A quasi-bound state implementation method based on symmetry breaking and area compensation

Abstract

The application discloses a quasi-bound state realization method based on symmetry breaking and area compensation and belongs to the technical field of micro-nano photonic devices. In view of the problem that the resonance wavelength is deviated when the quasi-bound state is realized by symmetry breaking, the application provides a dielectric metasurface unit cell supporting a symmetry-protected continuous domain bound state, adjusts the size of the air hole to introduce an asymmetric parameter to break the symmetry, and simultaneously implements area compensation to maintain the stability of the resonance wavelength, including compensation modes in the horizontal direction, the vertical direction or the bidirectional direction. The method can stabilize the quasi-bound state resonance wavelength near 1417.5 nanometers, the deviation is only 1 nanometer, and the quality factor can be adjusted in the range of 10³ to 10⁹, and can be used for high-sensitivity sensing and nanolaser.

Description

Technical Field

[0001] This invention belongs to the field of micro-nano photonic device technology, and particularly relates to a method for realizing quasi-bound states based on symmetry breaking and area compensation. Background Technology

[0002] Metallic metasurfaces exhibit significant ohmic losses in the visible and near-infrared bands, limiting their practical application in many high-precision photonic devices. All-dielectric metasurfaces, due to their high refractive index and low-loss characteristics, effectively avoid the ohmic losses of metallic materials, providing an important pathway for developing low-loss, high-performance photonic devices. All-dielectric structures can simultaneously support electric and magnetic dipole resonances, expanding the ability to control multidimensional optical parameters such as amplitude, phase, and polarization. Among these, the continuous-domain bound states achieved through symmetry protection have attracted considerable attention due to their theoretically infinite quality factor.

[0003] In practical applications, it is often necessary to couple this ideal bound state to the radiation channel to form a quasi-bound state that can be excited and utilized. This is usually achieved by deliberately breaking the intrinsic symmetry of the structure. However, during this symmetry breaking process, the effective refractive index of the structure often changes unexpectedly, directly leading to a significant shift in the resonant wavelength. This wavelength instability is a serious drawback in applications such as high-sensitivity biochemical sensing and narrow-linewidth lasers, because the accuracy of the sensing signal or the laser output wavelength will drift with structural fabrication errors or changes in operating conditions, making it difficult to control and repeat the device performance.

[0004] While methods such as band folding can alleviate the resonant wavelength shift in certain structures, their applicability and control mechanisms have inherent limitations, making them unsuitable for the widespread symmetry-protected continuum bound state systems. Therefore, developing a method to effectively suppress wavelength shift during the transition to quasi-bound states in the more common symmetry-protected continuum bound state systems, while simultaneously enabling precise and independent control of the quality factor, has become a critical technical challenge in this field. The difficulty in solving this problem lies in the need to skillfully compensate for optical parameter perturbations caused by geometric changes while simultaneously breaking symmetry to introduce radiative coupling, thereby achieving the decoupling and synergy of the two objectives of wavelength stability and quality factor control. Summary of the Invention

[0005] To address the aforementioned technical problems, this invention proposes a quasi-bound state realization method based on symmetry breaking and area compensation, thereby resolving the issues present in the prior art.

[0006] Firstly, to achieve the above objectives, the present invention provides a quasi-bound state realization method based on symmetry breaking and area compensation, comprising the following steps:

[0007] Provides a silicon dielectric layer unit cell with a central air hole;

[0008] Adjusting the dielectric size on one side of the air hole breaks the mirror symmetry of the silicon dielectric layer unit cell, thereby exciting the quasi-bound state;

[0009] Area compensation is implemented in the silicon dielectric layer unit cell, which is achieved by expanding the air hole boundary in at least one direction to maintain the resonant wavelength stability of the quasi-bound state.

[0010] Optionally, the process of adjusting the size of the medium includes:

[0011] Keep the original side length of the air hole unchanged;

[0012] Reduce the side length of the air hole on the other side to create an asymmetrical structure;

[0013] The parameter of an asymmetric structure is the difference between the original side length and the reduced side length.

[0014] Optionally, the process of implementing area compensation includes:

[0015] Determine the reduced air hole area on one side due to the disruption of symmetry;

[0016] The expansion is symmetrical along at least one boundary direction of the air hole, such that the increased area of ​​the air hole by the expansion is equal to the decreased area.

[0017] Optionally, the process of symmetrically expanding along at least one boundary direction of the air hole includes:

[0018] The two boundaries along the first direction of the air hole are simultaneously and symmetrically extended outward by a first dimension to implement area compensation in the first direction.

[0019] Optionally, the process of symmetrically expanding along at least one boundary direction of the air hole includes:

[0020] The two boundaries along the second direction of the air hole simultaneously extend outward symmetrically to a second dimension to implement area compensation in the second direction, which is perpendicular to the first direction.

[0021] Optionally, the process of symmetrically expanding along at least one boundary direction of the air hole includes:

[0022] The air hole extends symmetrically outwards simultaneously along its four boundaries to implement combined area compensation in the first and second directions.

[0023] Secondly, the present invention also provides a quasi-bound state realization system based on symmetry breaking and area compensation, used to implement a quasi-bound state realization method based on symmetry breaking and area compensation, the system comprising:

[0024] A cell configuration module for configuring silicon dielectric layer cell with a central air hole;

[0025] A symmetry breaking adjustment module is used to adjust the medium size on one side of the air hole to break the mirror symmetry of the unit cell and excite the quasi-bound state;

[0026] An area compensation implementation module is used to implement area compensation in the unit cell to maintain the resonant wavelength stability of the quasi-bound state by expanding the air hole boundary in at least one direction.

[0027] Thirdly, the present invention also provides a computer terminal device, comprising:

[0028] One or more processors;

[0029] A memory, coupled to the processor, for storing one or more programs;

[0030] When the one or more programs are executed by the one or more processors, the one or more processors implement the steps of the quasi-bound state realization method based on symmetry breaking and area compensation in the first aspect above.

[0031] 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, it implements the steps of the quasi-bound state realization method based on symmetry breaking and area compensation in the first aspect described above.

[0032] 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 quasi-bound state realization method based on symmetry breaking and area compensation in the first aspect described above.

[0033] Compared with the prior art, the present invention has the following advantages and technical effects:

[0034] This invention provides a quasi-bound state realization method based on symmetry breaking and area compensation. By introducing a synergistic mechanism of symmetry breaking and synchronous area compensation, this invention effectively suppresses the resonant wavelength shift caused by structural geometric changes during the excitation of quasi-bound states, achieving high wavelength stability. This invention allows for flexible adjustment of the mode quality factor over a wide range, thus meeting the differentiated requirements of various application scenarios for spectral linewidth and energy localization capabilities. The proposed multiple area compensation strategies, including horizontal, vertical, and multi-directional joint compensation, provide selectable control dimensions for wavelength stability and radiation loss management, enabling targeted adjustment of the quality factor and field distribution characteristics while maintaining wavelength stability. The structural design concept of this scheme is universal and can be extended to metasurface structures with air holes of different shapes, providing a reliable technical foundation for the development of high-performance, customizable micro / nano photonic devices, such as sensors and lasers. Attached Figure Description

[0035] 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:

[0036] Figure 1 This is a schematic diagram of the symmetrically broken air nanopore structure according to an embodiment of the present invention;

[0037] Figure 2 The mode features of the air nanopore symmetric structure in this embodiment of the invention are shown in (a) and (b), respectively, the mode magnetic field and electric field, (c) the wavelength position of the symmetry-protected BIC, and (d) the three-dimensional Q factor and far-field polarization field under symmetry protection.

[0038] Figure 3 This is a schematic diagram of air nanopore symmetry breaking in an embodiment of the present invention; wherein, (a) shows mode cancellation when the air nanopore has a symmetric structure, (b) shows mode leakage after the air nanopore symmetry breaking, (c) shows the change of Q factor value under changing asymmetry parameters, and (d) shows multipole mode decomposition after the symmetry breaking structure.

[0039] Figure 4 This invention relates to the variation of the mode magnetic field and resonant wavelength position by changing the asymmetry parameters from 0 nm to 90 nm in this embodiment.

[0040] Figure 5 This is a schematic diagram of area compensation in the x-direction according to an embodiment of the present invention; wherein (a) is an equal-proportional area compensation in the x-direction, (b) and (c) are schematic diagrams of the magnetic field before and after implementing area compensation in the x-direction with an asymmetry parameter of 60nm, and (d) is a comparison of the resonance peak positions before and after changing the asymmetry parameter and implementing area compensation in the x-direction.

[0041] Figure 6 This is a schematic diagram of area compensation in the y-direction according to an embodiment of the present invention; wherein (a) is an equal-proportional area compensation in the y-direction, (b) and (c) are schematic diagrams of the magnetic field before and after implementing area compensation in the y-direction with an asymmetry parameter of 60nm, and (d) is a comparison of the resonance peak positions before and after changing the asymmetry parameter and implementing area compensation in the y-direction.

[0042] Figure 7 This is a schematic diagram of area compensation in the x and y directions according to an embodiment of the present invention; wherein (a) shows simultaneous proportional area compensation in the x and y directions, (b) and (c) are schematic diagrams of the magnetic field before and after area compensation with an asymmetry parameter of 60nm, and (d) is a comparison of the resonance peak positions before and after changing the asymmetry parameter and implementing area compensation in the x and y directions. Detailed Implementation

[0043] 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.

[0044] 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.

[0045] Example 1

[0046] This embodiment provides a quasi-bound state realization method based on symmetry breaking and area compensation, including:

[0047] Provides a silicon dielectric layer unit cell with a central air hole;

[0048] Adjusting the dielectric size on one side of the air hole breaks the mirror symmetry of the silicon dielectric layer unit cell, thereby exciting the quasi-bound state;

[0049] Area compensation is implemented in the silicon dielectric layer unit cell, which is achieved by expanding the air hole boundary in at least one direction to maintain the resonant wavelength stability of the quasi-bound state.

[0050] As one implementation method in this embodiment, the process of adjusting the size of the medium includes:

[0051] Keep the original side length of the air hole unchanged;

[0052] Reduce the side length of the air hole on the other side to create an asymmetrical structure;

[0053] The parameter of an asymmetric structure is the difference between the original side length and the reduced side length.

[0054] This invention enables the quasi-bound state resonance wavelength to be stably maintained around 1417.5 nm under parameter variations, with an overall shift of only 1 nm. Simultaneously, its Q-factor can range from 10³ to 10⁻⁶. 9 Tuning within a range. Includes:

[0055] like Figure 1 , Figure 5 , Figure 6 , Figure 7 As shown, this embodiment of the invention provides a method for realizing wavelength-stable quasi-bound states based on symmetry breaking and area compensation of air nanopores, comprising: the silicon dielectric layer unit cell is a rectangular silicon dielectric microcavity arranged with a period of P = 800 nm and a thickness of H = 400 nm; a rectangular air hole is etched in the center of the microcavity, and the side length of the air hole is a1 = 400 nm; the mirror symmetry of the structure along the y-axis is broken by increasing the dielectric size on the right side of the structure to adjust the volume of the air hole; its asymmetry parameter α = a1 - a2 is defined as the difference between the original side length of the air hole a1 and the side length a2 after adding the dielectric on the right side.

[0056] Preferably, the asymmetric parameter takes values ​​in the range of (15 nm, 30 nm, 45 nm, 60 nm, 75 nm, 90 nm). This operation excites the quasi-continuous bound state, but at the same time causes a blue shift in the resonance wavelength.

[0057] As one implementation method in this embodiment, the process of implementing area compensation includes:

[0058] Determine the reduced air hole area on one side due to the disruption of symmetry;

[0059] The expansion is symmetrical along at least one boundary direction of the air hole, such that the increased area of ​​the air hole by the expansion is equal to the decreased area.

[0060] As one implementation method in this embodiment, the process of symmetrically expanding along at least one boundary direction of the air hole includes:

[0061] The two boundaries along the first direction of the air hole are simultaneously and symmetrically extended outward by a first dimension to implement area compensation in the first direction.

[0062] Optionally, the first direction is along both sides of the x-direction of the nano-air pores.

[0063] Optionally, the first dimension is Δx.

[0064] Specifically, proportional area compensation is performed symmetrically on both sides of the nano-air pore x-direction.

[0065] The left and right boundaries of the rectangular air hole are symmetrically extended outwards, with the lateral dimension of the extension also being Δx. This ensures that the area of ​​the silicon dielectric removed on the right side is equal to the area of ​​the air hole effectively increased by the extension on the left side. Through this operation, the total area of ​​the silicon dielectric within the unit cell is kept in dynamic equilibrium in the x-direction, effectively offsetting the change in the effective refractive index of the system caused by the reduction in volume on one side.

[0066] As one implementation method in this embodiment, the process of symmetrically expanding along at least one boundary direction of the air hole includes:

[0067] The two boundaries along the second direction of the air hole simultaneously extend outward symmetrically to a second dimension to implement area compensation in the second direction, which is perpendicular to the first direction.

[0068] Optionally, the second direction is along both sides of the y-direction of the nano-air pores.

[0069] Optionally, the second dimension is Δy.

[0070] Specifically, proportional area compensation is performed symmetrically on both sides along the y-direction of the nano-air pores.

[0071] refer to Figure 6 In (a), the upper and lower boundaries of the rectangular air hole are simultaneously and symmetrically expanded outwards, with a longitudinal dimension of Δy. Δy is adjusted so that the total area of ​​the air hole increased by the vertical expansion equals the area of ​​the air hole decreased by the contraction on the right side. This compensation strategy maintains wavelength stability while (see reference...) Figure 6 (d) in the image (wavelength stabilized around 1417.5nm) can better maintain a higher Q value.

[0072] As one implementation method in this embodiment, the process of symmetrically expanding along at least one boundary direction of the air hole includes:

[0073] The air hole extends symmetrically outwards simultaneously along its four boundaries to implement combined area compensation in the first and second directions.

[0074] Specifically, proportional area compensation is performed symmetrically on both sides of the nano-air pores along the x and y directions. The four boundaries of the square air pores (left, right, top, and bottom) are simultaneously and symmetrically expanded outwards. The expansion amount in each direction is adjusted so that the total increase in air pore area equals the area reduced due to the contraction on the right side.

[0075] refer to Figure 7 In (a), the four boundaries of the square air hole—left, right, top, and bottom—are simultaneously and symmetrically expanded outwards. The amount of expansion in each direction is adjusted so that the total increased area of ​​the air hole equals the area reduced due to the contraction on the right side.

[0076] like Figure 2 As shown, under the condition of maintaining a centrosymmetric structure without introducing any asymmetry, the magnetic field distribution of the air hole exhibits a highly symmetrical shape, with its intensity mainly concentrated at the edge of the air hole and in the adjacent medium region. The displacement current distribution exhibits the same rotational symmetry as the magnetic quadrupole moment, and the vector field lines form closed vortex loops in space. This closed characteristic is an essential feature of magnetic multipoles. The electric field distribution also exhibits symmetrical local characteristics, with hotspots mainly located within the air hole and concentrated in the medium region near the air hole. The eigenmodes supported by the symmetrical structure maintain centrosymmetric distributions in both the magnetic and electric fields. By continuously adjusting the geometric asymmetry parameter a2, a continuous transition from a fully bound, non-radiative ideal BIC to a radiation-controlled, wavelength-tunable QBIC can be achieved. Near a2 = 400 nm, the structure maintains perfect symmetry, and the mode is in an ideal BIC state. At this point, the mode is completely decoupled from radiation continuity, the resonant linewidth is zero, and it has an infinitely large quality factor, which symbolizes its topological protection characteristics of being bound in a continuous domain. As a2 changes from 400 nm to 310 nm, the symmetry of the structure is broken, and the mode is thus coupled to the radiation channels, transforming into an observable QBIC. To better observe the mode characteristics, the 3D quality factor and far-field polarization state of the mode in momentum space were further calculated. At the Γ point, the Q factor exhibits a sharp singularity, with theoretical values ​​tending towards infinity. Under this specific momentum, the intrinsic mode is completely decoupled from all radiation channels, becoming an ideal BIC that does not radiate any energy to the far field. From the Γ point, the wave vector decays rapidly towards the surrounding area, the Q factor forms a conical distribution, introducing radiation loss, and the mode transforms from a bound state to a leaky mode. By calculating the number of turns of the far-field polarization vector around the BIC in momentum space,

[0077] Topological charge q is defined as the circulation of a closed path C with polarization angle ϕ(k):

[0078]

[0079]

[0080] The calculated topological charge is q = -1. This conforms to system C. nv The topological charge set allowed at the Γ point under symmetry, and the obvious clockwise vortex characteristics of the far-field polarization vector field, further demonstrate the existence of SP-BIC.

[0081] By introducing perturbations by breaking the symmetry in the y-direction, the magnetic quadrupole mode transitions from an ideal BIC to an excitable and tunable quasi-BIC. The magnetic quadrupole moment is primarily dominated by a pair of magnetic moments in the xy-plane. Under symmetrical structure conditions, the magnetic moments are parallel and opposite in direction, with equal radiation intensity but a fixed phase difference. At this point, the vector sum of the two magnetic dipoles in each radiation channel is zero, thus forming a bound state with completely suppressed radiation, and the energy localized within the structure. To utilize this non-radiative dark mode, by altering the geometric symmetry of the air hole, such as reducing the volume of the air hole on the right, a difference in resonance intensity can be created between the originally symmetrical pair of magnetic moments. Once the symmetry is broken, the sum of their radiation vectors is no longer zero, and the non-zero dipole components form discrete trapped mode resonances within the metasurface unit, thereby achieving high-quality factor resonance dominated by the magnetic quadrupole moment. To further illustrate and understand the excitation mechanism of the mode, the origin of the quasi-bound state is studied by combining multipole decomposition theory, electromagnetic field, and current density distribution. According to multipole expansion theory, the radiation power of different multipole moments is calculated as follows:

[0082]

[0083]

[0084]

[0085]

[0086]

[0087] Here, w is the angular frequency; c is the speed of light; k = 2π / λ = w / c is the wave number; It is the vacuum permeability; α and β represent the Cartesian coordinate components x, y and z, respectively. , , , and These represent electric dipoles (ED), magnetic dipoles (MD), toroidal dipoles (TD), electric quadrupoles (EQ), and magnetic quadrupoles (MQ), respectively. Figure 3 As shown in (c), the results indicate that the magnetic quadrupole (MQ) is the main contributing source. The intensity of the MQ differs from that of other dipole modes by an exponential order of magnitude, thus suppressing other dipoles, consistent with previous mode analysis results. Effective tuning of the resonance mode quality factor can be achieved by adjusting the degree of symmetry breaking in the rectangular air-hole structure. Figure 3 As shown in (d) in the figure, with the asymmetric parameter As the wavelength changes from 10 nm to 90 nm, the Q factor exhibits a continuous and significant decreasing trend, with its value decreasing from close to 10. 9The high Q state is adjusted across three orders of magnitude to 10. 3 This allows for free adjustment of the Q factor over a wide range.

[0088] By introducing controllable symmetry breaking, SP-BIC can be transformed into Q-BIC. However, the change in the effective medium volume of the structure leads to an increase in the effective refractive index of the mode, resulting in a redshift of the resonant wavelength. This invention proposes three geometric compensation strategies to achieve relative wavelength stability while breaking the symmetry of the air hole structure through three different air hole area compensation methods. Specifically, compensation is performed in the x-direction, y-direction, and surrounding directions, with the size of the compensation area being the same as the broken area. After equal-area compensation of the air hole in the x-direction, as shown... Figure 5 As shown in (c), the overall energy center of gravity has recovered somewhat, but the horizontal magnetic field energy has further weakened. This is because the compensation in the x-direction exacerbates the asymmetry in the horizontal direction, causing the magnetic dipole component in the x-direction to weaken due to further radiation coupling, significantly increasing the radiation loss rate of the mode, and thus suppressing the Q value due to near-field energy leakage. This geometric adjustment essentially redistributes the spatial dipole moment distribution of the mode, precisely controlling the effective medium volume in the x-direction to offset the refractive index change caused by the previous symmetry breaking, and overall controlling the average energy density of the mode, causing the resonance peak to blue shift again.

[0089] The air holes are compensated for with equal area along the y-direction. Figure 6 Figure (a) shows a schematic diagram of symmetrically expanding equal areas along the y-axis on both the top and bottom sides. This compensation method maintains the symmetry characteristics of the dominant resonant mode's eigenfield. To investigate the impact of compensation on mode characteristics, Figure 6 (b) and Figure 6 The comparison in (c) shows the normalized magnetic field distribution before and after compensation. Figure 6 (b) corresponds to the case where the asymmetry parameter α = 60 nm and no compensation is provided, and its magnetic field distribution exhibits significant asymmetry in the x-direction. However, after implementing equal-area compensation in the y-direction, as shown in Figure (b), the magnetic field distribution in Figure (b) shows a different result. Figure 6 In (c), the overall symmetry of the magnetic field distribution is significantly improved, and the localization of the magnetic field intensity component in the horizontal direction is significantly enhanced. This is because the air hole compensation operation in the y-direction reduces the average dielectric constant in that direction, offsetting the redshift of the resonance peak caused by the increase in the overall effective refractive index of the system due to the defect. This makes the magnetic field energy more concentrated on the medium at the edge of the air hole, reducing the radiation loss and thus improving the Q value. The effect of this structure in modulating the wavelength has been directly verified in the spectral response. For example... Figure 6In (d), the blue dashed lines show that in the uncompensated case, as the asymmetry parameter α gradually increases, the effective refractive index of the medium changes, resulting in a systematic redshift of the resonance peaks. However, the red solid lines, representing the y-direction compensation results, show a trend of wavelength stability. Although the mode linewidth increases with the change of α, under the same asymmetry parameter, the linewidth remains highly consistent before and after compensation. This indicates that the Q-factor is almost lossless before and after y-direction compensation. All resonance peaks are densely distributed in the region around 1417.5 nm, successfully achieving low-loss adjustable Q-factor and effectively maintaining the stability of the resonance wavelength.

[0090] This invention utilizes COMSOL Multiphysics for simulation, and the specific steps are as follows:

[0091] Step 1: Set up an all-silicon dielectric layer structure with a cell period P = 800 nm, a symmetrical rectangular air hole etched in the center with a side length a1 = 400 nm, a thickness H = 400 nm, and a silicon refractive index Si = 3.48. The right side length of the asymmetrical rectangular air hole is a2, with a value between 400 nm and 310 nm.

[0092] Step 2: The volume of the air hole is adjusted by increasing the size of the medium on the right side of the structure, thereby breaking the mirror symmetry along the y-axis while maintaining C2 symmetry. The degree of this breaking is quantified by the asymmetry parameter α = a1 - a2, where α is defined as the difference between the side length of the original air hole and the side length after adding the medium on the right side. In the simulation, it is assumed that the metasurface is surrounded by air (background refractive index n = 1). Periodic boundary conditions are applied along the x and y axes, while a perfectly matched layer (PML) is used along the z direction to absorb the outgoing wave. Simultaneously, under y-polarized light, the asymmetry parameter is varied to 15 nm, 30 nm, 45 nm, 60 nm, 75 nm, and 90 nm. Figure 4 In (g), it was observed that after breaking the symmetry, the maximum redshift of the resonance wavelength was 30 nm.

[0093] Step 3: While introducing the aforementioned defect, area compensation is performed in the x-direction. Specifically, the left and right boundaries of the rectangular air hole are symmetrically extended outwards, with the lateral dimension of the extension also being Δx. This ensures that the area of ​​the removed right-side silicon dielectric is equal to the area of ​​the air hole effectively increased by the left-side extension. Through this operation, the total area of ​​the silicon dielectric within the unit cell is kept in dynamic equilibrium in the x-direction, effectively offsetting the change in the effective refractive index of the system caused by the reduction in volume on one side. Figure 5The transmission spectrum comparison in (d) shows that, without compensation (dashed line), the resonant wavelength blue shifts significantly (>30 nm) as Δx increases; after x-direction compensation (solid line), the resonant wavelength is stabilized in the range of λ0 ± 1 nm (e.g., around 1417.5 nm), and the full width at half maximum (FWHM) of the resonant peak increases with Δx, indicating that the device's quality factor (Q value) can achieve wide-range active tuning.

[0094] Step 4: The basic unit cell structure is the same as in Step 3. The symmetry breaking method is also to reduce the volume on the right side of the air pore. The area compensation method is different: see [link to relevant documentation]. Figure 6 In (a), the upper and lower boundaries of the rectangular air hole are simultaneously and symmetrically expanded outwards, with a longitudinal dimension of Δy. Δy is adjusted so that the total area of ​​the air hole increased by the vertical expansion equals the area of ​​the air hole decreased by the contraction on the right side. This compensation strategy maintains wavelength stability, as shown in [the diagram]. Figure 6 In (d), the wavelength is stabilized around 1417.5 nm, which better maintains a high Q value.

[0095] Step 5: Its basic unit cell structure is the same as in Step 3. The symmetry breaking method is also to reduce the volume on the right side of the air hole. The area compensation method is as follows: Figure 7 In (a), the four boundaries of the rectangular air hole—left, right, top, and bottom—are simultaneously and symmetrically expanded outwards. The expansion amount in each direction is adjusted so that the total increased air hole area equals the area reduced due to the contraction on the right side. This compensation strategy exhibits the best overall performance among the three schemes, such as... Figure 7 The (d) in the formula can suppress wavelength fluctuations within λ0 ± 1 nm (such as around 1417.5 nm) and has a narrow resonance peak linewidth, that is, the Q value remains at its highest.

[0096] After compensation from the surrounding area ( Figure 7 In (c), the horizontal magnetic field distribution is partially recovered, and the overall energy density is between that of single compensation in the x and y directions. The compensated magnetic field energy is significantly concentrated in the medium region, and the localization of the field strength is significantly enhanced. This is because the surrounding compensation evenly adjusts the effective medium distribution in all directions. Compared with unidirectional compensation, surrounding compensation reduces the effective volume of the medium in both the x and y directions, resulting in a comprehensive and uniform cancellation of changes in the effective refractive index of the mode. This geometric modulation suppresses anisotropic radiation leakage channels, reducing radiation loss while maintaining the stability of the resonant wavelength, achieving the optimal balance between wavelength stability and Q-factor preservation. Spectral results ( Figure 7Figure (d) further validates the effectiveness of this mechanism. The blue dashed line in the figure represents the uncompensated case. As the asymmetry parameter α increases from 0 nm to 90 nm, the resonance peaks exhibit a systematic redshift, with a wavelength drift exceeding 30 nm. In contrast, the surrounding compensation result, corresponding to the red solid line, shows that as the asymmetry parameter changes from 0 nm to 90 nm, all resonance peaks remain stable around 1417.5 nm, with fluctuations within approximately 1 nm. Notably, the spectral linewidth after surrounding compensation is generally narrower than that after x-direction compensation, indicating that under the same asymmetry parameter, the Q-factor attenuation is smaller with surrounding compensation. This demonstrates that this strategy can more effectively maintain a high Q-factor while achieving wavelength stabilization.

[0097] The quasi-BIC mode discovered in this invention is mainly dominated by a magnetic quadrupole. By adjusting the geometric parameters, while disrupting structural symmetry to excite a high-Q resonance, the effective refractive index change caused by the redistribution of material volume is compensated, thereby readjusting the mode's radiation loss and altering the resonance frequency. By introducing equal-area compensation in three corresponding directions (x, y, or surrounding directions), the resonance wavelength can be stabilized around 1417.5 nm under a wide range of asymmetry parameters, with an overall shift of only 1 nm. Moreover, different compensation strategies exhibit differentiated control characteristics: x-direction compensation increases radiation loss while stabilizing the wavelength, but achieves Q-value tuning and wavelength stability; y-direction compensation better maintains a higher Q value while stabilizing the wavelength; and surrounding compensation shows a comprehensive balance between wavelength stability and loss suppression.

[0098] The above embodiments use a rectangular air hole as an example, but the area compensation concept described in this invention is also applicable to other polygonal or elliptical air hole structures. The compensation directions (x, y, surrounding) can be used individually or in combination according to the required optical performance (wavelength stability, Q-value tuning range). The wavelength-stable, Q-value-tunable metasurface device provided by this invention can be widely used in fields such as high-sensitivity biochemical sensing, low-threshold nanolasers, nonlinear optical frequency conversion, and quantum light sources to enhance the interaction between light and matter.

[0099] Based on this, this invention provides a quasi-bound state realization method based on symmetry breaking and area compensation. The symmetry-breaking unit cell of the air nanopore is a rectangular silicon dielectric microcavity with a period of P = 800 nm and a thickness of H = 400 nm. A rectangular air hole with a side length of a1 = 400 nm is etched at the center of the microcavity. The volume of the air hole is adjusted by increasing the dielectric size on the right side of the structure, thereby breaking the mirror symmetry of the structure along the y-axis. The asymmetry parameter α = a1 - a2 is defined as the difference between the original side length of the air hole a1 and the side length a2 after adding dielectric on the right side. Area compensation is implemented to suppress the resonant wavelength shift. Specifically, three schemes are proposed: x-direction area compensation, y-direction compensation, and simultaneous x and y-direction area compensation.

[0100] By employing the technical solution of this invention, the quasi-bound state resonance wavelength can be stably maintained around 1417.5 nm under parameter variations, while its Q factor can range from 10³ to 10⁻⁶. 9 Tuning within the range. Simultaneously achieving a quasi-bound state with wavelength stability and adjustable Q-factor.

[0101] Example 2

[0102] In this embodiment, a computer terminal device is provided, including:

[0103] One or more processors;

[0104] A memory, coupled to the processor, for storing one or more programs;

[0105] 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 realizing quasi-bound states based on symmetry breaking and area compensation.

[0106] 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 realizing quasi-bound states based on symmetry breaking and area compensation.

[0107] 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 quasi-bound state realization method based on symmetry breaking and area compensation.

[0108] 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 quasi-bound state realization method based on symmetry breaking and area compensation.

[0109] 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.

[0110] 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.

[0111] This embodiment provides such a device or system. The system, referred to as a quasi-bound state realization system based on symmetry breaking and area compensation, includes:

[0112] A cell configuration module for configuring silicon dielectric layer cell with a central air hole;

[0113] A symmetry breaking adjustment module is used to adjust the medium size on one side of the air hole to break the mirror symmetry of the unit cell and excite the quasi-bound state;

[0114] An area compensation implementation module is used to implement area compensation in the unit cell to maintain the resonant wavelength stability of the quasi-bound state by expanding the air hole boundary in at least one direction.

[0115] As one implementation method in this embodiment, the symmetry breaking adjustment module includes:

[0116] An original size retention unit is used to keep the original side length of the air hole unchanged.

[0117] An asymmetric structure forming unit is used to reduce the side length of the other side of the air hole to form an asymmetric structure;

[0118] The parameter calculation unit is used to calculate the difference between the original side length and the reduced side length as an asymmetric parameter.

[0119] As one implementation method in this embodiment, the area compensation implementation module includes:

[0120] An area calculation unit is used to determine the area of ​​the air hole that is reduced on said side due to the breaking of symmetry;

[0121] A compensation execution unit is configured to expand symmetrically along at least one boundary direction of the air hole, such that the increased area of ​​the air hole due to the expansion is equal to the decreased area.

[0122] As one implementation method in this embodiment, the compensation execution unit includes:

[0123] A first-direction compensation subunit is configured to simultaneously and symmetrically expand outward by a first dimension along both boundaries of the air hole in a first direction to implement area compensation in the first direction.

[0124] As one implementation method in this embodiment, the compensation execution unit includes:

[0125] The second direction compensation subunit is used to simultaneously and symmetrically expand outward a second dimension along the two boundaries of the second direction of the air hole to implement area compensation in the second direction, which is perpendicular to the first direction.

[0126] As one implementation method in this embodiment, the compensation execution unit includes:

[0127] A combined compensation subunit is used to simultaneously and symmetrically expand outward along the four boundaries of the air hole to implement combined area compensation in the first direction and the second direction.

[0128] 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.

[0129] The above implementation method solves the problem of realizing quasi-bound states based on symmetry breaking and area compensation in related technologies, thereby ensuring that the problems existing in the prior art are resolved.

[0130] 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-bound states based on symmetry breaking and area compensation, characterized in that, Includes the following steps: Provides a silicon dielectric layer unit cell with a central air hole; Adjusting the dielectric size on one side of the air hole breaks the mirror symmetry of the silicon dielectric layer unit cell, thereby exciting the quasi-bound state; Area compensation is implemented in the silicon dielectric layer unit cell, which is achieved by expanding the air hole boundary in at least one direction to maintain the resonant wavelength stability of the quasi-bound state.

2. The method according to claim 1, characterized in that, The process of adjusting the size of the medium includes: Keep the original side length of the air hole unchanged; Reduce the side length of the air hole on the other side to create an asymmetrical structure; The parameter of an asymmetric structure is the difference between the original side length and the reduced side length.

3. The method according to claim 1, characterized in that, The process of implementing area compensation includes: Determine the reduced air hole area on one side due to the disruption of symmetry; The expansion is symmetrical along at least one boundary direction of the air hole, such that the increased area of ​​the air hole by the expansion is equal to the decreased area.

4. The method according to claim 3, characterized in that, The process of symmetrical expansion along at least one boundary direction of the air hole includes: The two boundaries along the first direction of the air hole are simultaneously and symmetrically extended outward by a first dimension to implement area compensation in the first direction.

5. The method according to claim 4, characterized in that, The process of symmetrical expansion along at least one boundary direction of the air hole includes: The two boundaries along the second direction of the air hole simultaneously extend outward symmetrically to a second dimension to implement area compensation in the second direction, which is perpendicular to the first direction.

6. The method according to claim 5, characterized in that, The process of symmetrical expansion along at least one boundary direction of the air hole includes: The air hole extends symmetrically outwards simultaneously along its four boundaries to implement combined area compensation in the first and second directions.

7. A quasi-bound state realization system based on symmetry breaking and area compensation, characterized in that, The system for implementing the method of any one of claims 1-6 comprises: A cell configuration module for configuring silicon dielectric layer cell with a central air hole; A symmetry breaking adjustment module is used to adjust the medium size on one side of the air hole to break the mirror symmetry of the unit cell and excite the quasi-bound state; An area compensation implementation module is used to implement area compensation in the unit cell to maintain the resonant wavelength stability of the quasi-bound state by expanding the air hole boundary in at least one direction.

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.

Images