Implementation method of ultra-high quality factor quasi-continuous domain bound state

Abstract

The invention discloses an ultra-high quality factor quasi-continuous domain bound state realization method, and relates to the field of micro-nano photonics resonators, and the method comprises the steps: designing a symmetric medium nano column, and exciting an internal Mie mode and a Fabry-Perot mode through adjusting the geometric parameters of the symmetric medium nano column; coupling of the two modes is accurately regulated and controlled, so that far-field radiation destructive interference is achieved, and a high-Q-value quasi-continuous domain bound state is formed under the condition of no symmetry breaking; the nano-columns are arranged into a periodic array, lattice constants are optimized, and the quality factor is improved to an ultrahigh level by using resonance coupling and collective interference effect between adjacent nano-columns. Symmetrical breaking is not needed, and higher structural robustness and preparation tolerance are achieved.

Description

Technical Field

[0001] This invention belongs to the field of micro-nano photonic resonator technology, and particularly relates to a method for realizing a quasi-continuous bound state with an ultra-high quality factor. Background Technology

[0002] Continuous-domain bound states are nonradiative states that exist within a radiation continuum but are completely localized. Their theoretical quality factor is infinite, and they hold immense potential for applications in low-threshold lasing, nonlinear enhancement, and sensing. However, ideal continuous-domain bound states are completely decoupled from external radiation channels and cannot be directly excited or utilized. To overcome this limitation, current techniques primarily introduce asymmetries into photonic structures, such as designing asymmetric pairs of nanopillars, elliptical holes, or tilted sidewalls to break the structure's mirror or rotational symmetry, thereby transforming ideal continuous-domain bound states into quasi-continuous-domain bound states that can weakly couple with free space. While this approach has been successful and has become the mainstream technique in this field, it has revealed a fundamental technical flaw in its application to practical applications.

[0003] This deficiency manifests as the fact that the quality factor of the quasi-continuous bound states achieved through symmetry breaking is extremely sensitive to minute changes in structural asymmetry parameters. Specifically, during micro- and nano-fabrication, any nanometer-level geometric perturbation, such as minute deviations in the size or shape of nanopillars, will lead to a drastic decrease in the quality factor of the quasi-continuous bound states. This means that to obtain and maintain high-Q resonance, the actual device manufacturing process requires extremely precise control over structural asymmetry, typically requiring sub-nanometer precision. This stringent process requirement poses a significant challenge to nanofabrication technologies such as photolithography and etching, directly resulting in extremely small fabrication tolerances, low processing yields, and high manufacturing costs. More importantly, even if the device is successfully fabricated, its performance lacks robustness in practical application environments. Minor temperature fluctuations or mechanical stresses can cause slight drifts in structural parameters, leading to significant degradation of the device's optical performance and affecting its long-term stability and reliability in systems such as lasers and sensors. Therefore, the strong dependence of existing technologies on the breaking of fine symmetry severely restricts the progress of bound states in quasi-continuous domains from laboratory principle verification to practical engineering applications, becoming a key technological bottleneck that urgently needs to be overcome. Summary of the Invention

[0004] To address the aforementioned technical problems, this invention proposes a method for realizing ultra-high quality factor quasi-continuous domain bound states, thereby resolving the issues present in the prior art.

[0005] In a first aspect, to achieve the above objective, the present invention provides a method for realizing a quasi-continuous domain bound state with an ultra-high quality factor, comprising the following steps: Design and construct a dielectric nanopillar structure with geometric symmetry; By adjusting the geometric parameters of the dielectric nanopillars, both Mie-type and Fabry-Pérot-type resonant modes can be excited simultaneously within them. By adjusting the coupling strength between the Mie-type resonant mode and the Fabry-Pérot-type resonant mode, the far-field radiation of the two modes undergoes destructive interference, thereby forming a quasi-continuous domain bound state in the dielectric nanopillar under the condition of no symmetry breaking. The dielectric nanopillars supporting the quasi-continuous domain bound states are arranged into a periodic array; The lattice constant of the periodic array is optimized to excite resonant coupling between the quasi-continuous bound state modes of adjacent dielectric nanopillars, thereby improving the quality factor of the quasi-continuous bound state through the collective interference effect induced by the coupling.

[0006] Optionally, the process of adjusting geometric parameters includes: The system scans the radius-to-height ratio of the dielectric nanopillars and determines the parameter region where the two modes are strongly coupled based on the anti-crossing phenomenon of Mie-type and Fabry-Pérot-type resonant modes in the scattering spectrum.

[0007] Optionally, the dielectric nanopillars are cylindrical structures made of dielectric materials with a dielectric constant greater than 10.

[0008] Optionally, the process of optimizing the lattice constant includes: The lattice constant of the periodic array was set in the range of 350 nm to 600 nm and scanned. The lattice constant that made the quality factor of the quasi-continuous domain bound state reach the peak was selected as the optimized working parameter.

[0009] Optionally, the optimized operating parameters are a lattice constant of 460 nm, at which point the quality factor of the quasi-continuous bound state reaches the order of 10 to the power of 6.

[0010] Optionally, the method further includes illuminating the periodic array from the side with a horizontally polarized plane wave to excite and observe the quasi-continuous bound states.

[0011] Secondly, the present invention also provides a system for realizing ultra-high quality factor quasi-continuous domain bound states, for implementing a method for realizing ultra-high quality factor quasi-continuous domain bound states, the system comprising: The mode excitation module is used to simultaneously excite Mie-type resonant modes and Fabry-Pérot-type resonant modes inside a geometrically symmetric dielectric nanopillar. The interference control module is used to control the coupling strength between the Mie-type resonant mode and the Fabry-Pérot-type resonant mode, so that the far-field radiation of the two modes undergoes destructive interference, so as to form a quasi-continuous bound state under the condition of no symmetry breaking. An array building module is used to arrange dielectric nanopillars supporting the quasi-continuous domain bound states into a periodic array; The coupling enhancement module is used to excite resonant coupling between quasi-continuous bound state modes of adjacent dielectric nanopillars by optimizing the lattice constant of the periodic array, thereby improving the quality factor of the quasi-continuous bound state through collective interference effect.

[0012] Thirdly, the present invention also provides a computer terminal device, comprising: One or more processors; A memory, coupled to the processor, for storing one or more programs; When the one or more programs are executed by the one or more processors, the one or more processors implement the steps of the method for implementing the ultra-high quality factor quasi-continuous domain bound state in the first aspect above.

[0013] Fourthly, the present invention also provides a computer-readable storage medium having a computer program stored thereon, wherein when the computer program is executed by a processor, the steps of the method for realizing the ultra-high quality factor quasi-continuous domain bound state in the first aspect are implemented.

[0014] Fifthly, the present invention also provides a computer program product, including a computer program that, when executed by a processor, implements the steps of the method for implementing the ultra-high quality factor quasi-continuous domain bound state in the first aspect described above.

[0015] Compared with the prior art, the present invention has the following advantages and technical effects: This invention provides a method for realizing quasi-continuous bound states with ultra-high quality factor. This invention completely eliminates the dependence on precise symmetry breaking. Through destructive interference between Mie-type and Fabry-Pérot-type resonant modes within dielectric nanopillars, quasi-continuous bound states with high quality factor are spontaneously formed under conditions of complete geometric symmetry. Furthermore, by constructing such nanopillars into a periodic array and optimizing the lattice constant, the collective interference effect induced by resonant coupling between adjacent units can be utilized to elevate the quality factor of the resonance to an ultra-high level. Compared to traditional schemes that rely on symmetry breaking, the high quality factor resonance achieved by this invention is insensitive to minor fluctuations in the manufacturing process, thereby significantly improving the robustness and fabrication tolerance of the structure. This provides a more practical technical foundation for developing high-performance, high-reliability nanolasers, nonlinear optical devices, and high-sensitivity sensors. Attached Figure Description

[0016] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an undue limitation of the invention. In the drawings: Figure 1 This is a schematic diagram of the structure of an embodiment of the present invention; Figure 1 (a) is a schematic diagram of a single dielectric nanocylinder in free space. Figure 1 (b) is a schematic diagram of a dielectric metasurface composed of periodically arranged nanocylinders; Figure 2 This is a schematic diagram of the scattering cross section according to an embodiment of the present invention; Figure 2 (a) in the figure represents the scattering cross section of a theoretical model that strongly couples the Mie mode with the Fabry-Pérot mode; Figure 2 (b) shows the scattering cross section of the dielectric nanocylinder and its corresponding quality factor distribution, calculated based on wavelength and aspect ratio. Figure 3 The electric field distribution of six modes on the scattering cross-section curve of this invention embodiment; Figure 4 Analysis of the results of embodiments of the present invention; Figure 4 In the figure (a), the quality factor of the quasi-BIC in the nanocylindrical metasurface varies with the lattice period a. Figure 4 (b) in the figure represents the electric field distribution corresponding to the selected period value; Figure 4 (c) shows the variation of the resonance wavelength of the quasi-BIC with the lattice period; Figure 4 In the figure, (d) represents fitting the Q value and the period; Figure 5 This is a flowchart of a method according to an embodiment of the present invention. Detailed Implementation

[0017] It should be noted that, unless otherwise specified, the embodiments and features described in the present invention can be combined with each other. The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0018] It should be noted that the steps shown in the flowchart in the accompanying drawings can be executed in a computer system such as a set of computer-executable instructions, and although a logical order is shown in the flowchart, in some cases the steps shown or described may be executed in a different order than that shown here. Example 1

[0019] like Figure 5 As shown, this embodiment provides a method for realizing a quasi-continuous bound state with an ultra-high quality factor, including: Design and construct a dielectric nanopillar structure with geometric symmetry; By adjusting the geometric parameters of the dielectric nanopillars, both Mie-type and Fabry-Pérot-type resonant modes can be excited simultaneously within them. By adjusting the coupling strength between the Mie-type resonant mode and the Fabry-Pérot-type resonant mode, the far-field radiation of the two modes undergoes destructive interference, thereby forming a quasi-continuous domain bound state in the dielectric nanopillar under the condition of no symmetry breaking. The dielectric nanopillars supporting the quasi-continuous domain bound states are arranged into a periodic array; The lattice constant of the periodic array is optimized to excite resonant coupling between the quasi-continuous bound state modes of adjacent dielectric nanopillars, thereby improving the quality factor of the quasi-continuous bound state through the collective interference effect induced by the coupling.

[0020] As one implementation method in this embodiment, the process of adjusting the geometric parameters includes: The system scans the radius-to-height ratio of the dielectric nanopillars and determines the parameter region where the two modes are strongly coupled based on the anti-crossing phenomenon of Mie-type and Fabry-Pérot-type resonant modes in the scattering spectrum.

[0021] As one embodiment of this example, the dielectric nanopillar is a cylindrical structure made of a dielectric material with a dielectric constant greater than 10.

[0022] like Figure 1 (a) and Figure 1 As shown in (b) of the present invention, this embodiment provides a method for achieving a quasi-BIC ultra-high quality factor that does not rely on symmetry breaking, comprising: S1. Establish a theoretical framework to reveal its physical mechanism. Take a thin dielectric cylinder with narrow resonance contribution as an example, which includes Mie resonance and Fabry-Perot resonance.

[0023] Specifically, in the theoretical model, the reflection coefficient of the Mie-type resonator reaches 1 at resonance, and the transmittance... t and reflectivity r It can be approximated using the Breit-Wigner form:

[0024]

[0025] in, ω 0 and γ These represent the resonant frequency and linewidth, respectively. Here, ω 0 and h (Cylinder diameter 2) RThe ratio is inversely proportional. Further considering the cylinder as analogous to a cylinder with a spacing of... h A Fabry-Pérot resonator is formed by two identical planar arrays. The transmission coefficient T of the array can be obtained using the Fabry-Pérot method:

[0026] Where k is the wave vector component perpendicular to the array.

[0027] Based on the above theoretical model, systematic theoretical calculations were performed using self-written MATLAB code, and the results are as follows. Figure 2 As shown in (a) above. It is noteworthy that the theoretical spectrum was analyzed using a normalized wavelength scale from 0 to 1. Within this range, two resonant branches that avoid crossing can be clearly observed. This avoidance of crossing stems from the strong coupling between the Mie resonance mode and the Fabry-Perot mode. Without intermode coupling, the energy levels of these two independent modes would cross directly, but their strong interaction causes a deviation from the original crossing trajectory, thus forming two non-crossing branches. The connection region between the two branches, in... Figure 2 In (a), a continuous transition line is observed, a direct result of this strong coupling effect. Within this region, the Mie mode and the Fabry-Pérot mode are no longer independent but evolve into a hybrid mode, which subsequent intrinsic mode analysis confirmed to be a synergistic combination of the TE320 and TE312 modes. This strong coupling-mediated hybridization, along with the destructive interference between the two modes in the far field, lays the foundation for radiation loss suppression and constitutes the core origin of quasi-BICs in a single dielectric nanocylinder.

[0028] S2. Design a quasi-BIC structure based on an ultra-high quality factor that does not depend on symmetry breaking, wherein the quasi-BIC structure is a single nanocylinder in a vacuum. Specifically, nanocylinders in a vacuum, such as Figure 1 As shown in (a) above. The relative permittivity of the nanocylinder is 13, the relative permittivity in vacuum is 1, and the height of the nanocylinder is... h =205nm, radius r =152nm, the ratio of radius to height r / h For fixed h Change r Due to the strong coupling between the Mie resonance mode and the Fabry-Pérot resonance mode, this structure can support quasi-bound states through Friedrich–Wintgen-type interference mechanisms.

[0029] As one implementation of this embodiment, the method further includes irradiating the periodic array from the side with a horizontally polarized plane wave to excite and observe the quasi-continuous bound state.

[0030] S3. Calculate the scattering cross section of the nanocylinder using simulation software to find the wavelength range where the cross curves are avoided; Specifically, a plane wave with horizontal electric field polarization is injected from the side for excitation, and the corresponding scattering cross section... Q sca The calculation formula is: Q sca ( λ )= P sca ( λ ) / [ I ( λ ) S ] in P sca ( λ ) represents the scattering intensity. I ( λ () represents the intensity of the incident wave. S =2 rh This represents the geometric cross-sectional area of ​​a nanocylinder, which is used as the aspect ratio ( r / h The aspect ratio of the isolated nanocylinder was calculated as a function of the excitation wavelength. The resonant response was studied by systematically varying the aspect ratio of the isolated nanocylinder and analyzing the scattering cross-section generated under horizontally incident plane wave excitation. The nanocylinder maintained perfect geometric symmetry. The scattering simulation in this embodiment was performed using the commercial electromagnetic solver COMSOL Multiphysics. Figure 2 As shown in (b), two distinct cross-resonance branches appear in the spectral range of 400 to 600 nm, indicating strong mode coupling. This is consistent with the derived theoretical model. The resonance modes at selected spectral positions on these branches are explicitly labeled as those of the upper branch. H 1. H 2. H 3 and the lower branch L 1. L 2. L 3.

[0031] As one implementation method in this embodiment, the process of optimizing the lattice constant includes: The lattice constant of the periodic array was set in the range of 350 nm to 600 nm and scanned. The lattice constant that made the quality factor of the quasi-continuous domain bound state reach the peak was selected as the optimized working parameter.

[0032] As one implementation method in this embodiment, the optimized operating parameters are a lattice constant of 460 nanometers, at which point the quality factor of the quasi-continuous domain bound state reaches the order of 10 to the power of 6.

[0033] S4. Extend the structure of a single resonator to a periodic metasurface to systematically study how lattice-induced coupling affects the formation and quality factor of this lattice-independent quasi-BIC.

[0034] Specifically, this structure is excited by optical pumping, such as... Figure 1 As shown in (b) above. When the period of the metasurface is large ( a At a wavelength of 600 nm, the optical response is primarily dominated by resonances within a single nanocylinder, while the coupling between resonators is negligible. This explanation is strongly supported by the electric field distribution, which is remarkably similar to that of an isolated nanocylinder (see [link to article]). Figure 4 (b) and Figure 1 (See illustration (a) for comparison), and the order of magnitude of the quality factors obtained for periodic and isolated structures is also quite similar. As the lattice period decreases systematically ( Figure 4 In (a) of the simulation, localized Mie-Fabry-Pérot modes supported by a single nanocylinder begin to interact within the lattice, leading to a gradual increase in coupling between adjacent resonators. This enhanced coupling between adjacent resonators is particularly evident in the simulated spectral response. At the optimal period... a At 460 nm, strong coupling was established between the Mie-Fabry-Pérot modes of adjacent nanocylinders. This coupling-induced mixing effect effectively suppressed radiation loss through decoherence of the radiation channels, thereby significantly improving the resonance quality factor to approximately 10. 6 . Figure 4 The corresponding electric field distribution shown in (b) clearly reflects this coupling state, which shows both the strong electric field concentration inside the single nanocylinder and the consistent periodic energy distribution throughout the metasurface lattice.

[0035] S5. Discuss the stability of the quasi-BIC resonance wavelength under the variation of the lattice period, and perform linear fitting on the Q value as a function of the lattice period.

[0036] Specifically, the resonant wavelength of the quasi-BIC exhibits significant stability, such as... Figure 4 As shown in (c) in the figure. In stark contrast to the significant change in the quasi-BIC resonance wavelength with broken symmetry, this improves operational stability and manufacturing tolerance.

[0037] To quantitatively characterize the sensitivity of the Q-factor to periodic deviation, a normalized periodic tuning parameter is defined. η =( α - β ) / β ,in β This represents the lattice period corresponding to the maximum Q factor. For example... Figure 4 As shown in (d) of the figure, the data plotted in a log-log coordinate system exhibits a clear linear relationship, indicating that the Q factor decays power-lawfully as the period deviates from its optimal value. In 0 < η Linear fitting within the range <0.10 yielded a slope of -2.18, indicating that radiation loss and periodic tuning deviation have an approximately quadratic relationship. This scaling characteristic originates from the collective coupling within the resonator lattice, fundamentally different from the parameter dependence determined by broken symmetry in traditional quasi-wideband isolator designs.

[0038] In summary, this invention presents a method for realizing high-quality quasi-BIC photonic crystals in all-dielectric nanostructures, independent of geometric symmetry. Through systematic analysis of an isolated dielectric nanocylinder, this invention demonstrates that quasi-BIC photonic crystals can be generated by destructive interferences involving interactions similar to Mie resonances and Fabry-Pérot modes, without relying on any form of geometric symmetry destruction. Through scattering analysis and mode characterization, this interference-induced quasi-BIC photonic crystal is shown to significantly suppress radiation loss at a specific size ratio. Extending the single resonator system to a periodic metasurface further demonstrates that mutual resonator coupling provides an efficient method for collectively enhancing and tuning the quality factor of quasi-BIC photonic crystals. While lattice periodicity provides a convenient external degree of freedom for tuning resonant quality, the fundamental quality factor constraint within each individual resonator remains determined by its inherent mode interference. Importantly, the resulting high-quality factor resonances persist in a fully symmetrical structure, a stark contrast to conventional quasi-BIC resonator designs with symmetry protection or destruction properties, in which the quality factor is highly sensitive to asymmetric perturbations. These results demonstrate that mode interference, as a physically transparent and robust mechanism, provides a symmetry-constraint-independent approach to the engineering design of high-quality factor resonances. The proposed platform offers greater fabrication tolerance and design flexibility, and may enable a range of applications requiring ultra-high-quality factor resonances, including low-threshold nanolasers, enhanced nonlinear light-matter interactions, and high-sensitivity optical sensing. Example 2

[0039] In this embodiment, a computer terminal device is provided, including: One or more processors; A memory, coupled to the processor, for storing one or more programs; When the one or more programs are executed by the one or more processors, the one or more processors implement the steps of the above-described method for implementing the quasi-continuous bound state of the ultra-high quality factor.

[0040] In this embodiment, a computer-readable storage medium is also provided, on which a computer program is stored. When the computer program is executed by a processor, it implements the steps of the above-described method for implementing the quasi-continuous bound state of the ultra-high quality factor.

[0041] In this embodiment, an electronic device is also provided, including a memory and a processor. The memory stores a computer program, and the processor is configured to run the computer program to execute the steps of the above-described method for implementing the quasi-continuous bound state of the ultra-high quality factor.

[0042] In this embodiment, a computer program product is also provided, including a computer program that, when executed by a processor, implements the steps of the above-described method for implementing the quasi-continuous bound state of the ultra-high quality factor.

[0043] The aforementioned program can run on a processor or be stored in memory (or a computer-readable medium). Computer-readable media includes both permanent and non-permanent, removable and non-removable media, and information storage can be achieved by any method or technology. Information can be computer-readable instructions, data structures, program modules, or other data. Examples of computer storage media include, but are not limited to, phase-change memory (PRAM), static random-access memory (SRAM), dynamic random-access memory (DRAM), other types of random-access memory (RAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), flash memory or other memory technologies, CD-ROM, digital versatile optical disc (DVD) or other optical storage, magnetic tape, magnetic disk storage or other magnetic storage devices, or any other non-transfer medium that can be used to store information accessible by a computing device.

[0044] These computer programs may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps for the functions specified in one or more boxes can be implemented by different modules for different steps.

[0045] This embodiment provides such an apparatus or system. The system, referred to as a system for realizing ultra-high quality factor quasi-continuous domain bound states, includes: The mode excitation module is used to simultaneously excite Mie-type resonant modes and Fabry-Pérot-type resonant modes inside a geometrically symmetric dielectric nanopillar. The interference control module is used to control the coupling strength between the Mie-type resonant mode and the Fabry-Pérot-type resonant mode, so that the far-field radiation of the two modes undergoes destructive interference, so as to form a quasi-continuous bound state under the condition of no symmetry breaking. An array building module is used to arrange dielectric nanopillars supporting the quasi-continuous domain bound states into a periodic array; The coupling enhancement module is used to excite resonant coupling between quasi-continuous bound state modes of adjacent dielectric nanopillars by optimizing the lattice constant of the periodic array, thereby improving the quality factor of the quasi-continuous bound state through collective interference effect.

[0046] As one implementation method in this embodiment, the mode excitation module includes: The parameter scanning unit is used to scan the ratio of the radius to the height of the medium nanopillars in the system. The mode analysis unit is used to determine the parameter region where the Mie-type resonant mode and the Fabry-Pérot-type resonant mode are strongly coupled based on the anti-crossing phenomenon in the scattering spectrum.

[0047] As one implementation method in this embodiment, the interference control module includes: A strongly coupled unit is used to finely adjust the geometry of the dielectric nanopillar within a defined parameter region, so that the Mie-type resonant mode and the Fabry-Pérot-type resonant mode enter a strongly coupled state. The far-field interferometer is used to achieve far-field radiation destructive interference of two modes under strong coupling conditions.

[0048] As one implementation method in this embodiment, the array construction module includes: Structural arrangement unit, used to arrange dielectric nanopillars in a two-dimensional periodic structure; An initial setting unit is used to set an initial lattice constant for the periodic array.

[0049] As one implementation method in this embodiment, the coupling enhancement module includes: The periodic optimization unit is used to scan within a preset lattice constant range and calculate the quality factor of the quasi-continuous domain bound state under different lattice constants. Resonant coupling units are used to excite resonant coupling between quasi-continuous bound state modes of adjacent dielectric nanopillars at the optimal lattice constant.

[0050] As one implementation method in this embodiment, the lattice constant of the period optimization unit is preset to be in the range of 350 nanometers to 600 nanometers; The optimal lattice constant of the resonant coupling unit is 460 nanometers.

[0051] The system or apparatus is used to implement the functions of the methods in the above embodiments. Each module in the system or apparatus corresponds to each step in the method, as has been described in the method and will not be repeated here.

[0052] The above implementation method solves the problem of realizing the quasi-continuous domain bound state of ultra-high quality factor in related technologies, thereby ensuring that the problems existing in the prior art are solved.

[0053] The above are merely preferred embodiments of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A method for realizing quasi-continuous bound states with ultra-high quality factor, characterized in that, Includes the following steps: Design and construct a dielectric nanopillar structure with geometric symmetry; By adjusting the geometric parameters of the dielectric nanopillars, both Mie-type and Fabry-Pérot-type resonant modes can be excited simultaneously within them. By adjusting the coupling strength between the Mie-type resonant mode and the Fabry-Pérot-type resonant mode, the far-field radiation of the two modes undergoes destructive interference, thereby forming a quasi-continuous domain bound state in the dielectric nanopillar under the condition of no symmetry breaking. The dielectric nanopillars supporting the quasi-continuous domain bound states are arranged into a periodic array; The lattice constant of the periodic array is optimized to excite resonant coupling between the quasi-continuous bound state modes of adjacent dielectric nanopillars, thereby improving the quality factor of the quasi-continuous bound state through the collective interference effect induced by the coupling.

2. The method according to claim 1, characterized in that, The process of adjusting geometric parameters includes: The system scans the radius-to-height ratio of the dielectric nanopillars and determines the parameter region where the two modes are strongly coupled based on the anti-crossing phenomenon of Mie-type and Fabry-Pérot-type resonant modes in the scattering spectrum.

3. The method according to claim 1, characterized in that, Dielectric nanopillars are cylindrical structures made of dielectric materials with a dielectric constant greater than 10.

4. The method according to claim 1, characterized in that, The process of optimizing the lattice constant includes: The lattice constant of the periodic array was set in the range of 350 nm to 600 nm and scanned. The lattice constant that made the quality factor of the quasi-continuous domain bound state reach the peak was selected as the optimized working parameter.

5. The method according to claim 4, characterized in that, The optimized operating parameters are a lattice constant of 460 nm, at which point the quality factor of the quasi-continuous bound state reaches the order of 10 to the power of 6.

6. The method according to claim 1, characterized in that, The method also includes illuminating the periodic array from the side with a horizontally polarized plane wave to excite and observe the quasi-continuous bound states.

7. A system for realizing quasi-continuous bound states with ultra-high quality factor, characterized in that, The system for implementing the method of any one of claims 1-6 comprises: The mode excitation module is used to simultaneously excite Mie-type resonant modes and Fabry-Pérot-type resonant modes inside a geometrically symmetric dielectric nanopillar. The interference control module is used to control the coupling strength between the Mie-type resonant mode and the Fabry-Pérot-type resonant mode, so that the far-field radiation of the two modes undergoes destructive interference, so as to form a quasi-continuous bound state under the condition of no symmetry breaking. An array building module is used to arrange dielectric nanopillars supporting the quasi-continuous domain bound states into a periodic array; The coupling enhancement module is used to excite resonant coupling between quasi-continuous bound state modes of adjacent dielectric nanopillars by optimizing the lattice constant of the periodic array, thereby improving the quality factor of the quasi-continuous bound state through collective interference effect.

8. A computer terminal device, characterized in that, include: One or more processors; A memory, coupled to the processor, for storing one or more programs; When the one or more programs are executed by the one or more processors, the one or more processors perform the steps of the method as described in any one of claims 1-6.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the steps of the method as described in any one of claims 1-6.

10. A computer program product, comprising a computer program, characterized in that, When the computer program is executed by a processor, it implements the steps of the method according to any one of claims 1-6.

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