CN111125900A - Method and system for calculating Casimir action force of anisotropic ferrite three-layer structure - Google Patents
Method and system for calculating Casimir action force of anisotropic ferrite three-layer structure Download PDFInfo
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Abstract
The invention discloses a method and a system for calculating the Casimir action of an anisotropic ferrite three-layer structure, and relates to a system for calculating the Casimir action of the anisotropic ferrite three-layer structure, which comprises the following steps: the establishing module is used for establishing a model of the anisotropic ferrite three-layer structure; a determination module for determining electromagnetic properties of the anisotropic ferrite; a first calculation module for calculating a transmission matrix of the uniaxial anisotropic material layer; the second calculation module is used for calculating a reflection coefficient matrix of the anisotropic material three-layer structure; and the third calculation module is used for calculating the Casimir acting force of the anisotropic ferrite three-layer structure model. According to the method, the Casimir acting force of the anisotropic ferrite three-layer structure is calculated according to the scattering theory, and the effect of the Casimir acting force of the anisotropic ferrite three-layer structure can be accurately calculated through the scattering theory.
Description
Technical Field
The invention relates to the technical field of quantum optics, in particular to a method and a system for calculating Casimir action force of an anisotropic ferrite three-layer structure.
Background
From the quantum mechanics perspective, the vacuum is not all nothing, and the change of the vacuum fluctuation zero energy generates the macroscopic interaction force, namely the Casimir effect. While the Casimir force is the most easily measured effect on quantum vacuum fluctuation in the macroscopic world, accurate knowledge of the Casimir force is also the key point for accurate force measurement in many distance ranges on the nanometer to millimeter scale. Casimir calculates the force between a pair of plates parallel to each other, and in the extreme case of zero temperature and perfect reflection he finds the force FCasThe force depends only on two basic constants of the plate separation, namely the speed of light and the planck constant. In particular, it is independent of the fine structure constants that appear in the expression of atomic van der waals forces. This general attribute is related to the perfect reflection hypothesis that Casimir uses in its derivation. More precise experiments were performed with metal mirrors that showed perfect reflection only at frequencies less than the characteristic plasma frequency, which depends on the nature of the conduction electrons in the metal.
Due to the non-trivial permeability of ferrite, it is possible to obtain a repulsive Casimir force condition, and to control the polarity of the force by adjusting the external magnetic field, the anisotropic ferrite tri-layer structure is necessarily significantly different from other material structures. Through retrieval, the research of Casimir acting force of an anisotropic ferrite three-layer structure is not related in the prior art. The invention will therefore suggest how to calculate the Casimir forces for an anisotropic ferrite tri-layer structure.
Disclosure of Invention
The invention aims to provide a method and a system for calculating the Casimir acting force of an anisotropic ferrite three-layer structure aiming at the defects of the prior art, and the method and the system can accurately analyze the scattering theory to calculate the Casimir acting force effect of the anisotropic ferrite three-layer structure.
In order to achieve the purpose, the invention adopts the following technical scheme:
a system for calculating a Casimir force for an anisotropic ferrite tri-layer structure, comprising:
the establishing module is used for establishing a model of the anisotropic ferrite three-layer structure;
a determination module for determining electromagnetic properties of the anisotropic ferrite;
a first calculation module for calculating a transmission matrix of the uniaxial anisotropic material layer;
the second calculation module is used for calculating a reflection coefficient matrix of the anisotropic material three-layer structure;
and the third calculation module is used for calculating the Casimir acting force of the anisotropic ferrite three-layer structure model.
Further, the model for establishing the anisotropic ferrite three-layer structure in the establishing module comprises a first ferrite material plate, a second ferrite material plate and other material plates without ferrite materials.
Further, the determining module specifically includes determining a magnetic permeability of the anisotropic ferrite material; the magnetic permeability is mu when being vertical to the external magnetic field⊥The magnetic permeability is mu when being parallel to the external magnetic fieldzThe expressions are respectively:
μz＝1
wherein, ω isex＝γHex；ωm＝4πMs(ii) a γ represents a gyromagnetic ratio; msRepresents ferrite saturation magnetization; hexRepresenting the strength of the external magnetic field; omegaexRepresenting the frequency of the external magnetic field; omegamRepresenting the material plate plasma frequency.
Further, the first calculating module specifically includes:
the optical axis is vertical to an interface which is taken as an x-y plane, the anisotropic medium is a half space with z >0, and the magnetic permeability tensor is as follows:
wherein, mu⊥Denotes the permeability, μ, perpendicular to the external magnetic fieldzRepresents the permeability parallel to the external magnetic field;
the influence of a plurality of interfaces is calculated by adopting a transmission matrix method, a quaternary vector consisting of x and y components of an electromagnetic field in a medium is defined for a j-th layer of uniaxial anisotropic medium in a multilayer structure, and the structural relation of the uniaxial anisotropic material is as follows:
solution of the wave equation of the electromagnetic field to
Wherein k isyA wave vector representing the y direction; q represents a wave vector in the z direction;
represents the electric field strength;
representing the magnetic field strength.
Further, the first computing module further comprises:
and obtaining equations about the TE wave and the TM wave by adopting a Maxwell equation system:
wherein c represents the speed of light; ω represents the fluctuation frequency; q. q.sTMA z-direction wave vector representing the TE wave; q. q.sTMRepresents the z-direction wave vector of the TM wave.
Further, the transmission matrix of the uniaxial anisotropic material layer in the first calculation module is:
wherein M denotes a transmission matrix of the uniaxial anisotropic material layer.
Further, the second calculation module calculates the reflection coefficient matrix of the three-layer structure of the anisotropic material, specifically, obtains the total reflection coefficient matrix of the multilayer structure by using the transmission matrix of the quaternary vector of the corresponding electromagnetic field of each layer of the multilayer material structure;
wherein, by adopting the electromagnetic field boundary conditions at each interface, the obtained reflection coefficient matrix R is:
wherein the content of the first and second substances,
wherein the content of the first and second substances,
wherein, theta0Denotes the angle of incidence, k||Represents the wave vector parallel to the interface; x is the number ofmnRepresenting a total transmission matrix, wherein m and n are 1, 2, 3 and 4;
let ω i ξ, imaginary frequency ξ and parallel wave vector k||The formed coordinate system takes a polar coordinate form:
the reflection coefficient matrix of the three-layer structure of the anisotropic material is as follows:
wherein, XNRepresenting a reflection coefficient matrix of the three-layer structure of the anisotropic material; m denotes a transmission matrix of the uniaxial anisotropic material layer.
Further, the third computing module comprises:
under the condition of a plane and a parallel mirror surface, a Fabry-Perot cavity with the length of a Fabry-Perot cavity is formed by the first ferrite material plate and the second ferrite material plate, the cavity length is a, the frequency of a field mode is omega, and the transverse wave vector is k; the loop function of the cavity's optical response to the input field is defined as:
wherein the content of the first and second substances,
and
representing open-loop and closed-loop functions, respectively, corresponding to one round trip in the cavity;
is an analytic function of frequency ω; sum of transverse wave vectors is expressed as quantized eigenvector k in the x, y direction bounding intervalx＝2πqx/axAnd ky＝2πqy/ayWhen a is summedx,ay→ ∞ time, the summation transitions to integral:
taking the airy function defined in classical optics as the ratio of the in-cavity energy to the out-of-cavity energy in a given mode:
wherein a z-direction wave vector k is definedz＝ik[ω]Factor of
Indicating the difference between the medial and lateral sides;
by using the analytic nature of the function, and applying Cauchy's theorem to the complex plane region of frequencies surrounding the quadrants Re [ omega ] >0 and Im [ omega ] >0, the expression of the Casimir force is:
wherein, FCasIndicating a Casimir force.
Further, the third computing module further comprises:
in the case of plate non-specular reflection, the expression for the Casimir energy between the first and second ferrite plates as the sum of the modes denoted by the notation ξ and m ≡ k, p is:
wherein the content of the first and second substances,
wherein the content of the first and second substances,
representing the phase difference obtained by the field mode when scattering on the cavity wall; the phase difference is rewritten by quantum field theory as the traces of the matrix defined on each mode of the sum of modes m ≡ k, p:
casimir forces for the anisotropic ferrite three-layer structure model:
correspondingly, a method for calculating Casimir force of the anisotropic ferrite three-layer structure is also provided, and comprises the following steps:
s1, establishing a model of an anisotropic ferrite three-layer structure;
s2, determining the electromagnetic property of the anisotropic ferrite;
s3, calculating a transmission matrix of the uniaxial anisotropic material layer;
s4, calculating a reflection coefficient matrix of the anisotropic material three-layer structure;
and S5, calculating the Casimir acting force of the anisotropic ferrite three-layer structure model.
Compared with the prior art, the invention has the following advantages:
1. according to the method, the Casimir acting force of the anisotropic ferrite three-layer structure is calculated according to the scattering theory, and the effect of the Casimir acting force of the anisotropic ferrite three-layer structure can be accurately calculated through the scattering theory.
2. The invention can accurately reflect the influence of the non-trivial magnetic permeability of the external static magnetic field with different strengths and the anisotropic ferrite material on the Casimir acting force.
3. The invention can accurately obtain a stable sandwich structure and a stable balance point, and can adjust the balance staying position of the middle plate by regulating and controlling the intensity of the external electrostatic magnetic field.
4. The method can accurately reflect the influence of external static magnetic fields in different directions on the Casimir repulsive force.
Drawings
FIG. 1 is a diagram of a system for calculating Casimir force of an anisotropic ferrite three-layer structure according to one embodiment;
FIG. 2 is a schematic diagram of a three-layer structure model of an anisotropic ferrite provided in the first embodiment;
FIG. 3 is a schematic diagram of input and output of the system according to the second embodiment;
FIG. 4 is a schematic view of a propagation direction of a field mode in each material layer according to an embodiment;
FIG. 5 is a schematic view of a space plate system according to an embodiment;
FIG. 6 is a graph showing normalized Casimir force of ferrite plate 1(A plate) in a ferrite-silver plate-ferrite sandwich structure under the application of static magnetic field of different intensity generated by simulation provided in example two;
FIG. 7 is a graph showing normalized Casimir force of the ferrite plate 1(A plate) in the ferrite-dielectric plate-ferrite sandwich structure under the application of static magnetic field of different intensity generated by simulation provided in the first embodiment;
FIG. 8 is a graph of normalized Casimir net force of a silver plate in a ferrite-silver plate-ferrite sandwich structure under the application of static magnetic fields in different directions generated by simulation provided by one embodiment.
Detailed Description
The embodiments of the present invention are described below with reference to specific embodiments, and other advantages and effects of the present invention will be easily understood by those skilled in the art from the disclosure of the present specification. The invention is capable of other and different embodiments and of being practiced or of being carried out in various ways, and its several details are capable of modification in various respects, all without departing from the spirit and scope of the present invention. It is to be noted that the features in the following embodiments and examples may be combined with each other without conflict.
The invention aims to provide a method and a system for calculating Casimir action force of an anisotropic ferrite three-layer structure aiming at the defects of the prior art.
Example one
The embodiment provides a system for calculating Casimir acting force of an anisotropic ferrite three-layer structure, as shown in FIG. 1, comprising:
the establishing module 11 is used for establishing a model of an anisotropic ferrite three-layer structure;
a determination module 12 for determining the electromagnetic properties of the anisotropic ferrite;
a first calculation module 13 for calculating a transmission matrix of the uniaxial anisotropic material layer;
a second calculating module 14, configured to calculate a reflection coefficient matrix of the anisotropic material three-layer structure;
and the third calculation module 15 is used for calculating the Casimir acting force of the anisotropic ferrite three-layer structure model.
In the building block 11, a model of the anisotropic ferrite three-layer structure is built.
As shown in fig. 2, the model for establishing the anisotropic ferrite three-layer structure includes a first ferrite material plate 1, a second ferrite material plate 3, and other material plates 2 including ferrite materials; wherein the other material plate 2 is made of ferrite material, such as a metal silver plate. The thicknesses of three plates in the first ferrite material plate 1, the second ferrite material plate 3 and the other material plates 2 without ferrite materials are d1、d3、d2. In the present embodiment, the first ferrite material plate 1 and the second ferrite material plate 3 are both ferrite materials, i.e., ∈1＝ε3Permeability mu of the other material sheet 2 containing ferrite material2Has a dielectric constant of ∈2。
In the determination module 12, the electromagnetic properties of the anisotropic ferrite are determined.
The model of the three-layer structure of anisotropic ferrite used in this example is shown in fig. 2, where the plates 1 and 3 are ferrite material plates and the plate 2 is a silver metal plate.
Firstly, the magnetic permeability of the ferrite material is determined, and the magnetic permeability is mu when being vertical to the external magnetic field⊥Permeability parallel to the external magnetic field is muzThe expressions are respectively:
μz＝1
wherein, ω isex＝γHex；ωm＝4πMs(ii) a Typical ferrite materials have dielectric constants in the range of 12-16; msRepresents ferrite saturation magnetization, and has a value of 135G-239G; gamma denotes a gyromagnetic ratio, and gamma is 1.8X 107S-1G-1Corresponding distance unit
In the centimeter or millimeter range; hexRepresenting the strength of the external magnetic field; omegaexRepresenting the frequency of the external magnetic field; omegamRepresenting the material plate plasma frequency.
In a first calculation module 13, the transmission matrix of the layer of uniaxial anisotropic material is calculated.
For the case where the optical axis is perpendicular to the interface, this embodiment selects the interface as the x-y plane and the anisotropic medium as the half-space defined by z >0, as shown in fig. 4, the permeability tensor is given by:
μ⊥denotes the permeability, μ, perpendicular to the external magnetic fieldzRepresents the permeability parallel to the external magnetic field;
the influence of a plurality of interfaces is calculated by adopting a transmission matrix method, a quaternary vector consisting of x and y components of an electromagnetic field in a medium is defined for a j-th layer of uniaxial anisotropic medium in a multilayer structure, and the structural relation of the uniaxial anisotropic material is as follows:
solution of the wave equation of the electromagnetic field to
Wherein k isyA wave vector representing the y direction; q represents the z directionA wave vector;
represents the electric field strength;
representing the magnetic field strength.
Combining Maxwell equations to obtain the equations about TE wave and TM wave:
wherein c represents the speed of light; ω represents the fluctuation frequency; q. q.sTEA z-direction wave vector representing the TE wave; q. q.sTMRepresents the z-direction wave vector of the TM wave.
TE wave (i.e., s wave): there is a magnetic field component in the direction of propagation but no electric field component, called a transverse electric wave. In a planar optical waveguide (closed cavity structure), electromagnetic field components have Ey, Hx and Hz, and the propagation direction is the z direction.
TM wave (i.e., p wave): there is an electric field component in the direction of propagation and no magnetic field component, called transverse magnetic wave. In a planar optical waveguide (closed cavity structure), electromagnetic field components are Hy, Ex and Ez, and the propagation direction is the z direction.
Then, the relation of the quaternary vectors at (x, y, z) and (x, y, z + z) in the material is used for deriving the concrete form of the transmission matrix of the uniaxial anisotropic medium material layer by using the relation of the transmission matrix M of the material:
wherein M denotes a transmission matrix of the uniaxial anisotropic material layer.
In the second calculation module 14, the anisotropic material three-layer structure reflection coefficient matrix is calculated.
In this embodiment, a transmission matrix of the quaternary vector of the electromagnetic field corresponding to each layer of the multilayer material structure is used to obtain a total reflection coefficient matrix of the multilayer structure. Substituting each layer of transmission matrix into field quantity quaternary vectors before and after electromagnetic waves enter the multilayer structure, wherein electromagnetic field boundary conditions at each interface are applied to obtain each matrix element of the reflection coefficient matrix:
wherein, each parameter is defined as:
wherein the content of the first and second substances,
wherein, theta0Denotes the angle of incidence, k||Represents the wave vector parallel to the interface; x is the number ofmnRepresenting a total transmission matrix, wherein m and n are 1, 2, 3 and 4;
let ω i ξ, imaginary frequency ξ and parallel wave vector k||The formed coordinate system takes a polar coordinate form:
total transmission matrix xmnThe reflection coefficient matrix is obtained by multiplying each layer of transmission matrix, so that the reflection coefficient matrix of the three-layer structure of the anisotropic material is as follows:
wherein, XNRepresenting a reflection coefficient matrix of the three-layer structure of the anisotropic material; m denotes a transmission matrix of the uniaxial anisotropic material layer.
In a third calculation module 15, the Casimir forces of the anisotropic ferrite three-layer structure model are calculated.
This embodiment begins with the original Casimir effect space structure with perfect planes and parallel mirrors, the planes extending in the x and y directions, as shown in FIG. 5. The first ferrite material plate 1(A plate) and the second ferrite material plate 3(B plate) are made into Fabry-Perot cavities with the length of a. The field mode is characterized by its frequency ω, a transverse wavevector k (which has components kx, ky in the plane of the plate), and a polarization state p. In the system of fig. 5, the frequency ω, the transverse wave-vector k ≡ (kx, ky) and the polarization p ═ TE, TM remains unchanged throughout scattering on the mirror or cavity. The scattering process couples only free vacuum modes with opposite sign of the sagittal longitudinal component kz. By using
Indicating the reflection amplitude of the wall j-a, B seen from the inside of the cavity.
The loop function characterizing the optical response of the cavity to the input field is defined as:
wherein the content of the first and second substances,
and
representing open-loop and closed-loop functions, respectively, corresponding to one round trip in the cavity;
is an analytic function of frequency ω; sum of transverse wave vectors is expressed as quantized eigenvector k in the x, y direction bounding intervalx＝2πqx/axAnd ky＝2πqy/ayWhen a is summedx,ay→ ∞ time, the summation transitions to integral:
taking the airy function defined in classical optics as the ratio of the in-cavity energy to the out-of-cavity energy in a given mode:
wherein a z-direction wave vector k is definedz＝ik[ω]Factor of
Indicating the difference between the medial and lateral sides;
by using the analytic nature of the function, applying Cauchy's theorem to the complex planar region of frequencies encompassing the quadrants Re [ omega ] >0 and Im [ omega ] >0, and considering that the contribution of higher frequencies is neglected by applying high frequency transparency characteristics, the Casimir force expression is:
wherein, FCasRepresenting the Casimir force, i.e. the integral over the complex frequency ω i ξ.
In the case of flat non-specular reflection, the expression between the first ferrite material plate 1(a plate), the second ferrite material plate 3(B plate) as the mode sum Casimir energy by the label ξ and m ≡ k, p is:
wherein the content of the first and second substances,
wherein the content of the first and second substances,
representing the phase difference obtained by the field mode when scattering on the cavity wall; the phase difference is rewritten by quantum field theory as the traces of the matrix defined on each mode of the sum of modes m ≡ k, p:
where R isAAnd RBThe reflection characteristics of the two cavity walls are given, which in turn leads to a more general formula for the corresponding Casimir forces. Therefore, the Casimir forces for the anisotropic ferrite three-layer structure model:
wherein the transverse wave-vector component k of the parallel interface is explicitly written as k||. And finally substituting the relevant parameters of the anisotropic ferrite into a formula to obtain the Casimir acting force of the anisotropic ferrite.
Compared with the prior art, the embodiment has the following advantages:
1. according to the method, the Casimir acting force of the anisotropic ferrite three-layer structure is calculated according to the scattering theory, and the effect of the Casimir acting force of the anisotropic ferrite three-layer structure can be accurately calculated through the scattering theory.
2. The invention can accurately reflect the influence of the non-trivial magnetic permeability of the external static magnetic field with different strengths and the anisotropic ferrite material on the Casimir acting force.
3. The invention can accurately obtain a stable sandwich structure and a stable balance point, and can adjust the balance staying position of the middle plate by regulating and controlling the intensity of the external electrostatic magnetic field.
4. The method can accurately reflect the influence of external static magnetic fields in different directions on the Casimir repulsive force.
Correspondingly, a method for calculating Casimir force of the anisotropic ferrite three-layer structure is also provided, and comprises the following steps:
s11, establishing a model of an anisotropic ferrite three-layer structure;
s12, determining the electromagnetic property of the anisotropic ferrite;
s13, calculating a transmission matrix of the uniaxial anisotropic material layer;
s14, calculating a reflection coefficient matrix of the anisotropic material three-layer structure;
and S15, calculating the Casimir acting force of the anisotropic ferrite three-layer structure model.
Example two
The difference between the system for calculating the Casimir acting force of the anisotropic ferrite three-layer structure and the first embodiment is that:
this example further illustrates a system for calculating the Casimir force for an anisotropic ferrite tri-layer structure.
In this embodiment, as shown in fig. 3. The A port is provided with three thicknesses of a first ferrite material plate 1(A plate), a second ferrite material plate 3(B plate) and other material plates 2(C plate) without ferrite materials. Inputting the dielectric constant and omega of anisotropic ferrite material at the B portexAnd inputting the dielectric constant, the magnetic permeability and the plasma frequency of other material plates at the C port. The Casimir force of the ferrite plate is output at the D port, and the Casimir net force of the other material plates is output at the E port.
In this embodiment, fig. 6 is a normalized Casimir diagram of the first ferrite plate 1(a plate) in the ferrite-silver plate-ferrite sandwich structure when a static magnetic field of different intensity is applied. In the figure, a first ferrite material plate 1(A plate) and a second ferrite material plate 3(B plate) are ferrite material plates, other material plates 2(C plate) without ferrite material are silver plates, and the thickness of the three plates is d1＝d3＝d2＝1.0λmDielectric constant ε of anisotropic ferrite material1＝ε3＝12，ωex1＝ωex2Permeability μ of silver plate 2(C plate)2Dielectric constant of 1
In which the plasma frequency omegam＝1.37×106rad/s. As can be seen from fig. 6, this example is able to analyze the characteristic in which the electromagnetic response characteristic of the ferrite material plate gradually increases under the condition that the applied magnetic field gradually decreases within the controllable range.
In this example, FIG. 7 is a normalized Casimir diagram of ferrite plate 1(A plate) in a ferrite-dielectric-ferrite sandwich structure with different applied static magnetic fields. In this figure the three plates have a thickness d1＝d3＝d2＝1.0λmDielectric constant ε of anisotropic ferrite material1＝ε3＝10，ωex1＝ωex2Permeability μ of silver plate 2(C plate)2Dielectric constant ε ═ 1210. As can be seen from FIG. 7, this example enables analysis of plates of ferrite material under conditions of gradual reduction of the applied magnetic field, within a controllable rangeThe electromagnetic response characteristic of (2) is gradually enhanced.
In this embodiment, fig. 8 is a normalized Casimir net force diagram of the silver plate in the ferrite-silver plate-ferrite sandwich structure for different external magnetic field strengths when the external magnetic field direction is the x-axis direction. In the figure, the plates 1 (A) and 3 (B) are ferrite plates, the other plate 2 (C) is a silver plate, and the thickness of the three plates is d1＝d3＝d2＝1.0λmDielectric constant ε of anisotropic ferrite material1＝ε3＝12，ωex1＝ωex2Permeability of silver plate mu2Dielectric constant of 1
In which the plasma frequency omegam＝1.37×106rad/s. This embodiment can analyze the characteristics that the magnetic response strength of the ferrite material is weakened, the Casimir repulsive force cannot be obtained, and further, a stable sandwich structure cannot be obtained under the condition that the direction of the applied magnetic field is the x-axis direction.
The Casimir acting force of the three-layer structure of the anisotropic ferrite is calculated based on the scattering theory, the influence of static magnetic fields with different strengths and non-trivial magnetic permeability of the anisotropic ferrite material on the Casimir acting force can be analyzed, a stable sandwich structure and a stable balance point can be obtained, and the stable balance position of the middle plate can be regulated and controlled by analyzing and adjusting the intensity parameter of the external magnetic field. Because the material cost is higher in practice, the theoretical model used in the invention is closer to the actual anisotropic ferrite material, and the theoretical model has application value when being used as a test model. The system can calculate the required Casimir acting force in the test, can provide a new application for anisotropic ferrite materials, and also provides a new way for researching the Casimir acting force.
It is to be noted that the foregoing is only illustrative of the preferred embodiments of the present invention and the technical principles employed. It will be understood by those skilled in the art that the present invention is not limited to the particular embodiments described herein, but is capable of various obvious changes, rearrangements and substitutions as will now become apparent to those skilled in the art without departing from the scope of the invention. Therefore, although the present invention has been described in greater detail by the above embodiments, the present invention is not limited to the above embodiments, and may include other equivalent embodiments without departing from the spirit of the present invention, and the scope of the present invention is determined by the scope of the appended claims.
Claims (10)
1. A system for calculating a Casimir force for an anisotropic ferrite tri-layer structure, comprising:
the establishing module is used for establishing a model of the anisotropic ferrite three-layer structure;
a determination module for determining electromagnetic properties of the anisotropic ferrite;
a first calculation module for calculating a transmission matrix of the uniaxial anisotropic material layer;
the second calculation module is used for calculating a reflection coefficient matrix of the anisotropic material three-layer structure;
and the third calculation module is used for calculating the Casimir acting force of the anisotropic ferrite three-layer structure model.
2. The system for calculating Casimir forces of an anisotropic ferrite tri-layer structure of claim 1, wherein the model of the anisotropic ferrite tri-layer structure built in the building block comprises a first plate of ferrite material, a second plate of ferrite material, and other plates of material including ferrite material.
3. The system for calculating Casimir forces of an anisotropic ferrite tri-layer structure of claim 2, wherein the determining means comprises in particular determining the permeability of the anisotropic ferrite material; the magnetic permeability is mu when being vertical to the external magnetic field⊥The magnetic permeability is mu when being parallel to the external magnetic fieldzThe expressions are respectively:
μz＝1
wherein, ω isex＝γHex；ωm＝4πMs(ii) a γ represents a gyromagnetic ratio; msRepresents ferrite saturation magnetization; hexRepresenting the strength of the external magnetic field; omegaexRepresenting the frequency of the external magnetic field; omegamRepresenting the material plate plasma frequency.
4. The system for calculating Casimir acting force of the anisotropic ferrite three-layer structure according to claim 3, wherein the first calculating module is specifically:
the optical axis is vertical to an interface which is taken as an x-y plane, the anisotropic medium is a half space with z >0, and the magnetic permeability tensor is as follows:
wherein, mu⊥Denotes the permeability, μ, perpendicular to the external magnetic fieldzRepresents the permeability parallel to the external magnetic field;
the influence of a plurality of interfaces is calculated by adopting a transmission matrix method, a quaternary vector consisting of x and y components of an electromagnetic field in a medium is defined for a j-th layer of uniaxial anisotropic medium in a multilayer structure, and the structural relation of the uniaxial anisotropic material is as follows:
solution of the wave equation of the electromagnetic field to
Wherein k isyA wave vector representing the y direction; q represents a wave vector in the z direction;
represents the electric field strength;
representing the magnetic field strength.
5. The system of calculating an anisotropic ferrite tri-layer structure Casimir force of claim 4, wherein the first calculation module further comprises:
and obtaining equations about the TE wave and the TM wave by adopting a Maxwell equation system:
wherein c represents the speed of light; ω represents the fluctuation frequency; q. q.sTEA z-direction wave vector representing the TE wave; q. q.sTMRepresents the z-direction wave vector of the TM wave.
6. The system for calculating Casimir forces of an anisotropic ferrite tri-layer structure of claim 5, wherein the transmission matrix of the uniaxial anisotropic material layer in the first calculation module is:
wherein M denotes a transmission matrix of the uniaxial anisotropic material layer.
7. The system for calculating Casimir acting force of an anisotropic ferrite three-layer structure according to claim 6, wherein the second calculation module calculates the reflection coefficient matrix of the anisotropic material three-layer structure, specifically, obtains the total reflection coefficient matrix of the multilayer structure by using the transmission matrix of the corresponding electromagnetic field quaternion vector of each layer of the multilayer structure;
wherein, by adopting the electromagnetic field boundary conditions at each interface, the obtained reflection coefficient matrix R is:
wherein the content of the first and second substances,
wherein the content of the first and second substances,
wherein, theta0Denotes the angle of incidence, k||Represents the wave vector parallel to the interface; x is the number ofmnRepresenting a total transmission matrix, wherein m and n are 1, 2, 3 and 4;
let ω i ξ, virtual frequencyξ and the parallel wave vector k||The formed coordinate system takes a polar coordinate form:
the reflection coefficient matrix of the three-layer structure of the anisotropic material is as follows:
wherein, XNRepresenting a reflection coefficient matrix of the three-layer structure of the anisotropic material; m denotes a transmission matrix of the uniaxial anisotropic material layer.
8. The system for calculating Casimir forces of an anisotropic ferrite tri-layer structure of claim 7, wherein the third calculation module comprises:
under the condition of a plane and a parallel mirror surface, a Fabry-Perot cavity with the length of a Fabry-Perot cavity is formed by the first ferrite material plate and the second ferrite material plate, the cavity length is a, the frequency of a field mode is omega, and the transverse wave vector is k; the loop function of the cavity's optical response to the input field is defined as:
wherein the content of the first and second substances,
and
each representing an open loop corresponding to one round trip in the cavityAnd a closed loop function;
is an analytic function of frequency ω; the sum of the transverse wave vectors k is represented as the quantized eigenvector k of the x, y-direction bounding volumex＝2πqx/axAnd ky＝2πqy/ayWhen a is summedx,ay→ ∞ time, the summation transitions to integral:
taking the airy function defined in classical optics as the ratio of the in-cavity energy to the out-of-cavity energy in a given mode:
wherein a z-direction wave vector k is definedz＝ik[ω]Factor of
Indicating the difference between the medial and lateral sides;
by using the analytic nature of the function, and applying Cauchy's theorem to the complex plane region of frequencies surrounding the quadrants Re [ omega ] >0 and Im [ omega ] >0, the expression of the Casimir force is:
wherein, FCasIndicating a Casimir force.
9. The system for calculating Casimir forces in an anisotropic ferrite tri-layer structure of claim 8, wherein the third calculation module further comprises:
in the case of plate non-specular reflection, the expression for the Casimir energy between the first and second ferrite plates as the sum of the modes denoted by the notation ξ and m ≡ k, p is:
wherein the content of the first and second substances,
wherein the content of the first and second substances,
representing the phase difference obtained by the field mode when scattering on the cavity wall; the phase difference is rewritten by quantum field theory as the traces of the matrix defined on each mode of the sum of modes m ≡ k, p:
casimir forces for the anisotropic ferrite three-layer structure model:
10. a method for calculating Casimir force of an anisotropic ferrite three-layer structure is characterized by comprising the following steps of:
s1, establishing a model of an anisotropic ferrite three-layer structure;
s2, determining the electromagnetic property of the anisotropic ferrite;
s3, calculating a transmission matrix of the uniaxial anisotropic material layer;
s4, calculating a reflection coefficient matrix of the anisotropic material three-layer structure;
and S5, calculating the Casimir acting force of the anisotropic ferrite three-layer structure model.
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