Coupled Oscillator Model Research Articles

Lower Exciton Number Strong Light Matter Interaction in Plasmonic TweezersSupported by the National Key Research and Development Program of China (Grant No. 2016YFA0301300), the Fundamental Research Funds for the Central Universities (Grant No. 2019XD-A09), and the National Natural Science Foundation of China (Grant No. 11574035).

The plasmonic nanocavity is an excellent platform for the study of light matter interaction within a sub-diffraction volume under ambient conditions. We design a structure of plasmonic tweezers, which can trap molecular J-aggregates and also serve as a plasmonic cavity with which to investigate strong light matter interaction. The optical response of the cavity is calculated via finite-difference time-domain methods, and the optical force is evaluated based on the Maxwell stress tensor method. With the help of the coupled oscillator model and virtual exciton theory, we investigate the strong coupling progress at the lower level of excitons, finding that a Rabi splitting of 230 meV can be obtained in a single exciton system. We further analyze the relationship between optical force and model volume in the coupling system. The proposed method offers a way to locate molecular J-aggregates in plasmonic tweezers for investigating optical force performance and strong light matter interaction.

Dynamic behaviors in two-layer coupled oscillator system

In this paper, we present a two-layer coupled oscillator model, in which the first layer is composed of the nearest neighbor coupled identical oscillator, the second layer is composed of the global coupled identical oscillator, and there is a one-way point-to-point drive from the second layer to the first layer. In this system, the driven layer changes from unsynchronized state to synchronized state with the change of parameters. During this transformation, we found the existence of chimer state. And the dynamic behavior of the system had been studied. The critical value for the state transition had been caught.

Ultrafast control of slow light in THz electromagnetically induced transparency metasurfaces

In this paper, we experimentally demonstrate ultrafast optical control of slow light in the terahertz (THz) range by combining the electromagnetically induced transparency (EIT) metasurfaces with the cut wire made of P+-implanted silicon with short carrier lifetime. Employing the optical-pump THz-probe spectroscopy, we observed that the device transited from a state with a slow light effect to a state without a slow light effect in an ultrafast time of 5 ps and recovered within 200 ps. A coupled oscillator model is utilized to explain the origin of controllability. The experimental results agree very well with the simulated and theoretical results. These EIT metasurfaces have the potential to be used as an ultrafast THz optical delay device.

Analysis and modeling of Fano resonances in coupled cantilevers

The coupled oscillators model has been used for decades to interpret the Fano interference in a variety of systems: optical, plasmonic, and microwave. Hence, Fano resonance can be modeled with a weak or tightly coupled mechanical oscillators system, which provide insight into the interaction dynamics of a radioactive continuum of propagation modes and a discrete state. Therefore, the coupled cantilevers model was implemented in a FEM routine, in order to study and discuss aspects of the Fano resonance. The study of the Fano resonance in coupled cantilevers shows that this model may be applied in the field of micromechanical sensors.

Active thermal modulation of electromagnetically induced transparency at terahertz frequencies

We present thermal control of electromagnetically induced transparency (EIT) by actively modulating the dark mode in terahertz (THz) metamaterials, including a cut wire and a split-ring resonator (SRR). By integrating indium antimonide (InSb) into the SRR and increasing the temperature, the active modulation of EIT is realized. The coupling mechanism is numerically analyzed through the coupled oscillator model, and the result of fitting the EIT intensity agrees well with the simulation results when the temperature changes from 200 to 240 K. By analyzing the electric field distribution, the physical mechanism is the change in the damping rate of the dark mode resonator due to the increase in InSb temperature. Our work has practical significance in designing tunable THz functional devices.

Enhanced circular dichroism of plasmonic system in the strong coupling regime* *Project supported by the National Key R&D Program of China (Grant No. 2016YFA0301300), the Fundamental Research Funds for the Central Universities, China (Grant No. 2019XD-A09), and the National Natural Science Foundation of China (Grant No. 11574035).

The circular dichroism (CD) signal of a molecule is usually weak, however, a strong CD signal in optical spectrum is desirable because of its wide range of applications in biosensing, chiral photo detection, and chiral catalysis. In this work, we show that a strong chiral response can be obtained in a hybridized system consisting of an artificial chiral molecule and a nanorod in the strong coupling regime. The artificial chiral molecule is composed of six quantum dots in a helix assembly, and its CD signal arises from internal Coulomb interactions between quantum dots. The CD signal of the hybridized system is highly dependent on the Coulomb interactions and the strong coupling progress through the electromagnetic interactions. We use the coupled oscillator model to analyze strong coupling phenomenon and address that the strong coupling progress can amplify the CD signal. This work provides a scenario for designing new plasmonic nanostructures with a strong chiral optical response.

Second Harmonic Generation from a Single Plasmonic Nanorod Strongly Coupled to a WSe2 Monolayer.

Monolayer transition metal dichalcogenides, coupled to metal plasmonic nanocavities, have recently emerged as new platforms for strong light-matter interactions. These systems are expected to have nonlinear-optical properties that will enable them to be used as entangled photon sources, compact wave-mixing devices, and other elements for classical and quantum photonic technologies. Here, we report the first experimental investigation of the nonlinear properties of these strongly coupled systems, by observing second harmonic generation from a WSe2 monolayer strongly coupled to a single gold nanorod. The pump-frequency dependence of the second-harmonic signal displays a pronounced splitting that can be explained by a coupled-oscillator model with second-order nonlinearities. Rigorous numerical simulations utilizing a nonperturbative nonlinear hydrodynamic model of conduction electrons support this interpretation and reproduce experimental results. Our study thus lays the groundwork for understanding the nonlinear properties of strongly coupled nanoscale systems.

Dynamically Switchable Multispectral Plasmon-Induced Transparency in Stretchable Metamaterials

We propose dynamically switchable multispectral plasmon-induced transparency (PIT) with high modulation depth in a three-dimensional metamaterial standing on a flexible substrate. The proposed metamaterial is composed of a pair of metal–insulator–metal (MIM) nano-cut-wires and a pair of insulator–metal–insulator (IMI) nano-cut-wires. Results show that two PIT windows can be achieved because of the near-field coupling between the dipole supported by the IMI nano-cut-wire and two quadrupoles supported by the MIM structures. These two PIT windows can be blue-shifted or even flipped over by stretching the substrate along one direction, or be switched off by stretching along the other direction. A classical coupled oscillator model is developed to quantitatively describe and explain these results. We expect this work will find promising applications in multispectral sensors, slow light devices and nonlinear optical devices.

Optical rotation and electromagnetically induced transparency in a chiral metamaterial with C4 symmetry

We design and fabricate a double-layered chiral metamaterial with 4-fold rotational symmetry, which simultaneously exhibits optical rotation and electromagnetically induced transparency (EIT) effects. Using analytical equivalent circuit model and Lorentz's coupled oscillator model, we interpret the physical mechanisms and derive material equations. Importantly, we find that magnetic dipole and electric quadrupole play important roles in optical rotation and keeping the symmetry of the material equations. Our work offers a better understanding of optical rotation in chiral metamaterials, and provides a new and simple approach to combine optical rotation and EIT effects into a single metamaterial.

Rabi splitting obtained in a monolayer BP-plasmonic heterostructure at room temperature

Hybrid exciton states can be formed under the strong coupling of plasmons excited by metal nanostructures and excitons. Because of the large exciton binding energy, black phosphorus (BP) is an ideal platform to investigate the strong coupling. In this paper, we first demonstrate the strong coupling between local surface plasmon modes of different metal nanostructures and excitons in monolayer BP by adjusting the dimensions of nanostructures and polarization angle at room temperature. Moreover, the exciton dispersion curves obtained from the coupled oscillator model show the anti-crossing behavior at the exciton energy. And the Rabi splitting energies of the two different BP-metal nanostructures heterostructure are 250 meV and 202 meV, respectively, which paves a way towards the development of BP photodetectors, sensors, and emitters.

Computational and theoretical analysis of electron plasma cooling by resonant interaction with a microwave cavity

Recent experiments demonstrated that the cyclotron cooling rate of an electron plasma in a Penning–Malmberg trap can be increased by placing the plasma in a cavity and adjusting the magnetic field to make the cyclotron motion resonant with a cavity mode. Here this physics is studied with a coupled oscillator model and analyzed both analytically and numerically. Plasma cooling performance is evaluated over a wide range of system parameters, including the number of electrons, the coupling to the local electric field, the magnetic field gradient, and the detuning between the cavity and cyclotron frequencies. Scaling the equations shows that the system is well-described by a few key dimensionless quantities.

Asymmetric graphene metamaterial for narrowband terahertz modulation

The properties of planar three-layer asymmetric split-ring metamaterial are studied analytically by a coupled oscillator model and equivalent circuit model. These results are verified using full-wave numerical simulations. The influence of geometrical parameters of the proposed metamaterial structure, as well as graphene properties on the device terahertz spectral characteristics, are investigated in details. Such a comprehensive approach in graphene metamaterial description allows to design efficient narrowband modulator for a wide range of specific tasks including applications in terahertz sensing and switching.

Conjecture about the general cosmological solution of Einstein’s equations

We introduce consideration of a new factor, synchronisation of spacetime Mixmaster oscillations, that may play a simplifying role in understanding the nature of the general inhomogeneous cosmological solution to Einstein's equations. We conjecture that, on approach to a singularity, the interaction of spacetime Mixmaster oscillations in different regions of an inhomogeneous universe can produce a synchronisation of these oscillations through a coupling to their mean field in the way first demonstrated by the Kuramoto coupled oscillator model.

Research on piezoelectric energy harvester based on coupled oscillator model for vehicle vibration utilizing a L-shaped cantilever beam

Piezoelectric energy harvester can replace the battery and provide energy for most kinds of micro devices. And due to its advantages of considerable output power and high output voltage, it has bright prospects. This paper presents a piezoelectric energy harvester based on coupled oscillator model utilizing a L-shaped cantilever beam to collect the vibration energy of the vehicle with the frequency band from 5 Hz to 25 Hz. The finite element analysis of the designed piezoelectric energy harvester is carried out by running ANSYS simulation software, including modal analysis, transient response analysis and harmonic response analysis. The results shows that under the coupling, the amplitude-frequency characteristic curve of each oscillator has two peak points, which widens the working frequency band of the energy harvester. Meanwhile, experimental research is carried out on the collector prototype. By analyzing the experimental results, the natural frequency of oscillator 1 is about 17.1 Hz, and the natural frequency of oscillator 2 is about 21.1 Hz. Therefore, these natural frequencies meet the need to collect vibration energy of 5 Hz to 25 Hz. In addition, by comparing the frequency response curves of the open circuit output voltage of the energy collectors working independently and under coupling, the results show that the operating frequency band of the energy collector is broadened under coupling.

Raman opalescence and central peak scattering near phase transition point in crystals

Comparison of isotemperature and isofrequency temperature dependences was used for revealing the soft mode behavior near phase transition points in ferroelectric and ferro-structural phase transitions in crystals. Sharp increase of the Raman scattering spectral intensity maximum near phase transition points was found and classified as soft mode Raman opalescence effect. Such phenomenon was observed in ferroelectric crystals LiNbO3, LiTaO3, and Pb5Ge3O11, and crystalline quartz. Presence of the high intensive and narrow central peak in low frequency area of light scattering spectra in vicinity of phase transition point was explained on the base of two coupled oscillator model.

Position-guided Fano resonance and amended GaussAmp model for the control of slow light in hybrid graphene–silicon metamaterials

Position-guided Fano resonance is observed in hybrid graphene-silicon metamaterials. An outstanding application of such resonance is slow-light metadevices. The maximum group delay is 9.73 ps, which corresponds to a group delay in free-space propagation of 2.92 mm. We employ a coupled oscillator model to illustrate anomalous transmission, where the intensity of the Fano peak increases with the Fermi level. Furthermore, we amend the GaussAmp model to serve as a suitable control equation for the group delay. The coefficient of correlation (R2) is as high as 0.99998, while the lowest values of the root-mean-square error and sum of squared errors are respectively 0.00421 and 0.00156. These results indicate that the amended GaussAmp model accurately controls the trend of the group delay. This work not only clarifies the mechanism of Fano resonance generation but also provides a promising platform for dynamically adjustable optical switches and multidimensional information sensors.

Fano Resonance in Artificial Photonic Molecules

AbstractThe spectral signatures of chemical molecules are dependent on the hybridization of electronic states. The artificial photonic molecules formed by structured optical microcavities, exhibiting Fano features with sharp asymmetric line shape and strong field enhancement, hold various potential applications in sensors, optical switches, lasing spasers, optical diodes, etc. To design high‐performance photonic devices, it is of great importance to gain the formation and modulation mechanisms of Fano resonance in various artificial photonic molecules. This review is focused on the Fano resonance in artificial photonic molecules. It starts by discussing the properties of Fano resonance, followed by a detailed discussion of the coupled oscillator model and coupled mode theory that could reveal the underlying mechanisms. Then, different types of photonic molecules for realizing Fano resonance are presented, and several representative exciting applications are introduced. Finally, a summary and a brief outlook on challenges are discussed for Fano resonance in artificial photonic molecules.

Mechanisms of Fano-resonant biosensing: Mechanical loading of plasmonic oscillators

Distinctively narrow and asymmetric line shape Fano resonances arise due to resonant interactions of sub-radiant and super-radiant modes in plasmonic nanostructures and metamaterials. A number of recent experimental studies have shown unique opportunities provided by highly dispersive Fano resonances in biosensing applications. However, there is limited understanding of Fano resonant optical response to biomolecular accumulation. Here, we introduce a phenomenological model that can precisely describe the intricate nature of the Fano resonances in plasmonic nanohole arrays and provide unambiguous physical insights into biosensing experiments. Using rigorous electromagnetic simulations and experimental measurements as benchmarking tools, we show that the non-trivial contribution of molecular accumulation to Fano resonant plasmonic response can be incorporated as a mechanical loading effect in a coupled-oscillator model. Quite remarkably, our phenomenological approach captures the complex spectral response of the Fano resonance profile and asymmetric linewidth broadening upon molecular accumulation. Furthermore, in strong agreement with our experimental measurements, we show that our parameterized​ model has predictive power in fine tuning the Fano resonant extraordinary light transmission lineshape using structural design parameters without resorting to electromagnetic simulations. Our phenomenological model provides a general analytical method that can be adapted to understand biomolecular detection measurements in different plasmonic and metamaterial systems.

A Computationally Efficient Integrated Coupled Opto-Electronic Oscillator Model

Coupled opto-electronic oscillators can generate microwave signals with very low phase noise. Several approaches for modelling these oscillators exist, but none of them include the fast carrier dynamics of the mode-locked laser, due to computational limitations. In this work, we present a new model, that is based on a computationally efficient model for semiconductor mode-locked lasers, which is capable of simulating both the fast laser dynamics and the long term phase stability. We use it to model the phase noise of a hybridly integrated coupled opto-electronic oscillator. The results show that a timing jitter of down to $\mathbf {\sim} \text{0.2}$ $\text{ps}$ in the integration range from $\text{10}$ $\text{kHz}$ to $\text{10}$ $\text{MHz}$ is achievable when using an integrated delay line of $\text{10.2}$ $\text{m}$ in the opto-electronic feedback path. It is also shown that by increasing both gain and bandwidth of the opto-electronic feedback link, the timing jitter is reduced. Together, these results present a path towards low phase noise performance of hybridly integrated coupled opto-electronic oscillators, and the model serves as a new design tool. Such oscillators might increase, for example, the spectral efficiency in future data communication systems and thus enable higher data rates.

Modulation of Robot Orientation Via Leg-Obstacle Contact Positions

We study a quadrupedal robot traversing a structured (i.e., periodically spaced) obstacle field driven by an open-loop quasi-static trotting walk. Despite complex, repeated collisions and slippage between robot legs and obstacles, the robot's horizontal plane body orientation (yaw) trajectory can converge in the absence of any body level feedback to stable steady state patterns. We classify these patterns into a series of “types” ranging from stable locked equilibria, to stable periodic oscillations, to unstable or mixed period oscillations. We observe that the stable equilibria can bifurcate to stable periodic oscillations and then to mixed period oscillations as the obstacle spacing is gradually increased. Using a 3D-reconstruction method, we experimentally characterize the robot leg-obstacle contact configurations at each step to show that the different steady patterns in robot orientation trajectories result from a self-stabilizing periodic pattern of leg-obstacle contact positions. We present a highly-simplified coupled oscillator model that predicts robot orientation pattern as a function of the leg-obstacle contact mechanism. We demonstrate that the model successfully captures the robot steady state for different obstacle spacing and robot initial conditions. We suggest in simulation that using the simplified coupled oscillator model we can create novel control strategies that allow multi-legged robots to exploit obstacle disturbances to negotiate randomly cluttered environments.