An optical topology conversion method and system based on a composite layered periodic structure of magneto-optical materials and a graphene-coated dielectric layer.

Abstract

This invention relates to an optical topology conversion method and system based on a composite layered periodic structure of magneto-optical material and a dielectric layer covered with graphene. The method includes (1) establishing a composite layered periodic structure model of the composite layer of magneto-optical material and a dielectric layer covered with graphene, which is composed of alternating layers of magneto-optical material and dielectric layers covered with graphene; (2) analyzing and calculating the dielectric tensor of the composite layered periodic structure; (3) calculating and determining the expressions for the magnetic field and electric field in the composite layered periodic structure and the corresponding boundary conditions; (4) calculating the transfer matrix of the composite layered periodic structure; (5) deriving the dispersion equation of the infinite periodic structure using Bloch's theorem; and (6) based on the dispersion equation, adjusting the applied magnetic field to obtain the change of the isofrequency surface, thereby realizing optical topology conversion. This invention utilizes the alternating arrangement of magneto-optical material layers and dielectric layers covered with graphene to construct a hyperbolic material, which makes it easier to realize optical topology conversion and obtain new topological characteristics.

Description

Technical Field

[0001] This invention belongs to the field of optoelectronic information, specifically relating to an optical topology conversion method and system based on a composite layered periodic structure of magneto-optical materials and a dielectric layer covered with graphene. Background Technology

[0002] The application of radio frequency transmission lines in anisotropic layered hyperbolic metamaterials provides a foundation for further research on hyperbolic metamaterials. Hyperbolic metamaterials exhibit isofrequency surface transformations, or optical topological transformations, resulting from the shifts in the positive and negative values ​​of various components of the electromagnetic response parameters. These optical topological transformations induce the emergence of some exotic electromagnetic states, such as enhanced nonlinear effects at the transformation frequency and abrupt changes in energy density. Recent research has primarily focused on common metal-dielectric hyperbolic periodic structures or nanowire arrays.

[0003] Therefore, there is an urgent need in this field to further study the transformation of isofrequency surface topologies using different layered structures such as other artificial metamaterials and considering the presence of dissipation. Summary of the Invention

[0004] To address the aforementioned shortcomings in existing technologies, the present invention aims to provide an optical topology conversion method and system based on a dielectric composite layered periodic structure of magneto-optical materials and a graphene-coated film. Specifically, a novel material structure is used, comprising a dielectric material covered with an electrically anisotropic graphene film and a magneto-optical material, to construct a layered periodic material. By adjusting the external field strength of the magneto-optical material and the fill factor of the periodic material layers, its optical topology conversion can be calculated and studied.

[0005] To achieve the above-mentioned objectives, the present invention adopts the following technical solution:

[0006] An optical topology conversion method based on a composite layered periodic structure of magneto-optical materials and a dielectric layer covered with graphene includes the following steps:

[0007] (1) Establish a composite layered periodic structure model of magneto-optical material and dielectric layer covered with graphene. The composite layered periodic structure model is composed of alternating layers of magneto-optical material and dielectric layer covered with graphene.

[0008] (2) Analyze and calculate the dielectric tensor of the composite layered periodic structure;

[0009] (3) Calculate and determine the expressions for the magnetic field and electric field in the composite layered periodic structure and the corresponding boundary conditions;

[0010] (4) Calculate the transmission matrix of the composite layered periodic structure;

[0011] (5) Derive the dispersion equation for an infinite periodic structure from Bloch's theorem;

[0012] (6) Based on the dispersion equation, the change of the isofrequency surface is obtained by adjusting the external magnetic field, thereby realizing optical topology conversion.

[0013] As a preferred embodiment, step (2) includes:

[0014] Because a very thin layer of graphene is covered on the surface of the dielectric, the thickness is negligible;

[0015] The dielectric tensor of magneto-optical materials is:

[0016]

[0017] Wherein, the dielectric constant is ε x =ε MO The layer thickness is d2, ε z For the z-direction component, ε y The component in the y-direction;

[0018] The dielectric layer has a material permeability of μ1, a dielectric constant of ε1, and a layer thickness of d1.

[0019] The unit cell thickness of the composite layered periodic structure model is h = d1 + d2;

[0020] The z-axis is the direction of material layer stacking. The optical axis of the magneto-optical material coincides with the z-axis, that is, the direction of the applied magnetic field is the z-axis; the conductivity σ of graphene is used to characterize the surface current.

[0021] σ is the electrical conductivity of graphene, and its expression is:

[0022]

[0023] As a preferred embodiment, step (3) includes:

[0024] Since magneto-optical materials are electrically anisotropic, they only exhibit hyperbolic properties under TM polarization; under TM polarization, the boundary conditions must be considered. Continuity; k 1z Let k be the z-direction component of the wave vector in region one. 2z Let k be the z-direction component of the wave vector in region two. x Let be the wave vector component in the x-direction. and These represent the negative and positive x-components of the magnetic field on the left side of region one, respectively. and These represent the negative and positive x-components of the magnetic field on the right side of region one, respectively; the same applies to other regions. H 1y H 2y H 3y These represent the y-direction components of the magnetic fields in regions one, two, and three respectively; E 1x E2x Let x be the component of the electric field in regions one and two in the x-direction.

[0025] Calculate the TM wave, where the time component e -iωt These are independent components; region 1 is the electrolyte, region 2 is the magneto-optical material, and region 3 is the dielectric.

[0026] The magnetic field expressions in regions 1 and 2 are as follows:

[0027]

[0028] The expression for the tangential electric field, derived from the boundary conditions and electromagnetic field relations, is as follows:

[0029]

[0030] Wherein, 1- and 1+ represent the left and right sides of the interface between the two material layers, respectively;

[0031] Interface 1 is the interface between the magneto-optical material in region 1 and the graphene dielectric layer in region 2; Interface 2 is the interface between the graphene dielectric layer in region 2 and the magneto-optical material layer in region 3; Interface 3 is the interface between the magneto-optical material in region 3 and the graphene dielectric layer in the next cycle of the material.

[0032] From the electromagnetic boundary conditions, it can be seen that at interface 1, the tangential component of the electric field is conserved, but the boundary conditions of the magnetic field change due to the generation of the surface current Js.

[0033]

[0034] in,

[0035] Then, at interface 1, there is:

[0036] H 1y (x,0)=H 2y (x,0)+J s (x,0)

[0037] E 2x (x,0)=E 1x (x,0)

[0038] And because:

[0039] J s =σE 1(2)x (x,0) is calculated to be:

[0040]

[0041] The results were:

[0042]

[0043] make:

[0044]

[0045] get:

[0046]

[0047] make Right now

[0048]

[0049] The final result is:

[0050]

[0051] As a preferred embodiment, step (4) includes:

[0052] The relationship between the left side of interface 2 and the left side of interface 1 is as follows:

[0053]

[0054] and These represent the negative and positive x-components of the magnetic field on the left side of region two, respectively. and These represent the negative and positive x-direction components of the magnetic field on the right side of region two, respectively; the same applies to other regions. and These represent the negative and positive x-direction components of the magnetic field on the left side of region three, respectively.

[0055] Therefore, the transmission matrix from the left side of interface 1 to the left side of interface 2 is M1. Similarly, the transmission matrix from the left side of interface 2 to the left side of interface 3 can be obtained as follows:

[0056]

[0057] in,

[0058]

[0059] Then we have:

[0060]

[0061] The transmission matrix for electromagnetic wave propagation through a cycle consisting of two material layers, i.e., from the left side of interface 1 to the left side of interface 3, is as follows:

[0062]

[0063] in,

[0064]

[0065] Then, within the entire structure, we can obtain:

[0066]

[0067] As a preferred embodiment, step (5) includes: In the double-layer periodic structure, according to Bloch's theorem, we have:

[0068]

[0069] The dispersion equation for an infinite periodic structure is obtained:

[0070]

[0071] Substituting the matrix elements, we get:

[0072]

[0073] In TM mode, the wave vector in the material layer is represented as:

[0074]

[0075] Where, ω p ω is the plasma frequency. p =7.85×10 11 Hz, where c is the speed of light.

[0076] As a preferred embodiment, step (6) includes:

[0077] With ω p As the normalization frequency, let k x c / ω p 、kc / ω p For planar coordinates, ω / ω p Draw a topology transformation diagram with the vertical axis as the ordinate;

[0078] Where, ω p =2πc / 200h, ε MO =14, d1=fh, d2=(1-f)h, ε MO / ε2=1.17;

[0079] Magneto-optical materials, as electrically anisotropic materials, only exhibit hyperbolic properties under TM polarization;

[0080] Let ω c / ω p With the fill factor f = 2 unchanged, compare the topological transformation of the isofrequency surface when the fill factor f = 0.6 and 0.8;

[0081] When f = 0.6, at ω / ω p New isofrequency surfaces, i.e. new topologies, appear when the frequency is equal to 0.367, 2.236, and 3.234.

[0082] This invention also provides an optical topology conversion system based on a composite layered periodic structure of magneto-optical materials and graphene, applying the optical topology conversion method described in any of the preceding embodiments. The optical topology conversion system includes:

[0083] The model building module is used to model the composite layered periodic structure of magneto-optical materials and dielectric layers covered with graphene. The composite layered periodic structure model consists of alternating layers of magneto-optical materials and dielectric layers covered with graphene.

[0084] The analysis and calculation module is used to analyze and calculate the dielectric tensor of the composite layered periodic structure, as well as to calculate and determine the magnetic field and electric field expressions and corresponding boundary conditions in the composite layered periodic structure, and to calculate the transmission matrix of the composite layered periodic structure.

[0085] The dispersive relation equation derivation module is used to derive the dispersive equation for an infinite periodic structure based on Bloch's theorem.

[0086] The optical topology conversion module is used to achieve optical topology conversion by adjusting the applied magnetic field based on the dispersion equation to obtain the change of the isofrequency surface.

[0087] Compared with the prior art, the beneficial effects of this invention are:

[0088] (1) This invention utilizes alternating layers of magneto-optical material and dielectric layers covered with graphene to construct a new hyperbolic material. It is not limited to existing metal-dielectric traditional hyperbolic materials, thus broadening the range of material selection and making it easier to achieve optical topological transformation and obtain new topological structural characteristics.

[0089] (2) This invention is mainly designed based on the transfer matrix and Bloch's theorem, which makes it easier to calculate and derive accurate dispersion relations, and the calculation process has smaller errors. Attached Figure Description

[0090] Figure 1 This is a schematic diagram of the composite layered periodic structure model of Embodiment 1 of the present invention;

[0091] Figure 2 This is a schematic diagram of the isofrequency surface topology transformation with a fill factor of 0.6 according to an embodiment of the present invention;

[0092] Figure 3 This is a schematic diagram of the topology transformation of the isofrequency surface with a fill factor of 0.8 according to an embodiment of the present invention;

[0093] Figure 4This is a schematic diagram of the new topology obtained in an embodiment of the present invention;

[0094] Figure 5 This is a schematic diagram of another new topology obtained from an embodiment of the present invention;

[0095] Figure 6 This is a schematic diagram of another new topology obtained from an embodiment of the present invention. Detailed Implementation

[0096] The technical solution of the present invention will be further explained and illustrated below through specific embodiments.

[0097] The optical topology conversion method based on a composite layered periodic structure of magneto-optical materials and a dielectric layer covered with graphene, according to an embodiment of the present invention, includes the following steps:

[0098] Step 1: Establish a composite layered periodic structure model of magneto-optical material and dielectric composite layer covered with graphene layer.

[0099] Specifically, the composite layered periodic structure model consists of alternating layers of magneto-optical material and dielectric layers covered with graphene, such as... Figure 1 As shown, a very thin graphene layer, negligible in thickness, is coated on the surface of the dielectric.

[0100] The second step is to analyze and calculate the dielectric tensor of the composite layered periodic structure.

[0101] Because a very thin layer of graphene is covered on the surface of the dielectric, the thickness is negligible;

[0102] The dielectric tensor of magneto-optical materials is:

[0103]

[0104] Wherein, the dielectric constant is ε x =ε MO The layer thickness is d2, ε z The z-axis component;

[0105] The dielectric layer has a material permeability of μ1, a dielectric constant of ε1, and a layer thickness of d1.

[0106] The unit cell thickness (i.e., the thickness of one periodic layer) of the composite layered periodic structure model is h = d1 + d2;

[0107] The z-axis represents the direction of material layer stacking. The optical axis of the magneto-optical material coincides with the z-axis, meaning the direction of the applied magnetic field is along the z-axis. The conductivity σ of graphene is used to characterize the dielectric constant ε. MODue to the symmetry of the material, the propagation characteristics of electromagnetic waves are discussed only in the xz plane; the y-direction is the same as the x-direction. Furthermore, considering the electrical anisotropy of the graphene layer, a surface current is generated when graphene adheres to a dielectric surface. In this case, for ease of analysis, the conductivity σ of graphene is used to characterize the surface current.

[0108] The third step is to calculate and determine the expressions for the magnetic and electric fields and the corresponding boundary conditions in the composite layered periodic structure.

[0109] Since magneto-optical materials are electrically anisotropic, they only exhibit hyperbolic properties under TM polarization. Therefore, we will only consider the case under TM polarization here; under TM polarization, we will consider the boundary conditions. Continuity;

[0110] k 1z Let k be the z-direction component of the wave vector in region one. 2z Let k be the z-direction component of the wave vector in region two. x Let be the wave vector component in the x-direction. and These represent the negative and positive x-components of the magnetic field on the left side of region one, respectively. and These represent the negative and positive x-components of the magnetic field on the right side of region one, and the same applies to other regions; H 1y H 2y H 3y These represent the y-direction components of the magnetic fields in regions one, two, and three respectively; E 1x E 2x Let x be the component of the electric field in regions one and two in the x-direction.

[0111] Calculate the TM wave, where the time component e -iωt These are independent components; region 1 is the electrolyte, region 2 is the magneto-optical material, and region 3 is the dielectric.

[0112] The magnetic field expressions in regions 1 and 2 are as follows:

[0113]

[0114] The expression for the tangential electric field, derived from the boundary conditions and electromagnetic field relations, is as follows:

[0115]

[0116] Wherein, 1- and 1+ represent the left and right sides of the interface between the two material layers, respectively; Interface 1 is the interface between the magneto-optical material in region one and the graphene dielectric layer in region two; Interface 2 is the interface between the graphene dielectric layer in region two and the magneto-optical material layer in region three; Interface 3 is the interface between the magneto-optical material in region three and the graphene dielectric layer in the next cycle of the material.

[0117] From the electromagnetic field boundary conditions, it can be seen that at interface 1, the tangential component of the electric field is conserved, but the boundary conditions of the magnetic field change due to the generation of surface current.

[0118]

[0119] in,

[0120] Then, at interface 1, there is:

[0121] H 1y (x,0)=H 2y (x,0)+J s (x,0)

[0122] E 2x (x,0)=E 1x (x,0)

[0123] And because:

[0124] J s =σE 1(2)x (x,0)

[0125] The calculation yielded:

[0126]

[0127] The results were:

[0128]

[0129] make:

[0130]

[0131] get:

[0132]

[0133] make Right now

[0134]

[0135] The final result is:

[0136]

[0137] Step 4: Calculate the transmission matrix of the composite layered periodic structure.

[0138] Specifically, the relationship between the left side of interface 2 and the left side of interface 1 is as follows:

[0139]

[0140] in, and These represent the negative and positive x-components of the magnetic field on the left side of region two, respectively. and These represent the negative and positive x-components of the magnetic field on the right side of region two, respectively; the same applies to other regions.

[0141] Therefore, the transmission matrix from the left side of interface 1 to the left side of interface 2 is M1. Similarly, the transmission matrix from the left side of interface 2 to the left side of interface 3 can be obtained as follows:

[0142]

[0143] in,

[0144]

[0145] Then we have:

[0146]

[0147] The transmission matrix for electromagnetic wave propagation through a cycle consisting of two material layers, i.e., from the left side of interface 1 to the left side of interface 3, is as follows:

[0148]

[0149] in,

[0150]

[0151]

[0152] Then, within the entire structure, we can obtain:

[0153]

[0154] and These represent the negative and positive x-direction components of the magnetic field on the left side of region three, respectively.

[0155] Step 5: Derive the dispersion equation for an infinite periodic structure using Bloch's theorem. Specifically, in a two-layer periodic structure, according to Bloch's theorem:

[0156]

[0157] The dispersion equation for an infinite periodic structure is obtained:

[0158]

[0159] Substituting the matrix elements, we get:

[0160]

[0161] In TM mode, the wave vector in the material layer is represented as:

[0162]

[0163] Where, ω p ω is the plasma frequency. p =7.85×10 11 Hz, where c is the speed of light.

[0164] Step 6: Based on the dispersion equation, adjust the applied magnetic field to obtain the change of the isofrequency surface and realize optical topological conversion.

[0165] With ω p As the normalization frequency, let k x c / ω p ,kc / ω p For planar coordinates, ω / ω p Using the vertical axis, a topological transformation diagram is plotted to study the composite structure at the subwavelength scale. The layer thickness is much smaller than the incident wavelength, and the covering graphene is very thin, with negligible thickness.

[0166] Where, ω p =2πc / 200h, ε MO =14, d1=fh, d2=(1-f)h, ε MO / ε² = 1.17. As an electrically anisotropic material, the magneto-optical material only exhibits hyperbolic characteristics under TM polarization. The effect of changes in the applied magnetic field strength is not considered. The process is as follows:

[0167] Let ω c / ω p With the fill factor f = 2 unchanged, compare the topological transformation of the isofrequency surface when the fill factor f = 0.6 and 0.8, as follows: Figure 2 , 3 As shown. From the topological transformation diagram, we obtain that when f = 0.6, at ω / ω p New isofrequency surfaces, i.e. new topologies, appear when the frequencies are 0.367, 2.236, and 3.234, such as... Figure 4 , 5 As shown in Figure 6.

[0168] Corresponding to the optical topology conversion method described in the embodiments of the present invention, the embodiments of the present invention also provide an optical topology conversion system based on a composite layered periodic structure of magneto-optical materials and graphene, including a model building module, an analysis and calculation module, a dispersion relation equation derivation module, and an optical topology conversion module.

[0169] Specifically, the model building module is used to model the composite layered periodic structure of magneto-optical materials and dielectric layers covered with graphene; wherein, the composite layered periodic structure model is composed of alternating layers of magneto-optical materials and dielectric layers covered with graphene, such as... Figure 1 As shown, a very thin layer of graphene is coated on the surface of the dielectric, with a thickness that is negligible.

[0170] The analysis and calculation module is used to analyze and calculate the dielectric tensor of the composite layered periodic structure, as well as to calculate and determine the expressions for the magnetic and electric fields and corresponding boundary conditions in the composite layered periodic structure, and to calculate the transfer matrix of the composite layered periodic structure.

[0171] (a) Analyze and calculate the dielectric tensor of the composite layered periodic structure;

[0172] Because a very thin layer of graphene is covered on the surface of the dielectric, the thickness is negligible;

[0173] The dielectric tensor of magneto-optical materials is:

[0174]

[0175] Wherein, the dielectric constant is ε x =ε MO The layer thickness is d2, ε z The z-axis component;

[0176] The dielectric layer has a material permeability of μ1, a dielectric constant of ε1, and a layer thickness of d1.

[0177] The unit cell thickness (i.e., the thickness of one periodic layer) of the composite layered periodic structure model is h = d1 + d2;

[0178] The z-axis represents the direction of material layer stacking. The optical axis of the magneto-optical material coincides with the z-axis, meaning the direction of the applied magnetic field is along the z-axis. The conductivity σ of graphene is used to characterize the dielectric constant ε. MO Due to the symmetry of the material, the propagation characteristics of electromagnetic waves are discussed only in the xz plane; the y-direction is the same as the x-direction. Furthermore, considering the electrical anisotropy of the graphene layer, surface currents will be generated when graphene adheres to the surface of a dielectric.

[0179] (b) Calculate and determine the expressions for the magnetic and electric fields and the corresponding boundary conditions in the composite layered periodic structure.

[0180] Since magneto-optical materials are electrically anisotropic, they only exhibit hyperbolic properties under TM polarization. Therefore, we will only consider the case under TM polarization here; under TM polarization, we will consider the boundary conditions. Continuity;

[0181] Calculate the TM wave, where the time component e-iωt These are independent components; region 1 is the electrolyte, region 2 is the magneto-optical material, and region 3 is the dielectric.

[0182] The magnetic field expressions in regions 1 and 2 are as follows:

[0183]

[0184] The expression for the tangential electric field, derived from the boundary conditions and electromagnetic field relations, is as follows:

[0185]

[0186]

[0187] Wherein, 1- and 1+ represent the left and right sides of the interface between the two material layers, respectively;

[0188] From the electromagnetic field boundary conditions, it can be seen that at interface 1, the tangential component of the electric field is conserved, but the boundary conditions of the magnetic field change due to the generation of surface current.

[0189]

[0190] in,

[0191] Then, at interface 1, there is:

[0192] H 1y (x,0)=H 2y (x,0)+J s (x,0)E 2x (x,0)=E 1x (x,0)

[0193] And because:

[0194] J s =σE 1(2)x (x,0)

[0195] The calculation yielded:

[0196]

[0197] The results were:

[0198]

[0199] make:

[0200]

[0201] get:

[0202]

[0203] make Right now

[0204]

[0205] The final result is:

[0206]

[0207] (c) Calculate the transmission matrix of the composite layered periodic structure.

[0208] Specifically, the relationship between the left side of interface 2 and the left side of interface 1 is as follows:

[0209]

[0210] Therefore, the transmission matrix from the left side of interface 1 to the left side of interface 2 is M1. Similarly, the transmission matrix from the left side of interface 2 to the left side of interface 3 can be obtained as follows:

[0211]

[0212] in,

[0213]

[0214] Then we have:

[0215]

[0216] The transmission matrix for electromagnetic wave propagation through a cycle consisting of two material layers, i.e., from the left side of interface 1 to the left side of interface 3, is as follows:

[0217]

[0218] in,

[0219]

[0220] Then, within the entire structure, we can obtain:

[0221]

[0222] The dispersive relation equation derivation module is used to derive the dispersive equation for infinite periodic structures based on Bloch's theorem. Specifically, in a two-layer periodic structure, according to Bloch's theorem, we have:

[0223]

[0224] The dispersion equation for an infinite periodic structure is obtained:

[0225]

[0226] Substituting the matrix elements, we get:

[0227]

[0228] In TM mode, the wave vector in the material layer is represented as:

[0229]

[0230] The optical topology conversion module is used to achieve optical topology conversion by adjusting the applied magnetic field based on the dispersion equation to obtain the change of the isofrequency surface.

[0231] Specifically, ω p The plasma frequency is ω. p As the normalization frequency, let k x c / ω p ,kc / ω p For planar coordinates, ω / ω p Using the vertical axis, a topological transformation diagram is plotted to study the composite structure at the subwavelength scale. The layer thickness is much smaller than the incident wavelength, and the covering graphene is very thin, with negligible thickness.

[0232] Where, ω p =2πc / 200h, ε MO =14, d1=fh, d2=(1-f)h, ε MO / ε² = 1.17. As an electrically anisotropic material, the magneto-optical material only exhibits hyperbolic characteristics under TM polarization. The effect of changes in the applied magnetic field strength is not considered. The process is as follows:

[0233] Let ω c / ω p With the fill factor f = 2 unchanged, compare the topological transformation of the isofrequency surface when the fill factor f = 0.6 and 0.8, as follows: Figure 2 , 3 As shown.

[0234] When f = 0.6, at ω / ω p New isofrequency surfaces, i.e. new topologies, appear when the frequencies are 0.367, 2.236, and 3.234, such as... Figure 4 , 5 As shown in Figure 6.

[0235] The above description is merely a detailed explanation of two embodiments and principles of the present invention. For those skilled in the art, there may be changes in the specific implementation based on the ideas provided by the present invention, and these changes should also be considered within the scope of protection of the present invention.

Claims

1. A method of optical topological conversion based on a composite layered periodic structure of magneto-optical material and a dielectric layer covering graphene layer, characterized in that, The method comprises the following steps: (1) establishing a composite layered periodic structure model of magneto-optical material and dielectric composite layer covering graphene layer, the composite layered periodic structure model being formed by alternately arranging magneto-optical material layer and dielectric layer covering graphene layer; (2) analyzing and calculating the dielectric tensor of the composite layered periodic structure; (3) calculating and determining the expressions of magnetic field and electric field in the composite layered periodic structure and corresponding boundary conditions; (4) calculating the transfer matrix of the composite layered periodic structure; (5) deriving the dispersion equation of the infinite periodic structure from the Bloch theorem; (6) adjusting the applied magnetic field to obtain the change of the iso-frequency surface based on the dispersion equation, so as to realize optical topological conversion; Step (2) comprises: Since the dielectric surface is covered with a graphene layer with extremely thin thickness, the thickness can be ignored; The dielectric tensor of the magneto-optical material is: wherein the dielectric constant is ε x = ε MO , the layer thickness is d2, ε z is the z-direction component, and ε y is the y-direction component; The material permeability of the dielectric layer is μ1, the dielectric constant is ε1, and the layer thickness is d1; The unit cell thickness of the composite layered periodic structure model is h = d1 + d2; The z-axis is the direction of material layering, the optical axis of the magneto-optical material coincides with the z-axis, that is, the direction of the applied magnetic field is the z-axis; the conductivity σ of graphene is used to represent the surface current; Step (3) comprises: Since the magneto-optical material is electric anisotropic material, there exists hyperbolic characteristic only under TM polarization. Under TM polarization, continuity of boundary condition is considered k 1z is the z-direction component of wave vector in region one, k 2z is the z-direction component of wave vector in region two, k x is the x-direction component of wave vector; and are the x-negative and positive direction components of magnetic field on the left side of region one, respectively, and are the x-negative and positive direction components of magnetic field on the right side of region one, respectively; H 1y , H 2y , H 3y are the y-direction components of magnetic field in region one, two and three, respectively; E 1x , E 2x are the x-direction components of electric field in region one and two, respectively; The TM wave is calculated, where the time component e -iωt is the independent component; region 1 is an electrolyte, region 2 is a magneto-optic material, and region 3 is a dielectric; The magnetic field expressions in regions 1 and 2 are: The tangential electric field expression is obtained from the boundary conditions and the electromagnetic field relationship: Wherein, 1- and 1+ represent the left side and the right side of the interface between the two material layers respectively; interface 1 is the interface between the magneto-optical material in region one and the graphene-covered dielectric layer in region two; interface 2 is the interface between the graphene-covered dielectric layer in region two and the magneto-optical material layer in region three; interface 3 is the interface between the magneto-optical material in region three and the graphene-covered dielectric layer in the next period of the material; From the boundary conditions of electromagnetic field, at the interface 1, the tangential component of electric field is conserved, but the magnetic field changes due to the generation of surface current J s , i.e. wherein Then, at the interface 1, there is: H 1y (x,0) = H 2y (x,0) + J s (x,0) E 2x (x,0) = E 1x (x,0) And because: J s = σE1(2) x (x,0) The calculation result is: After sorting, we get: Let: We get: Let That is Finally, we get: Step (4) comprises: The relationship between the left side of interface 2 and the left side of interface 1 is: Therefore, the transfer matrix from the left side of interface 1 to the left side of interface 2 is M1, and the transfer matrix from the left side of interface 2 to the left side of interface 3 is obtained in the same way: Wherein, Then we have: Therefore, the transfer matrix from the left side of interface 1 to the left side of interface 3 in a period composed of two material layers is: Wherein, Then in the whole structure, we get: wherein, and Bx2L and Bx2R are the magnetic field components in the negative and positive x-directions, respectively, on the left side of region two, and Bx3L and Bx3R are the magnetic field components in the negative and positive x-directions, respectively, on the left side of region three; and Bx3L and Bx3R are the magnetic field components in the negative and positive x-directions, respectively, on the left side of region three; Step (5) comprises: In the two-layer periodic structure, according to the Bloch theorem, we have: The dispersion equation of the infinite periodic structure is obtained: After substituting the matrix elements, we get: Wherein, in the TM mode, the wave vector in the material layer is represented as: where ω p is the plasma frequency, ω p = 7.85 x 10 11 Hz, and c is the speed of light.

2. The method of optical topology conversion based on a composite layered periodic structure of a magneto-optical material and a dielectric layer covering graphene according to claim 1, characterized in that, Step (6) comprises: with ω p As the normalized frequency, let k x c / ω p , kc / ω p , as the plane coordinates, and ω / ω p as the longitudinal coordinate, the topological conversion diagram is drawn; where ω p = 2πc / 200h, ε MO = 14, d1= fh, d2= (1-f)h, ε MO / ε2= 1.17; The magneto-optical material is an electrically anisotropic material, which has hyperbolic characteristics only under TM polarization; Let ω / ω p = 2 invariant, the equal frequency surface topology conversion case is compared when the filling factor f = 0.6, 0.

8. When f = 0.6, new isofrequency surfaces, i.e. new topologies, appear at ω / ω p New isofrequency surfaces, i.e. new topologies, appear at ω / ω 0.367, 2.236, 3.

234.

3. An optical topology conversion system based on a layered periodic structure of a magneto-optical material and graphene, applying the optical topology conversion method according to any one of claims 1-2, characterized in that, Comprises: A model building module is configured to build a composite layered periodic structure model of magneto-optical material and dielectric composite layer covering graphene layer, the composite layered periodic structure model being formed by alternately arranging magneto-optical material layer and dielectric layer covering graphene layer; An analysis and calculation module is configured to analyze and calculate the dielectric tensor of the composite layered periodic structure, and to calculate and determine the expressions of magnetic field and electric field in the composite layered periodic structure and corresponding boundary conditions, and to calculate the transfer matrix of the composite layered periodic structure; A dispersion relation equation derivation module is configured to derive a dispersion equation of the infinite periodic structure according to the Bloch theorem; An optical topology conversion module is configured to adjust the variation of the equifrequency surface by adjusting an applied magnetic field based on the dispersion equation, so as to realize optical topology conversion.

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