. First part of this work is focusing on the theorical study of the proposed resonators where the equations are obtained. Secondly, the proposed coupler is designed on FR4 susbtrate, and simulated by using the EM Solver (ADS from Agilent technologies and CST microwave studio) in order to operate in the ISM band. The obtained results show good agreement with the simulations and the coupler shows a good perfo6rmance in the hole bandwidth. The size of the proposed coupler is reduced around 50% compared to the conventional design. The last part conerns the fabrication and test of the proposed coupler. The measurement and simulation results are in good agreements.

Capture into first-order resonances and long-term stability of pairs of equal-mass planets

Massive planets form within the lifetime of protoplanetary disks and undergo orbital migration due to planet-disk interactions. When the first planet reaches the inner edge of the disk its migration stops and the second planet is locked in resonance. We detail the resonant trapping comparing semi-analytical formulae and numerical simulations in the case of two equal-mass coplanar planets trapped in first order resonances. We describe the family of resonant stable equilibrium points (zero-amplitude libration orbits) using expanded and non-expanded Hamiltonians. We show that during convergent migration the planets evolve along these families of equilibria. Eccentricity damping from the disk leads to a final equilibrium configuration that we predict analytically. The fact that observed multi-exoplanetary systems are rarely seen in resonances suggests that the resonant configurations achieved by migration can become unstable after the removal of the disk. We probe the stability of the resonances as a function of planetary mass. To do this, we fictitiously increase the masses of the planets, adiabatically maintaining the low-amplitude libration regime until instability. We discuss two hypotheses for instability: low-order secondary resonance of the libration frequency with a fast synodic frequency, and minimal approach distance between planets. We show that secondary resonances do not seem to impact resonant systems at low-amplitude of libration. Resonant systems are more stable than non-resonant ones for a given minimal distance at close encounters, but we show that the latter still play the decisive role in the destabilisation of resonant pairs. We show that, as the planetary mass increases and the minimal distance between planets gets smaller in terms of mutual Hill radius, the region of stability around the resonance center shrinks, until the equilibrium point itself becomes unstable.

Modeling Resonances of Dielectric Spheres in the Terahertz Range

We 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.

Computational Analysis of the New Approach for Studying Non-Linear Dynamics Response of a Thin Fractionally Damped Cylindrical Shell With Combinational Internal Resonance of the Second Order

Non-linear Non-linear damped vibrations of a cylindrical shell embedded into a fractional derivative medium are investigated for the case of the combinational internal resonance of the second order numerically, using two different numerical methods with further comparison of the results obtained. The damping properties of the surrounding medium are described by the fractional derivative Kelvin-Voigt model utilizing the Riemann-Liouville fractional derivatives. Within the first method, the generalized displacements of a coupled set of nonlinear ordinary differential are estimated using numerical solution of nonlinear multi-term fractional differential equations by the procedure based on the reduction of the problem to a system of fractional differential equations. According to the second method, the amplitudes and phases of nonlinear vibrations are estimated from the governing nonlinear differential equations describing amplitude-and-phase modulations for the case of the combinational internal resonance of second order. A good agreement in results is declared.

Interaction of Lower and Higher Order Hamiltonian Resonances

The tools of normal forms and recurrence are used to analyze the interaction of low and higher order resonances in Hamiltonian systems. The resonance zones where the short-periodic solutions of the low order resonances exist are characterized by small variations of the corresponding actions that match the variations of the higher order resonance; this yields cases of embedded double resonance. The resulting interaction produces periodic solutions that in some cases destabilize a resonance zone. Applications are given to the three dof [Formula: see text] resonance and to periodic FPU-chains producing unexpected nonlinear stability results and quasi-trapping phenomena.

Phase Noise Measurements of AlN Contour-Mode Resonators With Carrier Suppression Technique.

In this paper, the phase noise of aluminum nitride (AlN) contour-mode resonators is investigated using a passive measurement system with carrier suppression. The purpose is to make careful measurements of the performance of AlN resonators in order to better understand and clarify previously reported frequency instability in these devices. The resonant frequencies of the resonators are around 220 MHz. The motional parameters, the thermal behavior, and the nonlinear power effect of these resonators have been evaluated. Then, the principle of the noise measurement system is reviewed, and the resonator conditioning is shown. Finally, the noise measurements of the resonators are presented and discussed.

A Simulation of Order Resonance Phenomenon in a Supply Chain Triggered by Reinforcing Loop

A Simulation of Order Resonance Phenomenon in a Supply Chain Triggered by Reinforcing Loop