A method and system for realizing bound states on quasi-continuous domain on SIW

Abstract

The present invention discloses a method and system for realizing bound states on a quasi-continuous domain on an SIW, belonging to the field of substrate integrated waveguide technology. The method comprises: S1: calculating the cutoff frequency of the SIW and the resonant frequency of the SIW resonant cavity according to design requirements; S2: gradually constructing a SIW and SIW-SIW resonant cavity stacked structure model in simulation software; S3: setting the simulation frequency, boundary conditions and field monitor; S4: scanning multiple parameters to obtain an S-curve, and selecting different parameters according to the required bandwidth and amplitude; if there is no S-curve that meets the preset conditions, rescanning more parameters until an S-curve that meets the preset conditions is obtained; S5: adjusting the parameters according to the ratio of the required transmission resonant frequency to the maximum half-width of the resonance to realize bound states on the quasi-continuous domain on the SIW. Quasi-BIC is realized on the SIW, which reduces the processing difficulty and process complexity and is conducive to device miniaturization.

Description

Technical Field

[0001] The present invention relates to the technical field of substrate integrated waveguides, and in particular to a method and system for realizing bound states on a quasi-continuous domain on a SIW. Background Art

[0002] As the foundation of front-end design for modern communication systems, microwave filters play a vital role. Due to their low insertion loss and ease of integration, substrate integrated waveguides (SIWs) have become the optimal choice for RF filters. Therefore, the Q value of SIWs is a key performance indicator for modern communication systems.

[0003] Bound states in the continuum (BICs) have recently attracted considerable attention due to their infinite lifetimes, extending their reach from quantum physics to photonics. Unlike conventional bound states whose frequencies lie outside the continuum, BICs reside within the continuum, maintaining the characteristics of perfectly localized electromagnetic waves in the absence of radiation. They coexist with the continuous radiation spectrum without leaking energy. Therefore, ideally, BICs are invisible in the spectrum, meaning their resonant bandwidth is zero and their Q value is infinite.

[0004] Perfectly ideal BICs are difficult to achieve experimentally. With current experimental techniques, research on BIC applications tends to focus on bound states in the quasi-continuum (quasi-BICs). Quasi-BICs are a collapsed form of BICs, representing nearly bound states that, while coupled to radiative modes, exhibit minimal leakage, resulting in a finite but very high Q. Therefore, introducing quasi-BICs into SIWs can significantly improve the Q of SIW structures, enabling applications such as narrowband filtering.

[0005] Previous research has relied on implementing BIC on SIW structures by using air as a dielectric filling the substrate layer of the SIW structure. While simulations, experiments, and theory have perfectly demonstrated the existence of BIC in SIW-SIW resonant cavity systems, the processing and design of these prototypes is complex, and experimental test results differ significantly from simulations, limiting this design approach to theoretical verification and limiting its application. Using air as a lossless dielectric is difficult and complex to process, hindering miniaturization. Summary of the Invention

[0006] The object of the present invention is to overcome the deficiencies of the prior art and to provide a method, system and storage medium for realizing bound states on a quasi-continuous domain on an SIW.

[0007] The object of the present invention is achieved through the following technical solutions: In a first aspect, the present invention provides: a method for realizing bound states on a quasi-continuous domain on an SIW, comprising the following steps:

[0008] S1: Calculate the cutoff frequency of SIW and the resonant frequency of SIW resonant cavity according to design requirements;

[0009] S2: Gradually construct SIW and SIW-SIW resonant cavity stacking structure models in the simulation software;

[0010] S3: Set simulation frequency, boundary conditions, and field monitors;

[0011] S4: Scan multiple parameters to obtain an S-curve, and select different parameters according to the required bandwidth and amplitude. If there is no S-curve that meets the preset conditions, rescan more parameters until an S-curve that meets the preset conditions is obtained.

[0012] S5: Adjust the parameters according to the ratio of the required transmission resonance frequency to the maximum half-width of the resonance to realize the bound state on the quasi-continuous domain on the SIW.

[0013] Preferably, the cutoff frequency of the SIW is lower than the resonant frequency of the SIW resonant cavity. The resonant frequency of the SIW resonant cavity is calculated as follows:

[0014] ;

[0015] in c is the speed of light in a vacuum; m is the first resonant mode number; n is the second resonance mode number; is the dielectric constant; and is the equivalent width and length of the SIW resonant cavity, which are calculated using the equivalent formula of the full-wave finite element method:

[0016] ,

[0017] in L 1. W 1 is the length and width of the SIW resonant cavity; d is the metal via diameter; p is the distance between two adjacent through holes;

[0018] The cutoff frequency calculation formula of SIW is as follows:

[0019] ,

[0020] in h is the thickness of the SIW dielectric substrate.

[0021] Preferably, the S2 further comprises the following steps:

[0022] A SIW structure model was established in the simulation software, and coplanar waveguide transition structures were added at both ends of the SIW to match the impedance;

[0023] A coupling gap is opened at the center of the metal layer on the upper surface of the SIW to cut the surface current so that the energy is coupled into the SIW resonant cavity;

[0024] Build a SIW resonant cavity model above the SIW and set the tunable parameters y , so that the SIW resonant cavity y The value changes along y Axis translation.

[0025] Preferably, the S4 further comprises the following steps:

[0026] For tunable parameters y Perform a sweep and simulate using a frequency domain solver;

[0027] Adjust the center offset of the SIW resonant cavity about the symmetry axis of the coupling slot y , to destroy the symmetry protection state in the resonant mode, thereby adjusting the ratio of the transmission resonance frequency to the maximum half-width of the resonance, so that the coupling between the bound state in the SIW resonant cavity and the continuous state in the SIW below is enhanced, and the ability of the SIW resonant cavity to bind energy is weakened.

[0028] Preferably, spectrum analysis and coupled mode theory are used to determine whether a resonance conforms to the quasi-BIC phenomenon.

[0029] Preferably, the simulation software is CST Microwave Studio software.

[0030] A second aspect of the present invention provides: a system for realizing bound states on a quasi-continuous domain on an SIW, for realizing any of the above-mentioned methods for realizing bound states on a quasi-continuous domain on an SIW, comprising:

[0031] A calculation module is used to calculate the cutoff frequency of the SIW and the resonant frequency of the SIW resonant cavity according to design requirements;

[0032] Simulation module, used to gradually build SIW and SIW-SIW resonant cavity stack structure models in the simulation software; set simulation frequency, boundary conditions and field monitor;

[0033] The curve generation module is used to scan multiple parameters to obtain an S-curve, and select different parameters according to the required bandwidth and amplitude. If there is no S-curve that meets the preset conditions, more parameters will be scanned again until an S-curve that meets the preset conditions is obtained.

[0034] The adjustment module is used to adjust parameters according to the ratio of the required transmission resonance frequency to the maximum half-width of the resonance to realize the bound state on the quasi-continuous domain on the SIW.

[0035] The third aspect of the present invention provides: a computer-readable storage medium, wherein the computer-readable storage medium stores computer-executable instructions, and when the computer-executable instructions are loaded and executed by a processor, any of the above-mentioned methods for realizing bound states on a quasi-continuous domain on an SIW is implemented.

[0036] The beneficial effects of the present invention are:

[0037] 1) Quasi-BIC was implemented on SIW. The internal coupling topology of the system was established and deduced using CMT. The resonance characteristics of the coupling slot were controlled by the slot width. The appropriate quasi-BIC state can be selected according to the bandwidth and Q value requirements. It can be applied to narrowband filters or high-Q value sensors, reducing the processing difficulty and process complexity and facilitating device miniaturization. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] Figure 1 Flowchart of the method for realizing bound states on quasi-continuous domains on SIW;

[0039] Figure 2 It is a schematic diagram of SIW structural model;

[0040] Figure 3 For parameters y Schematic diagram of S parameters after change;

[0041] Figure 4 Q value varies with parameters y Schematic diagram of the changes;

[0042] Figure 5 For different y Contour plot of the transmission spectrum at ;

[0043] Figure 6 is a schematic diagram of electric field distribution;

[0044] Figure 7 Schematic diagram of the topological structure of the stacked SIW;

[0045] Figure 8 Schematic diagram of reflection curves for different slot widths. DETAILED DESCRIPTION

[0046] The following will clearly and completely describe the technical solutions of the present invention in conjunction with the embodiments. Obviously, the embodiments described are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative work shall fall within the scope of protection of the present invention.

[0047] See Figures 1-8 The first aspect of the present invention provides: a method for realizing bound states on a quasi-continuous domain on an SIW, comprising the following steps:

[0048] S1: Calculate the cutoff frequency of SIW and the resonant frequency of SIW resonant cavity according to design requirements;

[0049] S2: Gradually construct SIW and SIW-SIW resonant cavity stacking structure models in the simulation software;

[0050] S3: Set simulation frequency, boundary conditions, and field monitors;

[0051] S4: Scan multiple parameters to obtain an S-curve, and select different parameters according to the required bandwidth and amplitude. If there is no S-curve that meets the preset conditions, rescan more parameters until an S-curve that meets the preset conditions is obtained.

[0052] S5: Adjust the parameters according to the ratio of the required transmission resonance frequency to the maximum half-width of the resonance to realize the bound state on the quasi-continuous domain on the SIW.

[0053] In this embodiment, air filling is abandoned, and a SIW is printed on a PCB. A coupling slot is opened on its upper surface to radiate energy to another SIW resonant cavity, forming an improved SIW-SIW resonant cavity system that produces a quasi-BIC, thereby improving the Q value of the structure.

[0054] In some embodiments, the cutoff frequency of the SIW is lower than the resonant frequency of the SIW resonant cavity. The resonant frequency of the SIW resonant cavity is calculated as follows:

[0055] ;

[0056] in c is the speed of light in a vacuum; m is the first resonant mode number; n is the second resonance mode number; is the dielectric constant; and is the equivalent width and length of the SIW resonant cavity, which are calculated using the equivalent formula of the full-wave finite element method:

[0057] ,

[0058] in L 1. W 1 is the length and width of the SIW resonant cavity; d is the metal via diameter; p is the distance between two adjacent through holes;

[0059] The cutoff frequency calculation formula of SIW is as follows:

[0060] ,

[0061] in h is the thickness of the SIW dielectric substrate.

[0062] In this embodiment, the resonant frequency is first determined according to the design requirements. Since the SIW is essentially a waveguide structure, its characteristics are equivalent to a high-pass filter, and the SIW resonant cavity is excited by the slot coupling above the SIW. Therefore, it is necessary to ensure that the cutoff frequency of the SIW is lower than the resonant frequency of the SIW resonant cavity. The resonant frequency of the SIW resonant cavity can be calculated by analogy with the calculation of a rectangular metal resonant cavity.

[0063] Preliminary calculations TE 101 The resonant frequency of the mode is around 4.86 GHz. If you want to get the corresponding resonant frequency, you can substitute any and According to the formula, the cutoff frequency of the fundamental mode of SIW can be calculated to be around 3.62GHz, which is lower than TE 101 resonant frequency.

[0064] In some embodiments, the S2 further comprises the following steps:

[0065] A SIW structure model was established in the simulation software, and coplanar waveguide transition structures were added at both ends of the SIW to match the impedance;

[0066] A coupling gap is opened at the center of the metal layer on the upper surface of the SIW to cut the surface current so that the energy is coupled into the SIW resonant cavity;

[0067] Build a SIW resonant cavity model above the SIW and set the tunable parameters y , so that the SIW resonant cavity y The value changes along y Axis translation.

[0068] In this embodiment, the SIW structure model is as follows Figure 2 As shown, it is composed of two layers of PCB, each dielectric substrate is Rogers 5880 dielectric with a thickness of t = 0.8mm (relative dielectric constant =4.7, loss tangent tanδ=0.022), the metal on both sides is 0.035mm thick copper with a conductivity of 5.8×10 7 The lower layer is a SIW with a coplanar waveguide transition, with a slot opened horizontally at the top center to radiate energy to the SIW resonant cavity above it. d is the diameter of the metal via, pis the distance between two adjacent through holes. L 2 and W 2 represent the length and width of SIW respectively. L 1 and W 1 is the length and width of the SIW resonant cavity. The length and width of the coupling slot are L gap and W gap , by adjusting the center offset of the SIW resonant cavity about the symmetry axis of the coupling slot y , in order to achieve the quasi-BIC with the maximum Q value, the specific parameters are shown in Table 1.

[0069] Table 1 Variable values (unit: mm)

[0070]

[0071] In some embodiments, the S4 further comprises the following steps:

[0072] For tunable parameters y Perform a sweep and simulate using a frequency domain solver;

[0073] Adjust the center offset of the SIW resonant cavity about the symmetry axis of the coupling slot y , to destroy the symmetry protection state in the resonant mode, thereby adjusting the ratio of the transmission resonance frequency to the maximum half-width of the resonance, so that the coupling between the bound state in the SIW resonant cavity and the continuous state in the SIW below is enhanced, and the ability of the SIW resonant cavity to bind energy is weakened.

[0074] In this embodiment, y Perform parameter sweep and use frequency domain solver to simulate. When the center of the coupling slot is offset y = 0, the system structure is symmetrical, but its dielectric substrate is not lossless, which causes its internal energy to dissipate in the form of absorption loss. At this time, the resonant cavity mode is a quasi-BIC mode, and its transmission spectrum does not have a peak or depression like the symmetric protection BIC mode, but shows a slight convexity like the Fano resonance. y When the value increases, the amplitude of the resonant cavity increases, the convex phenomenon becomes more obvious, and the Q value decreases. This is due to the adjustment of the center offset of the coupling slot. y The SIW resonant cavity can be made along y The symmetry of the axis is broken, but along x The symmetry of the axis is maintained. However, this perturbation behavior that destroys the inversion symmetry of the structure plane causes the BIC, which was originally protected by symmetry, to produce radiation loss, increase the resonance line width, and transform into a quasi-BIC with high Q, such as Figure 3 As shown in the figure, it can be seen from the S parameters of the system that the transmission spectrum peak of the system is relatively sharp, and it will have a broad application in high-Q value narrowband filters and sensors in the future.

[0075] The Q mentioned above is the ratio of the transmission resonance frequency ω0 to the maximum half-width of the resonance ∆ω, that is: .according to Figure 3 The Q value of the system can be obtained from the transmission spectrum in (a). Figure 4 As shown, the horizontal axis is different y Value (unit: mm), the vertical axis is Q value. y As the value decreases, Q tends to infinity. k Presentation The attenuation relationship of the function, both BIC and quasi-BIC have this feature.

[0076] The system adjusts the center offset of the SIW resonant cavity about the symmetry axis of the coupling slot y This operation is to destroy the symmetric protection state in the resonant mode. Therefore, this quasi-BIC belongs to the symmetric protection type BIC. The symmetric protection characteristics are not only displayed in the structure and resonant mode, but also in the resonant cavity. y The direction of axis movement also shows symmetry. Figure 5 Shows that when the resonant cavity is y Moving the axial center zero point in any direction (positive or negative) shows an increase in the resonance linewidth (the 4.9 GHz dark blue area represents the bandwidth), with the resonance being minimized at the center zero point, which is the quasi-BIC point with maximum Q. When the system's structural symmetry is broken, the coupling between the bound states in the SIW resonator and the continuous states in the SIW below increases, weakening the SIW resonator's ability to bind energy.

[0077] The electric field pattern distribution of the system of the present invention is as follows Figure 6 As shown, y =0.4, the structural symmetry collapses, and different degrees of strong coupling effects induce rapid changes in the electric field in the SIW resonant cavity, that is, y The smaller the value, the larger the amplitude of the electric field tends to be, which also implies that the ability of this system to confine electromagnetic waves is enhanced, that is, the Q value increases.

[0078] In some embodiments, spectrum analysis and coupled mode theory are used to determine whether a resonance conforms to the quasi-BIC phenomenon.

[0079] In this embodiment, determining whether a resonance conforms to the quasi-BIC phenomenon requires not only spectrum analysis but also the use of the theoretical tool of Coupled Mode Theory (CMT). The present invention establishes a CMT topology structure based on the working principle of the stacked SIW. Figure 7 Energy The energy flowing from Port 1 is coupled to the resonant cavity through the coupling slot, and the other part flows to Port 2. The energy flowing to the SIW resonant cavity will also flow back to the SIW below, which are recorded as and ,and is the total output of Port2.

[0080] According to the classical CMT proposed in optical resonators, the following dynamic equations can be derived:

[0081] ,in, κ 、 d and T are the coupling coefficients between the incident wave and the SIW resonant cavity and between the incident wave and the outgoing wave, respectively; ω0 is the transmission resonance frequency; is the amplitude in the SIW resonant cavity About time t The differential of and They represent the radiation loss and absorption loss of the system respectively; and the total output wave of port 2 can be written as:

[0082] ;

[0083] According to the time inversion rule in Maxwell's equations, we can get the existence of , T =1, so the amplitude in the SIW resonant cavity The expression is as follows:

[0084] , where ω is the operating frequency, so S 21 Can be expressed as:

[0085] ; The amplitude and bandwidth of the coupling resonance are determined by the radiation loss and absorption loss. Therefore, the present invention adjusts the center offset of the coupling slot to y To change the coupling relationship and thus affect .

[0086] From the formula derived from the above coupled mode theory, it can be seen that the resonance bandwidth and amplitude of the resonant cavity of the present invention are given by and Decide, is inherent to the system, thus changing the radiation loss The value of is a direct way to control the resonance characteristics. The excitation source of the upper SIW resonant cavity comes from the SIW coupling below. In the previous section, the characteristics of the symmetry-protected BIC have been demonstrated (by adjusting the center offset of the SIW resonant cavity about the symmetry axis of the coupling slot). y ) to adjust the resonance bandwidth and amplitude.

[0087] In this system, the aperture of the coupling slot is also a key factor affecting the radiation loss. Here, the slot width is W gap The slot widths are 0.4mm, 0.6mm, and 0.8mm, and the effects of different slot widths on the resonance reflection curve in this system are studied. Figure 8 As shown, with the slot width W gap As the resonant frequency of the SIW cavity decreases, the resonant bandwidth becomes narrower and narrower. This is the difference between the different slot widths. W gap The impact of different disturbances on the system resonance. W gap The larger the value, the wider the resonance bandwidth, so the slot width is also one of the important parameters affecting the Q value.

[0088] In summary, based on the characteristics of bound states on the quasi-continuous domain and the derivation of coupled modes, it is obvious that the parameter y and W gap Both can achieve resonance control, which is conducive to future applications in filters, high-Q sensors, and other fields. When used as a high-Q sensor, the device will exhibit different resonance peaks in different solutions, such as amplitude and bandwidth. These peaks can be analyzed using algorithms to analyze information such as the dielectric constant, temperature, and concentration of the solution.

[0089] In some embodiments, the simulation software is CST Microwave Studio software.

[0090] A second aspect of the present invention provides: a system for realizing bound states on a quasi-continuous domain on an SIW, for realizing any of the above-mentioned methods for realizing bound states on a quasi-continuous domain on an SIW, comprising:

[0091] A calculation module is used to calculate the cutoff frequency of the SIW and the resonant frequency of the SIW resonant cavity according to design requirements;

[0092] Simulation module, used to gradually build SIW and SIW-SIW resonant cavity stack structure models in the simulation software; set simulation frequency, boundary conditions and field monitor;

[0093] The curve generation module is used to scan multiple parameters to obtain an S-curve, and select different parameters according to the required bandwidth and amplitude. If there is no S-curve that meets the preset conditions, more parameters will be scanned again until an S-curve that meets the preset conditions is obtained.

[0094] The adjustment module is used to adjust parameters according to the ratio of the required transmission resonance frequency to the maximum half-width of the resonance to realize the bound state on the quasi-continuous domain on the SIW.

[0095] The third aspect of the present invention provides: a computer-readable storage medium, wherein the computer-readable storage medium stores computer-executable instructions, and when the computer-executable instructions are loaded and executed by a processor, any of the above-mentioned methods for realizing bound states on a quasi-continuous domain on an SIW is implemented.

[0096] The foregoing description is merely a preferred embodiment of the present invention. It should be understood that the present invention is not limited to the form disclosed herein and should not be construed as excluding other embodiments. Rather, the present invention can be used in various other combinations, modifications, and environments and can be modified within the scope of the concept described herein through the above teachings or techniques or knowledge in the relevant field. Modifications and variations made by those skilled in the art that do not depart from the spirit and scope of the present invention are intended to be protected by the appended claims.

Claims

1. A method for realizing bound states on a quasi-continuous domain on an SIW, characterized by: The following steps are involved: S1: Calculate the cutoff frequency of SIW and the resonant frequency of SIW resonant cavity according to design requirements; S2: In the simulation software, SIW and SIW-SIW resonant cavity stacking structure models are gradually constructed. Air filling is abandoned, and a SIW is printed on the PCB with a coupling slot opened on its top surface to radiate energy to another SIW resonant cavity, forming an improved SIW-SIW resonant cavity system that produces quasi-BIC. S3: Set simulation frequency, boundary conditions, and field monitors; S4: Scan multiple parameters to obtain an S-curve, and select different parameters according to the required bandwidth and amplitude. If there is no S-curve that meets the preset conditions, rescan more parameters until an S-curve that meets the preset conditions is obtained. S5: Adjust the parameters according to the ratio of the required transmission resonance frequency to the maximum half-width of the resonance to achieve the bound state on the quasi-continuous domain on the SIW; The S2 further comprises the following steps: A SIW structure model was established in the simulation software, and coplanar waveguide transition structures were added at both ends of the SIW to match the impedance; A coupling gap is opened at the center of the metal layer on the upper surface of the SIW to cut the surface current so that the energy is coupled into the SIW resonant cavity; Build a SIW resonant cavity model above the SIW and set the tunable parameters y , so that the SIW resonant cavity y The value changes along y Axis translation; y The axis is the length direction of the SIW resonant cavity model; The S4 further comprises the following steps: For tunable parameters y Perform a sweep and use the frequency domain solver for simulation solution; Adjust the center offset of the SIW resonant cavity about the symmetry axis of the coupling slot y , to destroy the symmetry protection state in the resonant mode, thereby adjusting the ratio of the transmission resonance frequency to the maximum half-width of the resonance, so that the coupling between the bound state in the SIW resonant cavity and the continuous state in the SIW below is enhanced, and the ability of the SIW resonant cavity to bind energy is weakened.

2. The method for realizing bound states on a quasi-continuous domain on an SIW according to claim 1, characterized in that: The cutoff frequency of the SIW is lower than the resonant frequency of the SIW resonant cavity. The resonant frequency of the SIW resonant cavity is calculated as follows: ； in c is the speed of light in a vacuum; m is the first resonant mode number; n is the second resonance mode number; is the relative dielectric constant; and is the equivalent width and length of the SIW resonant cavity, which are calculated using the equivalent formula of the full-wave finite element method: ， in L 1. W 1 is the length and width of the SIW resonant cavity; d is the metal via diameter; p is the distance between two adjacent through holes; The cutoff frequency calculation formula of SIW is as follows: ， in h is the thickness of the SIW dielectric substrate.

3. The method for realizing bound states on a quasi-continuous domain on an SIW according to claim 1, characterized in that: Spectral analysis and coupled mode theory are used to determine whether a resonance conforms to the quasi-BIC phenomenon.

4. The method for realizing bound states on a quasi-continuous domain on an SIW according to any one of claims 1 to 3, characterized in that: The simulation software is CST Microwave Studio software.

5. A system for realizing bound states on a quasi-continuous domain on an SIW, characterized by: The method for realizing a bound state on a quasi-continuous domain on an SIW according to any one of claims 1 to 4 comprises: A calculation module is used to calculate the cutoff frequency of the SIW and the resonant frequency of the SIW resonant cavity according to design requirements; Simulation module, used to gradually build SIW and SIW-SIW resonant cavity stack structure models in the simulation software; set simulation frequency, boundary conditions and field monitor; The curve generation module is used to scan multiple parameters to obtain an S-curve, and select different parameters according to the required bandwidth and amplitude. If there is no S-curve that meets the preset conditions, more parameters will be scanned again until an S-curve that meets the preset conditions is obtained. The adjustment module is used to adjust parameters according to the ratio of the required transmission resonance frequency to the maximum half-width of the resonance to realize the bound state on the quasi-continuous domain on the SIW.

6. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores computer-executable instructions. When the computer-executable instructions are loaded and executed by the processor, the method for realizing bound states on a quasi-continuous domain on an SIW according to any one of claims 1 to 4 is implemented.

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