A method and system for simulating the wave absorption of a tunable plasma photonic crystal

Abstract

The application provides a tunable plasma photonic crystal wave-absorbing simulation method and system, and relates to the technical fields of microwave communication and electromagnetic wave absorption. The simulation method comprises the following steps: obtaining the structural parameters of a plasma photonic crystal and the physical parameters of plasma, and constructing a three-dimensional electromagnetic simulation model containing a periodic alumina dielectric column array, wherein the height and radius of the dielectric column are both one quarter of the wavelength corresponding to the working frequency band; determining the relative permittivity of the plasma according to the physical parameters and assigning the model; performing electromagnetic simulation calculation after simulation configuration and grid division, and identifying the wave-absorbing frequency points; adjusting the lateral positions of part of the dielectric columns according to the structural parameters, so that multiple wave-absorbing frequency points are offset and overlapped to form a wide-frequency absorption band, and the dynamic tuning of the wave-absorbing frequency band is realized. The application can realize wide-frequency tunable wave absorption through structural regulation, avoids the engineering difficulties of relying on high-voltage adjustment of plasma parameters, and provides an efficient simulation analysis method for tunable wave-absorbing device design.

Description

Technical Field

[0001] This invention relates to the field of microwave communication and electromagnetic wave absorption technology, and more specifically, to a simulation method and system for wave absorption of a tunable plasma photonic crystal. Background Technology

[0002] Plasmon photonic crystals are a novel type of artificial electromagnetic material that combines plasma with photonic crystal structures. Through the synergistic coupling effect between plasma and periodic dielectric structures, they can effectively control the transmission and absorption characteristics of electromagnetic waves, showing broad application prospects in microwave absorption, stealth technology, and electromagnetic compatibility. Compared to traditional absorbing materials (such as ferrites and carbon-based composites), which rely on their own dielectric or magnetic loss mechanisms and have fixed operating frequencies that are difficult to adjust, plasma photonic crystals have attracted widespread attention due to their strong structural designability and wide range of adjustable equivalent electromagnetic parameters.

[0003] Currently, existing technologies for controlling the absorption performance of plasma photonic crystals mainly focus on shifting the absorption frequency band by changing the electron density or plasma density of the plasma. Specifically, the plasma frequency is adjusted by applying an external voltage or changing the excitation power, thereby altering the equivalent dielectric constant and photonic bandgap of the plasma photonic crystal, and thus shifting the absorption frequency. However, this approach, which relies on plasma parameter control, faces significant technical difficulties in practical engineering applications: on the one hand, for solid-state plasma or gas discharge plasma, dynamically adjusting its electron density over a wide range typically requires applying a high-voltage bias of several thousand or even tens of thousands of volts, which places stringent requirements on the safety and reliability of the power supply system; on the other hand, the plasma state is greatly affected by factors such as ambient air pressure and temperature, making long-term operational stability difficult to guarantee. Therefore, how to achieve flexible adjustment of the absorption frequency band of plasma photonic crystals without complex high-voltage control methods has become a pressing technical challenge in this field.

[0004] Furthermore, most existing simulation analysis methods for plasma photonic crystals only perform single calculations of absorption performance under fixed structural parameters, lacking a systematic simulation strategy that uses structural parameters as dynamically adjustable degrees of freedom, making it difficult to guide the tunable design of actual absorbing devices. Summary of the Invention

[0005] The problem solved by this invention is one or more of the aforementioned related technical problems.

[0006] To address the aforementioned problems, this invention provides a method and system for simulating the absorption of tunable plasma photonic crystals.

[0007] In a first aspect, the present invention provides a method for simulating the absorption of a tunable plasma photonic crystal, comprising: Obtain modeling parameters, including the structural parameters of the plasma photonic crystal and the physical parameters of the plasma; A three-dimensional electromagnetic simulation model of a plasma photonic crystal is constructed based on the structural parameters. The plasma photonic crystal includes plasma, an array of alumina dielectric pillars arranged periodically in the plasma along mutually perpendicular x and y directions, steel metal side plates disposed on both sides of the alumina dielectric pillar array, an ITO conductive thin film transparent cover plate disposed on the top, and a steel base plate disposed on the bottom. The height and radius of the alumina dielectric pillars are both one-quarter of the wavelength corresponding to the operating frequency band. The relative permittivity of the plasma is obtained based on the physical parameters, and the relative permittivity is assigned to the plasma in the three-dimensional electromagnetic simulation model. The three-dimensional electromagnetic simulation model is configured and meshed to generate a computational mesh model; Electromagnetic simulation calculations are performed based on the computational grid model to obtain simulation results of the absorption performance of the plasma photonic crystal, and the absorption frequency points are identified based on the simulation results. Adjusting the lateral position of some alumina dielectric pillars in the alumina dielectric pillar array according to the structural parameters causes multiple identified absorption frequency points to shift and overlap, forming a broadband absorption band and achieving dynamic tuning of the absorption frequency band.

[0008] Optionally, the structural parameters include the arrangement period of the alumina dielectric columns, the lateral gap between the alumina dielectric columns and the steel metal side plate, and the longitudinal gap between the alumina dielectric columns and the ITO conductive film transparent cover plate.

[0009] Optionally, the physical parameters include the electron density and effective collision frequency of the plasma; obtaining the relative permittivity of the plasma based on the physical parameters specifically includes: The plasma frequency is obtained based on the electron density. The relative permittivity is obtained based on the plasma frequency and the effective collision frequency.

[0010] Optionally, the relative permittivity includes: ; in, The plasma frequency, , The electron density, The effective collision frequency, Let e ​​be the vacuum permittivity, and e be the electron charge. For electronic quality, The incident electromagnetic wave angular frequency.

[0011] Optionally, the step of configuring and meshing the three-dimensional electromagnetic simulation model to generate a computational mesh model includes: Based on the finite element method, an eigenfrequency solver and a frequency domain solver are set, boundary conditions are set, and a free tetrahedral mesh is used to mesh the three-dimensional electromagnetic simulation model to obtain the computational mesh model. The boundary conditions include: setting perfect electrical conductor boundary conditions at the upper and lower boundaries of the three-dimensional electromagnetic simulation model, setting periodic boundary conditions at the left and right boundaries, and setting the ITO conductive thin film transparent cover plate as a perfect electrical conductor boundary condition.

[0012] Optionally, the electromagnetic simulation calculation based on the computational grid model to obtain the simulation results of the absorption performance of the plasma photonic crystal includes: The band distribution of the plasma photonic crystal under no-excitation source condition is calculated by the intrinsic frequency solver, and the absorption frequency point is identified based on the band distribution. The near-field electric field distribution and electromagnetic wave transmission characteristics of the plasma photonic crystal after excitation are calculated by the frequency domain solver, and the simulation results of the absorption performance are obtained.

[0013] Optionally, the alumina dielectric column array is arranged in a rectangular pattern of 3 rows × n columns, where n is a positive integer greater than or equal to 3; and some of the alumina dielectric columns are the alumina dielectric columns in the middle row.

[0014] Optionally, the adjustment of the lateral position specifically involves: calculating the translation distance based on the arrangement period and the radius of the alumina medium column, and translating part of the alumina medium column along the x-direction by the translation distance; the translation distance is a / 2-d, where a is the arrangement period and d is the radius of the alumina medium column.

[0015] Optionally, after adjusting the lateral position of the alumina dielectric pillar, the microwave absorption simulation method of the tunable plasma photonic crystal further includes: The plasma photonic crystal with the adjusted structure was re-meshed and electromagnetically simulated to obtain the band distribution and near-field electric field distribution of the adjusted structure. Specifically, obtaining the adjusted band distribution of the structure includes: The band distribution of the supercell with a predetermined number of periods in the y-direction of the plasma photonic crystal after the structure adjustment is calculated and projected in the x-direction within the first irreducible Brillouin zone. The band overlap region is then identified. The band overlap region is used as the broadband absorption frequency point to verify the formation of the broadband absorption band.

[0016] In a second aspect, the present invention provides a microwave absorption simulation system for a tunable plasma photonic crystal, used to implement the microwave absorption simulation method for the tunable plasma photonic crystal described in the first aspect, the system comprising: The acquisition unit is used to acquire modeling parameters, which include the structural parameters of the plasma photonic crystal and the physical parameters of the plasma. A construction unit is used to construct a three-dimensional electromagnetic simulation model of a plasma photonic crystal based on the structural parameters. The plasma photonic crystal includes a plasma, an array of alumina dielectric pillars arranged periodically in the plasma along mutually perpendicular x and y directions, steel metal side plates disposed on both sides of the alumina dielectric pillar array, an ITO conductive thin film transparent cover plate disposed on the top, and a steel base plate disposed on the bottom. The height and radius of the alumina dielectric pillars are both one-quarter of the wavelength corresponding to the operating frequency band. The relative permittivity of the plasma is obtained based on the physical parameters, and the relative permittivity is assigned to the plasma in the three-dimensional electromagnetic simulation model. The three-dimensional electromagnetic simulation model is divided into units, and simulation configuration and mesh generation are performed on the three-dimensional electromagnetic simulation model to generate a computational mesh model. The simulation unit is used to perform electromagnetic simulation calculations based on the computational grid model to obtain the simulation results of the absorption performance of the plasma photonic crystal, and to identify the absorption frequency points based on the simulation results. The unit adjusts the lateral position of some of the alumina dielectric pillars in the alumina dielectric pillar array according to the structural parameters, so that the identified multiple absorption frequency points are shifted and overlap each other to form a broadband absorption band, thereby realizing dynamic tuning of the absorption frequency band.

[0017] The beneficial effects of the tunable plasma photonic crystal absorption simulation method and system of the present invention are: By acquiring the structural and physical parameters of the plasma photonic crystal, a three-dimensional electromagnetic simulation model was constructed, comprising plasma, a periodic array of alumina dielectric pillars, steel side plates, an ITO transparent cover plate, and a steel base plate. The height and radius of the dielectric pillars were set to one-quarter of the wavelength corresponding to the operating frequency band, ensuring the model accurately reflects the electromagnetic coupling characteristics between the plasma and the periodic dielectric structure. The relative permittivity of the plasma was calculated based on the physical parameters and assigned to the plasma in the model, guaranteeing a high degree of consistency between the simulation input parameters and the actual physical state, thus improving the reliability of the simulation results. Absorption frequencies were identified through simulation calculations, and the lateral positions of some alumina dielectric pillars were adjusted according to the structural parameters, causing multiple absorption frequencies to shift and overlap, forming a broadband absorption band, achieving dynamic tuning of the absorption band. This method effectively expands the absorption bandwidth, solving the technical challenges of existing fixed-structure plasma photonic crystal absorbers, such as difficulty in adjusting the absorption band and limited operating bandwidth. It provides an efficient simulation analysis tool for the design and performance optimization of tunable broadband absorbing devices. Attached Figure Description

[0018] Figure 1 This is a flowchart illustrating a simulation method for absorbing waves using a tunable plasma photonic crystal according to an embodiment of the present invention. Figure 2 This is a schematic diagram of the structure of a plasma photonic crystal according to an embodiment of the present invention; Figure 3 This is a simulation diagram of the wave absorption effect according to an embodiment of the present invention; Figure 4 This is a schematic diagram of the energy band structure of a unit cell of a tunable plasma photonic crystal in the first irreducible Brillouin zone according to an embodiment of the present invention. Figure 5 This is a band structure diagram of a tunable plasma photonic crystal according to an embodiment of the present invention, showing the band distribution of a supercell with a period number of 3 in the y-direction projected in the x-direction within the first irreducible Brillouin zone. Figure 6 This is a schematic diagram of a modified plasma photonic crystal structure capable of absorbing broadband electromagnetic waves according to an embodiment of the present invention. Figure 7 This is a band structure diagram of a tunable plasma photonic crystal with a modified structure, projected in the x-direction by a supercell with a period number of 3 in the y-direction within the first irreducible Brillouin zone, according to an embodiment of the present invention.

[0019] Explanation of reference numerals in the attached diagram: 1. Alumina dielectric column; 2. Plasma; 3. Steel metal side plate; 4. ITO conductive film transparent cover plate; 5. Steel base plate. Detailed Implementation

[0020] To make the above-mentioned objects, features, and advantages of the present invention more apparent and understandable, specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings. Although some embodiments of the present invention are shown in the drawings, it should be understood that the present invention can be implemented in various forms and should not be construed as limited to the embodiments set forth herein. Rather, these embodiments are provided to provide a more thorough and complete understanding of the present invention. It should be understood that the accompanying drawings and embodiments of the present invention are for illustrative purposes only and are not intended to limit the scope of protection of the present invention.

[0021] It should be understood that the various steps described in the method embodiments of the present invention may be performed in different orders and / or in parallel. Furthermore, the method embodiments may include additional steps and / or omit the steps shown. The scope of the present invention is not limited in this respect.

[0022] The term "comprising" and its variations as used herein are open-ended, meaning "including but not limited to"; the term "based on" means "at least partially based on"; the term "one embodiment" means "at least one embodiment"; the term "another embodiment" means "at least one additional embodiment"; the term "some embodiments" means "at least some embodiments"; and the term "optionally" means "optional embodiments". Definitions of other terms will be given in the following description. It should be noted that the concepts of "first," "second," etc., mentioned in this invention are used only to distinguish different devices, modules, or units, and are not intended to limit the order of functions performed by these devices, modules, or units or their interdependencies.

[0023] It should be noted that the terms "a" and "a plurality of" used in this invention are illustrative rather than restrictive. Those skilled in the art should understand that, unless otherwise expressly indicated in the context, they should be understood as "one or more".

[0024] The names of the messages or information exchanged between the multiple devices in the embodiments of the present invention are for illustrative purposes only and are not intended to limit the scope of these messages or information.

[0025] like Figure 1 As shown in the figure, an embodiment of the present invention provides a method for simulating the absorption of a tunable plasma photonic crystal, comprising: Step S100: Obtain modeling parameters, which include the structural parameters of the plasma photonic crystal and the physical parameters of the plasma.

[0026] Step S200: Construct a three-dimensional electromagnetic simulation model of the plasma photonic crystal based on the structural parameters. The plasma photonic crystal includes plasma, an array of alumina dielectric pillars 1 arranged periodically in the plasma along mutually perpendicular x and y directions, steel metal side plates 3 disposed on both sides of the array of alumina dielectric pillars 1, an ITO conductive thin film transparent cover plate 4 disposed on the top, and a steel base plate 5 disposed on the bottom. The height and radius of the alumina dielectric pillars 1 are both one-quarter of the wavelength corresponding to the working frequency band.

[0027] Specifically, the structural parameters of the plasma photonic crystal are used to determine its geometric configuration. These typically include: the arrangement period of the alumina dielectric pillars 1, i.e., the distance between the centers of adjacent alumina dielectric pillars 1, which determines the density of the pillar array and the size of the periodic repeating units; the height and radius of the alumina dielectric pillars 1, both set to one-quarter of the wavelength corresponding to the operating frequency band. This setting allows the dielectric pillars to produce effective coherent interference with the incident electromagnetic wave within the target frequency band, thus forming a photonic bandgap; the lateral gap between the alumina dielectric pillars 1 and the two steel metal side plates 3, which affects the distribution characteristics of the electromagnetic field at the boundary; and the longitudinal gap between the alumina dielectric pillars 1 and the top ITO conductive film transparent cover plate 4, which affects the electromagnetic coupling state at the top boundary. The physical parameters include the electron density and effective collision frequency of the plasma 2. Electron density is the core parameter determining the plasma frequency, while the effective collision frequency reflects the frequency of collisions between electrons and neutral particles in the plasma 2. Both together determine the response characteristics of the plasma 2 to electromagnetic waves. The above parameters serve as input conditions for subsequent modeling and simulation calculations, ensuring that the entire simulation process is based on solid evidence.

[0028] Plasma 2 serves as the background medium for the entire photonic crystal, filling the internal space of the model. Its electromagnetic properties are determined by the physical parameters obtained in step S100. In the plasma 2 background, alumina dielectric pillars 1 are periodically arranged along mutually perpendicular x and y directions, forming a two-dimensional periodic array structure. Viewed from above, the column extension direction of the alumina dielectric pillar array 1 is defined as the x-direction, and the row extension direction is defined as the y-direction. The x and y directions are perpendicular to each other. In this embodiment, the alumina dielectric pillar array 1 is a rectangular arrangement of 3 rows × n columns. Alumina, as a low-loss, high-dielectric-constant ceramic material, exhibits excellent electromagnetic properties in the microwave band. Its dielectric constant alternates periodically with the plasma 2 background, resulting in a photonic bandgap effect. Steel metal side plates 3 are provided on both sides of the alumina dielectric pillar array 1, an ITO conductive thin film transparent cover plate 4 is provided at the top of the array, and a steel base plate 5 is provided at the bottom of the array. These components together constitute the boundary constraint structure of the plasma photonic crystal.

[0029] In some embodiments, such as Figure 2 As shown, the structure of the plasma photonic crystal includes a plasma element 2, an alumina dielectric pillar 1, which is cylindrical in shape; the height of the dielectric pillar is 7 mm, the radius is 7 mm, which is one-quarter of the wavelength, the distance between the centers of the alumina dielectric pillar 1 is 30 mm, which is one period, a gap of 23 mm is introduced between the alumina dielectric pillar 1 at the edge and the steel metal side plate 3, and the gap between the alumina dielectric pillar 1 and the top cover plate is 5 mm.

[0030] During the modeling process, the height and radius of the alumina dielectric pillar 1 were both set to one-quarter of the wavelength corresponding to the operating frequency band. The physical significance of this setting is that when the geometry of the dielectric pillar satisfies the one-quarter wavelength condition, the pillar generates a one-quarter wavelength resonance effect on the incident electromagnetic wave, causing coherent interference of the electromagnetic wave on the surface of the pillar. This enhances the coupling between the electromagnetic wave and the plasma-dielectric interface, which is beneficial for localizing the electromagnetic wave energy near the structure surface. Simultaneously, the periodic arrangement of the alumina dielectric pillar 1 causes Bragg scattering by the plasma photonic crystal in the two-dimensional plane. Combined with the dispersive characteristics of the plasma 2 itself, this together determines the absorption frequency band position of the structure.

[0031] By uniformly setting the height and radius of the alumina dielectric pillars 1 to a quarter wavelength, the electromagnetic response of the structure in both the x and y directions is made consistent, providing a symmetrical geometric basis for subsequent structural control. The alumina dielectric pillars 1 are arranged in a rectangular lattice pattern along the x and y directions, with equal spacing along the row and column directions. The distance between the centers of adjacent alumina dielectric pillars 1 is determined by the arrangement period. A lateral gap is left between the alumina dielectric pillars 1 at the edge and the steel metal side plate 3, providing a transition area for the propagation of electromagnetic waves at the edge of the structure. Similarly, a longitudinal gap is provided between the alumina dielectric pillars 1 and the top ITO conductive film transparent cover plate 4, reserving space for the propagation of electromagnetic waves in the height direction.

[0032] The definitions of the x and y directions mentioned above also have clear simulation application directions: the x direction is the direction of lateral movement of some dielectric pillars in subsequent structural adjustments. That is, by translating the alumina dielectric pillar 1 in the middle row along the x direction, the translational symmetry of the structure in the x direction can be broken, thereby changing the dispersion relationship of electromagnetic waves in this direction and realizing the controllable shift and overlap fusion of absorption frequency points. At the same time, the x direction is also the direction of subsequent band projection. That is, the band distribution of the plasma photonic crystal projected along the x direction under the corresponding supercell is calculated to identify the absorption frequency point position and verify the formation of broadband absorption bands.

[0033] By acquiring the structural and physical parameters of the plasma photonic crystal and constructing a three-dimensional electromagnetic simulation model containing plasma 2, an array of periodic alumina dielectric pillars 1, steel metal side plates 3, an ITO conductive thin film transparent cover plate 4, and a steel base plate 5, a three-dimensional electromagnetic simulation model is constructed. The height and radius of the alumina dielectric pillars 1 are both set to one-quarter of the wavelength corresponding to the working frequency band, enabling the model to accurately reflect the electromagnetic coupling characteristics between plasma 2 and the periodic dielectric structure. The relative permittivity of plasma 2 is determined based on the physical parameters and assigned to plasma 2 in the model, ensuring a high degree of consistency between the simulation input parameters and the actual physical state, thereby improving the reliability of the simulation results. This modeling method provides a precise geometric basis and initial physical field conditions for subsequent dynamic tuning of the absorption band through structural adjustments, enabling the entire simulation method to achieve accurate prediction and optimized design of absorption performance without the need for complex high-voltage control methods.

[0034] Step S300: Obtain the relative permittivity of plasma 2 based on the physical parameters, and assign the relative permittivity to plasma 2 in the three-dimensional electromagnetic simulation model.

[0035] Specifically, plasma 2, as a dispersive medium, has a relative permittivity that is not a fixed value, but a complex number that varies with the frequency of the incident electromagnetic wave. This frequency-dependent characteristic is determined by the collective motion behavior of free electrons in plasma 2.

[0036] When determining the relative permittivity, calculations are performed based on the aforementioned physical parameters and the intrinsic physical model of plasma. The resulting relative permittivity is expressed in complex form. The real part of this complex number reflects the dispersion characteristics of plasma 2 to electromagnetic waves, determining the position of the photon bandgap; its imaginary part reflects the loss characteristics of plasma 2 to electromagnetic waves, determining the absorption intensity. After assigning the aforementioned frequency-dependent complex permittivity as a material property to the plasma 2 region in the three-dimensional electromagnetic simulation model, the simulation software will automatically call the corresponding permittivity value according to the current solution frequency in subsequent electromagnetic field calculations, thereby accurately simulating the propagation, reflection, and absorption behavior of electromagnetic waves in the periodic structure composed of plasma 2 and alumina dielectric pillar 1.

[0037] Based on the physical parameters of plasma, the complex relative permittivity varying with frequency is calculated according to the intrinsic physical model of plasma, and this is assigned as a material property to the plasma 2 region in the three-dimensional electromagnetic simulation model. This allows plasma 2 in the simulation model to accurately reflect the dispersion and loss characteristics of real plasma under applied bias conditions. This processing method ensures a high degree of consistency between the simulation input parameters and the actual physical state of plasma 2, avoiding simulation deviations caused by simplifying plasma 2 as a material with a constant permittivity. This significantly improves the accuracy and reliability of the microwave absorption performance simulation results, providing a reliable physical field basis for subsequent dynamic tuning of the absorption band through structural adjustments.

[0038] Step S400: Perform simulation configuration and mesh generation on the three-dimensional electromagnetic simulation model to generate a computational mesh model.

[0039] Specifically, in terms of simulation configuration, based on the physical structural characteristics and computational requirements of the constructed 3D electromagnetic simulation model, appropriate solution strategies and boundary constraints are configured. The configuration of the solution strategy determines the computational method and solution type used in subsequent electromagnetic field numerical calculations. Different computational objectives (such as eigenmode analysis or response analysis under external excitation) correspond to different solution configurations, which need to be set accordingly in the simulation environment. The configuration of boundary constraints is used to limit the electromagnetic field behavior at the boundaries of the computational region, so that the finite-size computational model can correctly reflect the physical characteristics of electromagnetic waves propagation, reflection, or periodic repetition at the structural boundaries. For regions with metal boundaries in the model, corresponding boundary conditions are set to simulate the reflection behavior of electromagnetic waves on the metal surface; for structures exhibiting periodic directions, corresponding boundary conditions are set to simulate the electromagnetic characteristics of an infinite periodic array, thereby utilizing the periodicity of the structure to reduce the computational scale. The above simulation configuration establishes correct physical constraints and computational frameworks for subsequent electromagnetic field numerical calculations.

[0040] In terms of mesh generation, mesh types suitable for complex 3D structures (such as free tetrahedral meshes) can be used to spatially discretize the 3D electromagnetic simulation model. Mesh generation is a crucial step in finite element simulation. Essentially, it discretizes a continuous geometric model into a finite number of mesh elements and nodes, transforming the infinite-dimensional electromagnetic boundary value problem into a finite-dimensional system of algebraic equations for numerical solution. The selection of the mesh type must comprehensively consider the complexity of the model's geometry. For 3D structures containing arrays of cylindrical dielectric pillars, a mesh type that can flexibly adapt to curved surface boundaries has good adaptability. In setting the mesh density, a balance between accuracy and efficiency is required: denser meshes are used in regions with drastic electromagnetic field changes (such as near the surface of the dielectric pillars and at the interface between plasma and the dielectric pillars) to ensure the accuracy of the field distribution solution; relatively sparse meshes are used in regions with gentle electromagnetic field changes to control the overall computational scale and resource consumption. Through the above mesh generation process, the continuous geometric model is discretized into a computational mesh model composed of a finite number of mesh elements and nodes. This model contains all the geometric discretization information and material property allocation information required for subsequent numerical solutions.

[0041] By configuring appropriate solution strategies and boundary constraints, a correct physical constraint and computational framework were established for subsequent electromagnetic simulation calculations, ensuring that the solution process can accurately reflect the actual electromagnetic boundary conditions of the plasma photonic crystal. By adopting a mesh type suitable for complex three-dimensional structures to spatially discretize the model containing the cylindrical dielectric column array, the computational scale was reasonably controlled while ensuring the accuracy of the electromagnetic field solution. The generated discretized computational mesh model provides a numerical solution basis with both accuracy and computational efficiency for subsequent band analysis and microwave absorption performance simulation.

[0042] Step S500: Perform electromagnetic simulation calculations based on the computational grid model to obtain the simulation results of the absorption performance of the plasma photonic crystal, and identify the absorption frequency points based on the simulation results.

[0043] Specifically, electromagnetic simulation calculations typically include two complementary types of calculations, serving two different analytical needs: intrinsic characteristic analysis and microwave absorption performance evaluation.

[0044] In the first type of calculation, the computational grid model is subjected to the condition of no external excitation source, i.e., no external electromagnetic wave incident inside the structure. The eigenvalue problem of Maxwell's equations, determined by the dispersive characteristics of plasma 2 and the periodic arrangement of alumina dielectric pillars 1, is solved, yielding a series of eigenfrequencys and their corresponding field distribution characteristics. This set of eigenfrequencys reflects the eigenfrequency distribution characteristics of the plasma photonic crystal, revealing the allowed states and bandgap distributions of electromagnetic waves in the periodic structure at different propagation directions and frequencies. Specifically, at the frequencies corresponding to allowed states, electromagnetic waves can propagate in the structure; at the frequencies corresponding to bandgap frequencies, propagation is suppressed. The position and width of the bandgap are jointly determined by the dielectric constant dispersive characteristics of plasma 2 and the periodic arrangement of alumina dielectric pillars 1. When a frequency falls within the bandgap, electromagnetic waves of that frequency cannot propagate in the structure and are reflected or absorbed. Therefore, by analyzing the position of the bandgap in the eigenfrequency distribution, the frequency range in which the plasma photonic crystal exhibits a significant response to electromagnetic waves can be preliminarily determined.

[0045] In the second type of calculation, an external electromagnetic wave excitation is applied to the generated computational grid model to simulate the physical process of electromagnetic waves incident on the surface of a plasma photonic crystal under real operating conditions. In this calculation, the external excitation source is incident from above the model as a plane wave of a specific frequency. After propagating to the surface of the plasma photonic crystal, part of the energy is reflected back into free space, part penetrates into the structure and undergoes multiple scatterings and interferences at the interface between plasma 2 and the alumina dielectric pillar 1, and the remaining energy is absorbed by plasma 2 and converted into heat. By solving Maxwell's equations in the frequency domain under this active condition, the spatial distribution characteristics and energy transmission paths of the electromagnetic waves inside and around the plasma photonic crystal can be obtained. The spatial distribution characteristics intuitively demonstrate the localization of electromagnetic wave energy in space; that is, when the electromagnetic wave is effectively absorbed, the electric field energy is mainly concentrated in a specific region near the structure surface. The energy transmission paths completely record the distribution ratio of electromagnetic wave energy in each stage of incident, propagation, scattering, and absorption. Combining the results of the two types of calculations allows for a comprehensive evaluation of the absorption performance of the plasma photonic crystal at different frequencies.

[0046] After completing the above electromagnetic simulation calculations, absorption frequencies are identified based on the simulation results. Absorption frequencies refer to the frequency positions where the plasma photonic crystal exhibits significant absorption of incident electromagnetic waves. The basic identification method is as follows: Simulation calculations are performed on a series of discrete frequency points one by one to obtain the absorption rate of electromagnetic wave energy in the structure at each frequency. The frequency positions where the absorption rate reaches a maximum value are marked as absorption frequencies. In the technical solution of this application, multiple absorption frequencies can be obtained through the above identification method. These frequencies correspond to the electromagnetic resonance modes formed by the periodic structure of plasma 2 and alumina dielectric column 1 at different frequencies. Each absorption frequency represents the structure's enhanced absorption capability of electromagnetic waves at a specific frequency.

[0047] like Figure 3 As shown in the diagram, the simulation of the absorption effect visually illustrates the absorption mechanism of the plasma photonic crystal by comparing the upper and lower images: The upper image shows the ideal absorption process. The image demonstrates that the energy of the electromagnetic wave is effectively "absorbed" on the lower surface of the structure, without diffusing in other directions, indicating successful localization and absorption of the electromagnetic wave energy. The lower image shows the propagation path of the electromagnetic wave within the structure. Here, we can see that the electromagnetic wave propagates arbitrarily within the structure, providing a comparative reference for the absorption effect in the upper image. Therefore, Figure 3 By comparing the two states of "absorbed" and "free propagation", it was verified that the structure can successfully control electromagnetic waves on the surface and achieve absorption.

[0048] By solving the intrinsic electromagnetic field problem under no external excitation, the intrinsic frequency distribution characteristics of the plasma photonic crystal were obtained, providing a theoretical basis for understanding the physical origin of the absorption frequency. By solving the electromagnetic field response under applied excitation, the spatial distribution characteristics and energy transmission paths of the electromagnetic field in the structure were obtained, intuitively presenting the localized distribution and transmission paths of electromagnetic wave energy in the structure, providing a visual basis for the qualitative evaluation of absorption performance. By combining the two types of calculation results and identifying the absorption frequency, a clear target frequency benchmark for subsequent structural adjustments to merge multiple frequency points into a broadband absorption band was provided, giving the entire tunable design process a clear optimization direction and quantitative evaluation standard.

[0049] Step S600: Adjust the lateral position of some alumina dielectric pillars 1 in the alumina dielectric pillar array according to the structural parameters, so that the identified multiple absorption frequency points are shifted and overlap each other to form a broadband absorption band, thereby realizing dynamic tuning of the absorption frequency band.

[0050] Specifically, such as Figure 2As shown, in a plasma photonic crystal, the periodic arrangement of the alumina dielectric pillar array 1 determines the translational symmetry of the structure. This symmetry is directly related to the dispersion relation and band distribution of electromagnetic waves within the structure. When all the alumina dielectric pillars 1 are evenly spaced according to a uniform periodic arrangement, the structure possesses complete translational symmetry. In this case, the band distribution and the position of the absorption frequency are uniquely determined by this fixed periodic structure. However, when the lateral position of some of the alumina dielectric pillars 1 shifts, the original translational symmetry is broken in the direction of the shift. This symmetry breakage leads to a reconstruction of the dispersion relation of electromagnetic waves within the structure. That is, the electromagnetic resonance mode originally formed at a specific frequency undergoes frequency drift due to local structural changes, and the corresponding absorption frequency also shifts towards lower or higher frequencies. The direction and magnitude of the frequency shift are closely related to the lateral displacement of the alumina dielectric column 1: when the displacement is small, the frequency shift is small and the frequency points have not yet overlapped; as the displacement increases to a certain value, the multiple independent absorbing frequency points that were originally dispersed gradually approach each other and eventually overlap on the frequency axis, merging into a continuous broadband absorption band.

[0051] During the aforementioned adjustment process, the lateral displacement of the alumina dielectric column 1 is not arbitrarily selected, but determined based on structural parameters. The arrangement period in the structural parameters determines the reference spacing between adjacent dielectric columns, while the radius of the dielectric column determines its own geometric dimensions. Together, they limit the movable range of the dielectric column within the periodic unit. The displacement calculated based on the aforementioned structural parameters ensures that the adjusted structure produces the expected frequency shift and overlap effects while avoiding geometric interference between dielectric columns or between the dielectric column and the side plate.

[0052] In this embodiment, the identified multiple absorption frequencies correspond to multiple independent absorption modes formed at different frequencies by the structure in its unadjusted state. These modes originate from the resonant coupling of electromagnetic waves with plasma 2 and the alumina dielectric pillar array 1 at different frequencies. By adjusting the lateral position of some alumina dielectric pillars 1, the frequency response of each resonant mode changes to varying degrees; that is, some modes drift towards lower frequencies, some drift towards higher frequencies, or all modes converge in the same direction. When the displacement reaches a specific value determined by the structural parameters, the modes change from a dispersed distribution to a continuous distribution on the frequency axis, the stopband between adjacent frequencies disappears, and the absorption effect that was originally achieved at multiple discrete frequencies is merged into a continuous frequency range, thereby forming a broadband absorption band and completing the dynamic transformation of the absorption band from discrete multi-point to continuous broadband.

[0053] It is worth emphasizing that the tuning of the absorption band in this embodiment relies entirely on the structural parameters themselves. That is, the electromagnetic response is controlled by changing the relative spatial position between the alumina dielectric pillars 1, rather than by changing the electron density of the plasma 2 or electrical parameters such as the applied bias voltage. This means that once the optimal combination of structural parameters that can achieve a wide absorption band is determined through simulation, the corresponding absorption performance can be obtained simply by processing according to these structural parameters in the actual device fabrication, without the need for a complex high-voltage power supply and control system.

[0054] By adjusting the lateral position of some dielectric pillars in the alumina dielectric pillar array 1, the translational symmetry of the original periodic structure is broken, causing the dispersion relation of electromagnetic waves in the structure to be reconstructed. The independent absorption modes originally dispersed at multiple frequency points are shifted on the frequency axis and overlap and merge with each other, merging multiple discrete absorption frequency points into a continuous broadband absorption band, effectively expanding the absorption bandwidth and overcoming the technical defect of the fixed absorption frequency band of the existing fixed structure plasma photonic crystal absorber. At the same time, this tuning process is entirely based on the adjustment of structural parameters, without relying on the high-voltage power supply system required for dynamic control of plasma electron density, which greatly reduces the engineering implementation difficulty and system complexity in practical applications, and provides a structure-oriented technical path for the simulation design and performance optimization of tunable broadband absorber devices.

[0055] In this embodiment, by acquiring the structural and physical parameters of the plasma photonic crystal, a three-dimensional electromagnetic simulation model is constructed, comprising plasma, a periodic alumina dielectric pillar array, steel metal side plates, an ITO transparent cover plate, and a steel base plate. The height and radius of the dielectric pillars are set to one-quarter of the wavelength corresponding to the operating frequency band, enabling the model to accurately reflect the electromagnetic coupling characteristics between the plasma and the periodic dielectric structure. The relative permittivity of the plasma is calculated based on the physical parameters and assigned to the plasma in the model, ensuring a high degree of consistency between the simulation input parameters and the actual physical state, thereby improving the reliability of the simulation results. Absorption frequencies are identified through simulation calculations, and the lateral positions of some alumina dielectric pillars are adjusted according to the structural parameters, causing multiple absorption frequencies to shift and overlap to form a broadband absorption band, achieving dynamic tuning of the absorption band. This method effectively expands the absorption bandwidth, solving the technical problems of existing fixed-structure plasma photonic crystal absorbers, such as difficulty in adjusting the absorption band and limited operating bandwidth, providing an efficient simulation analysis tool for the design and performance optimization of tunable broadband absorbing devices.

[0056] Optionally, the structural parameters include the arrangement period of the alumina dielectric columns 1, the lateral gap between the alumina dielectric columns 1 and the steel metal side plate 3, and the longitudinal gap between the alumina dielectric columns 1 and the ITO conductive film transparent cover plate 4.

[0057] Specifically, the arrangement period of the alumina dielectric pillars 1 refers to the distance between the centers of adjacent alumina dielectric pillars 1. This parameter determines the density of the dielectric pillar array and the size of the periodic repeating units. The value of the arrangement period is directly related to the position of the photonic bandgap; that is, the larger the period, the lower the frequency of the bandgap; the smaller the period, the higher the frequency of the bandgap. Therefore, the arrangement period is a fundamental structural parameter that determines the operating frequency band of the plasma photonic crystal.

[0058] The lateral gap between the alumina dielectric column 1 and the steel metal side plate 3 refers to the horizontal distance between the outer wall of the alumina dielectric column 1 and the inner wall of the steel metal side plate 3 at the edge. This lateral gap provides a transition area for the propagation of electromagnetic waves at the edge of the structure. Its size affects the distribution characteristics of the electromagnetic field at the boundary and the reflection and scattering behavior of electromagnetic waves at the edge of the structure, thus having a certain impact on the wave absorption performance.

[0059] The longitudinal gap between the alumina dielectric column 1 and the ITO conductive film transparent cover plate 4 refers to the vertical distance between the top of the alumina dielectric column 1 and the lower surface of the ITO conductive film transparent cover plate 4. This longitudinal gap provides space for the propagation of electromagnetic waves in the height direction. Its size affects the electromagnetic coupling state at the top boundary and the degree of localization of electromagnetic waves on the upper surface of the structure, thus having a certain impact on the wave absorption effect. At the same time, the ITO conductive film transparent cover plate 4 has both conductive and light-transmitting properties, which can both serve as a conductive boundary to participate in electromagnetic confinement and facilitate the observation of the internal structure in experiments.

[0060] The aforementioned structural parameters, as important components of the modeling parameters obtained in step S100, together constitute the geometric description system of the three-dimensional electromagnetic simulation model of the plasma photonic crystal, providing complete geometric input conditions for subsequent model construction, structural adjustment, and microwave absorption performance simulation.

[0061] By incorporating the arrangement period of the alumina dielectric pillars, the lateral gap between the dielectric pillars and the steel metal side plates, and the longitudinal gap between the dielectric pillars and the ITO conductive thin film transparent cover plate into the modeling parameter system, the geometric configuration characteristics of the plasma photonic crystal are fully described. This allows the constructed three-dimensional electromagnetic simulation model to accurately reflect the spatial layout and boundary conditions of the real structure. The above structural parameters together constitute the operational basis for subsequent structural adjustments. Among them, the arrangement period and the radius of the dielectric pillars jointly determine the calculation benchmark for the lateral displacement during structural adjustments, the lateral gap limits the movable range of the dielectric pillars, and the longitudinal gap ensures a reasonable representation of the electromagnetic coupling state at the top. This provides complete geometric constraints and operational basis for achieving dynamic tuning of the absorption band through structural adjustments.

[0062] Optionally, the physical parameters include the electron density and effective collision frequency of the plasma 2; obtaining the relative permittivity of the plasma 2 based on the physical parameters specifically includes: The plasma frequency is obtained based on the electron density. The relative permittivity is obtained based on the plasma frequency and the effective collision frequency.

[0063] Optionally, the relative permittivity includes: ; in, The plasma frequency, , The electron density, The effective collision frequency, Let e ​​be the vacuum permittivity, and e be the electron charge. For electronic quality, The incident electromagnetic wave angular frequency.

[0064] Specifically, in the electromagnetic simulation of the plasma photonic crystal, the material properties of plasma 2 are characterized by its relative permittivity. This relative permittivity is not a constant value, but a complex number that varies with the frequency of the incident electromagnetic wave. Its frequency-dependent characteristics are jointly determined by the physical parameters of plasma 2, namely the electron density and the effective collision frequency.

[0065] electron density It is the core physical quantity describing the concentration of free electrons in plasma 2. In plasma 2, free electrons oscillate collectively around the relatively stationary ion background under the influence of an electromagnetic field. This oscillation behavior has an inherent characteristic frequency, called the plasma frequency. The relationship between plasma frequency and electron density indicates that higher electron density means a greater number of free electrons per unit volume, stronger Coulomb interactions between electrons, and a correspondingly higher natural frequency of collective oscillations; conversely, lower electron density causes the plasma frequency to decrease. Therefore, the plasma frequency is essentially uniquely determined by the concentration of free electrons in plasma 2, serving as a crucial bridge connecting macroscopic electromagnetic responses and microscopic physical states.

[0066] The effective collision frequency describes how frequently electrons in plasma 2 collide with neutral particles or other charged particles. In actual plasma, electrons continuously collide with background particles during their directional motion, converting the directional energy they gain from the electromagnetic field into random thermal energy. This collision process is the physical source of the loss absorption of electromagnetic waves by plasma 2; that is, the more frequent the collisions, the higher the efficiency of converting electromagnetic wave energy into thermal energy in plasma 2, and correspondingly, the stronger the absorption capacity of plasma 2 for electromagnetic waves.

[0067] Based on the above physical parameters, the relative permittivity of plasma 2 and the angular frequency of the incident electromagnetic wave satisfy the frequency domain constitutive relationship embodied in the above formula; this reflects the frequency dispersion and loss characteristics of plasma 2. The angular frequency of the incident electromagnetic wave is the inherent frequency parameter of the electromagnetic wave, determined by the frequency of the external excitation source. When the electromagnetic wave frequency is low, the plasma frequency dominates relative to the incident electromagnetic wave angular frequency, the permittivity exhibits a large negative real part, and the plasma displays strong reflection characteristics of the electromagnetic wave. When the electromagnetic wave frequency is high and exceeds the plasma frequency, the permittivity gradually approaches the vacuum permittivity, and the plasma exhibits transmission characteristics of the electromagnetic wave. When the electromagnetic wave frequency approaches the plasma frequency, the imaginary part of the permittivity contributes significantly, and the plasma's energy absorption of the electromagnetic wave reaches its peak.

[0068] In the simulation model, the above formula describes the relative permittivity of plasma 2 in complex form: its real part reflects the dispersion characteristics of electromagnetic waves in plasma 2, determining the phase change and photon bandgap position when electromagnetic waves propagate in plasma 2; its imaginary part reflects the loss characteristics of electromagnetic waves in plasma 2, determining the intensity of electromagnetic wave energy absorbed in plasma 2. After assigning the above frequency-related complex permittivity as a material property to the plasma 2 region in the three-dimensional electromagnetic simulation model, the simulation software will automatically call the corresponding permittivity value at each solution frequency point in subsequent electromagnetic field calculations, thereby accurately simulating the propagation, reflection, and absorption behavior of electromagnetic waves in the periodic structure composed of plasma 2 and alumina dielectric pillar 1.

[0069] By obtaining the electron density and effective collision frequency of the plasma, the complex relative permittivity varying with frequency is calculated based on the intrinsic physical model of the plasma. This allows the plasma in the simulation model to accurately reflect the dispersion and loss characteristics of the real plasma. Among these parameters, electron density is the key parameter that determines the plasma frequency and thus the location of the absorption band, while the effective collision frequency is the key parameter that determines the absorption intensity. Together, they constitute a complete physical description of the electromagnetic properties of the plasma. This approach incorporates the complex plasma physical processes into the simulation framework with a precise mathematical model, ensuring a high degree of consistency between the simulation input parameters and the real physical state. This provides a core material property guarantee for the accuracy of subsequent absorption performance simulation calculations and also provides a reliable simulation modeling foundation for tunable absorption technology based on electron density control.

[0070] Optionally, the step of configuring and meshing the three-dimensional electromagnetic simulation model to generate a computational mesh model includes: Based on the finite element method, an eigenfrequency solver and a frequency domain solver are set, boundary conditions are set, and a free tetrahedral mesh is used to mesh the three-dimensional electromagnetic simulation model to obtain the computational mesh model. The boundary conditions include: setting perfect electrical conductor boundary conditions at the upper and lower boundaries of the three-dimensional electromagnetic simulation model, setting periodic boundary conditions at the left and right boundaries, and setting the ITO conductive thin film transparent cover plate 4 as a perfect electrical conductor boundary condition.

[0071] Specifically, in the simulation configuration and mesh generation stage, the solution strategy configuration, boundary condition application and spatial discretization processing of the three-dimensional electromagnetic simulation model that has been modeled and assigned material properties are performed based on the finite element method to generate a computational mesh model that can be directly used for subsequent electromagnetic simulation calculations.

[0072] The finite element method (FEM) is a computational method widely used for numerical solutions of electromagnetic fields. Its core idea is to discretize the continuous computational domain into a finite number of elements, constructing an approximate function on each element to approximate the actual field distribution. This transforms the boundary value problem of partial differential equations described by Maxwell's equations into a large-scale algebraic equation system that can be solved numerically. The FEM is well-suited for complex geometries and non-uniform material distributions, and is particularly well-suited for handling the three-dimensional plasma photonic crystal model containing an array of cylindrical dielectric pillars, as described in this application.

[0073] In terms of solution strategy configuration, two types of solvers are set up: an eigenfrequency solver and a frequency domain solver. The eigenfrequency solver is used to solve the intrinsic electromagnetic modes of the structure under no external excitation conditions, that is, to solve the eigenvalue problem of Maxwell's equations determined by the plasma dispersion characteristics and the periodic arrangement of the alumina dielectric pillars, obtaining the resonant frequencies of the structure itself and their corresponding field distributions. The frequency domain solver is used to solve the electromagnetic field response under external excitation conditions, that is, to solve the propagation, reflection, and absorption behavior of electromagnetic waves in the structure under incident electromagnetic wave excitation at a specific frequency. The two types of solvers work together to serve two different simulation needs: band structure analysis and wave absorption performance evaluation.

[0074] Regarding boundary condition configuration, specific types of boundary conditions are applied to the corresponding boundaries of the three-dimensional electromagnetic simulation model based on the physical structural characteristics of the plasma photonic crystal and the requirements of electromagnetic simulation. Boundary conditions are indispensable physical constraints in the numerical solution of electromagnetic fields, used to limit the electromagnetic field behavior at the boundaries of the computational domain, so that the finite-size computational model can accurately reflect the physical characteristics of electromagnetic waves such as propagation, reflection, or periodic repetition at the actual structural boundaries.

[0075] Perfectly conductive boundary conditions are set at the upper and lower boundaries of the three-dimensional electromagnetic simulation model. The perfectly conductive boundary condition is an idealized model among electromagnetic field boundary conditions; its mathematical essence is setting the tangential component of the electric field on the boundary to zero. This boundary condition is used to simulate lossless ideal metallic surfaces, such as grounded planes or symmetrical boundary conditions. In this application, the upper and lower boundaries are set as perfectly conductive boundary conditions to simulate the total internal reflection characteristics of electromagnetic waves on the steel metal side plates and steel base plates, ensuring that the electromagnetic wave energy is confined to the area defined by the upper and lower boundaries and does not leak into the external space. The ITO conductive thin film transparent cover is also set as a perfectly conductive boundary condition, utilizing its conductivity to participate in electromagnetic confinement while retaining its light transmission characteristics for experimental observation.

[0076] Periodic boundary conditions are set at the left and right boundaries. These periodic boundary conditions are used to simulate the electromagnetic properties of a structure that repeats infinitely in a certain direction. For an array of alumina dielectric pillars arranged periodically along the x and y directions, applying periodic boundary conditions at the left and right boundaries ensures that the electromagnetic field values ​​are equal at the corresponding periodic boundaries. Therefore, the electromagnetic response of the entire infinite periodic array can be obtained by calculating only one periodic element. This approach significantly reduces the computational scale, simplifying the complex problem of calculating the entire finite array to the calculation of a single periodic element, thus significantly improving computational efficiency while maintaining accuracy.

[0077] For mesh generation, a free tetrahedral mesh was used to spatially discretize the 3D electromagnetic simulation model. The tetrahedral mesh can flexibly adapt to complex geometries and exhibits good adaptability to 3D structures containing arrays of cylindrical alumina dielectric pillars. That is, the tetrahedral mesh can accurately fit both the curved boundaries of the cylindrical dielectric pillars and the arc-shaped interface between the dielectric pillars and the plasma. In setting the mesh density, a balance needs to be struck between computational accuracy and efficiency: in regions with drastic electromagnetic field changes, such as near the surface of the alumina dielectric pillars, at the interface between the plasma and the dielectric pillars, and near the boundaries, a denser mesh is used to ensure the accuracy of the field distribution solution; in regions with gentle electromagnetic field changes, a relatively sparse mesh is used to control the overall computational scale and resource consumption. Through this mesh generation process, the continuous geometric model is discretized into a computational mesh model composed of a finite number of mesh elements and mesh nodes. This model contains all the geometric discretization information and material property allocation information required for subsequent numerical solutions, serving as the direct physical basis for subsequent electromagnetic simulation calculations.

[0078] In some embodiments, the mesh size ranges from a maximum of 100µm to a minimum of 50µm, with a total of 32,820 domain elements, 9,134 boundary elements, and 905 edge elements. The mesh density affects the frequency point location, but the difference is ≤0.1GHz.

[0079] By employing the finite element method and configuring intrinsic frequency solvers and frequency domain solvers, a numerical computation framework for passive mode solutions and active response solutions is provided for subsequent band structure analysis and microwave absorption performance simulation, respectively. The two types of solvers work together to fully cover all computational requirements for the microwave absorption performance analysis of plasma photonic crystals. By setting perfect electrical conductor boundary conditions at the upper and lower boundaries and the ITO cover plate, the total internal reflection characteristics of electromagnetic waves on the metal surface are accurately simulated, effectively confining the electromagnetic wave energy within the computational region. By setting periodic boundary conditions at the left and right boundaries, the periodic characteristics of the structure are fully utilized, simplifying the simulation problem of an infinite periodic array to the calculation of a single periodic element, significantly reducing the computational scale. By using free tetrahedral meshes to spatially discretize the three-dimensional complex structure containing the cylindrical dielectric column array, computational resource consumption is reasonably controlled while ensuring the accuracy of electromagnetic field solutions. The generated discretized computational mesh model provides a reliable guarantee for the accuracy and efficiency of subsequent electromagnetic simulation calculations.

[0080] Optionally, the electromagnetic simulation calculation based on the computational grid model to obtain the simulation results of the absorption performance of the plasma photonic crystal includes: The band distribution of the plasma photonic crystal under no-excitation source condition is calculated by the intrinsic frequency solver, and the absorption frequency point is identified based on the band distribution. The near-field electric field distribution and electromagnetic wave transmission characteristics of the plasma photonic crystal after excitation are calculated by the frequency domain solver, and the simulation results of the absorption performance are obtained.

[0081] Specifically, electromagnetic simulation calculations include: The computational mesh model is solved using an eigenfrequency solver under conditions without external excitation. Since there is no incident external electromagnetic wave inside the structure, the solver calculates the eigenvalues ​​of Maxwell's equations, determined by the dispersion characteristics of plasma 2 and the periodic arrangement of alumina dielectric pillars 1, yielding a series of eigenfrequencys and their corresponding field distributions. This set of eigenfrequencys constitutes the band structure of the plasma photonic crystal. The band structure reflects the allowed and forbidden states of electromagnetic waves in the periodic structure at different propagation directions and frequencies; that is, electromagnetic waves can propagate in the structure at frequencies corresponding to allowed states, and their propagation is suppressed at frequencies corresponding to forbidden states. The position and width of the bandgap are jointly determined by the dielectric constant dispersion characteristics of plasma 2 and the periodic arrangement of alumina dielectric pillars 1. When a frequency falls within the bandgap, electromagnetic waves at that frequency cannot propagate in the structure and are reflected or absorbed. Therefore, by analyzing the position of the bandgap in the band structure, the frequency range in which the plasma photonic crystal exhibits a significant response to electromagnetic waves can be preliminarily determined, and the absorption frequency points can be identified based on the band structure.

[0082] In some embodiments, such as Figure 4 and Figure 5 As shown, Figure 4 This diagram illustrates the band structure of the plasma photonic crystal calculated using the intrinsic frequency solver under no-excitation conditions. Specifically, it shows a schematic diagram of the band structure of a single cell (i.e., the smallest periodically repeating unit) of the plasma photonic crystal, calculated at a specific plasma electron density. (The electron density values ​​are not specified in the original text.) , Figure 4 Its purpose is to demonstrate the intrinsic band characteristics of the basic structure. Figure 4 The x-coordinate is the wave vector (k), which, more precisely, is the path along certain specific directions on the boundary of the First Irreducible Brillouin Zone.

[0083] Figure 4 The letters on the horizontal axis (such as Γ, X, M) represent high symmetry points in the reciprocal space. For a two-dimensional square lattice, these points are typically defined as follows: Γ (Gamma) point: the center point of the first Brillouin zone. X point: a point located on the boundary of the first Brillouin zone along one principal axis of the lattice (the axis corresponding to the x-direction (i.e., the column direction of the periodic lattice arrangement), used to analyze the band structure when electromagnetic waves propagate along this specific direction. The other principal axis (y-direction) usually corresponds to the Γ→Y path). M point: a point located at the corner of the first Brillouin zone along its diagonal direction. Figure 4 The x-axis is a scan starting from point Γ along the lines connecting these high symmetry points (such as Γ-X, XM, M-Γ), representing the change path of the wave vector k propagating in the crystal in these specific directions.

[0084] Figure 5 The diagram shows the band structure projection along the x-direction into the first irreducible Brillouin zone for a supercell with a period number of 3 in the y-direction (i.e., a finite-width structure with 3 rows × n columns). The diagram marks the intersections in the band structure (the marked intersections are the absorption frequencies), which correspond to the absorption frequencies where the structure significantly absorbs external electromagnetic waves. Figure 5 Compared to Figure 4 The restrictions of "supercell with a period number of 3 in the y-direction" and "projection in the x-direction" have been added. That is... Figure 5 The x-direction projected band distribution of the original supercell before adjustment was used to mark three independent absorption frequencies (marked as 6.9 GHz, 6.6 GHz, and 6.4 GHz in the figure).

[0085] The computational mesh model is solved using a frequency domain solver under the condition of external electromagnetic wave excitation. The external excitation source is incident from above the model in the form of a plane wave. After the electromagnetic wave propagates to the surface of the plasma photonic crystal, part of the energy is reflected back to free space, part of the energy penetrates into the structure and undergoes multiple scattering and interference at the interface between plasma 2 and alumina dielectric pillar 1, and part of the energy is absorbed by plasma 2 and converted into heat energy. By solving the frequency domain Maxwell's equations under this active condition, the near-field electric field distribution and electromagnetic wave propagation characteristics inside and around the plasma photonic crystal can be obtained. The near-field electric field distribution intuitively shows the degree of localization of electromagnetic wave energy in space, while the electromagnetic wave propagation characteristics fully record the distribution ratio of electromagnetic wave energy in each stage of incident, propagation, scattering, and absorption. Combining the two types of calculation results allows for a comprehensive evaluation of the absorption performance of the plasma photonic crystal at different frequencies and the acquisition of simulation results of absorption performance.

[0086] The intrinsic frequency solver solves the computational grid model under no-excitation conditions to obtain the band distribution of the plasma photonic crystal, providing a band theory basis for understanding the physical origin of the absorption frequency. The frequency domain solver solves the computational grid model under applied excitation conditions to obtain the near-field electric field distribution and electromagnetic wave propagation characteristics, providing a visual basis for the qualitative evaluation of absorption performance. The two types of solvers work together to fully cover all computational needs for plasma photonic crystal absorption performance analysis, providing a clear target frequency benchmark for subsequent dynamic tuning of the absorption band through structural adjustments.

[0087] Optionally, the alumina media column array 1 is arranged in a rectangular pattern of 3 rows × n columns, where n is a positive integer greater than or equal to 3; the alumina media column 1 in the middle row is the alumina media column 1.

[0088] Optionally, the adjustment of the lateral position specifically involves: calculating the translation distance based on the arrangement period and the radius of the alumina medium column 1, and translating part of the alumina medium column 1 along the x-direction by the translation distance; the translation distance is a / 2-d, where a is the arrangement period and d is the radius of the alumina medium column 1.

[0089] Specifically, such as Figure 6 As shown, the translation distance is calculated based on the arrangement period 'a' and the radius 'd' of alumina media column 1. This is used to move a portion of alumina media column 1 (i.e., the alumina media column 1 in the middle row). Figure 6 The row indicated by the middle arrow is shifted along the x-direction by this shift distance. The shift distance is a / 2-d, where a is the arrangement period and d is the radius of alumina medium column 1.

[0090] In the original periodic structure, all alumina dielectric pillars 1 are evenly spaced according to a uniform arrangement period, and the structure possesses complete translational symmetry. At this point, the band distribution and absorption frequency position are uniquely determined by this fixed periodic structure. When the middle row of alumina dielectric pillars 1 is translated a distance a / 2-d along the x-direction, the original translational symmetry is broken in the x-direction. This symmetry breakage leads to a reconstruction of the dispersion relation of electromagnetic waves within the structure. The electromagnetic resonance modes originally formed at specific frequencies experience frequency drift due to local structural changes, and the corresponding absorption frequencies shift towards lower or higher frequencies.

[0091] The physical meaning of the translation distance a / 2-d is that when the middle row of dielectric pillars is translated by this distance, the relative position between the middle row of dielectric pillars and the upper and lower rows of dielectric pillars changes specifically, causing the absorption modes originally dispersed at multiple independent frequency points to gradually approach each other on the frequency axis and eventually overlap. After multiple absorption frequency points shift and overlap, the absorption effect originally achieved at multiple discrete frequencies is merged into a continuous frequency range, forming a broadband absorption band. This process realizes the dynamic transformation of the absorption band from discrete multi-point to continuous broadband, and it depends entirely on the structural parameters themselves, that is, by changing the relative spatial position between the alumina dielectric pillars 1 to control the electromagnetic response, rather than by changing the electron density of plasma 2 or external bias voltage and other electrical parameters.

[0092] The translation distance a / 2-d is calculated based on the arrangement period and the radius of the dielectric column. The alumina dielectric column in the middle row is translated by this distance along the x-direction, breaking the translation symmetry of the original periodic structure. This causes multiple independent absorption frequency points to shift and overlap and merge on the frequency axis, forming a continuous broadband absorption band, effectively expanding the absorption bandwidth. This tuning process is entirely based on the adjustment of structural parameters, without relying on the high-voltage power supply system required for dynamic control of plasma electron density. This greatly reduces the engineering implementation difficulty and system complexity in practical applications, providing a structure-oriented technical path for the simulation design and performance optimization of tunable broadband absorbing devices.

[0093] Optionally, after adjusting the lateral position of the alumina dielectric pillar 1, the microwave absorption simulation method of the tunable plasma photonic crystal further includes: The plasma photonic crystal with the adjusted structure was re-meshed and electromagnetically simulated to obtain the band distribution and near-field electric field distribution of the adjusted structure. Specifically, obtaining the adjusted band distribution of the structure includes: The band distribution of the supercell with a predetermined number of periods in the y-direction of the plasma photonic crystal after the structure adjustment is calculated and projected in the x-direction within the first irreducible Brillouin zone. The band overlap region is then identified. The band overlap region is used as the broadband absorption frequency point to verify the formation of the broadband absorption band.

[0094] Specifically, after adjusting the lateral position of the alumina dielectric column 1, it is necessary to perform simulation verification on the plasma photonic crystal after the adjustment structure to confirm whether the broadband absorption band has been successfully formed.

[0095] The verification process begins with re-meshing and performing electromagnetic simulations on the adjusted plasma photonic crystal. Because the structural adjustment altered the spatial positions of some alumina dielectric pillars 1, the model's geometry has locally changed, rendering the original computational mesh unsuitable for the new structure. Therefore, a new mesh generation based on the adjusted geometry is necessary to produce a computational mesh model adapted to the new structure. Following this, electromagnetic simulations are performed again on the adjusted model using an eigenfrequency solver to obtain the band structure and near-field electric field distribution of the adjusted structure.

[0096] The specific method for obtaining the band distribution of the adjusted structure is as follows: The band distribution of the adjusted plasma photonic crystal is calculated by projecting a supercell with a predetermined number of periods in the y-direction onto the x-direction within the first irreducible Brillouin zone. A supercell refers to a combination of periodic units containing a predetermined number of periods (e.g., 3 periods) in the y-direction, used to reflect the band characteristics of a finite-width structure. The first irreducible Brillouin zone is the smallest symmetric unit of the periodic structure in reciprocal lattice space; calculating the band distribution within this region yields complete band information. Projection along the x-direction refers to projecting the band structure along the x-direction, thus presenting the band distribution on the frequency axis.

[0097] After calculating the x-direction projected band distribution of the adjusted structure, the band overlap region is identified. The band overlap region refers to the continuous region formed by multiple independent bands that were originally dispersed at different frequency positions before adjustment, but which have shifted and overlapped along the frequency axis after structural adjustment. This band overlap region is represented by a continuous interval rather than discrete frequency points, corresponding to the structure's enhanced absorption of electromagnetic waves within a continuous frequency band. Using this band overlap region as the broadband absorption frequency point verifies the successful formation of the broadband absorption band; that is, the frequency range of the band overlap region is the operating frequency band of the broadband absorption band, and the width of the band overlap region is the bandwidth of the broadband absorption band.

[0098] In some embodiments, such as Figure 7 As shown, Figure 7 The band structure of the modified tunable plasma photonic crystal is shown as the band distribution of the supercell with a period number of 3 in the y-direction projected into the first irreducible Brillouin zone in the x-direction.

[0099] Figure 7 This demonstrates the translation of the middle row of alumina dielectric columns along the x-direction by a distance a / 2. After calculating d (where a is the arrangement period and d is the radius of the alumina dielectric pillar), the recalculated supercell x-direction projected band distribution is the band distribution diagram of the supercell projected in the first irreducible Brillouin zone in the y-direction by a supercell with a preset number of periods. This is the band distribution diagram of the plasma photonic crystal after structural adjustment projected in the x-direction by a supercell with a preset number of periods in the y-direction. Figure 5 compared to, Figure 7 The energy bands, originally dispersed across three independent frequency points (6.9 GHz, 6.6 GHz, and 6.4 GHz), underwent significant frequency shifts, forming an overlapping region on the frequency axis. This overlapping region corresponds to a frequency range of 6.5–6.7 GHz, which is the broadband absorption band formed after structural adjustments. The figure also shows the electromagnetic field mode distribution characteristics within the overlapping region, indicating that electromagnetic wave energy is effectively localized near the structure's surface within the overlapping frequency band.

[0100] Figure 7 In this study, the overlapping region of the energy bands is used as the broadband absorption frequency point to verify the formation of the broadband absorption band. This figure also demonstrates from the perspective of energy band theory that the technical solution of merging multiple independent absorption frequencies into a continuous broadband absorption band through structural adjustments is feasible, providing direct simulation verification evidence for achieving dynamic tuning of the absorption band solely through structural parameter control.

[0101] By re-meshing and performing electromagnetic simulation calculations on the plasma photonic crystal after structural adjustment, it was ensured that the model still had an accurate computational grid basis after the geometric configuration change. By calculating the band distribution diagram of the supercell with a preset number of periods in the y-direction after structural adjustment and projecting it in the x-direction within the first irreducible Brillouin zone, and identifying the band overlap region as a broadband absorption frequency point, the successful formation of the broadband absorption band was verified from the physical mechanism level based on band theory. This provides a reliable simulation verification method for achieving dynamic tuning of the absorption band through structural adjustment.

[0102] This invention provides a simulation system for the absorption of a tunable plasma photonic crystal, used to implement the simulation method for the absorption of a tunable plasma photonic crystal as described in the first aspect. The system includes: The acquisition unit is used to acquire modeling parameters, which include the structural parameters of the plasma photonic crystal and the physical parameters of the plasma. A construction unit is used to construct a three-dimensional electromagnetic simulation model of a plasma photonic crystal based on the structural parameters. The plasma photonic crystal includes a plasma 2, an array of alumina dielectric pillars 1 arranged periodically along mutually perpendicular x and y directions in the plasma 2, steel metal side plates 3 disposed on both sides of the array of alumina dielectric pillars 1, an ITO conductive film transparent cover plate 4 disposed on the top, and a steel base plate 5 disposed on the bottom. The height and radius of the alumina dielectric pillars 1 are both one-quarter of the wavelength corresponding to the operating frequency band. The relative permittivity of the plasma 2 is obtained according to the physical parameters, and the relative permittivity is assigned to the plasma 2 in the three-dimensional electromagnetic simulation model. The three-dimensional electromagnetic simulation model is divided into units, and simulation configuration and mesh generation are performed on the three-dimensional electromagnetic simulation model to generate a computational mesh model. The simulation unit is used to perform electromagnetic simulation calculations based on the computational grid model to obtain the simulation results of the absorption performance of the plasma photonic crystal, and to identify the absorption frequency points based on the absorption performance simulation results; and to adjust the lateral position of some of the alumina dielectric pillars 1 in the array of alumina dielectric pillars 1 according to the structural parameters, so that the identified multiple absorption frequency points are shifted and overlap each other to form a broadband absorption band, thereby realizing dynamic tuning of the absorption frequency band.

[0103] The present invention provides a microwave absorption simulation device for a tunable plasma photonic crystal, comprising a memory and a processor; the memory is used to store a computer program; the processor is used to implement the microwave absorption simulation method for the tunable plasma photonic crystal as described above when the computer program is executed.

[0104] This invention provides a computer-readable storage medium storing a computer program. When the computer program is executed by a processor, it implements the microwave absorption simulation method of the tunable plasma photonic crystal as described above.

[0105] While the present invention has been disclosed above, its scope of protection is not limited thereto. Those skilled in the art can make various changes and modifications without departing from the spirit and scope of the present invention, and all such changes and modifications will fall within the scope of protection of the present invention.

Claims

1. A simulation method for wave absorption of a tunable plasma photonic crystal, characterized in that, include: Obtain modeling parameters, including the structural parameters of the plasma photonic crystal and the physical parameters of the plasma; A three-dimensional electromagnetic simulation model of a plasma photonic crystal is constructed based on the structural parameters. The plasma photonic crystal includes a plasma (2), an array of alumina dielectric pillars (1) arranged periodically in the plasma (2) along mutually perpendicular x and y directions, steel metal side plates (3) disposed on both sides of the array of alumina dielectric pillars (1), an ITO conductive film transparent cover plate (4) disposed on the top, and a steel base plate (5) disposed on the bottom. The height and radius of the alumina dielectric pillars (1) are both one-quarter of the wavelength corresponding to the working frequency band. The relative permittivity of the plasma (2) is obtained based on the physical parameters, and the relative permittivity is assigned to the plasma (2) in the three-dimensional electromagnetic simulation model. The three-dimensional electromagnetic simulation model is configured and meshed to generate a computational mesh model; Electromagnetic simulation calculations are performed based on the computational grid model to obtain simulation results of the absorption performance of the plasma photonic crystal, and the absorption frequency points are identified based on the simulation results. Adjusting the lateral position of some alumina dielectric pillars (1) in the alumina dielectric pillar (1) array according to the structural parameters causes multiple identified absorption frequency points to shift and overlap, forming a broadband absorption band and realizing dynamic tuning of the absorption frequency band.

2. The microwave absorption simulation method for tunable plasma photonic crystals according to claim 1, characterized in that, The structural parameters include the arrangement period of the alumina dielectric column (1), the lateral gap between the alumina dielectric column (1) and the steel metal side plate (3), and the longitudinal gap between the alumina dielectric column (1) and the ITO conductive film transparent cover plate (4).

3. The microwave absorption simulation method for tunable plasma photonic crystals according to claim 1, characterized in that, The physical parameters include the electron density and effective collision frequency of the plasma (2); the relative permittivity of the plasma (2) obtained based on the physical parameters specifically includes: The plasma frequency is obtained based on the electron density. The relative permittivity is obtained based on the plasma frequency and the effective collision frequency.

4. The microwave absorption simulation method for tunable plasma photonic crystals according to claim 3, characterized in that, The relative permittivity includes: ； in, The plasma frequency, , The electron density, The effective collision frequency, Let e ​​be the vacuum permittivity, and e be the electron charge. For electronic quality, The incident electromagnetic wave angular frequency.

5. The microwave absorption simulation method for tunable plasma photonic crystals according to claim 1, characterized in that, The process of configuring and meshing the three-dimensional electromagnetic simulation model to generate a computational mesh model includes: Based on the finite element method, an eigenfrequency solver and a frequency domain solver are set, boundary conditions are set, and a free tetrahedral mesh is used to mesh the three-dimensional electromagnetic simulation model to obtain the computational mesh model. The boundary conditions include: setting perfect electrical conductor boundary conditions at the upper and lower boundaries of the three-dimensional electromagnetic simulation model, setting periodic boundary conditions at the left and right boundaries, and setting the ITO conductive thin film transparent cover plate (4) as a perfect electrical conductor boundary condition.

6. The microwave absorption simulation method for tunable plasma photonic crystals according to claim 5, characterized in that, The electromagnetic simulation calculation based on the computational grid model yields simulation results of the absorption performance of the plasma photonic crystal, including: The band distribution of the plasma photonic crystal under no-excitation source condition is calculated by the intrinsic frequency solver, and the absorption frequency point is identified based on the band distribution. The near-field electric field distribution and electromagnetic wave transmission characteristics of the plasma photonic crystal after excitation are calculated by the frequency domain solver, and the simulation results of the absorption performance are obtained.

7. The microwave absorption simulation method for tunable plasma photonic crystals according to claim 1, characterized in that, The alumina media columns (1) array is arranged in a rectangular pattern of 3 rows × n columns, where n is a positive integer greater than or equal to 3; the alumina media columns (1) are the alumina media columns (1) in the middle row.

8. The microwave absorption simulation method for tunable plasma photonic crystals according to claim 7, characterized in that, The adjustment of the lateral position specifically involves: calculating the translation distance based on the arrangement period and the radius of the alumina medium column (1), and translating part of the alumina medium column (1) along the x direction by the translation distance; the translation distance is a / 2-d, where a is the arrangement period and d is the radius of the alumina medium column (1).

9. The method for simulating the absorption of a tunable plasma photonic crystal according to claim 1, characterized in that, After adjusting the lateral position of the alumina dielectric column (1), the microwave absorption simulation method of the tunable plasma photonic crystal further includes: The plasma photonic crystal with the adjusted structure was re-meshed and electromagnetically simulated to obtain the band distribution and near-field electric field distribution of the adjusted structure. Specifically, obtaining the adjusted band distribution of the structure includes: The band distribution of the supercell with a predetermined number of periods in the y-direction of the plasma photonic crystal after the structure adjustment is calculated and projected in the x-direction within the first irreducible Brillouin zone. The band overlap region is then identified. The band overlap region is used as the broadband absorption frequency point to verify the formation of the broadband absorption band.

10. A simulation system for absorbing waves using a tunable plasma photonic crystal, characterized in that, A method for simulating the absorption of a tunable plasma photonic crystal according to any one of claims 1 to 9, the system comprising: The acquisition unit is used to acquire modeling parameters, which include the structural parameters of the plasma photonic crystal and the physical parameters of the plasma. A construction unit is used to construct a three-dimensional electromagnetic simulation model of a plasma photonic crystal based on the structural parameters. The plasma photonic crystal includes a plasma (2), an array of alumina dielectric pillars (1) arranged periodically in the plasma (2) along mutually perpendicular x and y directions, steel metal side plates (3) disposed on both sides of the array of alumina dielectric pillars (1), an ITO conductive film transparent cover plate (4) disposed on the top, and a steel base plate (5) disposed on the bottom. The height and radius of the alumina dielectric pillars (1) are both one-quarter of the wavelength corresponding to the working frequency band. The relative permittivity of the plasma (2) is obtained according to the physical parameters, and the relative permittivity is assigned to the plasma (2) in the three-dimensional electromagnetic simulation model. The three-dimensional electromagnetic simulation model is divided into units, and simulation configuration and mesh generation are performed on the three-dimensional electromagnetic simulation model to generate a computational mesh model. The simulation unit is used to perform electromagnetic simulation calculations based on the computational grid model to obtain the simulation results of the absorption performance of the plasma photonic crystal, and to identify the absorption frequency points according to the simulation results of the absorption performance; and to adjust the lateral position of some of the alumina dielectric pillars (1) in the alumina dielectric pillar (1) array according to the structural parameters, so that the identified multiple absorption frequency points are shifted and overlap each other to form a broadband absorption band, thereby realizing the dynamic tuning of the absorption frequency band.

Images