Microwave transmission controller based on double semi-Dirac-like points and preparation method thereof

Abstract

The present invention provides a microwave transmission controller based on double semi-quasi-Dirac points and a preparation method, which relates to the fields of wireless communication technology and photonic crystal physics technology. The controller includes a plurality of three-dimensional anisotropic photonic crystal model lattice units arranged in an array, and the controller is a rectangular parallelepiped, wherein the three-dimensional anisotropic photonic crystal has two semi-quasi-Dirac points at the same time. The controller designed by the present invention can realize anisotropic transmission of electromagnetic waves at a frequency of 10GHz. The present invention can adjust the central operating frequency by changing the geometric parameters and electromagnetic parameters of the photonic crystal. The present invention can adjust the direction of anisotropic transmission of electromagnetic waves by rotating the direction of the photonic crystal. When the electromagnetic wave is incident along the Z direction, the controller designed by the present invention can obtain a high transmission result at a small angle regardless of whether the electric field is fixed along the X direction or the magnetic field is fixed along the Y direction.

Description

Technical Field

[0001] The present invention relates to the technical fields of wireless communication technology and photonic crystal physics, and in particular to a microwave transmission controller based on double semi-Dirac points and a preparation method thereof. Background Art

[0002] With the rapid development of the fifth generation mobile communication technology (5G), the global communication field has ushered in unprecedented technological innovation. As an extension of 4G technology, 5G not only greatly improves the data transmission rate and bandwidth, but also realizes open, integrated and innovative changes in communication architecture. This change has brought about a leap in user experience rate, but also puts higher requirements on the underlying support of communication technology. Among them, photonic crystals, as an important material for regulating microwaves, play a vital role in 5G communications.

[0003] Photonic crystals have a special band structure that enables efficient control of electromagnetic waves. In 5G communications, photonic crystals are widely used in microwave manipulation to achieve efficient signal transmission and processing. Among them, photonic crystals with Dirac-like point dispersion are particularly eye-catching. The Dirac-like point is a special case in which the photonic crystal band appears multiple degenerates at the center of the Brillouin zone. This situation mostly occurs in isotropic photonic crystals. When we transform the isotropic photonic crystal into anisotropic photonic crystals, the original Dirac-like point will be transformed into a semi-Dirac-like point. In a two-dimensional system, the Dirac-like point is usually a triple degeneracy realized by two dipoles and a monopole at the gamma point, which can exhibit the high transmission properties of a double-zero medium (that is, both the dielectric constant and the magnetic permeability are zero). The semi-quasi-Dirac point is a linear degenerate monopole and dipole in only one direction. Its remarkable characteristic is that it can realize anisotropic transmission of electromagnetic waves, that is, it exhibits the double-zero medium properties of the Dirac point in this direction, and the single-zero medium properties (that is, the dielectric constant or magnetic permeability is zero) in the vertical direction. The anisotropic transmission characteristics of semi-quasi-Dirac materials can be used to achieve efficient control of electromagnetic waves.

[0004] However, although photonic crystals have shown great application potential in 5G communications, existing technologies still have some obvious shortcomings and challenges. First, traditional photonic crystal bandgap electromagnetic wave controllers are mainly limited to the reflection control of electromagnetic waves, and do not involve other more complex control methods. This limitation has limited its application in 5G communications to a certain extent.

[0005] Secondly, for electromagnetic wave controllers of Dirac point-like structures, their high transmission control is limited by the incident angle. This means that in practical applications, such controllers can only control the transmission of electromagnetic waves with normal incidence, but cannot effectively control electromagnetic waves with oblique incidence or other angles. This undoubtedly limits the application of electromagnetic wave controllers of Dirac point-like structures in complex communication environments.

[0006] In addition, the semi-quasi-Dirac points of the two-dimensional model also face challenges in the anisotropic transmission control of electromagnetic waves. Since they are severely limited to the polarization direction, this type of controller can only perform anisotropic transmission control on a single TE or TM mode electromagnetic wave. Moreover, the control of electromagnetic waves by semi-quasi-Dirac points in two-dimensional photonic crystals is mainly limited to the XY directions, and does not involve the transmission in the Z direction. This limits its ability to fully control electromagnetic waves in three-dimensional space.

[0007] In summary, although photonic crystals have shown great application potential in 5G communications, existing technologies still have many challenges and limitations. Summary of the invention

[0008] To this end, an embodiment of the present invention provides a microwave transmission controller based on dual semi-quasi-Dirac points and a preparation method, which are used to solve the problems that the traditional photonic crystal bandgap electromagnetic wave controller in the prior art is mainly limited to the reflection control of electromagnetic waves, and does not involve other more complex control methods; for the electromagnetic wave controller of the quasi-Dirac point, its control ability is mainly concentrated in the transmission aspect, and also lacks diversity; the anisotropic transmission control of electromagnetic waves by the semi-quasi-Dirac point of the existing two-dimensional model is severely limited to the polarization direction, and its control range is limited to the XY directions, and it fails to achieve all-round electromagnetic wave control.

[0009] In order to solve the above problems, an embodiment of the present invention provides a microwave transmission controller based on dual semi-Dirac-like points, wherein the controller comprises a plurality of three-dimensional anisotropic photonic crystal model lattice units arranged in an array, and the controller is in the form of a rectangular parallelepiped, wherein the three-dimensional anisotropic photonic crystal simultaneously has two semi-Dirac-like points.

[0010] In one embodiment of the present invention, the lattice unit of the three-dimensional anisotropic photonic crystal model is composed of three dielectric pillars crossing along three vertical directions under an air background.

[0011] In one embodiment of the present invention, the three dielectric columns crossing along three vertical directions have different sizes, and the cross sections along the vertical directions are all square.

[0012] In one embodiment of the present invention, the three dielectric columns crossing in three vertical directions are made of the same material.

[0013] In one embodiment of the present invention, the material includes but is not limited to silicon and composite ceramics.

[0014] In one embodiment of the present invention, the structural parameters of the three dielectric columns crossing along three vertical directions are: s Between 5-30, x Between 0.1a-0.15a, l y , l z are between 0.3a-0.35a, among which ζ s represents the dielectric constant of three dielectric pillars crossing in three perpendicular directions, l x , l y and l z They represent the cross-sectional side lengths of the dielectric column along the x-axis, y-axis and z-axis respectively, and a represents the photonic crystal lattice constant.

[0015] In one embodiment of the present invention, the photonic crystal lattice constant a has a value range of 3 mm-1 m, wherein the photonic crystal lattice constant a represents the side length of a lattice unit of a three-dimensional anisotropic photonic crystal model.

[0016] The embodiment of the present invention further provides a method for preparing a microwave transmission controller based on a double semi-Dirac point, the method comprising:

[0017] Constructing a plurality of three-dimensional anisotropic photonic crystal model lattice units, wherein the three-dimensional anisotropic photonic crystal has two semi-Dirac-like points simultaneously;

[0018] A plurality of three-dimensional anisotropic photonic crystal model lattice units are arranged in an array to obtain a rectangular controller.

[0019] In one embodiment of the present invention, the lattice unit of the three-dimensional anisotropic photonic crystal model is composed of three dielectric pillars crossing along three vertical directions under an air background, the three dielectric pillars crossing along three vertical directions have different sizes, and the cross-sections along the vertical directions are all square, and the three dielectric pillars crossing along three vertical directions are made of the same material, which includes but is not limited to silicon and composite ceramics.

[0020] In one embodiment of the present invention, the structural parameters of the three dielectric columns crossing along three vertical directions are: ε s Between 5-30, x Between 0.1a-0.15a, l y , l z are all between 0.3a-0.35a, where a represents the photonic crystal lattice constant, and the value range of the photonic crystal lattice constant a is 3mm-1m. The photonic crystal lattice constant a represents the side length of the lattice unit of the three-dimensional anisotropic photonic crystal model, εs represents the dielectric constant of three dielectric pillars crossing in three perpendicular directions, l x , l y and l z Respectively represent the cross-sectional side lengths of the dielectric column along the x-axis, y-axis, and z-axis directions.

[0021] It can be seen from the above technical solutions that the present invention has the following beneficial effects:

[0022] The embodiment of the present invention provides a microwave transmission controller based on a double semi-Dirac point and a preparation method. The controller designed by the present invention can realize anisotropic transmission of electromagnetic waves at a frequency of 10 GHz. The present invention can adjust the central operating frequency by changing the geometric parameters and electromagnetic parameters of the photonic crystal. The present invention can adjust the direction of anisotropic transmission of electromagnetic waves by rotating the direction of the photonic crystal. When the electromagnetic wave is incident along the Z direction, the controller designed by the present invention can obtain a high transmission result at a small angle regardless of whether the electric field is fixed along the X direction or the magnetic field is fixed along the Y direction. The present invention gives full play to the role of photonic crystals in 5G communications and explores more advanced photonic crystal control technologies, which will help promote the further development of 5G communication technology and lay a solid foundation for future communication technologies. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] In order to more clearly illustrate the implementation cases of the present invention or the technical solutions in the prior art, the following is a brief description of the drawings required for use in the embodiments. By referring to the drawings, the features and advantages of the present invention will be more clearly understood. The drawings are schematic and should not be understood as limiting the present invention in any way. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work. Among them:

[0024] Figure 1 A schematic structural diagram of a microwave transmission controller based on double semi-Dirac-like points provided in an embodiment;

[0025] Figure 2 is a schematic diagram of the structure of a lattice unit of a three-dimensional anisotropic photonic crystal model in an embodiment,

[0026] Figure 3 A schematic diagram of a lattice unit and its energy band structure of a three-dimensional anisotropic photonic crystal model in an embodiment;

[0027] Figure 4 Schematic diagram of electromagnetic waves entering the photonic crystal array along the X direction and the electric field entering the photonic crystal array along the Z direction in the embodiment;

[0028] Figure 5 Schematic diagram of the effect of frequency and incident angle on transmittance when the electromagnetic wave is incident along the Z direction with the electric field and magnetic field directions fixed respectively in the embodiment;

[0029] Figure 6 Schematic diagram of the effect of frequency and incident angle on transmittance when the electromagnetic wave is incident along the Z direction with the electric field and magnetic field directions fixed respectively in the embodiment;

[0030] Figure 7 The present invention is a flow chart of a method for preparing a microwave transmission controller based on double semi-Dirac points provided in an embodiment.

[0031] Figure numerals in the specification: 1. lattice unit of three-dimensional anisotropic photonic crystal model; 11. dielectric column along the x-axis direction; 12. dielectric column along the y-axis direction; 13. dielectric column along the z-axis direction. DETAILED DESCRIPTION

[0032] In order to make the purpose, technical solution and advantages of the embodiments of the present invention clearer, the technical solution in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0033] Embodiment 1

[0034] Solve the problems that the traditional photonic crystal bandgap electromagnetic wave controller in the prior art is mainly limited to the reflection control of electromagnetic waves, and does not involve other more complex control methods; for the electromagnetic wave controller of the Dirac point, its control ability is mainly concentrated in the transmission, and also lacks diversity; the anisotropic transmission control of electromagnetic waves by the semi-Dirac point of the existing two-dimensional model is severely limited to the polarization direction, and its control range is limited to the XY direction, and it fails to achieve all-round electromagnetic wave control. Figure 1 As shown, an embodiment of the present invention provides a microwave transmission controller based on dual semi-Dirac-like points, the controller comprising a plurality of three-dimensional anisotropic photonic crystal model lattice units 1 arranged in an array, the controller being in the shape of a rectangular parallelepiped, wherein the three-dimensional anisotropic photonic crystal simultaneously has two semi-Dirac-like points.

[0035] It can be seen from the above technical solution that the present invention proposes a microwave transmission controller based on double semi-class Dirac points, which includes a plurality of three-dimensional anisotropic photonic crystal model lattice units arranged in an array, realizing the simultaneous existence of two types of semi-class Dirac points of three-dimensional anisotropic photonic crystals. Specifically, one type of semi-class Dirac points: a triple degenerate mode of two electric dipoles + one magnetic dipole; the second type of semi-class Dirac points: a triple degenerate mode of two magnetic dipoles + one electric dipole. The model structure designed by the present invention can realize double-zero dielectric properties in four cases within a frequency range of 10GHz: (1) transmission in the Z direction, the electric field is along the X direction; (2) transmission in the Z direction, the electric field is along the Y direction; (3) transmission in the Y direction, the electric field is along the X direction; (4) transmission in the Y direction, the electric field is along the X direction. And the present invention can achieve high transmission properties within a small incident angle range. The present invention gives full play to the role of photonic crystals in 5G communications and explores more advanced photonic crystal control technologies, which will help promote the further development of 5G communication technology and lay a solid foundation for future communication technologies.

[0036] In this embodiment, Figure 2 The structure diagram of the lattice unit of the three-dimensional anisotropic photonic crystal model is shown in FIG. The structure is composed of three dielectric pillars crossing along three vertical directions (x-axis, y-axis, and z-axis) under an air background, namely, dielectric pillar 11 along the x-axis direction, dielectric pillar 12 along the y-axis direction, and dielectric pillar 13 along the z-axis direction. The three dielectric pillars crossing along the three vertical directions are made of the same material, including but not limited to silicon and composite ceramics.

[0037] In this embodiment, the three dielectric pillars crossing along three vertical directions have different sizes, and the cross-sections along the vertical directions are all square. Specifically, the structural parameters of the three dielectric pillars crossing along three vertical directions are: ε s Between 5-30, x Between 0.1a-0.15a, l y , l z are between 0.3a-0.35a, where ε s represents the dielectric constant of three dielectric pillars crossing in three perpendicular directions, l x , l y and l z They represent the cross-sectional side lengths of the dielectric column along the x-axis, y-axis and z-axis respectively, and a represents the photonic crystal lattice constant.

[0038] It should be noted here that after a lot of calculations we concluded that: ε s Between 5-30, x Between 0.1a-0.15a, l y , l zWhen both are between 0.3a-0.35a, we can always obtain a double semi-Dirac-like point.

[0039] Specifically, the value range of the photonic crystal lattice constant a is 0.01 mm-3 mm, wherein the photonic crystal lattice constant a represents the side length of a lattice unit of a three-dimensional anisotropic photonic crystal model.

[0040] It should be noted here that the selection of the specific value of a depends on the operating frequency to be adopted.

[0041] In order to further illustrate the advantages of the present invention, Figures 3 to 6 To elaborate.

[0042] In a specific embodiment of the present application, Figure 3 (a) is a schematic diagram of the structure of the lattice unit of the three-dimensional anisotropic photonic crystal model, where the photonic crystal lattice constant a = 1.68 cm; the dielectric constant ε of the three dielectric pillars crossing along three vertical directions s =9.85; the cross-sectional side length l of the dielectric column 11 along the x-axis direction x =0.126a, the cross-sectional side length l of the dielectric column 12 along the y-axis direction y =0.32a, the cross-sectional side length l of the dielectric column 13 in the z-axis direction z =0.32a. Figure 3 (b) is a schematic diagram of the band structure of the photonic crystal, with the path being 0.2Y-Γ-0.2X. We can see that at a frequency of 10 GHz, the band structure has two semi-Dirac-like points at the gamma point, f SD1 =9.65GHz, f SD2 =10.6GHz. The low frequency f SD1 The semi-quasi-Dirac point is a triple degenerate composed of a magnetic dipole in the X direction and an electric dipole in the YZ direction. SD2 A semi-quasi-Dirac point is a triple degenerate consisting of a point dipole in the X direction and a magnetic dipole in the YZ direction.

[0043] By analyzing the various degenerate modes of the band structure, we can infer the effective parameter components of this photonic crystal. Through the effective medium theory, the originally complex photonic crystal can be analyzed as a simple uniform material, and the effective dielectric constant ε eff and effective magnetic permeability μ eff Due to the anisotropy of the structure, the effective dielectric constant ε eff is a tensor whose components along the x-axis, y-axis, and z-axis are ε x,eff , ε y,eff and ε z,eff Similarly, the effective magnetic permeability μ effIt is also a tensor whose components along the x-axis, y-axis, and z-axis are μ x,eff , μ y,eff and μ z,eff At the low-frequency semi-Dirac-like point, its effective parameter component is ε y,eff =ε z,eff =μ x,eff = 0, through the effective parameters we can get: if the electromagnetic wave is incident along the Z direction, the electric field is along the Y direction, or the electromagnetic wave is incident along the Y direction, the electric field is along the Z direction, the double zero material properties can be achieved at the low-frequency semi-quasi-Dirac point. At the high-frequency semi-quasi-Dirac point, its effective parameter component is ε x,eff =μ z,eff =μ y,eff = 0, through the effective parameters we can get: if the electromagnetic wave is incident along the Z direction and the electric field is along the X direction, or the electromagnetic wave is incident along the Y direction and the electric field is along the X direction, double zero material properties can be achieved at the high-frequency semi-quasi-Dirac point. If the electromagnetic wave is incident along the X direction and the electric field is along the Y / Z direction, single zero material properties are exhibited at both semi-quasi-Dirac points.

[0044] In order to verify the correctness of the effective parameters, we incident electromagnetic waves into the photonic crystal array (the controller designed by the present invention) from three directions and at different angles.

[0045] Figure 4 (a) is a schematic diagram of electromagnetic waves entering the photonic crystal array along the X direction and the electric field along the Z direction, where N x is the number of lattice periods in the X direction. Figure 4 (b) is N x = 10, and the electromagnetic wave transmittance is affected by the frequency and the incident angle when the electric field direction is fixed along the Z direction. It is worth noting that N here has no range limit, we just randomly select one to verify the above energy band analysis. The dotted lines in the figure represent the frequencies corresponding to the two semi-quasi-Dirac points.

[0046] Figure 5 When the electromagnetic wave is incident along the Z direction, the frequency and incident angle have an effect on the transmittance when the electric field and magnetic field directions are fixed. z = 10, and the electric field direction is fixed in the X direction. The relationship between the transmittance and the incident angle in the yz plane and the frequency of the electromagnetic wave. z =10, and the magnetic field direction is fixed in the Y direction. The relationship between the transmittance and the incident angle in the xz plane and the frequency of the electromagnetic wave.

[0047] Figure 6 When the electromagnetic wave is incident along the Z direction, the frequency and incident angle have an effect on the transmittance when the electric field and magnetic field directions are fixed. z= 10, and the electric field direction is fixed in the Y direction. The relationship between the transmittance and the incident angle in the xz plane and the frequency of the electromagnetic wave. z =10, and the direction of the magnetic field is fixed in the X direction. The relationship between the transmittance and the incident angle in the xz plane and the frequency of the electromagnetic wave.

[0048] Comparison conclusion:

[0049] When the electromagnetic wave is incident along the X direction, f SD1 to f SD2 There is total reflection between them, which is consistent with the conclusion corresponding to the energy band. When the electromagnetic wave is incident along the Z direction and the electric field is incident along the X direction, f SD2 It is the high transmission property of the double-zero medium, and there is also high transmission that does not fluctuate with frequency within the small angle range of incidence; when the magnetic field is fixed along the Y direction, there is also high transmission at small angles. When the electromagnetic wave is incident along the Z direction and the electric field is incident along the Y direction, f SD1 The double-zero medium has high transmittance properties, and also has high transmittance that fluctuates with frequency within a small angle of incidence; when the magnetic field is fixed along the X direction, there is also high transmittance at a small angle, but the effect is poor.

[0050] Embodiment 2

[0051] like Figure 7 As shown, the present invention provides a method for preparing a microwave transmission controller based on a double half-Dirac point. The system is used to prepare the microwave transmission controller based on a double half-Dirac point of the above embodiment 1, and specifically includes:

[0052] Constructing a plurality of three-dimensional anisotropic photonic crystal model lattice units, wherein the three-dimensional anisotropic photonic crystal has two semi-Dirac-like points simultaneously;

[0053] A plurality of three-dimensional anisotropic photonic crystal model lattice units are arranged in an array to obtain a rectangular controller.

[0054] In this embodiment, the lattice unit 1 of the three-dimensional anisotropic photonic crystal model is composed of three dielectric pillars crossing along three vertical directions under the air background. The three dielectric pillars crossing along three vertical directions have different sizes, and the cross-sections along the vertical directions are all square. The three dielectric pillars crossing along three vertical directions are made of the same material, including but not limited to silicon and composite ceramics.

[0055] In this embodiment, the structural parameters of three dielectric columns crossing in three vertical directions are: s Between 5-30, x Between 0.1a-0.15a, l y , l zare all between 0.3a-0.35a, where a represents the photonic crystal lattice constant, and the value range of the photonic crystal lattice constant a is 3mm-1m. The photonic crystal lattice constant a represents the side length of the lattice unit of the three-dimensional anisotropic photonic crystal model, ε s represents the dielectric constant of three dielectric pillars crossing in three perpendicular directions, l x , l y and l z Respectively represent the cross-sectional side lengths of the dielectric column along the x-axis, y-axis, and z-axis directions.

[0056] A method for preparing a microwave transmission controller based on double and half-Dirac points in this embodiment is used to prepare the aforementioned microwave transmission controller based on double and half-Dirac points. Therefore, the specific implementation method of the method for preparing a microwave transmission controller based on double and half-Dirac points can be found in the embodiment section of the microwave transmission controller based on double and half-Dirac points in the previous text. In order to avoid redundancy, it will not be repeated here.

[0057] Note that the above are only preferred embodiments of the present invention and the technical principles used. Those skilled in the art will understand that the present invention is not limited to the specific embodiments described herein, and that various obvious changes, readjustments and substitutions can be made by those skilled in the art without departing from the scope of protection of the present invention. Therefore, although the present invention has been described in more detail through the above embodiments, the present invention is not limited to the above embodiments, and may include more other equivalent embodiments without departing from the concept of the present invention, and the scope of the present invention is determined by the scope of the appended claims.

Claims

1. A microwave transmission controller based on double semi-Dirac points, characterized in that: The invention comprises a plurality of three-dimensional anisotropic photonic crystal model lattice units arranged in an array, wherein the controller is a rectangular parallelepiped, wherein the three-dimensional anisotropic photonic crystal has two semi-quasi-Dirac points at the same time; the three-dimensional anisotropic photonic crystal model lattice unit is composed of three dielectric pillars crossing along three vertical directions under an air background; the three dielectric pillars crossing along three vertical directions have different sizes, and the cross sections along the vertical direction are all square.

2. The microwave transmission controller based on double semi-Dirac points according to claim 1 is characterized in that: The three dielectric columns crossing in three vertical directions are made of the same material.

3. The microwave transmission controller based on double semi-Dirac points according to claim 2 is characterized in that: The materials include but are not limited to silicon and composite ceramics.

4. The microwave transmission controller based on double semi-Dirac points according to claim 1, characterized in that: The structural parameters of the three dielectric columns crossing in three vertical directions are: Between 5-30, Between 0.1 -0.15 between, , Both between 0.3 -0.35 between Represents the dielectric constant of three dielectric pillars crossing in three perpendicular directions, , and Respectively indicate along axis, Axis and The cross-sectional side length of the dielectric column in the axial direction, represents the photonic crystal lattice constant.

5. The microwave transmission controller based on double semi-Dirac points according to claim 4 is characterized in that: The photonic crystal lattice constant The value range is 3mm-1m, where the photonic crystal lattice constant Represents the side length of the lattice unit of the three-dimensional anisotropic photonic crystal model.

6. A method for preparing a microwave transmission controller based on double semi-Dirac points, characterized in that: The method is used to prepare the microwave transmission controller based on the double semi-Dirac point according to any one of claims 1 to 5, comprising: Constructing a plurality of three-dimensional anisotropic photonic crystal model lattice units, wherein the three-dimensional anisotropic photonic crystal has two semi-Dirac-like points simultaneously; A plurality of three-dimensional anisotropic photonic crystal model lattice units are arranged in an array to obtain a rectangular controller.

7. The method for preparing a microwave transmission controller based on double semi-Dirac points according to claim 6, characterized in that: The lattice unit of the three-dimensional anisotropic photonic crystal model is composed of three dielectric pillars crossing along three vertical directions under an air background. The three dielectric pillars crossing along three vertical directions have different sizes, and the cross-sections along the vertical directions are all square. The three dielectric pillars crossing along three vertical directions are made of the same material, which includes but is not limited to silicon and composite ceramics.

8. The method for preparing a microwave transmission controller based on double semi-Dirac points according to claim 6, characterized in that: The structural parameters of the three dielectric columns crossing in three vertical directions are: Between 5-30, Between 0.1 -0.15 between, , Both between 0.3 -0.35 Between, among them, represents the photonic crystal lattice constant, photonic crystal lattice constant The value range is 3mm-1m, and the photonic crystal lattice constant represents the side length of the lattice unit of the three-dimensional anisotropic photonic crystal model, Represents the dielectric constant of three dielectric pillars crossing in three perpendicular directions, , and Respectively indicate along axis, Axis and The cross-sectional side length of the dielectric column in the axial direction.

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