Optical Bound States in the Continuum Enabled by Magnetic Resonances Coupled to a Mirror

An ultrathin all-dielectric terahertz metamaterial with quasi-BIC induced angular dispersion

One typical characteristic of conventional all-dielectric terahertz metamaterials is their thickness, which is designed to be dozens of, or even one hundred microns, to reduce the leakage of the resonant field to the substrate. In the frequency range of 2 THz to 3 THz, we propose a substrate-free ultra-thin all-dielectric terahertz metamaterial (UATM) composed of a silicon (Si) dual-ellipse array and silicon dioxide (SiO2) supporting layer with thicknesses of 5 μm and 2 μm, respectively. The UATM exhibits quasi-bound state in the continuum (quasi-BIC) modes related to the tilt angle and period parameters. Moreover, due to the strong electromagnetic field near the interfaces and large interaction area, the UATM exhibits a high refractive index sensitivity exceeding 1.00 THz per RIU. Furthermore, at oblique incident angles ranging from 0° to 25°, the resonant quality factor (Q-factor) of the UATM remains higher than 100, and the sensitivities to the incident angle are 22.53 and 26.17 GHz per degree with a linear range of 0.498 THz and 0.438 THz, respectively. These properties indicate the potential applications of the UATM in high sensitivity biochemical sensing and multifunctional narrowband filtering fields.

Nonlinear van der Waals Metasurfaces with Resonantly Enhanced Light Generation

Efficient nonlinear wave mixing is of paramount importance for a wide range of applications. However, weak optical nonlinearities pose significant challenges for accessing nonlinear light-matter interaction in compact systems. Here, we experimentally study second harmonic generation in deeply subwavelength 3R-MoS2 metasurfaces (<λ/13 thick). Our measurements, supported by theoretical analysis, reveal a complex interplay and coupling between geometric resonances, optical extinction, and exciton-driven strong nonlinear susceptibility dispersion. We further demonstrate >150-fold enhancement in second harmonic signal at 740 nm mediated by the A exciton resonance. Additionally, our theoretical studies predict an enhancement of more than 106 in second harmonic generation in <100 nm thick structures exhibiting bound states in the continuum resonance. These findings provide insight into accessing and harnessing the unprecedented 3R-MoS2 nonlinearities at a subwavelength scale, paving the way to ultracompact nonlinear photonic devices.

Broadband and efficient third-harmonic generation from black phosphorus-hybrid plasmonic metasurfaces in the mid-infrared

Black phosphorus (BP), with a mid-infrared (MIR) bandgap of 0.34 eV, presents itself as a promising material for MIR nonlinear optical applications. We report the realization of MIR third-harmonic generation (THG) in both BP and BP-hybrid plasmonic metasurfaces (BPM). BP exhibits a high third-order nonlinear susceptibility ([Formula: see text]) exceeding 10-18 m2/V2 in the MIR region with a maximum value of 1.55 × 10-17 m2/V2 at 5000 nm. The BP flake achieves a THG conversion efficiency of 1.4 × 10-5, surpassing that of other 2D materials by over one order of magnitude. To further enhance this nonlinear performance, a BPM is designed and fabricated to achieve a two-order-of-magnitude enhancement in THG, leading to a record conversion efficiency of 6.5 × 10-4, exceeding the performance of previously reported metasurfaces by more than one order of magnitude. These findings establish BP as a promising platform for next-generation MIR nonlinear optical devices.

Strong coupling between high-Q guided mode resonance and excitons in a mirror-coupled WS2 grating structure

High-quality resonant metasurfaces that utilize guided mode resonance (GMR) or bound states in the continuum (BICs), in conjunction with the strong coupling potential of transition metal dichalcogenides (TMDs), present new opportunities for achieving significant Rabi splitting and nonlinear optical phenomena. In this study, we present a mirror-coupled WS2 grating structure specifically designed to enhance GMR-exciton coupling. By integrating a WS2 grating with a Si3N4 dielectric spacer and an Ag reflective mirror, the structure enables the generation of BIC modes within a narrow spectral range. Additionally, strong GMR-exciton coupling is demonstrated, resulting in a Rabi splitting of 220 meV, as supported by the coupled-mode theory (CMT). This work advances the understanding of optical mode dynamics and coupling mechanisms in hybrid grating systems, offering a versatile platform for next-generation photonic and optoelectronic technologies.

Angularly tunable second-harmonic generation from a structural-symmetry-broken silicon metasurface with bound states in the continuum

Second-harmonic generation (SHG) is usually suppressed in centrosymmetric materials such as silicon, due to their intrinsic inversion symmetry. Here, we report a significantly enhanced SHG from an amorphous silicon metasurface with symmetry-broken unit cells through accidental bound states in the continuum (BICs). Our experiments show a 40-fold increase of SHG compared to a flat silicon film. The accidental BIC mode can be modified by tuning the incident angle of the pump laser beam from 35° to 50°. Accordingly, a SHG output is achieved from 370.0 nm to 382.5 nm. Our results demonstrate an intriguing strategy for enhancing SHG by adjusting the incident angle of the fundamental beam.

Polarization-Independent Enhancement of Third-Harmonic Generation Empowered by Doubly Degenerate Quasi-Bound States in the Continuum

Recent advancements in nonlinear nanophotonics are driven by the exploration of sharp resonances within high-index dielectric metasurfaces. In this work, we leverage doubly degenerate quasi-bound states in the continuum (quasi-BICs) to demonstrate the robust enhancement of third-harmonic generation (THG) in silicon metasurfaces. These quasi-BICs are governed by C4v symmetry and therefore can be equally excited with the pump light regardless of polarization. By tailoring the geometric parameters, we effectively control Q-factors and field confinement of quasi-BICs and thus regulate their resonantly enhanced THG process. A maximum THG conversion efficiency up to 1.03 × 10-5 is recorded under a pump intensity of 5.85 GW/cm2. Polarization-independent THG profiles are further confirmed by mapping their signals across the polarization directions. This work establishes foundational strategies for the ultracompact design of robust and high-efficiency photon upconversion systems.

Hybrid Plasmonic Symmetry-Protected Bound state in the Continuum Entering the Zeptomolar Biodetection Range

Photonics bound states in the continuum (BICs) are peculiar localized states in the continuum of free-space waves, unaffected by far-field radiation loss. Although plasmonic nano-antennas squeeze the optical field to nanoscale volumes, engineering the emergence of quasi-BICs with plasmonic hotspots remains challenging. Here, the origin of symmetry-protected (SP) quasi-BICs in a 2D system of silver-filled dimers, quasi-embedded in a high-index dielectric waveguide, is investigated through the strong coupling between photonic and plasmonic modes. By tailoring the hybridizing plasmonic/photonic fractions, a trade-off is selected at which the quasi-BIC exhibits both high intrinsic Q-factor and strong near-field enhancement because of dimer-gap hotspot activation. Not only radiation loss is damped but in a configuration sustaining a lattice of plasmonic hotspots. This leads to an advantageous small modal volume for enhancing light-matter interaction. The layout of nearly embedded dimers is designed to maximize the spatial overlap between the optical field and the target molecules, enhancing reactive sensing efficiency. The architecture is evaluated for its ability to detect transactive response DNA-binding protein 43. The refractometric sensitivity outperforms current label-free biosensing platforms, reaching the zeptomolar range. The approach highlights the potential of combining plasmonic and dielectric nanomaterials for advanced sensing technologies.

Topologically Protected Plasmonic Bound States in the Continuum

Experimental realizations of bound states in the continuum (BICs) with strong robustness and advanced maneuverability in optical loss systems remain a long-standing challenge in nanophotonics. Here, we propose and fabricate a paradigm of diatomic metagratings incorporating the Su-Schrieffer-Heeger model into the design of plasmonic nanocavities to demonstrate optical resonators with a continuous "quasi-BICs (qBICs)-BICs-qBICs" transition. These resonators feature a topological band inversion, making high-quality (Q) resonances immune to the perturbation of incident angles and geometrical parameters. Furthermore, we strive to establish theoretical models to verify the topological nature of BICs-inspired resonances and introduce nonlinear optical probes to quantify strongly enhanced local fields at high-Q resonances. Our findings may provide a simple yet feasible design strategy for facilitating the dissipationless manipulation of surface/interface-enhanced light-matter interactions at the nanoscale, substantially broadening the functional scope of metaphotonics.

Tuning Multipolar Mie Scattering of Particles on a Dielectric-Covered Mirror

Optically resonant particles are key building blocks of many nanophotonic devices such as optical antennas and metasurfaces. Because the functionalities of such devices are largely determined by the optical properties of individual resonators, extending the attainable responses from a given particle is highly desirable. Practically, this is usually achieved by introducing an asymmetric dielectric environment. However, commonly used simple substrates have limited influences on the optical properties of the particles atop. Here, we show that the multipolar scattering of silicon microspheres can be effectively modified by placing the particles on a dielectric-covered mirror, which tunes the coupling between the Mie resonances of microspheres and the standing waves and waveguide modes in the dielectric spacer. This tunability allows selective excitation, enhancement, suppression, and even elimination of the multipolar resonances and enables scattering at extended wavelengths, providing transformative opportunities in controlling light-matter interactions for various applications. We further demonstrate with experiments the detection of molecular fingerprints by single-particle mid-infrared spectroscopy and with simulations strong optical repulsive forces that could elevate the particles from a substrate.

Enhancement of third-harmonic generation in all-dielectric kite-shaped metasurfaces driven by quasi-bound states in the continuum

We develop a new all-dielectric metasurface for designing high quality-factor (Q-factor) quasi-bound states in the continuum (quasi-BICs) using asymmetry kite-shaped nanopillar arrays. The Q-factors of quasi-BICs follow the quadratic dependence on the geometry asymmetry, and meanwhile their resonant spectral profiles can be readily tuned between Fano and Lorentzian lineshapes through the interplay with the broadband magnetic dipole mode. The third-harmonic signals of quasi-BIC modes exhibit a gain from 43.4- to 634-fold enhancement between samples with an axial-length difference of 15 nm and 75 nm when reducing the numerical aperture of the illuminating objective lenses in nonlinear measurement, which is attributed to the increasing illumination spot size and the less contribution from the large oblique incident light for establishing quasi-BIC modes with high-Q spectral profile and strong near-field intensity. The silicon-based metasurfaces with their simple geometry are facile for large-area fabrication and open new possibilities for the optimization of upconversion processes to achieve efficient nonlinear devices.

Realizing high-efficiency third harmonic generation via accidental bound states in the continuum

The bound states in the continuum (BICs) have attracted much attention in designing metasurface due to their high Q-factor and effectiveness in suppressing radiational loss. Here we report on the realization of the third harmonic generation (THG) at a near-ultraviolet wavelength (343 nm) via accidental BICs in a metasurface. The absolute conversion efficiency of the THG reaches 1.13 × 10-5 at a lower peak pump intensity of 0.7 GW/cm2. This approach allows the generation of an unprecedentedly high nonlinear conversion efficiency with simple structures.

High-Sensitivity Optical Sensors Empowered by Quasi-Bound States in the Continuum in a Hybrid Metal-Dielectric Metasurface

Enhancing light-matter interaction is a key requisite in the realm of optical sensors. Bound states in the continuum (BICs), possessing high quality factors (Q factors), have shown great advantages in sensing applications. Recent theories elucidate the ability of BICs with hybrid metal-dielectric architectures to achieve high Q factors and high sensitivities. However, the experimental validation of the sensing performance in such hybrid systems remains equivocal. In this study, we propose two symmetry-protected quasi-BIC modes in a metal-dielectric metasurface. Our results demonstrate that, under the normal incidence of light, the quasi-BIC mode dominated by dielectric can achieve a high Q factor of 412 and a sensing performance with a high bulk sensitivity of 492.7 nm/RIU (refractive index unit) and a figure of merit (FOM) of 266.3 RIU-1, while the quasi-BIC mode dominated by metal exhibits a stronger surface affinity in the biotin-streptavidin bioassay. These findings offer a promising approach for implementing metasurface-based sensors, representing a paradigm for high-sensitivity biosensing platforms.

Third Harmonic Generation Enhancement and Wavefront Control Using a Local High-Q Metasurface

High quality factor optical nanostructures provide a great opportunity to enhance nonlinear optical processes such as third harmonic generation. However, the field enhancement in these high quality factor structures is typically accompanied by optical mode nonlocality. As a result, the enhancement of nonlinear processes comes at the cost of their local control as needed for nonlinear wavefront shaping, imaging, and holography. Here we show simultaneous strong enhancement and spatial control over third harmonic generation with a local high-Q metasurface relying on higher-order Mie resonant modes. Our results demonstrate third harmonic generation at an efficiency of up to 3.25 × 10-5, high quality wavefront shaping as illustrated by a third harmonic metalens, and a flatband, angle independent, third harmonic response up to ±11° incident angle. The demonstrated high level of local control and efficient frequency conversion offer promising prospects for realizing novel nonlinear optical devices.

Unlocking Efficient Ultrafast Bound-Electron Optical Nonlinearities via Mirror Induced Quasi Bound States in the Continuum

The operation of photonic devices often relies on modulation of their refractive index. While the sub-bandgap index change through bound-electron optical nonlinearity offers a faster response than utilizing free carriers with an overbandgap pump, optical switching often suffers from inefficiency. Here, we use a recently observed metasurface based on mirror-induced optical bound states in the continuum, to enable superior modulation characteristics. We achieve a pulsewidth-limited switching time of 100 fs, reflectance change of 22%, remarkably low energy consumption of 255 μJ/cm2, and an enhancement of modulation contrast by a factor of 440 compared to unpatterned silicon. Additionally, the narrow photonic resonance facilitates the detection of the dispersive nondegenerate two-photon nonlinearity, allowing tunable pump and probe excitation. These findings are explained by a two-band theoretical model for the dispersive nonlinear index. The demonstrated efficient and rapid switching holds immense potential for applications, including quantum photonics, sensing, and metrology.

Modal Phase-Matched Bound States in the Continuum for Enhancing Third Harmonic Generation of Deep Ultraviolet Emission

Coherent deep ultraviolet (DUV) light sources are crucial for various applications such as nanolithography, biomedical imaging, and spectroscopy. DUV light sources can be generated by using conventional nonlinear optical crystals (NLOs). However, NLOs are limited by their bulky size, inadequate transparency at the DUV regime, and stringent phase-matching requirements for harmonic generation. Recently, dielectric metasurfaces support high Q-factor resonances and offer a promising approach for efficient harmonic generation at short wavelengths. In this study, we demonstrated a crystalline silicon (c-Si) metasurface simultaneously exciting modal phase-matched bound states in the continuum (BIC) resonance at the fundamental wavelength of 840 nm with a higher degree of freedom for precise control of the BIC resonance and a plasmonic resonance at the wavelength of 280 nm in the DUV to enhance third harmonic generation (THG). We experimentally achieved a Q-factor of ∼180 owing to the relatively large refractive index of the c-Si and the geometric symmetry breaking of the structure. We realized THG at a wavelength of 280 nm with a power of 14.5 nW by using a peak power density of 15 GW/cm2 excitation. The measured THG power is 14 times higher than the state-of-the-art THG dielectric metasurfaces using the same peak power density in the DUV regime, and the maximum obtained THG power enhancement factor is up to 48. This approach relies on the significant third-order nonlinear susceptibility of c-Si, the interband plasmonic nature of the c-Si in the DUV, and the strong field confinement of BIC resonance to boost overall nonlinear conversion efficiency to 5.2 × 10-6% in the DUV regime. Our work shows the potential of c-Si BIC metasurfaces for developing efficient and ultracompact DUV light sources using high-efficacy nonlinear optical devices.

Quasi-bound states in the continuum in a metal nanograting metasurface for a high figure-of-merit refractive index sensor

In this work, we investigate the bound states in the continuum (BICs) in a gold nanograting metal-insulator-metal metasurface structure at oblique angles of incidence. The nanograting metasurface consists of a gold nanograting patterned on a silicon dioxide dielectric film deposited on a thick gold film supported by a substrate. With rigorous full-wave finite difference time domain simulations, two bound states in the continuum are revealed upon transverse magnetic wave angular incidence. One BIC is formed by the interference between the surface plasmon polariton mode of the gold nanograting and the FP cavity mode. Another BIC mode is formed by the interference between the metal-dielectric hybrid structure guided mode resonance mode and the FP cavity mode. While true BIC modes cannot be observed, quasi-BIC modes are investigated at angles of incidence slightly off from the corresponding true BIC angles. It is shown that quasi-BIC modes can suppress radiation loss, resulting in narrow resonance spectral linewidths and high quality-factors. The quasi-BIC mode associated with the surface plasmon polariton mode is investigated for refractive index sensing. As a result, a high sensitivity refractive index sensor with a large figure-of-merit of 364 has been obtained.

Terahertz absorber based on vanadium dioxide with high sensitivity and switching capability between ultra-wideband and ultra-narrowband

The terahertz perfect absorber can be applied in the control, sensing and modulation of optical fields in micro- and nanostructures. However, they are only single function, complex device structure and low sensing sensitivity. Based on this, by introducing the bound state in the continuum (BIC) with infinite quality factor and field enhancement effect, and taking advantage of the phase transition characteristics of vanadium dioxide (VO2), we designed a terahertz perfect absorber device which can actively switch between ultra-wideband and ultra-narrowband. The absorption mechanism is explained by multipole analysis theory, impedance matching theory and electromagnetic field distribution. The broadband absorption is mainly due to the electric dipole resonance on metallic VO2 materials, and the absorption is more than 99% across 3.64-6.96 THz, and it has excellent characteristics such as robustness. Ultra-narrowband perfect absorption has a quality factor greater than 2200 due mainly to the implementation of symmetrically protected BIC with a sensing sensitivity of 2.575 THz per RIU. Therefore, this research could be widely used in the fields of integrated optical circuits, optoelectronic sensing and perceptual modulation of energy, as well as providing additional design ideas for the design of terahertz multifunctional devices.

Advances in nonlinear metasurfaces for imaging, quantum, and sensing applications

Metasurfaces, composed of artificial meta-atoms of subwavelength size, can support strong light-matter interaction based on multipolar resonances and plasmonics, hence offering the great capability of empowering nonlinear generation. Recently, owing to their ability to manipulate the amplitude and phase of the nonlinear emission in the subwavelength scale, metasurfaces have been recognized as ultra-compact, flat optical components for a vast range of applications, including nonlinear imaging, quantum light sources, and ultrasensitive sensing. This review focuses on the recent progress on nonlinear metasurfaces for those applications. The principles and advances of metasurfaces-based techniques for image generation, including image encoding, holography, and metalens, are investigated and presented. Additionally, the overview and development of spontaneous photon pair generation from metasurfaces are demonstrated and discussed, focusing on the aspects of photon pair generation rate and entanglement of photon pairs. The recent blossoming of the nonlinear metasurfaces field has triggered growing interest to explore its ability to efficiently up-convert infrared images of arbitrary objects to visible images and achieve spontaneous parametric down-conversion. This recently emerged direction holds promising potential for the next-generation technology in night-vision, quantum computing, and biosensing fields.

Merging bound states in the continuum in all-dielectric metasurfaces for ultrahigh-Q resonances

The concept of symmetry-protected bound states in the continuum (BICs) offers a simple approach to engineer metasurfaces with high-quality (Q) factors. However, traditional designs driven by symmetry-protected BICs require an extremely small perturbation parameter to obtain very large Q factors, complicating fabrication and limiting practical applications. Here, we demonstrate a BIC-driven structure composed of two coupled all-dielectric metasurfaces that enables ultrahigh-Q resonances even at large perturbations. The underlying mechanism enabling this is to merge the symmetry-protected BIC and Fabry-Pérot BIC in the parameter space by tuning the distance between the two metasurfaces, thereby altering the intrinsic radiation behavior of the isolated symmetry-protected BIC. It is found that this simple strategy results in Q factors that are three orders of magnitude higher than those with isolated-BIC configurations. Our approach provides a promising route for designing high-Q BIC nanostructures promising in exciting device applications as sensors and filters.

High-Q Quasi-Bound States in the Continuum in Terahertz All-Silicon Metasurfaces

Bound states in the continuum (BIC)-based all-silicon metasurfaces have attracted widespread attention in recent years because of their high quality (Q) factors in terahertz (THz) frequencies. Here, we propose and experimentally demonstrate an all-silicon BIC metasurface consisting of an air-hole array on a Si substrate. BICs originated from low-order TE and TM guided mode resonances (GMRs) induced by (1,0) and (1,1) Rayleigh diffraction of metagratings, which were numerically investigated. The results indicate that the GMRs and their Q-factors are easily excited and manipulated by breaking the lattice symmetry through changes in the position or radius of the air-holes, while the resonance frequencies are less sensitive to these changes. The measured Q-factor of the GMRs is as high as 490. The high-Q metasurfaces have potential applications in THz modulators, biosensors, and other photonic devices.

Observation of the bound states in the continuum supported by mode coupling in a terahertz metasurface

Metasurface supporting bound states in the continuum (BIC) provides a unique approach for the realization of intense near-field enhancement and high quality factor (Q-factor) resonance, which promote the advancement of various applications. Here we experimentally demonstrate a Friedrich-Wintgen BIC based on the mode coupling in the terahertz metasurface, which produces BIC by the coupling of the LC mode and dipole mode resonances. The transition from ideal BIC to quasi-BIC is caused by the mismatch of the coupling, and the mode decay rate during this process is analyzed by temporal coupled mode theory. The Q-factor and the electric field enhancement of the quasi-BIC resonance are significantly increased, which provides enormous potential in sensing, nonlinear optics, and topological optics.

Dual Control of Enhanced Quasi-Bound States in the Continuum Emission from Resonant c-Si Metasurfaces

Optical bound states in the continuum (BICs) offer strong interactions with quantum emitters and have been extensively studied for manipulating spontaneous emission, lasing, and polariton Bose-Einstein condensation. However, the out-coupling efficiency of quasi-BIC emission, crucial for practical light-emitting devices, has received less attention. Here, we report an adaptable approach for enhancing quasi-BIC emission from a resonant monocrystalline silicon (c-Si) metasurface through lattice and multipolar engineering. We identify dual-BICs originating from electric quadrupoles (EQ) and out-of-plane magnetic dipoles, with EQ quasi-BICs exhibiting concentrated near-fields near the c-Si nanodisks. The enhanced fractional radiative local density of states of EQ quasi-BICs overlaps spatially with the emitters, promoting efficient out-coupling. Furthermore, coupling the EQ quasi-BICs with Rayleigh anomalies enhances directional emission intensity, and we observe inherent opposite topological charges in the multipolarly controlled dual-BICs. These findings provide valuable insights for developing efficient nanophotonic devices based on quasi-BICs.

Photonic spin-selective perfect absorptance on planar metasurfaces driven by chiral quasi-bound states in the continuum

Optical metasurfaces with high-quality-factor resonances and selective chirality simultaneously are desired for nanophotonics. Here, an all-dielectric planar chiral metasurface is theoretically proposed and numerically proved to support the astonishing symmetry-protected bound state in the continuum (BIC), due to the preserved π rotational symmetry around the z axis and up-down mirror symmetry simultaneously. Importantly, such BIC is a vortex polarization singularity enclosed by elliptical eigenstate polarizations with non-vanishing helicity, owing to the broken in-plane mirror symmetry. Under the oblique incidence, companied by the BIC transforming into a quasi-BIC (Q-BIC), the strong extrinsic chirality manifests. Assisted by the single-port critical coupling, the planar metasurface can selectively and near-perfectly absorb one circularly polarized light but non-resonantly reflect its counterparts. The circular dichroism (CD) approaching 0.812 is achieved. Intriguingly, the sign of CD (namely, the handedness of the chiral metasurface) can be flexibly manipulated only via varying the azimuthal angle of incident light, due to the periodic helicity sign flip in eigen polarizations around the BIC. Numerical results are consistent with the coupled-mode theory and multipole decomposition method. The spin-selective metasurface absorber empowered by the physics of chiral Q-BICs undoubtedly may promise various applications such as optical filters, polarization detectors, and chiral imaging.

Ultrasensitive Frequency Shifting of Dielectric Mie Resonance near Metallic Substrate

Dielectric resonators on metallic surface can enhance far-field scattering and boost near-field response having promising applications in nonlinear optics and reflection-type devices. However, the dependence of gap size between dielectric resonator and metallic surface on Mie resonant frequency is complex and desires a comprehensive physical interpretation. Here, we systematically study the effect of metallic substrate on the magnetic dipole (MD) resonant frequency at X-band by placing a high permittivity CaTiO₃ ceramic block on metallic substrate and regulating their gap size. The simulated and experimental results show that there are two physical mechanisms to codetermine the metallic substrate-induced MD frequency. The greatly enhanced electric field pair in the gap and the coupling of MD resonance with its mirror image are decisive for small and large gaps, respectively, making the MD resonant frequency present an exponential blue shift first and then a slight red shift with increasing gap size. Further, we use the two mechanisms to explain different frequency shifting properties of ceramic sphere near metallic substrate. Finally, taking advantage of the sharp frequency shifting to small gaps, the ceramic block is demonstrated to accurately estimate the thickness or permittivity of thin film on metallic substrate through a governing equation derived from the method of symbolic regression. We believe that our study will help to understand the resonant frequency shifting for dielectric particle near metallic substrate and give some prototypes of ultrasensitive detectors.