Third-order Signal Research Articles

Third-Harmonic and Intermodulation Distortion in Bulk Acoustic-Wave Resonators

This article discusses on the measured third-order intermodulation (IMD3) products and third harmonics (H3) appearing in a set of six different solidly mounted resonators (SMR) and bulk acoustic-wave (BAW) resonators with different shapes and stack configurations. The discussion is supported by a comprehensive nonlinear distributed circuit model that considers the nonlinear effects potentially occurring in any layer of the resonator stack. The aluminum-nitride (AlN) and silicon-dioxide (SiO2) layers are identified as the most significant contributors to the IMD3 and H3. The frequency profile of the third-order spurious signals also reveals that, in temperature-compensated resonators, where the SiO2 layers are usually thicker, the remixing effects from the second-order nonlinear terms are the major contributors to the IMD3 and H3. These second-order terms are those that explain the second-harmonic (H2) generation, whose measurements are also reported in this article. Unique values of the nonlinear material constants can explain all the measurements despite the resonators have different shapes, resonance frequencies, and stack configurations.

A refined PCPF algorithm for estimating the parameters of multicomponent polynomial-phase signals

This paper considers the parameter estimation of multicomponent polynomial-phase signals (mc-PPSs) with orders greater than two. The proposed method combines the product cubic phase function (PCPF) and high-order ambiguity function (HAF) when the mc-PPS orders exceed three. In the proposed method, the HAF is first applied to the observed mc-PPS to produce a cubic phase signal. Second, the algorithm is modified to estimate the parameters of mc-PPS using the CPF. To obtain accurate estimates of the two highest-order parameters (i.e., $$ a_{P} $$ and $$ a_{P - 1} $$ of each component), all possible $$ a_{P} $$ and $$ a_{P - 1} $$ must be obtained in this step in all combinations of the instantaneous frequencies; then, the maximum absolute value of all sum values must be identified by dechirping with all possible $$ a_{P} $$ and $$ a_{P - 1} $$ . In addition, non-uniformly-spaced signal sample methods are used to employ fast Fourier transformation in the CPF. The proposed method is different from the PCPF–HAF method proposed by other researchers; it is referred to as the improved PCPF–HAF method and can remedy the shortcomings of the traditional method when estimating mc-PPS parameters. Additionally, the PCPF–HAF method cannot be used to treat multicomponent third-order polynomial-phase signals, but the proposed method can treat them using non-uniformly-spaced signal sample methods. The cross-terms can also be restrained more effectively than with the CPF, resulting in higher accuracy of the estimated parameters and a lower signal-to noise ratio threshold. Theoretical analysis and simulations are presented to support these claims.

Theory of three-pulse photon echo spectroscopy with dual frequency combs

A theoretical analysis is carried out for the recently developed three-pulse photon echo spectroscopy employing dual frequency combs (DFC) as the light sources. In this method, the molecular sample interacts with three pulse trains derived from the DFC and the generated third-order signal is displayed as a two-dimensional (2D) spectrum that depends on the waiting time introduced by employing asynchronous optical sampling method. Through the analysis of the heterodyne-detected signal interferogram using a local oscillator derived from one of the optical frequency combs, we show that the 2D spectrum closely matches the spectrum expected from a conventional approach with four pulses derived from a single femtosecond laser pulse and the waiting time between the second and third field-matter interactions is given by the down-converted detection time of the interferogram. The theoretical result is applied to a two-level model system with solvation effect described by solvatochromic spectral density. The model 2D spectrum reproduces spectral features such as the loss of frequency correlation, dephasing, and spectral shift as a function of the population time. We anticipate that the present theory will be the general framework for quantitative descriptions of DFC-based nonlinear optical spectroscopy.

Power quality improvement of single phase weak grid interfaced hybrid solar PV and wind system using double fundamental signal extracter‐based control

In this study, a double fundamental signal extracter using third-order signal integrator-based control technique is used for the improvement of power quality of single phase grid interfaced with hybrid wind energy generation system (WEGS) and solar photovoltaic (PV) array under weak grid conditions. The control algorithm is proposed for the extraction of dual fundamental components of load current and to extract fundamental grid voltage for synchronisation to the grid. The main objective of the system is to establish secure, reliable and safe integration while mitigating several power quality issues such as total harmonic distortion (THD) of the grid current, DC current injection. The system operates in distribution static compensator mode in the absence of renewable energy sources and also, maintains the grid current THD as per the limit of the IEEE-519 standard. For optimal power extraction from WEGS as well as the solar PV array, perturb and observe algorithm is used. The prototype developed in the laboratory is tested under different operating conditions such as variable wind speed, grid voltage sag/swell, variable solar insolation, and varying load conditions.

The ultra-sensitive visual biosensor based on thermostatic triple step functional nucleic acid cascade amplification for detecting Zn2+

Here, we present an ultra-sensitive visual biosensor based on thermostatic triple step functional nucleic acid cascade amplification for detecting Zn2+. A Zn2+-assisted cDNAzyme assay is conducted and the Zn2+ is successfully converted into nucleic acids to achieve the first circular amplification within 1 h. The cleavage products prompted Hybridization Chain Reaction (HCR), forming multiple DNA nanowire structures with branched chains. And the Strand Displacement Amplification (SDA) were further empowered by the HCR products with the addition of the amplification enzyme and the endonuclease. In just 80 min, the second and third-order signal amplifications are reached. With the addition of Hemin and chromogenic substrates, the visual signal output is achieved in 15 min based on the large amount of G-quadruplex (G4) DNAzymes. This biosensor can detect levels as low as 1.075 pM Zn2+, showing a good linear range within 10 pM–100 nM. It shows considerable potential for the Zn2+ quantitative detection.

Simplification of control design for driftless nonholonomic systems based on rough path anlaysis

This paper provides a strict system formulation for a class of nonholonomic systems with Lie bracket motions via rough path analysis. The dynamics of the resulting systems are represented by rough differential equations as augmented versions of ordinary differential equations. The rough differential equations are allowed to have rough signals generated by unbounded-variation functions and derived by classifying the functions according to “orders” of the boundedness. This paper clarifies rough differential equations driven by third-order rough signals, and the validity for control design problems is confirmed by considering a fourth-order chained system, which is a typical form of driftless affine nonholonomic systems.

A Modulator-Free Photonic Triangular Pulse Generator Based on Semiconductor Lasers

A modulator-free photonic triangular pulse generator is proposed and demonstrated based on two semiconductor lasers. In this method, a direct-modulated semiconductor laser is employed to generate a fundamental frequency component. Meanwhile, a third-order harmonic signal is generated by external optical injection together with 1/3 subharmonic microwave modulation of another semiconductor laser. After properly setting the amplitude and time delay between the fundamental and third-order harmonics, the combined signal composes a triangular waveform. The generation of a 11.4-GHz triangular pulse train is experimentally demonstrated. Without using any modulator, the proposed approach is a promising method for triangular pulse generation with low cost and simple structure.

Tunable high-order single-sideband signal generator with optical carrier suppression using dual-parallel Mach–Zehnder modulator

A tunable high-order single-sideband signal generator with optical carrier suppression (SSB-OCS generator) is proposed, which is based on frequency multiplication operation using dual-parallel Mach–Zehnder modulator (DPMZM) and Mach–Zehnder interferometer (MZI). By changing all the modulators at maximum or minimum transmission point simultaneously, the amplitude of input radio frequency (RF) signals and the phase difference between input RF signals, two high-order even or odd signals with opposite amplitude of one sideband, are generated by upper DPMZM and lower DPMZM, respectively. Then, two optical signals are coupled to reserve one sideband, and the coupled SSB-OCS signal is injected into an MZI to suppress high-order intermodulation components. The simulated results show that the first-, second-, and third-order SSB-OCS signals can be achieved, and the suppression ratio is over 30 dB, which agrees well with the theoretical prediction. This scheme is featured by the capability to generate tunable high-order SSB-OCS signal with high suppression ratio, and the operation is simple and flexible. Finally, an experiment was carried out to demonstrate the feasibility of the proposed scheme, and a first- and second-order SSB-OCS signal were obtained, respectively, and the suppression ratio is over 24 dB.

Axial point source localization using variable displacement–change point detection

A three-dimensional point-source localization technique is demonstrated using two-photon photoluminescence and four-wave mixing nonlinear optical signals from plasmonic gold nanorods (AuNRs), imaged at the single-particle level. Introduction of position-dependent latitudinal astigmatisms into the imaging system, in combination with a change point detection (CPD) algorithm, resulted in localization of single particles with high precision in three dimensions. Astigmatisms were generated using axial sample-position displacements spanning the range from ±10 to ±90 nm with a minimum step-size resolution of ±3 nm. Based on the current data, 20 nm point source localization was achieved in the axial dimension using a single imaging objective. This technique is named variable displacement–change point detection (VD-CPD). The influence of plasmon enhancement on achievable axial localization was also quantified. Two AuNR systems with different length-to-diameter aspect ratios (AR, where AR=1.86 and 3.90) were selected for this purpose; the AR=1.86 and AR=3.90 had nonresonant and resonant longitudinal surface plasmon resonances (LSPR) energies, respectively, with the laser fundamental. Matching the fundamental wave LSPR energies resulted in increased axial localizations. Power-dependent analysis of the LSPR-mediated nonlinear optical images revealed that resonantly excited AuNRs results in third-order signals. The axial localization provided by VD-CPD exceeds what could be obtained using astigmatic imaging alone by a factor of 2.5. This advance will facilitate the in-depth study of photonic materials and complex biological environments that can benefit from increased axial position determinations.

Communication: Probing the interaction of infrared antenna arrays and molecular films with ultrafast quantum dynamics.

Narrowband vibrational molecular transitions interacting with the broadband resonance of infrared plasmonic antennas lead to Fano lineshapes observed in linear (FTIR) and third-order (transient absorption and 2DIR) spectroscopic experiments. Both molecular and plasmonic components are inherently dissipative, and the effects associated with their coupling can be observed, in principle, when measuring the corresponding ultrafast quantum dynamics. We used 2DIR spectroscopy to study the waiting time evolution of quantum coherence excited in the carbonyl stretching modes of rhodium (acetylacetonato) dicarbonyl molecules, which were embedded in an 80 nm-thick polymer film spin-coated on an array of infrared half-wavelength gold antennas. Despite the pronounced Fano lineshapes obtained for the molecular transitions, and up to a four order of magnitude enhancement of the third-order signals, which taken together, indicate the coupling between the plasmonic and molecular transitions, the dynamics of the quantum coherence were identical to that obtained with 3 μm-thick film without the interaction with the plamson mode. This suggests that the coupling rate between the molecular and plasmonic excitations is significantly smaller than the relaxation rates of the molecular excitations monitored in the experiment. Here, the Fano lineshape, observed at the frequency of the molecular transition, can result from the mutual radiation damping of the molecular and plasmon modes.

Modelling nonlinearity in superconducting split ring resonator and its effects on metamaterial structures

Superconducting materials are intrinsically nonlinear, because of nonlinear Meissner effect (NLME). Considering nonlinear behaviors, such as harmonic generation and intermodulation distortion (IMD) in superconducting structures, are very important. In this paper, we proposed distributed nonlinear circuit model for superconducting split ring resonators (SSRRs). This model can be analyzed by using Harmonic Balance method (HB) as a nonlinear solver. Thereafter, we considered a superconducting metamaterial filter which was based on split ring resonators and we calculated fundamental and third-order IMD signals. There are good agreement between nonlinear results from proposed model and measured ones. Additionally, based on the proposed nonlinear model and by using a novel method, we considered nonlinear effects on main parameters in the superconducting metamaterial structures such as phase constant (β) and attenuation factor (α).

Control scheme for grid‐tied distributed generation inverter under unbalanced and distorted utility conditions with power quality ancillary services

This study proposes a control scheme with a new fundamental sequence components extractor for grid interfaced distributed generation inverter under polluted grid conditions. The proposed sequence extractor is realised using third-order sinusoidal signal integrator-based frequency adaptive filters. It has an excellent ability to decompose the three-phase voltage and current signals into positive and negative sequence components under distorted grid scenario. The proposed control scheme is immune to frequency variations and is capable of providing power quality ancillary services such as reactive power compensation and harmonics rejection in addition to basic power injection. The performance of the proposed system under various grid disturbances and loading conditions is evaluated through simulation and experimental studies.

On-chip temperature-compensated Love mode surface acoustic wave device for gravimetric sensing

Love mode surface acoustic wave (SAW) sensors have been recognized as one of the most sensitive devices for gravimetric sensors in liquid environments such as bio sensors. Device operation is based upon measuring changes in the transmitted (S21) frequency and phase of the first-order Love wave resonance associated with the device upon on attachment of mass. However, temperature variations also cause a change in the first order S21 parameters. In this work, shallow grooved reflectors and a “dotted” single phase unidirectional interdigitated transducer (D-SPUDT) have been added to the basic SAW structure, which promote unidirectional Love wave propagation from the device's input interdigitated transducers. Not only does this enhance the first-order S21 signal but also it allows propagation of a third-order Love wave. The attenuation coefficient of the third-order wave is sufficiently great that, whilst there is a clear reflected S11 signal, the third-order wave does not propagate into the gravimetric sensing area of the device. As a result, whilst the third-order S11 signal is affected by temperature changes, it is unaffected by mass attachment in the sensing area. It is shown that this signal can be used to remove temperature effects from the first-order S21 signal in real time. This allows gravimetric sensing to take place in an environment without the need for any other temperature measurement or temperature control; this is a particular requirement of gravimetric biosensors.

Photonic Generation of Reconfigurable Orders Ultrawideband Signals by Using Cascaded RSOAs

We experimentally demonstrate an ultrawideband (UWB) signals generation scheme with reconfigurable orders using cascaded reflective semiconductor optical amplifiers. Through controlling the gain saturation effect of this cascaded structure, a quasi-high-pass radio frequency filter with tunable cutoff frequency is realized. After passing through this filter, the coded Gaussian like pulse is converted to first-, second-, and third-order UWB signals. All achieved UWB signals accord with the Federal Communications Commission regulations and the third-order UWB signal can eliminate interference with other wireless communications in low frequency range.

Simple Recipes for Separating Excited-State Absorption and Cascading Signals by Polarization-Sensitive Measurements

The dependence of four-wave mixing and six-wave mixing signals on the polarization of the laser pulses is analyzed. Assuming that the dipole moments of the electronic transitions are not all parallel, we show that the excited-state absorption signal can be separated from the total pump-probe signal by two measurements with different polarizations of the pump and probe pulses. We show, furthermore, that cascading (third-order) signals can be separated from the fifth-order signal by two polarization-sensitive six-wave mixing measurements. We provide simple explicit formulas that express the excited-state absorption and cascading contributions, respectively, in terms of polarization-sensitive signals.

Fully absorptive 3D IR spectroscopy using a dual mid-infrared pulse shaper.

This paper presents the implementation of 3D IR spectroscopy by adding a second pump beam to a two-beam 2D IR spectrometer. An independent mid-IR pulse shaper is used for each pump beam, which can be programmed to collect its corresponding dimension in either the frequency or time-domains. Due to the phase matching geometry employed here, absorptive 3D IR spectra are automatically obtained, since all four of the rephasing and non-rephasing signals necessary to generate absorptive spectra are collected simultaneously. Phase cycling is used to isolate the fifth-order from the third-order signals. The method is demonstrated on tungsten hexacarbonyl (W(CO)6) and dicarbonylacetylacetonato rhodium (I), for which the eigenstates are extracted up to the third excited state. Pulse shaping affords a high degree of control over 3D IR experiments by making possible mixed time- and frequency-domain experiments, fast data acquisition and straightforward implementation.

Polaron dynamics in two-dimensional photon-echo spectroscopy of molecular rings

We have developed a new approach to the computation of third-order spectroscopic signals of molecular rings, by incorporating the Davydov soliton theory into the nonlinear response function formalism. The Davydov D1 and D Ansätze have been employed to treat the interactions between the excitons and the primary phonons, allowing for a full description of arbitrary exciton-phonon coupling strengths. As an illustration, we have simulated a series of optical 2D spectra for two models of molecular rings.

Perception of second- and third-order orientation signals and their interactions

Orientation signals, which are crucial to many aspects of visual function, are more complex and varied in the natural world than in the stimuli typically used for laboratory investigation. Gratings and lines have a single orientation, but in natural stimuli, local features have multiple orientations, and multiple orientations can occur even at the same location. Moreover, orientation cues can arise not only from pairwise spatial correlations, but from higher-order ones as well. To investigate these orientation cues and how they interact, we examined segmentation performance for visual textures in which the strengths of different kinds of orientation cues were varied independently, while controlling potential confounds such as differences in luminance statistics. Second-order cues (the kind present in gratings) at different orientations are largely processed independently: There is no cancellation of positive and negative signals at orientations that differ by 45°. Third-order orientation cues are readily detected and interact only minimally with second-order cues. However, they combine across orientations in a different way: Positive and negative signals largely cancel if the orientations differ by 90°. Two additional elements are superimposed on this picture. First, corners play a special role. When second-order orientation cues combine to produce corners, they provide a stronger signal for texture segregation than can be accounted for by their individual effects. Second, while the object versus background distinction does not influence processing of second-order orientation cues, this distinction influences the processing of third-order orientation cues.

Calculation of third-order signals via driven Schrödinger equations: General results and application to electronic 2D photon echo spectroscopy

We present the wavefunction (WF) version of the equation-of-motion phase-matching approach (EOM-PMA) for the calculation of four-wave-mixing (4WM) optical signals. For the material system, we consider a general electronic-vibrational Hamiltonian, comprising the electronic ground state, a manifold of singly-excited electronic states, and a manifold of doubly-excited electronic states. We show that the calculation of the third-order polarization for particular values of the pulse delay times and in a specific phase-matching direction requires 6 independent WF propagations within the rotating wave approximation. For material systems without optical transitions to doubly-excited electronic states, the number of WF propagations is reduced to 5. The WF EOM-PMA automatically accounts for pulse-overlap effects and allows the efficient numerical calculation of 4WM signals for vibronically coupled multimode material systems. The application of the method is illustrated for model systems with strong electron-vibrational and electronic inter-state couplings.

Design of Circular Polarization Antenna With Harmonic Suppression for Rectenna Application

A microstrip antenna design that effectively attains circular polarization (CP) and harmonic suppression is proposed. By modifying the size and position of two peripheral cuts, two orthogonal modes that have equal amplitude and are 90 out of phase are simultaneously excited. The four right-angle slits embedded in the antenna can block the second- and third-order harmonic signals. This property is especially suitable for nonlinear circuit applications, such as active integrated antenna (AIA) and rectifying antenna (rectenna). The adopted CP antenna built on a low-cost FR4 substrate has a measured bandwidth of 137 MHz (10-dB return loss) and a 30-MHz CP bandwidth (3-dB axial ratio). A rectenna that comprises the proposed antenna and a rectifying circuit is built for verifying the characteristics of the proposed antenna. The measured results of the proposed antenna are in good performances and steady efficiency.