Higher-order Resonances Research Articles

Second harmonic generation in metasurfaces with multipole resonant coupling

Abstract We report on the numerical demonstration of enhanced second harmonic generation (SHG) originating from collective resonances in plasmonic nanoparticle arrays. The nonlinear optical response of the metal nanoparticles is modeled by employing a hydrodynamic nonlinear Drude model implemented into Finite-Difference Time-Domain (FDTD) simulations, and effective polarizabilities of nanoparticle multipoles in the lattice are analytically calculated at the fundamental wavelength by using a coupled dipole–quadrupole approximation. Excitation of narrow collective resonances in nanoparticle arrays with electric quadrupole (EQ) and magnetic dipole (MD) resonant coupling leads to strong linear resonance enhancement. In this work, we analyze SHG in the vicinity of the lattice resonance corresponding to different nanoparticle multipoles and explore SHG efficiency by varying the lattice periods. Coupling of electric quadrupole and magnetic dipole in the nanoparticle lattice indicates symmetry breaking and the possibility of enhanced SHG under these conditions. By varying the structure parameters, we can change the strength of electric dipole (ED), EQ, and MD polarizabilities, which can be used to control the linewidth and magnitude of SHG emission in plasmonic lattices. Engineering of lattice resonances and associated magnetic dipole resonant excitations can be used for spectrally narrow nonlinear response as the SHG can be enhanced and controlled by higher multipole excitations and their lattice resonances. We show that both ED and EQ–MD lattice coupling contribute to SHG, but the presence of strong EQ–MD coupling is important for spectrally narrow SHG and, in our structure, excitation of narrow higher-order multipole lattice resonances results in five times enhancement.

Effect of Symmetry Breaking on Plasmonic Coupling in Nanoring Dimers

Breaking the morphological and compositional symmetries of metallic nanoparticle (NP) dimers provides a novel approach to modulate plasmon coupling between the NPs. In this study, we theoretically investigate the effect of symmetry breaking on the plasmonic coupling in morphologically asymmetric Au nanoring-nanodisk (NR-ND) dimer, compositionally heterogeneous Au-Ag nanoring dimer, and compositionally as well as morphologically asymmetric Au-Ag NR-ND heterodimers. It has been found that when the inner radii of symmetrical Au NR dimer is decreased, the scattering spectral intensity of coupled bonding mode and higher-order coupled bonding mode drastically decreases and increases, respectively. Besides, the effect of aspect ratio on the plasmon resonance modes is investigated. Furthermore, with fixed geometric parameters of one NR and by morphing the shape of the other NR into ND through inner radius, we show the generation and modification of a Fano resonance. As a result of introducing morphological and compositional asymmetry separately, single Fano-type spectral feature is observed in the scattering spectra. We demonstrate that the double Fano resonances can be easily achieved in compositionally and morphologically asymmetric heterodimer with double symmetry breaking. These dual modes are caused by the interference of dipolar bright mode (localized LSPR modes) of Ag NP with the quadrupole and hexapole modes (interband transitions) of the Au NP. Finally, at optimum asymmetric heterodimers, we discussed the effect of refractive index on the Fano-type resonance. These new and simple designs provide a novel insight to modulate optical response and the generation of higher-order Fano resonances, which have many potential applications such as in photonics and refractive index sensing.

A Ku-Band Oscillator Utilizing Overtone Lithium Niobate RF-MEMS Resonator for 5G

This letter presents a 12.9-GHz silicon germanium (SiGe) Pierce oscillator using a third antisymmetric overtone in a lithium niobate (LiNbO3) resonator for 5G communications. Quarter-wave resonators are used to satisfy the Barkhausen oscillation conditions for the third overtone while suppressing the fundamental and higher order resonances. The oscillator achieves a measured phase noise of -70 and -111 dBc/Hz at 1 and 100-kHz offsets from a 12.9-GHz carrier while consuming 20 mW of dc power. The oscillator achieves a figure-of-merit of 200 dBc/Hz at 100-kHz offset, surpassing the state-of-the-art electromagnetic (EM) and overtone MEMS oscillators. The achieved oscillation frequency is the highest reported to date for an MEMS oscillator. The demonstrated performance shows the strong potential of microwave acoustic oscillators for 5G frequency synthesis. This work will enable low-power 5G transceivers featuring high speed, high sensitivity, and high selectivity in small form factors.

Optical design of connecting electrodes for tandem organic light-emitting diodes.

Connecting electrodes play a crucial role to assist charge injection into the adjacent electroluminescent units in tandem organic light-emitting diodes (OLEDs). In this study, we demonstrate that Mg:Ag alloy is an effective connecting electrode for bottom- and top-emitting tandem OLEDs. Optical cavity design and simulation are also conducted to predict the luminance of tandem OLEDs. It is found that the theoretical luminance of tandem OLEDs is close to but not higher than twofold enhancement over the luminance of a single OLED optimized to the first resonance mode, which is theoretically higher than high-order resonance modes. It is also found that the optical properties of Mg:Ag connecting electrodes, while having relatively small influence on weak microcavity bottom-emitting tandem OLEDs, have large influence on strong microcavity top-emitting tandem OLEDs.

Manipulating the frequency response of small high-frequency atomic force microscope cantilevers

We study small (less than 10 µm-long) high-frequency (greater than 1 MHz) cantilevers specially designed for visualization of biomolecular processes in high-speed atomic force microscopes. The frequency responses of the first three flexural eigenmodes are investigated for the modified geometries. It is found that the Q-factors can be significantly altered in the desired way by reengineering the cantilever geometry without affecting its main operational parameters, such as the spring constant and the resonance frequency of the first flexural eigenmode in an air environment. In addition, higher-order flexural resonances can be moved away from the fundamental resonance with these geometrical modifications. The Q-factors in liquid, on the other hand, do not show a significant difference due to high viscous damping of the medium. Regular cantilevers modified by a focused ion beam are used to demonstrate the validity of the finite element simulation model.

Wide-Angle Frequency-Scanning Array Antenna Using Dual-Layer Finger Connected Interdigital Capacitor Based CRLH Unit Cell

In this paper, a wide-angle frequency-scanning array antenna is presented for three-dimensional (3D) radar. Initially, a modified composite right/left-handed (CRLH) unit cell based on a dual-layer finger-connected interdigital capacitor (FCIDC) is analyzed. Compared with its conventional counterpart, the proposed unit cell eliminates the undesired high-order resonances and has a lower right/left-handed passband. Then, a broadband frequency-scanning feeding network, which has a large scanning angle, is designed using the proposed CRLH unit cell. The responses of the four output ports indicate that the network can offer desired amplitude and phase difference to scan towards both negative and positive elevation angles. To validate its performance, a tightly coupled planar quasi-Yagi antenna array is fed to synthesize an array antenna. The measured results show that the designed array antenna has an impedance bandwidth ($\vert \text{S}_{11}\vert <; -10$ dB) of 118.7% (2.55-10 GHz) and gains larger than 5dBi in the bulk of the band. Besides, the radiated beam can scan from -47° to 46° continuously when the frequency ranges from 3GHz to 9GHz.

Exploiting Localized Surface Plasmon Resonances in Subwavelength Spiral Disks for THz Thin Film Sensing

In this paper, we studied the sensing performance of metasurfaces comprised by spiral-disk-shaped metallic elements patterned on polypropylene substrates, which exhibited localized surface plasmon resonances in the low-frequency region of the terahertz (THz) spectrum (0.2–0.5 THz). Optimal designs of spiral disks with C-shaped resonators placed near the disks were determined and fabricated. The experimentally measured transmittance spectra of the samples coated with very thin photoresistive layers (d ~ 10−4–10−3 λ) showed good agreement with the simulations. The resonance frequency shift Δf increases with increasing d, while saturating near d = 50 µm. The narrow-band magnetic dark modes excited on symmetrical spiral disks with a 90° C-resonator demonstrated very high figure of merit (FOM) values reaching 1670 (RIU·mm)−1 at 0.3 μm thick analyte. The hybrid high order resonances excited on asymmetrical densely packed spiral disks showed about two times larger FOM values (up to 2950 (RIU·mm)−1) compared to symmetrical distantly spaced spirals that resembled the best FOM results found in the literature for metasurfaces fabricated with a similar technique. The demonstrated high sensing performance of spiral disks is evaluated to be promising for bio-sensing applications in the THz range.

On the Detuned $$2\!{:}\!4$$ Resonance

We consider families of Hamiltonian systems in two degrees of freedom with an equilibrium in 1:2 resonance. Under detuning, this "Fermi resonance" typically leads to normal modes losing their stability through period-doubling bifurcations. For cubic potentials this concerns the short axial orbits and in galactic dynamics the resulting stable periodic orbits are called "banana" orbits. Galactic potentials are symmetric with respect to the co-ordinate planes whence the potential -- and the normal form -- both have no cubic terms. This $\mathbb{Z}_2 \times \mathbb{Z}_2$-symmetry turns the 1:2 resonance into a higher order resonance and one therefore also speaks of the 2:4 resonance. In this paper we study the 2:4 resonance in its own right, not restricted to natural Hamiltonian systems where $H = T + V$ would consist of kinetic and (positional) potential energy. The short axial orbit then turns out to be dynamically stable everywhere except at a simultaneous bifurcation of banana and "anti-banana" orbits, while it is now the long axial orbit that loses and regains stability through two successive period-doubling bifurcations.

Switchable All-Dielectric Magnetic-Electric Mirror Based on Higher-Order Dipoles

Both magnetic and electric mirrors have great applied values in military, medical, and signal-transmission technology because of their electromagnetic properties. Although many kinds of artificial magnetic conductors, such as arrays of Mie resonance--based dielectric cubes or disks, have been demonstrated to be able to approximate a magnetic mirror, most of them, however, work within a narrow and invariable frequency band, and most attention is paid to magnetic dipole resonance of first order. Here, we investigate the resonant mechanism of dielectric cuboids and employ the dipole resonance of higher order to obtain a bifunctional and reconfigurable all-dielectric electric and magnetic mirror controlled by temperature. A prototype device is designed and fabricated with $\mathrm{Ca}$-${\mathrm{La}}_{2}{\mathrm{O}}_{3}$-${\mathrm{Ti}\mathrm{O}}_{2}$ ferroelectric cuboids as building blocks, and its reflecting effects are successfully demonstrated, as well as the tunability of working frequency by varying temperature. Moreover, electric and magnetic dipole resonances of higher order are proved to have superior resonant characteristics to the primary ones, which can effectively suppress the spectral overlapping between the adjacent magnetic and electric resonances and thus makes such all-dielectric reflector possible to switch between magnetic mirror and electric mirror. Furthermore, the proposed cuboids have the potential to expand to active phase-control metasurface devices and Huygens' sources with better impedance matching. Our work reveals the specific optical properties of higher-order dipolar resonances and opens the door towards the realization of tunable and reconfigurable magnetic-electric mirrors.

Optical multi-stability in a nonlinear high-order microring resonator filter

We theoretically analyze and experimentally demonstrate optical bi-stability and multi-stability in an integrated nonlinear high-order microring resonator filter based on high-index contrast doped silica glass. We use a nonlinear model accounting for both the Kerr and thermal effects to analyze the instability behavior of the coupled-resonator based filter. The model also accurately predicts the multi-stable behavior of the filter when the input frequency is slightly detuned. To understand the role of the intracavity power distribution, we investigate the detuning of the individual rings of the filter from the optical response with a pump–probe experiment. Such a measurement is performed scanning the filter with a low-power probe beam tuned a few free spectral ranges away from the resonance where the pump is coupled. A comprehensive understanding of the relationship between the nonlinear behavior and the intracavity power distribution for the high-order microring resonator filter will help the design and implementation of future all-optical switching systems using this type of filter.

Design, control and comparative analysis of an LCLC coupling hybrid active power filter

This study provides the design, control and comparative analysis of the proposed LCLC coupling hybrid active power filter (LCLC-HAPF). Compared with the conventional L filter coupling active power filters (APFs), LC filter and LCL filter coupling HAPFs (LC-HAPFs and LCL-HAPFs), the proposed LCLC-HAPF provides better switching frequency harmonics elimination, lower dc-link voltage rating and switching loss. Although the LCLC-HAPF has some advantages, two main challenges will still be confronted in practical implementations. Those are stability problems caused by resonance of LCLC filter, and parameter design for the LCLC filter. In this study, a new active damping method is proposed to overcome the high order resonance problem existing in the proposed LCLC-HAPF. After that, the stability analysis and parameter design are given for the proposed LCLC-HAPF. Finally, the effectiveness of the proposed LCLC-HAPF topology is validated through both simulation and experimental studies in comparison with the conventional APFs and HAPFs.

Bound states in the continuum of higher-order topological insulators

We show that lattices with higher-order topology can support corner-localized bound states in the continuum (BICs). We propose a method for the direct identification of BICs in condensed matter settings and use it to demonstrate the existence of BICs in a concrete lattice model. Although the onset for these states is given by corner-induced filling anomalies in certain topological crystalline phases, additional symmetries are required to protect the BICs from hybridizing with their degenerate bulk states. We demonstrate the protection mechanism for BICs in this model and show how breaking this mechanism transforms the BICs into higher-order topological resonances. Our work shows that topological states arising from the bulk-boundary correspondence in topological phases are more robust than previously expected, expanding the search space for crystalline topological phases to include those with boundary-localized BICs or resonances.

Dynamics of a non-linearly damped microresonator under parametric excitation and its application in developing sensitive inertial sensors with ultra-wide dynamic ranges

We model and investigate the response of a nonlinear cantilever beam under principal parametric excitation. The design is initially assessed, optimized, and tuned using three-dimensional finite element analysis (FEA) to ensure the presence of fundamental parametric resonance and the absence of other internal and higher-order parametric resonances. The derived governing differential equation represents a modified generalized parametrically excited dynamic system under principal parametric excitation. The nonlinear dynamic system is developed and presented in the context of resonators with extensive applications in developing sensors, filters, and switches. The quadratic and cubic nonlinearities include second- and third-order deflection, velocity, acceleration terms describing stiffness, damping, and inertial nonlinearities. To explore and investigate the corresponding generalized nonlinear Mathieu equation, the method of multiple-scales along with the reconstitution method are used and modulation equations are obtained and solved to obtain closed-form amplitude and phase equations. The quadratic damping is modeled and approximated using a Fourier series and analytical models are generated in both Cartesian and Polar frames. To further explore the dynamic system and its applications, a resonator is designed to measure external acceleration and investigated for two cases. It is discussed and shown how the external acceleration modifies the dynamic system, the corresponding reduced-order model, and the modulation equations. The external acceleration affects the amplitude, phase, and frequency of oscillation providing means to estimate the input. These results indicate that the proposed resonator design (dynamic system) is able to significantly improve the dynamic range of shock/acceleration sensors.

Structural Colors Enabled by Lattice Resonance on Silicon Nitride Metasurfaces

Artificial color pixels based on dielectric Mie resonators are appealing for scientific research as well as practical design. Vivid colors are imperative for displays and imaging. Dielectric metasurface-based artificial pixels are promising candidates for developing flat, flexible, and/or wearable displays. Considering the application feasibility of artificial color pixels, wide color gamuts are crucial for contemporary display technology. To achieve a wide color gamut, ensuring the purity and efficiency of nanostructure resonance peaks in the visible spectrum is necessary for structural color design. Low-loss dielectric materials are suitable for achieving vivid colors with structural color pixels. However, high-order Mie resonances prevent color pixels based on dielectric metasurfaces from efficiently generating highly saturated colors. In particular, fundamental Mie resonances (electric/magnetic dipole) for red can result in not only a strong resonance peak at 650 nm, but also high-order Mie resonances at shorter wavelengths, which reduces the saturation of the target color. To address these problems, we fabricated silicon nitride metasurfaces on quartz substrates and applied Rayleigh anomalies at relatively short wavelengths to successfully suppress high-order Mie resonances, thus creating vivid color pixels. We performed numerical design, semianalytic considerations, and experimental proof-of-concept examinations to demonstrate the performance of the silicon nitride metasurfaces. Apart from traditional metasurface designs that involve transmission and reflection modes, we determined that lateral light incidence on silicon nitride metasurfaces can provide vivid colors through long-range dipole interactions; this can thus extend the applications of such surfaces to eyewear displays and guided-wave illumination techniques.

Time-step dependent force interpolation scheme for suppressing numerical Cherenkov instability in relativistic particle-in-cell simulations

The WT scheme, a piecewise polynomial force interpolation scheme with time-step dependency, is proposed in this paper for relativistic particle-in-cell (PIC) simulations. The WT scheme removes the lowest order numerical Cherenkov instability (NCI) growth rate for arbitrary time steps allowed by the Courant condition. While NCI from higher order resonances is still present, the numerical tests show that for smaller time steps, the numerical instability grows much slower than using the optimal time step found in previous studies. The WT scheme is efficient for improving the quality and flexibility of relativistic PIC simulations.

Ultra-narrowband dielectric metamaterial absorber for sensing based on cavity-coupled phase resonance

We propose an ultra-narrowband dielectric metamaterial absorber with dielectric-dielectric-metal (DDM) structure where a dielectric cavity layer is inserted between the top compound periodic dielectric microstructures and bottom metal substrate. The results show that this absorber has an ultra-narrowband absorption with a full width at half-maximum (FWHM) of 0.028 nm and quality factor larger than 50,000 in the near-infrared regime. The electric field distribution shows that the phase resonance excited in the microstructures slits is coupled with the cavity resonance occurring in the middle dielectric layer which can greatly narrow the absorption bandwidth. More importantly, the absorption bandwidth can be flexibly manipulated by adjusting the thickness of the dielectric cavity layer. Due to the ultra-narrow absorption bandwidths and electric field concentrated in the slits, we can get a huge figure of merit (FOM) of 6731 which is much larger than those of the reported absorbers in the near-infrared regime. In addition, the larger FOM of 20,366 can be attained with higher-order mode resonance in the dielectric cavity layer. The proposed metamaterials have the great potentials in sensing applications.

Nekhoroshev Estimates for the Survival Time of Tightly Packed Planetary Systems

Abstract N-body simulations of nonresonant, tightly packed planetary systems have found that their survival time (i.e., time to first close encounter) grows exponentially with their interplanetary spacing and planetary masses. Although this result has important consequences for the assembly of planetary systems by giant collisions and their long-term evolution, this underlying exponential dependence is not understood from first principles, and previous attempts based on orbital diffusion have only yielded power-law scalings. We propose a different picture, where large deviations of the system from its initial conditions is due to a few slowly developing high-order resonances. Thus, we show that the survival time of the system T can be estimated using a heuristic motivated by Nekhoroshev’s theorem, and obtain a formula for systems away from overlapping two-body mean-motion resonances as , where P is the average Keplerian period, a is the average semimajor axis, Δa ≪ a is the difference between the semimajor axes of neighboring planets, μ is the planet-to-star mass ratio, and c 1 and c 2 are dimensionless constants. We show that this formula is in good agreement with numerical N-body experiments for c 1 = 5 × 10−4 and c 2 = 8.

Local Ultrasonic Resonance Spectroscopy: A Demonstration on Plate Inspection

Local ultrasonic resonance spectroscopy (LURS) is a new approach to ultrasound signal analysis, which was necessitated by a novel inspection method capable of the contact-free, localized, broadband generation and detection of ultrasound. By performing a LURS scan, it is possible to detect local mechanical resonances of various features and of the specimen itself. They are highly sensitive to local mechanical properties. By observing different parameters in the frequency spectrum (e.g., resonance amplitude and resonance peak frequency), geometrical, material and condition properties can be visualized for all of the scanning positions. We demonstrate LURS for inspection of a carbon fiber reinforced polymer plate. Local defect resonances of delaminations and a flat-bottom hole were detected in the frequency range from 25 to 110 kHz. Analyzing the higher frequency range (0.3 MHz to 1.5 MHz) of the same scan, the shift of the thickness resonance frequency of the plate and its higher-order resonance frequencies carry the information about the aluminum inclusions. LURS shows an advantage in characterizing the localized features of the specimens via contact-free ultrasonic inspection.

Studying localized surface plasmon resonances in the THz region for subwavelength spiral disks

Spoof localized surface plasmon resonances (LSPRs) in the THz range are promising for bio-sensing and spectroscopy. Using long spiral grooves allows improving the surface mode confinement of LSPRs in the long-wavelength region. Our numerical simulations of sub-wavelength spiral gold disks in the range of 0.04–6 THz have shown that in case of Drude conductivity and normal incidence of EM radiation only the first- and second-order dipole localized surface plasmon resonances (LSPRs) are excited. High order resonances arise at inclined incidence. The spectra and 2D distributions of the EM field at the resonant frequencies depend on the number of spiral arms and symmetry of the spiral structure.

High-sensitivity temperature sensor based on Fano resonance in an optofluidic microcapillary resonator.

In this paper we demonstrate a high-sensitivity temperature sensor based on high-order Fano resonance (FR) in an optofluidic microcapillary resonator. High-order FR modes (Q∼3000) are excited in an ethanol-filled optofluidic microcapillary resonator for temperature sensing. Due to the high thermo-optic coefficient of ethanol and a large energy fraction of high-order modes in the core liquid, the sensitivity as high as -0.402nm/∘C and the detection limit of 0.026°C can be achieved. Also the sensitivity and free spectral range of different order radial modes are calculated theoretically. The experimental results agree well with the theoretical results. Through the comparison between the theoretical and experimental results, the radial order number of the mode used for temperature sensing is estimated to be 10.