Critical Coupling Point Research Articles

Spatial organisation of the mesoscale connectome: A feature influencing synchrony and metastability of network dynamics.

Significant research has investigated synchronisation in brain networks, but the bulk of this work has explored the contribution of brain networks at the macroscale. Here we explore the effects of changing network topology on functional dynamics in spatially constrained random networks representing mesoscale neocortex. We use the Kuramoto model to simulate network dynamics and explore synchronisation and critical dynamics of the system as a function of topology in randomly generated networks with a distance-related wiring probability and no preferential attachment term. We show networks which predominantly make short-distance connections smooth out the critical coupling point and show much greater metastability, resulting in a wider range of coupling strengths demonstrating critical dynamics and metastability. We show the emergence of cluster synchronisation in these geometrically-constrained networks with functional organisation occurring along structural connections that minimise the participation coefficient of the cluster. We show that these cohorts of internally synchronised nodes also behave en masse as weakly coupled nodes and show intra-cluster desynchronisation and resynchronisation events related to inter-cluster interaction. While cluster synchronisation appears crucial to healthy brain function, it may also be pathological if it leads to unbreakable local synchronisation which may happen at extreme topologies, with implications for epilepsy research, wider brain function and other domains such as social networks.

Design of hollow metasurfaces for absorption sensors and surface enhanced infrared absorption

Absorption sensors detect variations in the imaginary part of refractive index with selectivity in sensing since analytes can be distinguished according to their characteristic absorption bands. In this study we combine the theoretical analysis based on temporal coupled mode theory and numerical calculations in order to derive design principles of optimal metasurfaces aimed for absorption sensing and surface enhanced infrared absorption (SEIRA). We consider hollow metal–insulator-metal metasurfaces with an empty space between two metallic layers. This space acts as a channel for the infiltration of fluid analytes in the region with the maximal electric field enhancement, which provides high sensitivity. We demonstrate that optimal metasurfaces operate in overcoupled regime where radiative decay rate of the resonant mode is larger than non-radiative decay rate. The operation in this regime is adjusted by choosing appropriate channel thickness (the vertical distance between two metallic layers), which should be around three times larger than the channel thickness at the critical coupling point, associated with equal decay rates and zero reflectance. Metasurface period should be as large as possible, whereas the operating frequency should be equal to the resonant frequency of metasurfaces. The same conclusions hold for hollow metasurfaces aimed for SEIRA, while in addition, their resonant frequency should match the vibrational frequency of an analyte under investigation. The absorption sensitivity (reflectance change divided by the change in the imaginary part of refractive index) of an optimal metasurface is larger than , which provides detection of the imaginary part of refractive index below .

Unified treatment of scattering, absorption, and luminescence spectra from a plasmon–exciton hybrid by temporal coupled-mode theory

Plasmonic nanostructures are capable of tailoring the emission of a nearby emitter by increasing (or reducing) the brightness, shortening (or prolonging) the lifetime, and shaping the spectrum. Experimental characterization of such coupled plasmon-exciton (plexciton) systems usually relies on the acquisition and comparison of scattering, absorption, or luminescence spectra. However, theoretical accounts of these optical spectra, which are key to distinguishing between the coupling regimes and to standardizing the coupling criteria, often scatters in different frameworks, varying from classical to quantum-mechanical. Therefore, developing a unified and simple formalism that can simultaneously compare all these spectral signatures in different coupling regimes is nontrivial. Here, we use a temporal coupled-mode formalism to reproduce the scattering, absorption, and luminescence spectra of a plexciton system and find that its luminescence reaches a maximum at a critical coupling point, featuring a light-emitting plexciton with intense brightness and ultrafast lifetime. This simple approach provides a unified and phenomenological treatment of these spectra by simply including or excluding an external driving term. It therefore allows for a direct comparison of different spectroscopic signatures from the plexciton system and provides an easy-to-use guidance for the design of broadband light-emitting devices.

Silicon-coupled tantalum pentoxide microresonators with broadband low thermo-optic coefficient.

Stable microresonators are important integrated photonics components but are difficult to achieve on silicon-on-insulator due to silicon intrinsic properties. In this work, we demonstrate broadband thermally stable tantalum pentoxide microresonators directly coupled to silicon waveguides using a micro-trench co-integration method. The method combines in-foundry silicon processing with a single step backend thin-film deposition. The passive response of the microresonator and its thermal behavior are investigated. We show that the microresonator can operate in the overcoupled regime as well as near the critical coupling point, boasting an extinction ratio over 25 dB with no higher-order mode excitation. The temperature dependent wavelength shift is measured to be as low as 8.9 pm/K and remains below 10 pm/K over a 120 nm bandwidth.

Refractive index sensing with hollow metal–insulator–metal metasurfaces

Refractive index sensing with metal–insulator–metal (MIM) metasurfaces featuring a continuous dielectric film between two metallic layers suffers from a low spatial overlap between high field enhancement regions and the analyte placed above. Recent studies have thus turned toward hollow MIM metasurfaces, particularly suited for fluid analytes which can infiltrate the hollow cavities. Here we describe a general procedure for reaching the optimal design in three most relevant configurations: mushroom-type structures with narrow dielectric pedestals carrying the top metallic ribbon array, hollow structures with the metallic ribbon array resting on a distant lateral support, and hollow structures in which the metallic ribbons are carried by an encapsulating layer from top. We contend that since a majority of the resonant eigenmode energy is contained within the analyte, very high refractive index sensitivities are possible for three different measurement methods: spectral, reflectance and phase interrogation. This is confirmed by numerical simulations demonstrating terahertz spectral sensitivities of above 700 GHz RIU−1 with a normalized sensitivity of around 0.6 (RIU stands for refractive index unit). Detection limits and dynamic ranges are estimated for both bulk refractive index sensing and thin film detection. Refractive index sensitivities and corresponding figure-of-merit factors are shown to reach maxima in the critical coupling regime characterized by equal radiative and non-radiative decay rates of the resonant mode which is controlled by cavity height. Since this regime is associated with a zero reflectance which prevents measurements of any signal, metasurfaces should operate close to the critical coupling point where reflected beam is still measurable. The final optimization is done by decay rate engineering in order to achieve narrower resonances and improve sensing performance.

Quasi‐Bound States in the Continuum with Temperature‐Tunable Q Factors and Critical Coupling Point at Brewster's Angle

AbstractQuasibound state in the continuum (quasi‐BIC) is a long‐lived state with a high quality factor (Q factor). Here quasi‐BICs in nematic liquid crystal (LC) layer embedded between a distributed Bragg reflector (DBR) and a metal layer are studied. First, a special class of true BICs between the DBR and the metal film with field localization provided by the Brewster transverse electric (TE) reflection in the DBR is experimentally demonstrated. It is demonstrated that the Q factor of the quasi‐BIC can be tuned by the LC optical axis rotation in a wide range being only restricted by metal losses. The change of coupling with the radiation channel leads to a critical coupling condition, providing a total absorption of incident light. The acquired quasi‐BIC resonance is extremely sensitive to the temperature due to the narrow nematic temperature range of the LC. The quasi‐BIC transforms to BIC at the LC‐isotropic clearing point, due to closing of the radiation channel.

Critical coupling vortex with grating-induced high Q-factor optical Tamm states.

We investigate optical Tamm states supported by a dielectric grating placed on top of a distributed Bragg reflector. It is found that under certain conditions the Tamm state may become a bound state in the continuum. The bound state, in its turn, induces the effect of critical coupling with the reflectance amplitude reaching an exact zero. We demonstrate that the critical coupling point is located in the core of a vortex of the reflection amplitude gradient in the space of the wavelength and angle of incidence. The emergence of the vortex is explained by the coupled mode theory.

\u03c0-phase modulated monolayer supercritical lens

The emerging monolayer transition metal dichalcogenides have provided an unprecedented material platform for miniaturized opto-electronic devices with integrated functionalities. Although excitonic light–matter interactions associated with their direct bandgaps have received tremendous research efforts, wavefront engineering is less appreciated due to the suppressed phase accumulation effects resulting from the vanishingly small thicknesses. By introducing loss-assisted singular phase behaviour near the critical coupling point, we demonstrate that integration of monolayer MoS2 on a planar ZnO/Si substrate, approaching the physical thickness limit of the material, enables a π phase jump. Moreover, highly dispersive extinctions of MoS2 further empowers broadband phase regulation and enables binary phase-modulated supercritical lenses manifesting constant sub-diffraction-limited focal spots of 0.7 Airy units (AU) from the blue to yellow wavelength range. Our demonstrations downscaling optical elements to atomic thicknesses open new routes for ultra-compact opto-electronic systems harnessing two-dimensional semiconductor platforms with integrated functionalities.

Dynamical phase transition and selective energy exchange in dual-cavity optochanical systems

<sec> In recent years, the cavity quantum photomechanics has been developed rapidly, and played a very important role in quantum information processing, quantum basic principle verification, and high-precision measurement. The kinds of quantum mechanical behaviors have also been explored and discovered in the study of cavity mechanics. By placing the Kerr medium in the system, quantum nonlinearity is introduced into the optomechanical system. Quantum phase transition is a relatively important part in the research of condensed matter physics. Since Dicke quantum phase transition was successfully observed experimentally, the problem of quantum phase transition in the optical cavity has attracted more attention. The spin-coherent-state variation method and the Holstein-Primakoff transformation are used to theoretically calculate the ground state energy functional, and the rich structure of the macroscopic multi-particle quantum state is given by adjusting the parameters. The quantum phase transition evolution equation describes the relationship between each phase and the time of generating a new phase when reaching the critical phase transition point. At the same time, the mode squeezing of multi-mode hybrid optomechanical system has also became one of the basic problems of quantum mechanical behavior in cavity quantum dynamics.</sec><sec> In this article, we explore the quantum dynamics of optomechanical devices including single-cavity and dual-cavities. We find that the system will undergo a dynamic phase transition, which is similar to the Dicke-Hepp-Lieb superradiant type phase transition, and a new dynamic critical point appears in the coupling between the momentum quadratures of the two optical fields. By manipulating the coupling parameters, we can achieve selective energy exchange between any two modes and the critical coupling point corresponds to selective energy exchange. Mode squeezing, which is easy to measure by applying the quantum uncertainty relationship, is also revealed and consistent with selective energy exchange. The study of coordinate and momentum variances gives us the revelation that the compressed orthogonal variables are the most suitable for measurement because of the small quantum noise. In fact, phononic modes can store energy in a longer duration, while photonic modes can transfer energy in a long distance. This phenomenon makes the hybrid optomechanical cavities useful in the next-generation quantum communications and quantum information processing units.</sec>

Spectral phase singularity in a transmission-type double-layer metamaterial

Phase singularities are seen in optical vortex beams, which are located in a two-dimensional spatial plane. Phase singularities in optical spectra are not common, but exploiting the extreme phase behavior around the singularity point could improve conventional optical devices for molecular-/bio-sensing, large phase modulation, etc. Recently, spectral phase singularities have been reported in reflection-type metamaterials but have not yet been reported in transmission. In this work, we demonstrate a spectral phase singularity in a transmission-type double-layer metamaterial. We attribute the mechanism to two different types of resonances in the double-layer metamaterial, namely a hybrid resonance and an anti-parallel dipole resonance. By controlling the lattice size of the double-layer metamaterial, we can manipulate the coupling of the two types of resonances. At a critical-coupling point, the phase singularity occurs in a spectrum-lattice diagram. We developed film metamaterial devices to experimentally demonstrate the phase singularity. Our results could enable investigation of coupled resonator systems, and may have applications in tunable metamaterial device design and improved sensing techniques.

Characterize and optimize the four-wave mixing in dual-interferometer coupled silicon microrings**Project supported by the National Key Research and Development Program of China (Grant No. 2017YFA0303700), the National Natural Science Foundation of China (Grant Nos. 61632021, 11627810, 11690031, and 11621091), and Open Funds from the State Key Laboratory of High Performance Computing of China (HPCL, National University of Defense Technology).

By designing and fabricating a series of dual-interferometer coupled silicon microrings, the coupling condition of the pump, signal, and idler beams can be engineered independently and then we carried out both the continuous-wave and pulse pumped four-wave mixing experiments to verify the dependence of conversion efficiency on the coupling conditions of the four interacting beams, respectively. Under the continuous-wave pump, the four-wave mixing efficiency gets maximized when both the pump and signal/idler beams are closely operated at the critical coupling point, while for the pulse pump case, the efficiency can be enhanced greatly when the pump and converted idler beams are all overcoupled. These experiment results agree well with our theoretical calculations. Our design provides a platform for explicitly characterizing the four-wave mixing under different pumping conditions, and offers a method to optimize the four-wave mixing, which will facilitate the development of on-chip all-optical signal processing with a higher efficiency or reduced pump power.

Quantum Criticality in the Biased Dicke Model.

The biased Dicke model describes a system of biased two-level atoms coupled to a bosonic field, and is expected to produce new phenomena that are not present in the original Dicke model. In this paper, we study the critical properties of the biased Dicke model in the classical oscillator limits. For the finite-biased case in this limit, We present analytical results demonstrating that the excitation energy does not vanish for arbitrary coupling. This indicates that the second order phase transition is avoided in the biased Dicke model, which contrasts to the original Dicke model. We also analyze the squeezing and the entanglement in the ground state, and find that a finite bias will strongly modify their behaviors in the vicinity of the critical coupling point.

Gain-assisted critical coupling for high-performance coherent perfect absorbers.

Balanced radiation and absorption rates of an optical resonator are necessary for coherent perfect light absorption in many active device applications. This balance is referred to as critical coupling condition. We propose a gain-assisted method for exact access to critical coupling conditions without altering any structure parameters. In a coherent absorber with additional internal gain media, critical coupling with arbitrarily high coherent signal extinction can be obtained by continuously tuning optical pumping density. Assuming a surface-plasmon resonance grating covered by a gain layer as a promising architecture, we numerically demonstrate gain-assisted continuous access to its critical coupling point with experimentally probable settings. In addition, the gain tuning further introduces switching of the coherent-absorber's functionality to a conventional lossless beam splitter.

Tunable Q-factor silicon microring resonators for ultra-low power parametric processes.

A compact silicon ring resonator is demonstrated that allows simple electrical tuning of the ring coupling coefficient and Q-factor and therefore the resonant enhancement of on-chip nonlinear optical processes. Fabrication-induced variation in designed coupling fraction, crucial in the resonator performance, can be overcome using this post-fabrication trimming technique. Tuning of the microring resonator across the critical coupling point is demonstrated, exhibiting a Q-factor tunable between 9000 and 96,000. Consequently, resonantly enhanced four-wave mixing shows tunable efficiency between -40 and -16.3 dB at an ultra-low on-chip pump power of 0.7 mW.

Analysis and Performance Improvement of Independent Electric Coupled Resonance WPT System with Impedance Transformer

Wireless power transfer (WPT) technology is expected for the next generation power feeding system, which could supply the power to portable devices without any wires. Compare to the magnetic coupled resonance; a WPT system uses electric coupled resonance could provide a higher position of flexibility. In this paper, the concepts of independent electric coupled resonance type WPT system is investigated by using equivalent circuit including: power transfer function, critical coupling point, frequency splitting and optimum port impedance. After a pair of matching loops are added into source and receive side, the power transfer efficiency could has a great improvement is confirmed by using simulation and experiment.

Robustness of a partially interdependent network formed of clustered networks.

Clustering, or transitivity, a behavior observed in real-world networks, affects network structure and function. This property has been studied extensively, but most of this research has been limited to clustering in single networks. The effect of clustering on the robustness of coupled networks, on the other hand, has received much less attention. Only the case of a pair of fully coupled networks with clustering has recently received study. Here we generalize the study of clustering of a fully coupled pair of networks and apply it to a partially interdependent network of networks with clustering within the network components. We show, both analytically and numerically, how clustering within networks affects the percolation properties of interdependent networks, including the percolation threshold, the size of the giant component, and the critical coupling point at which the first-order phase transition changes to a second-order phase transition as the coupling between the networks is reduced. We study two types of clustering, one proposed by Newman [Phys. Rev. Lett. 103, 058701 (2009)] in which the average degree is kept constant while the clustering is changed, and the other by Hackett et al. [Phys. Rev. E 83, 056107 (2011)] in which the degree distribution is kept constant. The first type of clustering is studied both analytically and numerically, and the second is studied numerically.

Inverted-wedge silica resonators for controlled and stable coupling

Silica microresonators with an inverted-wedge shape were fabricated using conventional semiconductor fabrication methods. The measured quality factors of the resonators were greater than 10(6) in 1550 nm band. Controllable coupling from undercoupling to the overcoupling regime through the critical coupling point was demonstrated by horizontally moving a fiber taper while in touch with the top surface of the resonator. The thin outer ring of the resonator provided a support for the fiber taper leading to robust stable coupling.

Plasmonic racetrack resonator with high extinction ratio under critical coupling condition

In this paper, an ultracompact plasmonic racetrack resonator based on single mode metal-insulator-metal plasmonic gap waveguide with high coupling efficiency is investigated both analytically and numerically. The coupling properties of a plasmonic waveguide to a racetrack resonator at 1.55 μm wavelength are studied with various coupling lengths. An extinction ratio of −34.5 dB and a free-spectral range of 303 nm at the critical coupling point can be achieved. Such a plasmonic resonator design provides a promising realization for highly effective modulators and wide band filters.

Taper-microsphere coupling with numerical calculation of coupled-mode theory

We have numerically studied a taper-microsphere coupling system with coupled-mode theory by introducing a mode-coupling mechanism. Transmission and reflection coefficients have been obtained directly through numerical calculation for a spherical silica microcavity. In the presence of the modal coupling mechanism, the optimal condition for transferring the light energy into the microsphere is no longer the critical coupling point. Instead, it should be in the under-coupling regime and can be reached by optimizing the size of the fiber taper and the taper-microsphere gap.

Pulse advancement and delay in an integrated-optical two-port ring-resonator circuit: direct experimental observations

We report experimental observations of the negative-group-velocity (v(g)) phenomenon in an integrated-optical two-port ring-resonator circuit. We demonstrate that when the v(g) is negative, the (main) peak of output pulse appears earlier than the peak of a reference pulse, while for a positive v(g), the situation is the other way around. We observed that a pulse splitting phenomenon occurs in the neighborhood of the critical-coupling point. This pulse splitting limits the maximum achievable delay and advancement of a single device as well as facilitating a smooth transition from highly advanced to highly delayed pulse, and vice versa, across the critical-coupling point.