Wave Vector Research Articles

Metastable and unstable hydrodynamics in multiphase lattice Boltzmann.

Metastability in liquids is at the foundation of complex phase transformation dynamics such as nucleation and cavitation. Intermolecular interaction details, beyond the equationof state, and thermal hydrodynamic fluctuations play a crucial role. However, most numerical approaches suffer from a slow time and space convergence, thus hindering the convergence to the hydrodynamic limit. This work shows that the Shan-Chen lattice Boltzmann model has the unique capability of simulating the hydrodynamics of the metastable state. The structure factor of density fluctuations is theoretically obtained and numerically verified to a high precision, for all simulated wave vectors, reduced temperatures, and pressures, deep into the metastable region. Such remarkable agreement between the theory and simulations leverages the exact implementation at the lattice level of the mechanical equilibrium condition. The static structure factor is found to consistently diverge as the temperature approaches the critical point or the density approaches the spinodal line at a subcritical temperature. Theoretically predicted critical exponents are observed in both cases. Finally, the phase separation in the unstable branch follows the same pattern, i.e., the generation of interfaces with different topology, as observed in molecular dynamics simulations.

Probing rotated Weyl points on one-dimensional sonic crystals

Recently, researchers have devoted their intense efforts to investigating Weyl physics in synthetic space. In this Letter, we study the intriguing topological rotated Weyl physics in a three-dimensional parameter space, which consists of two extra structural parameters and the wave vector of a simple one-dimensional sonic crystal. In our ultrasonic experiments, we observe that the topological interface states propagate along the interface formed by two sonic crystals of distinct chirality caused by the rotated Weyl points. We detect the rotated synthetic Weyl points and measure the singularities of the reflection phase, which results in the robustness of the interface states. At the same time, it also shows the advantages of synthetic dimensions in exploring high-dimensional physics problems in low-dimensional systems.

Topological Phase Singularities in Light Reflection from Non‐Hermitian Uniaxial Media

AbstractPerfect light transmission into a dielectric at the Brewster angle is one of the simplest effects of macroscopic electromagnetism. The common wisdom states that absorption in the dielectric violates Brewster angle and leads to a non‐vanishing reflection. Yet, incorporating anisotropy may recover perfect transmission of p‐polarized light into the absorbing medium. Unlike the ordinary “lossless” Brewster angle, perfect transmission in this case is accompanied by phase singularities of the reflection amplitude. In this paper, phase singularities and the associated topological charges are theoretically examined as emerging in the wavelength‐incidence angle space upon perfect transmission into absorbing uniaxial dielectrics. The analytical criterion of perfect light transmission into an anisotropic medium is derived, phase singularities are demontrated in these scenarios, and their dynamics are studied as a function of material parameters. Finally, by lowering the symmetry of the problem, this phenomenon is translated into a different parameter space of wave vector components, and illustrate the feasibility of this phenomenon with available optically anisotropic materials. The results may become valuable for the development of novel analog computing schemes and holography approaches.

Temperature-dependent evolution of micromagnetic structure of B20-type Fe1-xCoxGe studied by Mössbauer spectroscopy

The non-collinear magnetic structures hosted in magnets with broken central inversion symmetry, some of which are topologically non-trivial, have unique physical properties and application prospects. This paper presents a detailed study of the temperature evolution of the micromagnetic structures of B20-type Fe1-xCoxGe (x = 0, 0.05, 0.10) polycrystalline samples using 57Fe Mössbauer spectroscopy. We take the relatively weak electric quadrupole interaction as a perturbation of the hyperfine magnetic interaction to obtain the distribution of the hyperfine magnetic field Hhf (φ) in the plane perpendicular to the magnetic propagation vector ks. It is found that the geometric features of Hhf (φ) are sensitive to the relative orientation of ks regarding the electric field gradient at the iron nucleus, as well as to the spin texture. The temperature dependence of Hhf (φ) provides a distinct signal of first-order phase transition when ks shifts from [100] to [111]. The doping of cobalt atoms leads to out-of-plane component and in-plane component aggregation of the neighboring iron magnetic moments. These results are instructive for understanding the dynamical behavior of spiral magnets with long-periods.

Transit‐Time Instability Mechanism in Lateral Graphene n+‐i‐n‐i‐n+ Structure with Transverse Terahertz Pasmonic Resonant Cavity

The terahertz (THz) plasmonic instability in the lateral graphene structure (LGS) with the n+‐i‐n‐i‐n+ junction in its graphene channel (GC) is analyzed. The i‐regions in the LGS n+‐i‐n‐i‐n+ GC plays the role of the transit spaces of the electrons emitted from the n+‐regions (the emitters) and collected by the gated n‐region (collector) and the side contact to the latter. The interband Zener–Klein tunneling (ZKT) in the i‐regions also contributes to the currents received by the n‐region. Simultaneously, the n‐region constitutes the transverse resonant plasmonic cavity, in which the plasmons with the wave vector directed perpendicular to the electron propagation direction are excited. The plasmonic instability in the LGSs is associated with the transit‐time negative dynamic conductance of the i‐regions supported by the plasmonic resonances in the n‐region. The self‐excitation of plasmonic oscillations associated with the instability in the LGS with sub‐micrometer i‐regions and supplied with a proper antenna can lead to the emission of THz radiation. The LGS can form periodic arrays, which can serve as an active distributed antenna.

Investigation of a Pyramid-like Optical Absorber with High Absorptivity in the Range of Ultraviolet A to Middle Infrared

In this study, a simple pyramid-like ultra-wideband absorber was designed to explore high absorptivity across a wide bandwidth. The absorber consisted of eight layers organized into four groups, and each group comprised a metal layer followed by an oxide layer, both of which were square with equal side lengths. Specifically, the chosen oxides, arranged from bottom to top, included SiO2 (t7 layer), Al2O3 (t5 layer), SiO2 (t3 layer), and Al2O3 (t1 layer). In the initial design phase, the thickness of the t8 Ti layer was set to 50 nm and assigned initial values to the thicknesses of the t7-t1 layers, and the widths of the four groups w4, w3, w2, and w1, decreased successively from bottom to top, creating a structure reminiscent of a pyramid. Comsol (version 6.0) was utilized to simulate and systematically vary one parameter at a time, ranging from the thicknesses of the t7-t1 layers to the widths of w4-w1, in order to identify the most suitable structural parameters. Our analyses demonstrated that multimode resonance arose due to the emergence of absorption peaks at lower wavelengths between larger and smaller areas. Additionally, surface plasmon resonance and interference effects between various layers and materials were attributed to the alternating arrangement of metal and oxide layers. The enhancements in the electric field observed at different resonance peak wavelengths illustrated the Fabry–Perot cavity effect, while the impedance matching effect was observed through variations in the real and imaginary parts of the optical impedance with respect to the wave vector. After simulating using these optimally found thicknesses and widths, the aforementioned effects manifested in the pyramid-like ultra-wideband absorber we designed, with its absorptivity surpassing 0.900 across the spectrum from ultraviolet A (335 nm) to middle infrared (4865 nm).

Analytical study of linear optical properties of metal nanoparticle trimers: the impact of dipole-dipole interaction on different modes of configuration

In this study, we theoretically investigate the linear properties of a metal nanoparticle (MNP) trimer. Three identical spherical nanoparticles (NPs) whose centers are equidistantly oriented on a same straight line are considered. Using the solid core approximation for NPs and considering interaction between particles through induced electric dipoles, the motion equation of each NP conduction electrons is analytically solved. Some appropriately approximated expressions are derived for the permittivity of each NP based on a Drude-like model, allowing the clear observation of the contribution of inter-particle interaction. Depending on the orientation of the trimer axis and incident laser beam geometry (i.e., orientation of electromagnetic (EM) fields and wave vector of laser beam), three different configurations or modes are considered. The extinction efficiency of each NP as a function of wavelength is plotted, revealing that when the laser electric field is perpendicular to the symmetry axis of the trimer, it increases compared to the case of non-interactional single NP, and its plasmon resonance peak experiences a red shift. For other cases where the electric field of the laser beam is parallel to the trimer axis, the extinction efficiency of each NP decreases, and its peak shifts to the blue. In all cases, the effect of interaction on the optical properties of the middle NP is greater than on the other NPs.

Switching the spin cycloid in BiFeO3 with an electric field

Bismuth ferrite (BiFeO3) is a multiferroic material that exhibits both ferroelectricity and canted antiferromagnetism at room temperature, making it a unique candidate in the development of electric-field controllable magnetic devices. The magnetic moments in BiFeO3 are arranged into a spin cycloid, resulting in unique magnetic properties which are tied to the ferroelectric order. Previous understanding of this coupling has relied on average, mesoscale measurements. Using nitrogen vacancy-based diamond magnetometry, we observe the magnetic spin cycloid structure of BiFeO3 in real space. This structure is magnetoelectrically coupled through symmetry to the ferroelectric polarization and this relationship is maintained through electric field switching. Through a combination of in-plane and out-of-plane electrical switching, coupled with ab initio studies, we have discovered that the epitaxy from the substrate imposes a magnetoelastic anisotropy on the spin cycloid, which establishes preferred cycloid propagation directions. The energy landscape of the cycloid is shaped by both the ferroelectric degree of freedom and strain-induced anisotropy, restricting the spin spiral propagation vector to changes to specific switching events.

On the Wave‐Normal Distribution of Lightning‐Generated Whistlers and Their Propagation Modes

AbstractObservations from Van Allen Probes are analyzed to obtain the statistical wave normal distribution of lightning‐generated whistlers (LGWs). An automatic algorithm is developed to identify burst mode waveform data with LGW signals and analyze the wave polarization information for these LGW signals. The spatial distribution of the LGW occurrence and the probabilities of different propagation types demonstrate that most LGWs can be observed in the low L‐shell region (L < 3), where the dominant propagation type is oblique outward. Parallel propagation dominates in the high L‐shell region, but the LGW occurrence is very small. Additionally, a small group of oblique but inwardly propagating LGWs are observed at low altitudes (<0.2RE). A ray tracing simulation is performed not only to confirm predominant oblique and outward wave vectors in the vast region of the plasmasphere but also to verify the existence of these inward propagating LGW signals at low altitudes near the topside ionosphere.

Comparative Studies of Phonon Frequency Spectrum of HTSCs GdBa2Cu3O7 and SmBa2Cu3O7 Through Normal Co-Ordinate Analysis

The prime application of Nano technology is High temperature superconductor. The Raman spectroscopy of HTSC explains that the role played by the phonons in the mechanism of superconductivity in the perovskite family of superconductors is not fully understood although a large series of experimental results has shown considerable coupling of some phonons to electronic excitation in these systems. Optical spectroscopy and especially Raman and Infrared spectroscopy revealed strong direct influences of the changes in the electronic states to the phonon at the center of the Brillouin. However, it is indispensable to have a precise knowledge of the zone –boundary phonons to investigate the contribution of electron-phonon coupling to Tc which can be achieved by neutron scattering techniques. The most commonly employed model is the valence force field model for computing phonon frequencies based on stretching bond and bending bond coordinates. Such models have the advantage of being well adopted to describe a covalent bonding but ignored the long–range Coulomb forces and wave vector dependence of the phonon spectrum. Even though a fairly good amount of literature is available on the vibrational spectra of high temperature superconductors, still some specific feature in the experimental vibration spectra could not be assigned reliable to a definite type of vibration. Hence a normal coordinate analysis (NCA) which is applicable to zero wave-vector normal-mode vibrations have been carried out for the high temperature superconductors and the assignment of specific features like phonon softening and hardening were looked in for the clear understanding of the superconducting mechanism in these new class materials. In the normal coordinate analysis, PED play an important role for characterization of the relative contributions from each internal coordinate to the total potential energy associated with particular normal coordinate of the molecule. The contribution to the potential energy from the individual diagonal elements give rise to a conceptual link between the empirical analysis of infrared spectra of complex molecules dealing with characteristic group frequencies and the theoretical approach from the computation of the normal modes. NCA gives complete assessment of all normal vibration modes of the system.

Electronic and Optical Characteristics of Phosphorus-Doped Two-Dimensional Hexagonal Boron Arsenide: The Effects of Doping Concentration and Mechanical Strain

Abstract The present study investigates the impact of P doping and stretching loads on phonon dispersion, electronic properties, and optical characteristics of P-doped hexagonal boron arsenide (h-BAs(1-x)Px), where the doping level x varies from 0 to 1, employing the density functional theory (DFT) method. The findings reveal that the chemical bonds in h-BAs(1-x)Px monolayers are indeed covalent. Furthermore, an increase in P concentration from 0.0% to 100% leads to enhancement in the band gap, approximately 18.42%. However, regardless of variations in P concentration or the application of tensile strains up to 4%, the electronic nature of h-BAs(1-x)Px remains unaltered. These monolayers continue to exhibit characteristics of a direct band gap semiconductor at the K wave vector. On the other hand, there exists an intricate interplay between strain and optical properties. Investigating the dielectric functions, absorption coefficient, refractive index, and reflectivity coefficient of h-BAs(1-x)Px monolayers provides insights into their behavior in the ultraviolet spectrum.

Tuning optical properties of Au thin film using electric field for surface plasmon resonance biosensor application

The effect of electric field application on the optical properties of gold (Au) thin film for spectroscopic ellipsometry-based surface plasmon resonance (SPR) biosensor applications has been successfully studied. The optical properties, such as the complex refractive index, complex dielectric constant, real optical conductivity, and absorption coefficient, were determined by fitting data from the ψ and Δ functions obtained through measurements using a homemade rotating analyzer ellipsometer. The applied electric fields of 0.8 V/cm, 1.6 V/cm, 2.4 V/cm, and 3.2 V/cm were induced by applying voltages of 1 V, 2 V, 3 V, and 4 V for ellipsometer tests, and 1.6 V/cm to 3.2 V/cm for the SPR test. The Au thin film was deposited onto a glass slide using an evaporator for ellipsometer testing and a BK7 half-cylinder prism was employed for SPR testing. The experimental results show that the real part of the refractive index (n) increases in the spectral range from 1.5 eV to 2.2 eV and from 3 eV to 5 eV and tends to be constant in the range from 2.3 eV to 2.8 eV. Conversely, the imaginary part of the refractive index (k) decreases from 2.8 eV to 3.6 eV and tends to remain consistent from 3.9 eV to 5.0 eV. The dielectric constant (ε1) consistently shows a significant increase within the spectral range of 3 eV–5.0 eV, with a tendency to decrease between 2.1 eV and 2.4 eV. Meanwhile, the imaginary part (ε2) demonstrates an increase in the spectral range of 1.5 eV–2.4 eV and 3.3 eV–5.0 eV while maintaining relatively stable values in the energy spectral range of 2.6 eV–3.0 eV. Moving to the real part of optical conductivity (σ1), it increases within the spectral range from 1.5 eV to 2.4 eV and from 3.5 eV to 5 eV, with relatively constant values between 2.6 eV and 3.1 eV. The absorption coefficient (α) exhibits a decrease in the spectrum between 2.8 eV and 3.6 eV, but the values remain stable within the range of 3.9 eV–5.0 eV. The α slightly decreases in the energy range of 1.8 eV–2.6 eV. The outcomes obtained from these experiments are directly linked to the SPR results, revealing a noticeable shift in the SPR angle (θSPR) of 45.51°, 45.61°, and 45.73° and an increase in the minimum reflectance (Rmin) of 0.05, 0.09, and 0.13 for electric field strengths of 0 V/cm, 1.6 V/cm, and 3.2 V/cm, respectively. These results imply that the application of an external electric field to the surface of the Au thin film disrupts the matching condition between the evanescent wave vector and the surface plasmon wave vector, thereby altering the reflected light under resonance conditions indicated by an increase in the minimum reflectance and SPR angle. This development holds significant promise to further enhance the sensitivity of electro-optic modulation-based biosensors.

Classical stochastic approach to quantum mechanics and quantum thermodynamics

We derive the equations of quantum mechanics and quantum thermodynamics from the assumption that a quantum system can be described by an underlying classical system of particles. Each component φ j of the wave vector is understood as a stochastic complex variable whose real and imaginary parts are proportional to the coordinate and momentum associated with a degree of freedom of the underlying classical system. From the classical stochastic equations of motion, we derive a general equation for the covariance matrix of the wave vector, which turns out to be of the Lindblad type. When the noise changes only the phase of φ j , the Schrödinger and the quantum Liouville equations are obtained. The component ψ j of the wave vector obeying the Schrödinger equation is related to the stochastic wave vector by |ψj|2=⟨|ϕj|2⟩ .

On some structural phase transitions in coupled quantum wires at finite temperature

In this paper, we explore some structural phase transitions in GaAs-based coupled electron-electron (e-e) and electron-hole (e-h) quantum wires at finite temperature. To this endeavour, the intra- and inter-wire static-structure factors, pair-correlation functions and static (charge) density susceptibilities are calculated over a wide range of temperature T, particle number density parameter r se and some selected values of inter-wire spacing d. The particle exchange-correlations (xc) are included using the dynamic version of self-consistent mean-field theory of Singwi et al (the qSTLS theory), and the results have been compared with the static STLS model. It has been found that in the e-h system, the inclusion of dynamic nature of xc leads to the formation of Wigner crystal (WC) state in the close proximity of two wires at wave-vector q ∼ 3.5k Fe . However, a charge-density-wave (CDW) instability is observed at q ∼ 2k Fe when the xc are treated statically (k Fe being the electron’s Fermi wave vector). On the other hand, the e-e system shows comparatively small signatures of the WC phase when wires are kept sufficiently far apart, but, a long-wavelength instability is encountered in close vicinity of the wires. Interestingly, the CDW phase is completely missing in the e-e system at the investigated parameters. Expectedly, the quantum phase transitions are predicted to occur in the strongly correlated regime i.e. at sufficiently small T and high r se .

Direct-write 3D printing of plasmonic nanohelicoids by circularly polarized light

Chiral plasmonic surfaces with 3D "forests" from nanohelicoids should provide strong optical rotation due to alignment of helical axis with propagation vector of photons. However, such three-dimensional nanostructures also demand multi-step nanofabrication, which is incompatible with many substrates. Large-scale photonic patterns on polymeric and flexible substrates remain unattainable. Here, we demonstrate the substrate-tolerant direct-write printing and patterning of silver nanohelicoids with out-of-plane 3D orientation using circularly polarized light. Centimeter-scale chiral plasmonic surfaces can be produced within minutes using inexpensive medium-power lasers. The growth of nanohelicoids is driven by the symmetry-broken site-selective deposition and self-assembly of the silver nanoparticles (NPs). The ellipticity and wavelength of the incident photons control the local handedness and size of the printed nanohelicoids, which enables on-the-fly modulation of nanohelicoid chirality during direct writing and simple pathways to complex multifunctional metasurfaces. Processing simplicity, high polarization rotation, and fine spatial resolution of the light-driven printing of stand-up helicoids provide a rapid pathway to chiral plasmonic surfaces, accelerating the development of chiral photonics for health and information technologies.

Vectorgastrogram: dynamic trajectory and recurrence quantification analysis to assess slow wave vector movement in healthy subjects.

Functional gastric disorders entail chronic or recurrent symptoms, high prevalence and a significant financial burden. These disorders do not always involve structural abnormalities and since they cannot be diagnosed by routine procedures, electrogastrography (EGG) has been proposed as a diagnostic alternative. However, the method still has not been transferred to clinical practice due to the difficulty of identifying gastric activity because of the low-frequency interference caused by skin-electrode contact potential in obtaining spatiotemporal information by simple procedures. This work attempted to robustly identify the gastric slow wave (SW) main components by applying multivariate variational mode decomposition (MVMD) to the multichannel EGG. Another aim was to obtain the 2D SW vectorgastrogram VGGSW from 4 electrodes perpendicularly arranged in a T-shape and analyse its dynamic trajectory and recurrence quantification (RQA) to assess slow wave vector movement in healthy subjects. The results revealed that MVMD can reliably identify the gastric SW, with detection rates over 91% in fasting postprandial subjects and a frequency instability of less than 5.3%, statistically increasing its amplitude and frequency after ingestion. The VGGSW dynamic trajectory showed a statistically higher predominance of vertical displacement after ingestion. RQA metrics (recurrence ratio, average length, entropy, and trapping time) showed a postprandial statistical increase, suggesting that gastric SW became more intense and coordinated with a less complex VGGSW and higher periodicity. The results support the VGGSW as a simple technique that can provide relevant information on the "global" spatial pattern of gastric slow wave propagation that could help diagnose gastric pathologies.

Two‐Dimensional Hybrid Simulation of the Second‐Harmonic Generation of EMIC Waves in the Inner Magnetosphere

AbstractTwo‐dimensional (2‐D) hybrid model is developed to investigate the second harmonic (SH) generation of electromagnetic ion cyclotron (EMIC) waves. Applying the singular value decomposition method to simulated fields, we show that the SH exhibits wave properties analogous to typical EMIC waves generated by ion cyclotron instabilities, that is, left‐hand polarization and small wave normal angle. However, the bicoherence index inferred from simulated fields reflects a strong phase coupling between the fundamental wave (FW) and the SH, illustrating the nonlinear generation of the SH by the FW. The necessary conditions, especially for the wave vector relation, are further verified from a 2‐D perspective. The simulated amplitude ratios well meet the theoretical results only in the SH saturation stage, while the necessary conditions remain satisfied almost throughout the simulation. This study provides a comprehensive analysis of the SH excitation in a 2‐D simulation domain, contributing to a deeper understanding of EMIC wave nonlinear generation.

The Shocks in Josephson Transmission Line Revisited

We continue our previous studies of the shocks in the lossy Josephson transmission line (JTL). The article consists of two parts. In the first part, we analyze the scattering of the “sound” (small amplitude small wave vector harmonic wave) on the shock wave and calculate the reflection and the transmission coefficients. In the second part, we show that the kinks, which we previously studied only in the lossless JTL, exist also in the lossy JTL and study the similarities and the dissimilarities between the shocks and the kinks there. We find that the nonlinear equation describing the weak kinks and the weak shocks can be integrated (in particular cases) in terms of elementary functions. We also show that the profile of the shock in the lossy JTL demonstrates oscillatory behavior with leading peaks resembling solitary waves if the losses are weak.

Applications of the kinetic theory for a model of a confined quasi-two dimensional granular mixture: Stability analysis and thermal diffusion segregation

The Boltzmann kinetic theory for a model of a confined quasi-two dimensional granular mixture derived previously [Garzó et al., “Navier–Stokes transport coefficients for a model of a confined quasi-two dimensional granular binary mixture,” Phys. Fluids 33, 023310 (2021)] is considered further to analyze two different problems. First, a linear stability analysis of the hydrodynamic equations with respect to the homogeneous steady state (HSS) is carried out to identify the conditions for stability as functions of the wave vector, the coefficients of restitution, and the parameters of the mixture. The analysis, which is based on the results obtained by solving the Boltzmann equation by means of the Chapman–Enskog method to first order in spatial gradients, takes into account the (nonlinear) dependence of the transport coefficients and the cooling rate on the coefficients of restitution and applies in principle to arbitrary values of the concentration, and the mass and diameter ratios. In contrast to the results obtained in the conventional inelastic hard sphere (IHS) model, the results show that all the hydrodynamic modes are stable so that the HSS is linearly stable with respect to long enough wavelength excitations. On the other hand, this conclusion agrees with previous stability analysis performed in earlier studies for monocomponent granular gases. As a second application, segregation induced by both a thermal gradient and gravity is studied. A segregation criterion based on the dependence of the thermal diffusion factor Λ on the parameter space of the mixture is derived. In the absence of gravity, the results indicate that Λ is always positive, and hence, the larger particles tend to accumulate near the cold plate. However, when gravity is present, our results show the transition between Λ>0 (larger particles tend to move toward the cold plate) to Λ<0 (larger particles tend to move toward the hot plate) by varying the parameters of the system (masses, sizes, composition, and coefficients of restitution). Comparison with previous results derived from the IHS model is carried out.

Indefinite metacavities coupled to a mirror: bound states in the continuum with anomalous resonance scaling

Indefinite metacavities (IMCs) made of hyperbolic metamaterials show great advantages in terms of extremely small mode volume due to large wave vectors endowed by the unique hyperbolic dispersion. However, quality (Q) factors of IMCs are limited by Ohmic loss of metals and radiative loss of leaked waves. Despite the fact that Ohmic loss of metals is inevitable in IMCs, the radiative loss can be further suppressed by leakage engineering. Here we propose a mirror coupled IMC structure which is able to operate at Fabry–Pérot bound states in the continuum (BICs) while the hyperbolic nature of IMCs is retained. At the BIC point, the radiative loss of magnetic dipolar cavity modes in IMCs is completely absent, resulting in a considerably increased Q factor (>90). Deviating from the BIC point, perfect absorption bands (>0.99) along with a strong near-field intensity enhancement (>1.8×104) appear when the condition of critical coupling is almost fulfilled. The proposed BICs are robust to the geometry and material composition of IMCs and anomalous scaling law of resonance is verified during the tuning of optical responses. We also demonstrate that the Purcell effect of the structure can be significantly improved under BIC and quasi-BIC regimes due to the further enhanced Q factor to mode volume ratio. Our results provide a new train of thought to design ultra-small optical nanocavities that may find many applications benefitting from strong light–matter interactions.