Multimode Oscillator Research Articles

Some Results on Oscillation Stability in Multi-Mode Harmonic Oscillators

We study the stability of oscillation in two different multi-mode harmonic oscillators by means of Barkhausen’s criterion, involving a minimum of mathematical machinery in favor of a more intuitive, circuit-based approach. The results of the theoretical analysis match very closely those obtained through transient simulations, confirming occasionally surprising outcomes of the latter.

Tunable Microwave Frequency Comb Generation Based on Actively Mode-Locked OEO

A novel photonics-assisted method for tunable microwave frequency comb (MFC) generation based on an actively mode-locked optoelectronic oscillator (AML-OEO) is proposed and experimentally demonstrated in this letter. Two key factors for the proposed system, periodic gain modulation and widely tunable center frequency, are implemented by an externally introduced intensity-modulated optical signal and a microwave photonic filter (MPF) based on the phase-shifted fiber Bragg grating (PS-FBG) respectively. Unlike a conventional OEO with only one dominant oscillation mode, an AML-OEO operates in a stable multimode oscillation state and thus can generate MFC signal. Through simply adjusting the center frequency of the PS-FBG-based MPF, the center frequency of the generated MFC changes accordingly. In the proof-of-principle experiment, two sets of MFC signals with center frequency tuning from 3.5 GHz to 6.5 GHz and frequency intervals of 1.02 MHz and 340.46 kHz are generated.

Coherent Quantum LQG Controllers with Luenberger Dynamics

This paper is concerned with the coherent quantum linear-quadratic-Gaussian control problem of minimising an infinite-horizon mean square cost for a measurement-free field-mediated interconnection of a quantum plant with a stabilising quantum controller. The plant and the controller are multimode open quantum harmonic oscillators, governed by linear quantum stochastic differential equations and coupled to each other and the external multichannel bosonic fields in the vacuum state. We discuss an interplay between the quantum physical realizability conditions and the Luenberger structure associated with the classical separation principle. This leads to a quadratic constraint on the controller gain matrices, which is formulated in the framework of a swapping transformation for the conjugate positions and momenta in the canonical representation of the controller variables. For the class of coherent quantum controllers with the Luenberger dynamics, we obtain first-order necessary conditions of optimality in the form of algebraic equations, involving a matrix-valued Lagrange multiplier.

Nanoscale subparticle imaging of vibrational dynamics using dark-field ultrafast transmission electron microscopy

An understanding of nanoscale energy transport and acoustic response is important for applications of nanomaterials but hinges on a complete characterization of their structural dynamics. The precise determination of the structural dynamics within nanoparticles, however, is still challenging and requires high spatiotemporal resolution and detection sensitivity. Here we present a centred dark-field imaging approach based on ultrafast transmission electron microscopy that is capable of directly mapping the picosecond-scale evolution of intrananoparticle vibration with a spatial resolution down to 3 nm. Using this approach, we investigated the photo-induced vibrational dynamics in individual gold heterodimers composed of a nanoprism and a nanosphere. We observed not only the retardation of in-plane vibrations in the nanoprisms, which we attribute to thermal and vibrational energy transferred from adjacent nanospheres mediated by surfactants, but also the existence of a complex multimodal oscillation and its spatial variation within individual nanoprisms. This work represents an advance in real-space mapping of vibrational dynamics on the subnanoparticle level with a high detection sensitivity.

Differential evolution reveals the effect of polar and nonpolar solvents on carotenoids: A case study of astaxanthin optical response modeling

• Unique software that simulates optical response of biological pigments was developed • Differential evolution is used for finding the best model to fit experimental data • Multimode Brownian oscillator models were created to simulate carotenoid absorption • The optimal settings of Differential evolution allowing fast convergence were found • Differential evolution allowed distinguishing models for polar and nonpolar solvents The task to simulate realistic absorption spectra of electronic transitions in pigment molecules takes the form of the art of optimization, particularly if one must choose between the quality of the results obtained and the calculation time necessary to get such quality. The semiclassical theory of optical response provides us with a good opportunity to escape a so-called sum-over-state procedure of considering the innumerable number of vibronic states of a pigment by applying a correlation function approach. This approach, known as the multimode Brownian oscillator model (MBOM), involves replacing an infinite set of vibronic states, which interacts with an electronic transition, with a finite set of effective vibronic modes. Thus, the parameters of effective vibronic modes and an electronic transition can be found only by fitting experimental data. This situation gives rise to the following problem: as the number of free parameters increases, it becomes more difficult to find a single solution. To overcome this obstacle, differential evolution (DE), a method of global optimization, which is based on the idea of natural selection, seems to be the right choice. To test the efficiency of DE in solving quantum mechanical problems, we simulated absorption spectra of astaxanthin (AST) in 18 different organic solvents by using the MBOM. To do so, we developed software that implements both the DE algorithm and linear absorption modeling procedures. We have shown that simulating practically identical AST spectra, DE allows determining the effect of polar and nonpolar solvents on several parameters of MBOM of AST with high accuracy.

Vortex-induced vibration of a two degree-of-freedom flexibly mounted circular cylinder in the crossflow direction

Vortex-induced vibration (VIV) of a two degree-of-freedom (DOF) circular cylinder, placed in the test section of a recirculating water tunnel and free to oscillate in its first two vibrational modes in the crossflow direction, is studied experimentally. The dynamic response of the cylinder is studied for a reduced velocity range of $U^*=4\unicode{x2013}30$ for eigenfrequency ratios in the range of 1.3–3.0. For the two DOF system, while the onset of the VIV response followed a similar lock-in region as those observed for a classical VIV response of a single DOF system, by increasing the reduced velocity a secondary lock-in region was observed over which the oscillations of the cylinder were locked into the system's second mode. In addition, there existed an intermediate range of reduced velocity over which the VIV response consisted of oscillations at a combination of the first two natural modes of the system. As the eigenfrequency ratio between the first two modes increased, the secondary lock-in range was extended to higher reduced velocities and the reduced velocity range over which multi-modal oscillations were observed was decreased. A full map of vortex dynamics in the wake of the cylinder was developed qualitatively and quantitatively using hydrogen bubble flow visualization and time-resolved volumetric particle tracking velocimetry techniques, respectively. A Q-criterion analysis revealed the existence of highly three-dimensional vortex structures in the wake of the cylinder. The spatiotemporal mode analysis using the proper orthogonal decomposition technique revealed strong coupling between the vortex shedding modes in the wake of the cylinder and the structural vibration modes.

Tunable Microwave Pulse Generation Based on an Actively Mode-Locked Optoelectronic Oscillator

A tunable microwave-pulse-generation scheme is proposed and demonstrated by employing an actively mode-locked optoelectronic oscillator (OEO) based on a microwave photonic filter (MPF). The MPF mainly consists of a phase-shifted fiber Bragg grating (PS-FBG) and a phase modulator. The microwave pulse trains with variable repetition rates are achieved by injecting an external signal, of which the frequencies are equal to an integer multiple of the free spectrum range (FSR) of the OEO. The multi-mode oscillation mechanism is discussed in detail theoretically and experimentally. A microwave pulse train with a central frequency of 9.25 GHz and repetition rate of 1.68 MHz is demonstrated by setting the injecting signal frequency to be the same with the FSR of the OEO. A tunable center frequency of the microwave pulses from 5.47 GHz to 18.91 GHz can be easily generated by tuning the laser frequency benefit from adopting the MPF. Furthermore, the microwave pulses with different pulse periods of 297.62 ns, 198.69 ns, and 148.81 ns are also realized by harmonic mode-locking. The proposed tunable microwave-pulse-generation method has potential applications in the pulse Doppler radar and communications.

Low-Power Low-Complexity FM-UWB Hybrid Transceiver for Communication and Ranging

A frequency-modulated ultrawideband (FM-UWB) hybrid transceiver, with a high system reuse ratio up to 90%, is fabricated in the 65-nm CMOS process for both short-range wireless communication and high-resolution radar ranging. The radio frequency (RF) front-ends (RFFEs) based on module stacking and current reuse achieve significant RF power savings of about 30% and 50% for the transmitter and the receiver (RX), respectively. The presented IF zero-crossing delay discrimination benefits a high radar resolution less than 1 cm. A multimode relaxation oscillator (OSC) for the reconfigured triangular subcarrier generation and a dual-path ring voltage-controlled oscillator (VCO) for the linear FM, stacked by a wideband push–pull power amplifier (PA), generate an FCC-compliant UWB signal. An active balun embedded low-noise amplifier (LNA) and two symmetric-detuning band-passed filters (BPFs) are stacked with the bandwidth extension to linearly demodulate the UWB FM signal. Experimental results show that the 3.75–4.25-GHz hybrid transceiver has an energy efficiency of 1.9 nJ/bit with an active area of 0.7 mm2 and a power dissipation of 1.9 mW and achieves the RX sensitivity of −71 dBm and the transmitted power of −14.1 dBm, with a bit error rate (BER) of 10−4 at a distance of 4 m under the data rate (DR) of 0.1–1.0 Mbps. The transceiver also achieves the noise figure (NF) of 4.8 dB and the phase noise of −78.6 dBc/Hz at 1-MHz offset frequency.

Self-starting spatiotemporal mode-locking using Mamyshev regenerators.

Bridging multi-mode fibers and Mamyshev regenerators holds promise for pulse energy scaling in fiber lasers. However, initialization of a multi-mode Mamyshev oscillator remains a practical challenge. Here we report self-starting spatiotemporal mode-locking (STML) in a multi-mode Mamyshev oscillator without active assistance. The first initialized mode-locking is unstable, but stable STML can be attained by increasing the filter separation. Simulations verify the capability of reaching self-starting STML using Mamyshev regenerators and unveil the effect of filter separation on the self-starting ability.

Stabilization of spatiotemporal dissipative solitons in multimode fiber lasers by external phase modulation

In this work, we introduce a method for the stabilization of spatiotemporal (ST) solitons. These solitons correspond to light bullets in multimode optical fiber lasers, energy-scalable waveguide oscillators and amplifiers, localized coherent patterns in Bose–Einstein condensates, etc. We show that a three-dimensional confinement potential, formed by a spatial transverse (radial) parabolic graded refractive index and dissipation profile, in combination with quadratic temporal phase modulation, may permit the generation of stable ST dissipative solitons. This corresponds to combining phase mode-locking with the distributed Kerr-lens mode-locking. Our study of the soliton characteristics and stability is based on analytical and numerical solutions of the generalized dissipative Gross–Pitaevskii equation. This approach could lead to higher energy (or condensate mass) harvesting in coherent spatio-temporal beam structures formed in multimode fiber lasers, waveguide oscillators, and weakly-dissipative Bose–Einstein condensates.

Experimental evidence of coupled-mode flutter in a two-meter-long non-rotating wind turbine blade

We have conducted a series of experiments on a 30:1 scale wind turbine blade and observed coupled-mode flutter. This observation validates the theoretical studies that predict larger wind turbine blades are susceptible to coupled-mode flutter. To conduct these experiments, we built a scaled-down model of the 61-meter NREL 5 MW blade. The blade was approximately 2 meters long and was built such that the ratios between its first torsional natural frequency and the flapwise natural frequencies were similar to those of the full-scale blade. This was important, because the theoretical predictions suggest that coupled-mode flutter occurs when one of the flapwise modes and the first torsional mode of the blade coalesce. In our experiments, as the wind speed was increased, turbulence induced vibrations were observed initially in the form of oscillations of the blade’s first flapwise mode, and then its second flapwise mode, with a region of multi-modal oscillations in between. It was observed that the first torsional natural frequency of the blade decreased with increasing wind speed and the second flapwise natural frequency increased slightly. Then at a critical wind speed, the second flapwise mode and the first torsional mode merged into a flutter mode, indicating coupled-mode flutter has occurred at this wind speed.

Simulation of Emission Spectra of Transition Metal Dichalcogenide Monolayers with the Multimode Brownian Oscillator Model.

The multimode Brownian oscillator model is employed to simulate the emission spectra of transition metal dichalcogenide (TMD) monolayers. Good agreement is obtained between measured and simulated photoluminescence spectra of WSe2, WS2, MoSe2, and MoS2 at various temperatures. The Huang-Rhys factor extracted from the model can be associated with that from the modified semiempirical Varshni equation at high temperatures. Individual mechanisms leading to the unique temperature-dependent emission spectra of those TMDs are validated by the multimode Brownian oscillator (MBO) fitting, while it is, in turn, confirmed that the MBO analysis is an effective method for studying the optical properties of TMD monolayers. Parameters extracted from the MBO fitting can be used to explore exciton-photon-phonon dynamics of TMDs in a more comprehensive model.

Theoretical calculation and particle-in-cell simulation of a multi-mode relativistic backward wave oscillator operating at low magnetic field

Increasing the dimensions of high power microwave devices is an efficient method to improve the power capacity. However, an overmoded structure usually results in mode competition and a low beam-wave conversion efficiency. In this paper, a multi-mode operation mechanism is used to avoid mode competition and increase the efficiency. The calculation results of nonlinear theory of beam-multimode interaction show that the optimized conversion efficiency is up to 48% when TM01 mode, TM02 mode, and TM03 mode are all considered. As only the TM01 mode, TM02 mode, or TM03 mode is taken into account independently, the corresponding efficiency is 38%, 22%, or 20%. Based on this, a multi-mode relativistic backward wave oscillator is proposed with the ratio of the mean diameter of the slow wave structure (SWS) to the wavelength of the output microwave to be 3.5. The non-uniform SWS is used to increase the beam-wave conversion efficiency, and a combined reflector is adopted to reflect partial of the mixed microwave modes and make the device compact. The particle-in-cell simulations show that as the diode voltage is 1.1 MV, the beam current is 22.8 kA, and the external magnetic field is 0.76 T, the conversion efficiency is 45%, and the output microwave of 11.3 GW is the mixed modes of TM01 mode, TM02 mode, and TM03 modes with the corresponding power ratio of 74%, 7%, and 19%, respectively.

Searching for a Unique Exciton Model of Photosynthetic Pigment–Protein Complexes: Photosystem II Reaction Center Study by Differential Evolution

Studying the optical properties of photosynthetic pigment–protein complexes (PPCs) in the visible light range, both experimentally and theoretically, is one of the ways of gaining knowledge about the function of the photosynthetic machinery of living species. To simulate the PPC optical response, it is necessary to use semiclassical theories describing the effect of external fields–matter interaction, energy migration in molecular crystals, and electron–phonon coupling. In this paper, we report the results of photosystem II reaction center (PSIIRC) linear optical response simulations. Applying the multimode Brownian oscillator model and the theory of molecular excitons, we have demonstrated that the absorption, circular and linear dichroism, and steady-state fluorescence of PSIIRC can be accurately fitted with the help of differential evolution (DE), the multiparametric evolutionary optimization algorithm. To explore the effectiveness of DE, we used the simulated experimental data as the target functions instead of those actually measured. Only 2 of 10 DE strategies have shown the best performance of the optimization algorithm. With the best tuning parameters of DE/rand-to-best/1/exp strategy determined from the strategy tests, we found the exact solution for the PSIIRC exciton model and fitted the spectra with a reasonable convergence rate.

Theoretical Studies on the Photophysical Properties of the Ag(I) Complex for Thermally Activated Delayed Fluorescence Based on TD-DFT and Path Integral Dynamic Approaches.

Theoretical calculation not only is a powerful tool to deeply explore photophysical processes of the emitters but also provides a theoretical basis for material renewal and design strategy in the future. In this work, the interconversion and decay rates of the thermally activated delayed fluorescence (TADF) process of the rigid Ag(dbp)(P2-nCB) complex are quantitatively calculated by employing the optimally tuned range-separated hybrid functional (ω*B97X-D3) method combined with the path integral approach to dynamics considering the Herzberg–Teller and the Duschinsky rotation effects within a multimode harmonic oscillator model. The calculated results show that the small energy splitting ΔE(S1–T1) = 742 cm–1 (experimental value of 650 cm–1) of the lowest singlet S1 and triplet T1 state and proper vibrational spin–orbit coupling interactions facilitate the reverse intersystem crossing (RISC) processes from the T1 to S1 states. The kRISC rate is estimated to be 1.72 × 108 s–1 that is far more than the intersystem crossing rate kISC of 7.28 × 107 s–1, which will greatly accelerate the RISC process. In addition, the multiple coupling routes of zero-field splitting (ZFS) interaction can provide energetically nearby lying states, to speed up the RISC pathway, and restrict the phosphorescence decay rate. A smaller ZFS D-tensor of 0.143 cm–1, E/D ≈ 0.094 ≪ 1/3, and Δg > 0 are obtained, indicating that the excited singlet states are hardly mixed into the T1 state; thus, a lower phosphorescence decay rate (kp = 9.29 × 101 s–1) is expected to occur, and the T1 state has a long lifetime, which is helpful for the occurrence of the RISC process. These works are in excellent agreement with the experimental observation and are useful for improving and designing efficient TADF materials.

Weak RF signal detection with high resolution and no blind zone based on ultra-simple multi-mode optoelectronic oscillation

Weak RF signal detection with high resolution and no blind zone based on directly modulated multi-mode optoelectronic oscillation has been proposed. The high-sensitivity optical modulators and optical filters are avoided because multi-mode oscillation is obtained based on directly modulating the semiconductor laser at the relaxation oscillation frequency. For the directly modulated optoelectronic oscillator, the detection characteristics such as gain for the RF signal, resolution, noise floor, and sensitivity are firstly analyzed. The experimental results are consistent with the simulated results. For the RF signal of unknown frequency, it can be detected out and amplified by tuning the bias current and delay time of the loop. There is no blind zone within 1–4.5 GHz. The system provides a maximum gain of 17.88 dB for the low-power RF signal. The sensitivity of the system can reach as high as -95 dBm. The properties such as gain dynamic range and power stability are also investigated. The system has potential for weak RF signal detection, especially for the RF signal with unknown frequency.

Nanoscale Visualization of a Photoinduced Plasmonic Near-Field in a Single Nanowire by Free Electrons.

Swift electrons can undergo inelastic interactions not only with electrons but also with near-fields, which may result in an energy loss or gain. Developments in photon-induced near-field electron microscopy (PINEM) enable direct imaging of the plasmon near-field distribution with nanometer resolution. Here, we report an analysis of the surface plasmonic near-field structure based on PINEM observations of silver nanowires. Single-photon order-selected electron images revealed the wavelike and banded structure of electric equipotential regions for a confined near-field integral associated with typical absorption of photon quanta (nℏω). Multimodal plasmon oscillations and second-harmonic generation were simultaneously observed, and the polarization dependence of plasmon wavelength and symmetry properties were analyzed. Based on advanced imaging techniques, our work has implications for future studies of the localized-field structures at interfaces and visualization of novel phenomena in nanostructures, nanosensors, and plasmonic devices.

Onset of periodic oscillations as a precursor of a transition to pore-generating turbulence in laser melting

• Narrowband oscillations of laser absorption precede multimodal oscillations. • Melt pool hydrodynamics drive oscillations when laser is stationary or scanned. • Simulations and X-ray imaging shows pore formation during multimodal oscillations. Laser melting technologies in welding and additive manufacturing, such as laser powder bed fusion, promises to revolutionize manufacturing. However, a challenge remains in preventing pore defects produced by melt pool instabilities, which degrade part quality. Using X-ray imaging synchronized with ultrahigh-speed (40 ns) absorption radiometry and coupled with high-fidelity simulations, we discovered that periodic oscillations in the melt pool's morphology existed prior to a transition to chaotic and pore-generating turbulence. Over-extension by recoil waves followed by surface-tension driven recession created temporary pores that persisted longer in a multimodal regime. This non-linear hydrodynamics exists in both shallow and deep melt pools, but most strongly affects the latter. Early prevention of this transition will help improve the quality of manufactured parts. This work demonstrates that remote sensing of these oscillations is possible by very high time resolution total light scattering measurements, which is more readily achievable in an industrial setting than 2-dimensional melt pool imaging.

Photosynthetic pigment-protein complexes optical response modeling optimized by Differential evolution: algorithm convergence study

Photosynthetic pigment-protein complexes are the essential parts of thylakoid membranes of higher plants and cyanobacteria. Besides many organic and inorganic molecules they contain pigments like chlorophyll, bacteriochlorophyll, and carotenoids, which absorb the incident light and transform it into the energy of the excited electronic states. The semiclassical theories such as molecular exciton theory and the multimode Brownian oscillator model allows us to simulate the linear and nonlinear optical response of any pigment-protein complex, however, the main disadvantage of those approaches is a significant amount of effective parameters needed to be found in order to reproduce the experimental data. To overcome these difficulties we used the Differential evolution method (DE) that belongs to the family of evolutionary optimization algorithms. Based on our preliminary studies of the linear optical properties of monomeric photosynthetic pigments using DE, we proceed to more complex systems like the reaction center of photosystem II isolated from higher plants (PSIIRC). PSIIRC contains only eight chlorophyll pigments, and therefore it is potentially a very promising subject to test DE as a powerful optimization procedure for simulation of the optical response of a system of interacting pigments. Using the theoretically simulated linear spectra of PSIIRC (absorption, circular dichroism, linear dichroism, and fluorescence), we investigated the dependence of the algorithm convergence on DE settings: strategies, crossover, weighting factor; eventually finding the optimal mode of operation of the optimization procedure.

Electronic dephasing in mixed quantum–classical molecular systems using the spin-boson model

Pure electronic dephasing is investigated using the spin-boson Hamiltonian in mixed quantum–classical environment. The spin-boson model used here is a composite system made up of a quantum subsystem, an electronic 2-level subsystem linearly coupled to harmonic vibrations, interacting with a classical bath. Experimental results for a multitude of molecular systems indicate that the zero-phonon line (ZPL) profile is determined by electronic dephasing, which is not accounted for in the multimode Brownian oscillator (MBO) model due to the unphysical contribution from the MBO bath modes to the ZPL profile. Mixed quantum–classical dynamics formalism of non-equilibrium systems is employed to assess the contribution of the bath modes to pure electronic dephasing by probing the ZPL profile when coupled to a classical bath in the mixed quantum–classical condensed systems. Pure electronic dephasing is discussed in the context of mixed quantum–classical dynamics formalism which starts with mixed quantum–classical Liouville equation in a mixed quantum–classical environment. It is noteworthy, however, that the fundamental difference between the fully quantum MBO model and the mixed quantum–classical Brownian oscillator, is that the zero-phonon line calculated by the former shows unphysical asymmetry on the low-energy side as it has not been observed in real systems, whereas the ZPL reported herein eliminates this asymmetry. A systematic approach using matrix mechanics is developed to treat this phenomenon. To this end, a closed-form expression of linear and nonlinear optical electronic transition dipole moment time correlation functions in a dissipative media are derived. Linear absorption spectra and 4-wave mixing signals at various temperatures showing a sound thermal broadening, temporal decay, and accurate pure dephasing further ratify the applicability and correctness of the mixed quantum–classical dynamics approach to spectroscopy and dynamics are computed.