Critical Coupling Condition Research Articles

Numerical Verification of a Polarization-Insensitive Electrically Tunable Far Infrared Band-Stop Meta-Surface Filter

Tunable filters have many potential applications in diverse fields, including high-capacity communications, dynamic beam shaping and spectral imaging. Although providing a high-performance solution for actively tunable devices, metasurface combined with tunable materials faces the great challenges of limited tuning range and modulation depth. Here, we propose a far-infrared tunable band-stop filter based on Fabry-Perot (FP) resonators and graphene surface plasmons. By switching the wavelength of the critical coupling condition of the filter via the gate voltage applied on graphene, achieving the dynamically tunable band-stop filtering at the central wavelengths from 12.4 μm to 14.1 μm with a modulation depth of more than 99%. Due to the symmetry of the proposed meta-atoms, the filter is insensitive to the polarization direction of the incident light. And it can realize more than 85% filtering efficiency within 60° angle of incidence around the vertical direction. By adjusting the geometry of the meta-atoms structure, it is feasible to move the operational range from the near-infrared to terahertz bands.

Enhancing circular dichroism with anisotropic heterogeneous-structure based on MQBIC resonance

Metasurfaces based on quasi-bound states in the continuum (QBIC) typically require careful tuning of structural parameters to meet critical coupling condition, thereby maximizing circular dichroism (CD). In this study, we propose an innovative heterogeneous-structure comprising four pairs of symmetry-breaking silicon dielectric rods embedded in an anisotropic polymer. The resonance of magnetic QBIC (MQBIC) within the dielectric rods generates a CD response, while the polymer effectively modulates the chirality of the heterogeneous-structure and enhances the CD. This enhancement occurs because the resonance of the MQBIC in the diagonal direction of the heterogeneous-structure is confined, leading to a break in mirror symmetry. Further investigations reveal that even when critical coupling condition are not satisfied, CD can still be maximized through rotational modulation. Additionally, the critical coupling condition for the resonance of MQBIC in the heterogeneous-structure are more readily achievable, allowing the CD response to remain unconstrained by lattice constants. This research is anticipated to have a significant impact on the fields of biosensing and medical imaging in the future.

T-matrix of piezoelectric shunt inclusions on a thin plate

Developing piezoelectric-based plate-like metamaterials necessitates an effective modeling method to elucidate the omnidirectional wave properties of piezoelectric coupled inclusions on a thin plate. The commonly used methods, such as the transfer-matrix method and finite element method, are inadequate for analyzing the transmission and reflection of omnidirectional waves in a two-dimensional elastic medium. Unlike the existing methods, the multiple scattering method employs Bessel functions as the displacement-basis methods which can accurately describe the propagation and scattering characteristics of omnidirectional waves. This paper develops a novel T-matrix formulation to support the multiple scattering method, representing the input-output relationship between incident and reflected waves from a piezoelectric shunt inclusion on a host thin plate. The piezoelectric shunt inclusion comprises a varying-thickness substrate bonded with piezoelectric shunting patches. The T-matrix of the piezoelectric shunt inclusion is formulated by integrating the wave-based method with Rayleigh-Ritz method. The derived T-matrix is then used to semi-analytically analyze the far-field scattering and reflection properties of a single inclusion. Numerical results capture the scattering properties resulting from trapped mode resonances of the piezoelectric shunt inclusion. Additionally, the capability of the piezoelectric shunt damping to design and tune multiple critical coupling conditions for axisymmetric modes of thin plates is parametrically investigated by varying the values of inductors and resistors.

Graphene-based hybrid metasurfaces with quasi-bound states in the continuum for manipulating terahertz absorption

We present a graphene-based hybrid metasurface with quasi-bound states in the continuum (BICs) for manipulating terahertz (THz) wave absorption. By the strategic application of structural perturbations for the THz metasurface, the symmetry-protected BICs transforms into quasi-BICs. The incorporation of graphene adeptly satisfies the critical coupling condition, thereby facilitating the attainment of the theoretical maximum absorption of 0.5 for the quasi-BICs in the THz region. And the Q-factor of the quasi-BIC can be up to 2755. Moreover, the metasurface exhibits a distinctive ability for unique tuning and efficient absorption of terahertz waves by varying the asymmetry parameter and Fermi levels. This work provides promising strategies for manipulating terahertz wave absorption.

Experimental Demonstration of High-Efficiency Harmonic Generation in Photonic Moiré Superlattice Microcavities.

Integrated photonic microcavities have demonstrated powerful enhancement of nonlinear effects, but they face a challenge in achieving critical coupling for sufficient use of incident pump power. In this work, we first experimentally demonstrate that highly efficient third-harmonic generation (THG) and detectable second-harmonic generation (SHG) can be produced from high-Q photonic moiré superlattice microcavities, where a critical coupling condition can be achieved via selecting a magic angle. Furthermore, at the magic angle of 13.17°, critical coupling is satisfied, resulting in a normalized THG conversion efficiency of 136%/W2 at a relatively low peak pump power of 6.8 MW/cm2, which is 3 orders of magnitude higher than the best results reported previously. Our work shows the power of photonic moiré superlattices in enhancing nonlinear optical performances through flexible and feasible engineering resonant modes, which can be applied in integrated frequency conversion and generation of quantum light sources.

Transverse magneto-optical Kerr effect enhanced by surface plasmon resonances at the critical coupling condition

Nanostructures possessing plasmonic and magnetic properties can enhance the transverse magneto-optical Kerr effect (TMOKE) by exciting surface plasmon resonances (SPRs). This provides a promising platform for magneto-optical SPR sensors with significantly improved sensing performance. Here, we propose a high-performance magneto-optical SPR sensor, which consists of a bilayer Au/Co grating placed on a gold film. By tuning the structural parameters, a Fano-like TMOKE spectrum with a linewidth of only 0.0135 nm and an amplitude approaching the theoretical maximum is obtained. We attribute the optimal TMOKE signal achieved by the sensor to the critical coupling concept which is associated with the trade-off between scattering and intrinsic decay rates of the system. The optimized nanostructure sensor demonstrates a sensitivity of 1432 nm/RIU to refractive index fluctuations as small as 0.0001 in air, and all figures of merit (FOM) up to 105 RIU−1, making it suitable for gas sensor fabrication.

Polarization-insensitive terahertz third-harmonic generation from degenerate pairs of mirror-coupled super-BICs

Resonant nanostructures have emerged as versatile photonic platforms for boosting optical nonlinear responses on a subwavelength scale for their ability to confine intense electromagnetic fields while relaxing the phase-matching requirements. Recent significant advances in this field are associated with the utilization of non-radiative eigenmodes above the light cone, termed bound states in the continuum (BICs), which provide a unique mechanism for light trapping to realize excitation of ultrahigh quality (Q) factor resonances. Nevertheless, the current studies on BICs predominantly focus on symmetry-protected BICs (SP-BICs), whose excitation requires symmetry breaking, and Q factors are limited by fabrication imperfections. Here, we demonstrate a simple and feasible scheme for creating degenerate pairs of mirror-coupled super-BICs by harnessing magnetic dipole resonances coupled to their mirror images in adjacent metal films. Unlike trivial SP-BICs, mirror-coupled BICs showcases the huge enhancement of Q factors and are resilient against fabrication imperfections. By combining mirror-coupled resonance with the engineered radiative loss, we obtain a perfect absorber with near-unity absorption and ultra-narrow bandwidth at a critical coupling condition. Finally, we numerically demonstrate the terahertz (THz) regime, polarization-insensitive highly efficient third-harmonic generation benefiting from the maximum field enhancement localized within the perfect absorber. Our work not only paves the way toward unlocking the full potential of BIC resonance but also promise valuable insights for developing efficient THz optoelectronic devices and metadevices across a wide range of fields.

High-efficiency and stable laser transmission for laser and electrochemical machining

Laser and electrochemical machining (LECM) has been increasingly adopted to improve the efficiency and surface quality of micromachining. The coupling and high-efficiency transmission of laser in electrolyte are critical to the implementation of LECM, which were rarely studied in previous research. In this study, the geometric and simulation model of laser coupling and transmission within the electrolyte jet has been established for laser and shaped tube electrochemical machining (Laser-STEM). The critical coupling condition and transmission efficiency of laser beam was investigated theoretically. Influences of laser coupling errors on the laser transmission efficiency and laser power intensity distribution at the exit of hybrid tool electrode were explored. Results indicated that the angular offset had the greatest impact on laser transmission efficiency, while the longitudinal offset impact the least, which were accordance with the experimental results. The thresholds of laser power intensity and the frequency of the laser-induced electrolyte breakdown were measured. The thresholds for laser-induced breakdown in NaNO3 solution were higher than that in NaCl solution. The laser power intensity threshold of laser-induced electrolyte breakdown increased with the increase of focal length, and the frequency of smaller than 4.5 could be obtained with the laser power density ranging from 2.35e9 to 1.06e10 W/cm2 at the focal spot. The distribution trended to more uniform at the exit with the increase of hybrid tool electrode length. A laser coupling efficiency of larger than 81.2 % has been achieved by utilizing the hybrid tool electrode with NA of 0.534 and acceptance angle of 32.3°. Finally, experiments with a designed raster-shaped workpiece were conducted to verify the feasibility of laser transmission in large depth in the Laser-STEM process. The high aspect-ratio small holes with a depth of 50 mm, and a diameter of 1.3 mm have been processed by using Laser-STEM.

WITHDRAWN: The periodic evolution of the resonant mode in a lossy microfiber coil resonator with three turns

The periodic evolution of the resonant mode in a lossy microfiber coil resonator with three turns is unraveled, and two types of loss conditions are assumed to investigate the characteristics of resonant mode with respect to the coupling state by means of numerical modeling. Under a given loss condition, the resonant mode exhibits periodic evolution between normal resonance, white-light cavity effect and resonance mode splitting as the change of the phase shift and coupling state. When the coupling state exceeds a certain threshold under a specific loss coefficient, the microfiber coil resonator predominantly exhibits normal resonance with characteristics akin to a single-ring resonator. Once the coupling state decreases to this threshold and matches the loss, white-light cavity effect will be activated. Moreover, as the coupling state falls below this threshold, the degeneracy of the resonance mode is raised and the resonant phase undergoes a bifurcation. The excitation conditions for each resonant mode have been derived, and the critical coupling conditions exist for both normal resonance and mode splitting in the case of relatively small losses. It’s found that there exists a threshold loss at which the critical coupling states of normal resonance and mode splitting coincide with the condition of white-light cavity effect. The characteristics of each mode have also been discussed.

Two-peak envelope spectrum of a subwavelength grating microring resonator for wide-range and high-sensitivity refractive index sensing

The detectable range and sensitivity play a key role in the accuracy and range of applications available for lab-on-a-chip sensing systems. Here, we propose and numerically demonstrate an on-chip refractive index sensor simultaneously possessing wide detectable range and high sensitivity through monitoring the two-peak envelope spectrum of a subwavelength grating microring resonator. The principle lies in the combination of the envelope spectrum tracking scheme and the light field releasing in subwavelength grating waveguides. The structure of the subwavelength grating microring resonator is designed to adjust the wavelength dependence of its critical coupling condition, so that the two-peak envelope spectrum can be formed and centered at critically coupled wavelengths. By probing the drift of the two-peak envelope spectrum within the C+L band (1530–1625 nm), we lift the free spectral range constraint on the detectable range and broaden it up to 0.46 RIU. Meanwhile, a sensitivity of 444 nm/RIU is achieved. This investigation provides an attractive candidate for high performance integrated sensors, and thus may pave the way for lab-on-chip sensing, especially in application scenarios demanding both wide detectable range and high sensitivity.

From weak to strong coupling: quasi-BIC metasurfaces for mid-infrared light-matter interactions.

Thanks to their giant, yet tunable, Q-factor resonances, all-dielectric metasurfaces supporting the quasi-bound states in the continuum (q-BIC) resonances are well-suited to provide a promising platform for quantum-coherent light-matter interactions. Yet, the strong coupling regime, characterized by the hybrid light-matter states - polaritons, has not yet been fully explored in the mid-infrared regime. This paper investigates the parameter space of vibrational strong coupling (VSC) between material and metasurface cavities supporting q-BIC resonances in the mid-infrared spectral range. We outline the effects of transition dipole strength, damping rate, and the number of molecules coupled to a single cavity, as well as the cavity damping rates, to understand their respective impacts on VSC. By tuning the Q-factor of the metasurface and material parameters, a new transition light-matter coupling zone is introduced, bridging the gap between weak and strong coupling, where polaritons form but their linewidths prohibit their spectral identification. The study further identifies the effects of cavity linewidth on polariton peak separability in strongly coupled systems, highlighting that the cavities with smaller nonradiative losses and narrower linewidths facilitate better polariton separability. Moreover, we found that matching cavity and material loss, satisfying the critical strong coupling condition, enhances the coupling strength between cavity and material. Overall, these findings can guide the design of photonic cavities suited for VSC experiments, contributing to the burgeoning fields of polaritonic chemistry, light-mediated modulation of chemical reactivity, and highly sensitive molecular spectroscopy.

Efficient excitation and control of integrated photonic circuits with virtual critical coupling

Critical coupling in integrated photonic devices enables the efficient transfer of energy from a waveguide to a resonator, a key operation for many applications. This condition is achieved when the resonator loss rate is equal to the coupling rate to the bus waveguide. Carefully matching these quantities is challenging in practice, due to variations in the resonator properties resulting from fabrication and external conditions. Here, we demonstrate that efficient energy transfer to a non-critically coupled resonator can be achieved by tailoring the excitation signal in time. We rely on excitations oscillating at complex frequencies to load an otherwise overcoupled resonator, demonstrating that a virtual critical coupling condition is achieved if the imaginary part of the complex frequency equals the mismatch between loss and coupling rate. We probe a microring resonator with tailored pulses and observe a minimum intensity transmission T=0.11\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$T=0.11$$\\end{document} in contrast to a continuous-wave transmission T=0.58\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$T=0.58$$\\end{document}, corresponding to 8 times enhancement of intracavity intensity. Our technique opens opportunities for enhancing and controlling on-demand light-matter interactions for linear and nonlinear photonic platforms.

Optimum asymmetry for nanofabricated refractometric sensors at quasi-bound states in the continuum

A symmetry-protected bound state in the continuum (BIC) is one of the bases for high-resolution photonic refractometric sensors that rely on spectral shifts. However, a trade-off exists between the quality (Q) factors and the resonance amplitudes when the asymmetries of the unit cell are changed, making it difficult to intuitively determine the optimal nanostructural geometry. In this study, we present a theoretical and experimental approach for identifying the asymmetry parameters of dielectric metasurfaces that yield the lowest limit of detection (LOD). Silicon-based metasurfaces with asymmetric pair-rod arrays are fabricated experimentally, and the minimum LOD is obtained under a critical coupling condition with equal radiative and nonradiative Q factors. The results agree well with the theoretical model derived from the temporal coupled-mode theory. We reveal that the LOD and the optimum asymmetry are significantly influenced by nonradiative losses in the nanostructure, emphasizing the importance of loss reduction in dielectric metasurfaces at quasi-BICs for high-performance refractometric sensors.

Linear Terahertz Frequency Conversion in a Temporal‐Boundary Metasurface

AbstractLinear frequency conversion enabled by a temporal boundary of a resonant cavity provides a promising alternative to generating new frequency components, where the temporal boundary can be introduced by rapidly modifying the refractive index of the cavity. However, the perturbed photon dynamics during the ultrafast linear process is still vague. Here, the photon dynamics based on temporal coupled‐mode theory are explored and the phenomena are demonstrated with a silicon metasurface via simulations and experiments in the terahertz regime. With the time‐varying real and imaginary parts of the refractive index, a periodic modulation (Td) of the amplification coefficient of the newly generated photons is observed where the optimized coefficient occurs in the first period at td = Td /2. It further establishes a dynamic critical coupling condition to improve the amplification coefficient in the dynamic process. The scheme of linear frequency conversion via temporal boundary can revolutionize the paradigm of parametric amplification from nonlinear to linear processes, and conversion efficiency will be improved in a high‐quality factor cavity. The ultrafast modulation will find applications in optical signal processing, modulators, and reconfigurable intelligent surfaces for development of the next‐generation communications.

Maximum chirality of THz metasurfaces with quasi-bound states in the continuum.

Metasurfaces hold great promise for terahertz (THz) chiral-optical devices. Here, we proposed a chiral THz metasurface with quasi-bound state in the continuum (BIC) for maximum chirality. By exploiting structural perturbations of the dipole displacement and the diverging angle for the THz metasurface, the symmetry-protected BIC transforms into quasi-BIC. The critical coupling condition is satisfied by the introduction of graphene, enabling the theoretical maximum absorption of the quasi-BIC. Subsequently, the perturbations are balanced to obtain maximum chirality. The numerical simulations show that the THz metasurface exhibits strong linear chirality with the circular dichroism (CD) of 0.99 at the quasi-BIC. Additionally, the chiral third harmonic generation (THG) is achieved, characterized by high efficiency up to 19% and strong THG-CD as high as 0.99. It is expected that the THz metasurfaces has great potential for applications in chiral sensing and imaging.

High-speed metasurface modulator using perfectly absorptive bimodal plasmonic resonance

Free-space electro-optic (EO) modulators operating at gigahertz and beyond are attractive for a wide range of emerging applications, including high-speed imaging, free-space optical communication, microwave photonics, and diffractive computing. Here, we experimentally demonstrate a high-speed plasmonic metasurface EO modulator operating in a near-infrared wavelength range with a gigahertz modulation bandwidth. To achieve efficient intensity modulation of reflected light from an ultrathin metasurface layer, we utilize the bimodal plasmonic resonance inside a subwavelength metal–insulator–metal grating, which is precisely tuned to satisfy the critical coupling condition. As a result, perfect absorption of −27 dB (99.8%) and a high quality (Q) factor of 113 are obtained at a resonant wavelength of 1650 nm. By incorporating an EO polymer inside the grating, we achieve a modulation depth of up to 9.5 dB under an applied voltage of ±30 V. The 3-dB modulation bandwidth is confirmed to be 1.25 GHz, which is primarily limited by the undesired contact resistance and the output impedance of the driver. Owing to the high electrical conductivity of metallic gratings and a compact device structure with a minimal parasitic capacitance, the demonstrated device can potentially operate at several tens of gigahertz, which opens up exciting opportunities for ultrahigh-speed active metasurface devices in various applications.

Machine learning assisted design of acoustic metamaterials with broadband sound-absorbing and superior mechanical performance

It remains challenging to design lightweight metamaterials with superior sound-absorbing and load-bearing capacities. One promising approach is using multiple coherently coupled resonators to serve as sound absorbers and reinforced grid cores of sandwich panels. However, with too many design parameters each requiring careful tuning to reach the stringent critical coupling condition, achieving an optimal design based on experience alone is challenging. An autoencoder-like neural network is constructed that, once well trained, significantly promote the inverse design process thanks to the highly efficient computational speed. Particularly, a probabilistic model is inserted into the network to tackle ill-posed inverse problems requiring man-made and probably unreal spectrum as an input, and can provide multiple ultra-thin (32 mm) and broadband designs. We have fabricated and tested the optimized metallic sandwich structures, showing broadband capacity of using solely nine resonators to achieve quasi-perfect sound absorption (over 0.9) from 399 to 675 Hz. The static compression and dynamic impact testing also verify the superior mechanical performance with high yield strength (21.2 MPa) and large normalized energy absorption (0.29) at lower relative density (13.5%). We believe this work is encouraging to accelerate the design of multifunctional absorbers targeted especially for low-frequency noise control in engineering.

Dual-mode tunable absorber based on quasi-bound states in the continuum.

In this Letter, we propose a novel, to the best of our knowledge, dual-mode tunable absorber that utilizes quasi-bound states in the continuum (q-BIC) based on the periodically arranged silicon cylinders tetramer. By introducing asymmetry perturbation through manipulating the diameters of diagonal cylinders in the all-dielectric structure, the symmetry-protected BIC (SP-BIC) transforms into q-BIC, leading to the emergence of one transmission and one reflection Fano-like resonant mode. The relationship between the quality factor of each mode and the asymmetry parameter α is analyzed, revealing an exponential dependence with an exponent of -1.75, i.e., Q ∝ α-1.75. To explain the underlying physics, multipole decomposition analysis and Aleksandra's theory are applied. Subsequently, a monolayer graphene is introduced to the all-dielectric structure to demonstrate the application of the dual-mode tunable absorber. When the critical coupling condition is satisfied, each mode can achieve the theoretical maximum absorption, demonstrating the distinctive capability of our proposed absorber for tuning and efficient light absorption. This research provides valuable insights into light-matter interactions and opens up possibilities for optical modulation and the development of graphene-based devices.

Perfect Absorption and Reflection Modulation Based on Asymmetric Slot-Assisted Gratings without Mirrors.

As a perfect graphene absorber without any external mirrors, we proposed asymmetric slot-assisted grating structures supporting two degenerate resonant modes of the guided-mode resonances (GMR) and the quasi-bound states in the continuum (quasi-BIC). The GMR mode functions as an internal mirror in conjunction with the background scattering, while the quasi-BIC, which is responsible for perfect graphene absorption, stems from the horizontal symmetry breaking by an asymmetric slot. By properly shifting the slot center from the grating center, the leakage rate of quasi-BIC can be controlled in such a way as to satisfy the critical coupling condition. We provide a comprehensive study on the coupling mechanism of two degenerate resonant modes for a one-port system mimicking the resonance. We also numerically demonstrated that our proposed grating structures show an excellent reflection-type modulation performance at optical wavelength ranges when doped double-layer graphene is applied. Due to the perfect absorption at the OFF state, a high modulation depth of ~50 dB can be achieved via a small Fermi level variation of ~0.05 eV. To obtain the lower insertion loss at the ON state, the higher Fermi level is required to decrease the graphene absorption coefficient.

Principles of progressive slow-sound and critical coupling condition in broadband sonic black hole absorber

Recent advances in sonic black hole (SBH) provide new opportunities for controlling sound waves and designing wave manipulation devices. SBH is a device that consists of partitions with gradually decreasing inner radii inserted into an acoustic duct. Several studies have reported that SBH can achieve a broadband sound absorption coefficient close to 1, avoiding the issue of alternating high and low absorption coefficients observed in traditional sound absorbers. However, the fundamental mechanisms and principles behind this behavior are not yet fully understood. This study aims to investigate the detailed sound absorption mechanisms of SBH, including the progressive slow-sound effect and the critical coupling condition that leads to broadband sound absorption. To achieve this goal, an analytical model based on the effective medium approach is developed to investigate the layer-by-layer retardation in sound propagation. The sound absorption coefficient is then determined based on the surface impedance calculation. The effective medium analysis reveals that SBH enables a unique condition to progressively decelerate wave propagation across its layers. As a result, the critical coupling condition becomes more easily established with smoothly increasing SBH partitions and more discretised layers, as elucidated by the complex frequency analysis results. The physical insights gained from this study reveal the distinctive features of SBH compared to classical sound absorbers, paving the way for its engineering applications.