CN112231947B - Simulation method and system for double anisotropic waveguides - Google Patents
Simulation method and system for double anisotropic waveguides Download PDFInfo
- Publication number
- CN112231947B CN112231947B CN202010975266.3A CN202010975266A CN112231947B CN 112231947 B CN112231947 B CN 112231947B CN 202010975266 A CN202010975266 A CN 202010975266A CN 112231947 B CN112231947 B CN 112231947B
- Authority
- CN
- China
- Prior art keywords
- dual
- anisotropic
- waveguide
- anisotropic waveguide
- equation
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Active
Links
- 238000000034 method Methods 0.000 title claims abstract description 34
- 238000004088 simulation Methods 0.000 title claims abstract description 28
- 230000009977 dual effect Effects 0.000 claims abstract description 53
- 230000008878 coupling Effects 0.000 claims abstract description 44
- 238000010168 coupling process Methods 0.000 claims abstract description 44
- 238000005859 coupling reaction Methods 0.000 claims abstract description 44
- 239000011159 matrix material Substances 0.000 claims abstract description 35
- 238000012360 testing method Methods 0.000 claims abstract description 28
- 230000035699 permeability Effects 0.000 claims abstract description 15
- 230000005684 electric field Effects 0.000 claims abstract description 12
- 230000006870 function Effects 0.000 claims description 35
- 238000006243 chemical reaction Methods 0.000 claims description 4
- 239000000463 material Substances 0.000 abstract description 9
- 238000004422 calculation algorithm Methods 0.000 description 7
- 238000004364 calculation method Methods 0.000 description 5
- 239000004020 conductor Substances 0.000 description 5
- 238000010586 diagram Methods 0.000 description 5
- 238000013461 design Methods 0.000 description 4
- 230000003287 optical effect Effects 0.000 description 4
- 238000011161 development Methods 0.000 description 3
- 238000005253 cladding Methods 0.000 description 2
- 230000009286 beneficial effect Effects 0.000 description 1
- 230000005540 biological transmission Effects 0.000 description 1
- 230000008859 change Effects 0.000 description 1
- 230000000052 comparative effect Effects 0.000 description 1
- 230000007423 decrease Effects 0.000 description 1
- 230000007547 defect Effects 0.000 description 1
- 230000001419 dependent effect Effects 0.000 description 1
- 238000009795 derivation Methods 0.000 description 1
- 239000000835 fiber Substances 0.000 description 1
- 238000012986 modification Methods 0.000 description 1
- 230000004048 modification Effects 0.000 description 1
- 230000009466 transformation Effects 0.000 description 1
Classifications
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/20—Design optimisation, verification or simulation
- G06F30/23—Design optimisation, verification or simulation using finite element methods [FEM] or finite difference methods [FDM]
-
- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
- Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
- Y02E60/00—Enabling technologies; Technologies with a potential or indirect contribution to GHG emissions mitigation
Landscapes
- Engineering & Computer Science (AREA)
- Physics & Mathematics (AREA)
- Theoretical Computer Science (AREA)
- Computer Hardware Design (AREA)
- Evolutionary Computation (AREA)
- Geometry (AREA)
- General Engineering & Computer Science (AREA)
- General Physics & Mathematics (AREA)
- Optical Integrated Circuits (AREA)
Abstract
The invention provides a simulation method and a simulation system of a double anisotropic waveguide, comprising the following steps: determining an eigen equation of the dual anisotropic waveguide based on parameters of the dual anisotropic waveguide; the parameters include: electromagnetic coupling coefficient, magneto-electric coupling coefficient, relative permeability tensor, relative dielectric tensor; performing interpolation test on the eigenvalue to obtain a weak form partial differential equation of the eigenvalue; converting the weak form partial differential equation into a matrix equation; and solving to obtain the propagation constant and the electric field distribution of the eigenmodes of the dual-anisotropic waveguide based on the matrix equation. The invention greatly saves the time for simulating the double anisotropic structure, and a user can arbitrarily define the double anisotropic item of the material and simulate the double anisotropic waveguide structure with arbitrary complexity.
Description
Technical Field
The invention belongs to the fields of electromagnetics and optical waveguides, and particularly relates to a simulation method and a simulation system of a double-anisotropy waveguide.
Background
The finite element method is a common numerical calculation means in computational electromagnetics, and the idea of grid division enables the method to solve any complex structure, so that the method is widely applied to the design of optical devices. From the birth of 1940, as the computing power of computers is greatly improved, finite elements are also developed and mature step by step, and relatively general commercial software such as COMSOL, ANSYS and the like is formed.
With the rapid development of metamaterials in recent years, the structure required for calculation is more and more complex. Structures such as split-rings require a significant amount of memory to be consumed in finite element simulations. The complex structure of the split ring has to be equivalent by an optical parameter, i.e. the double anisotropy, also called magneto-electric (electromagnetic) coupling coefficientThe equivalent greatly reduces the memory required by calculation, does not need to simulate a real structure any more, and only needs to define the double anisotropic parameters of the material. However, in software such as COMSOL, the double anisotropy term cannot be defined, which brings great inconvenience to the study.
In 2015, yang Rui et al published paper "Fundamental modal properties of SRRmetamaterials and metamaterial basedwaveguiding structures" on Optics Express, the first study of the optical transmission characteristics of rectangular waveguides based on doubly anisotropic materials. Their structure is too simple, the rectangular waveguide is covered around by perfect electrical conductors, and its analytical solution is readily available in the case of such a structure with high symmetry and ideal boundaries. However, the development of metamaterials is not limited to this simplest structure, and when the structure is more complex, such as an elliptic fiber, the analytical solution is no longer available. Thus, there is an urgent need for a method that can solve complex dual anisotropic waveguides.
Disclosure of Invention
Aiming at the defects of the prior art, the invention aims to provide a simulation method and a simulation system of a double-anisotropic waveguide, and aims to solve the problem that no complex double-anisotropic waveguide solving method exists at present.
To achieve the above object, in a first aspect, the present invention provides a simulation method of a dual anisotropic waveguide, including the steps of:
determining an eigen equation of the dual anisotropic waveguide based on parameters of the dual anisotropic waveguide; the parameters include: electromagnetic coupling coefficient, magneto-electric coupling coefficient, relative permeability tensor, relative dielectric tensor;
performing interpolation test on the eigenvalue to obtain a weak form partial differential equation of the eigenvalue;
converting the weak form partial differential equation into a matrix equation;
and solving to obtain the propagation constant and the electric field distribution of the eigenmodes of the dual-anisotropic waveguide based on the matrix equation.
In an alternative embodiment, the eigen equation is:
wherein χ is eh Is the electromagnetic coupling coefficient of the double anisotropic waveguide, χ he Is the magneto-electric coupling coefficient of the dual anisotropic waveguide,is the relative permeability tensor of the dual anisotropic waveguide, < >>Is the relative dielectric tensor, k of the dual anisotropic waveguide 0 As propagation constant in vacuum, e= [ E t E z ] T e -γz Is the electric field distribution of the intrinsic mode of the dual-anisotropic waveguide, gamma is the propagation constant of the light wave in the dual-anisotropic waveguide, E t For the cross-section field, E z For the longitudinal field, z is the propagation direction.
In an alternative embodiment, the weak form partial differential equation of the eigenequation is:
wherein,hamiltonian for section field, +.>Is a unit vector in the x direction, +.>Is a unit vector in the y direction; />For the test function of the ith cross-sectional field, < >>For the j-th cross-sectional field interpolation function, +.>For the mth longitudinal fieldTest function(s)>Interpolation function for the nth longitudinal field; a, a j ，a n The coefficients before the interpolation function to be solved are respectively.
In an alternative embodiment, the weak form partial differential equation is converted into a matrix equation, specifically:
wherein:
where dS represents the small triangle after the discretization, Δe represents the e-th small triangle,the third column term, χ, is the third row of the dielectric tensor eh,zz Is the third row and the third column of the electromagnetic coupling item, χ he,zz For a third row and a third column of magneto-electric coupling items, alpha represents a test function and an interpolation function of a section field, subscript i, j represents an ith, j, alpha represents a test function of a longitudinal field, and subscript m, n represents an mth, n;
wherein χ is eh,tt Columns 1, 2, χ representing rows 1, 2 of the electromagnetic coupling term he,tt Columns 1 and 2 of rows 1 and 2 of magneto-electric coupling items,column 1, 2 of row 3 representing the dielectric tensor>A third column representing rows 1, 2 of the dielectric tensor;
and +.>Are coefficients of the matrix equation.
In an alternative embodiment, the simulation method of the dual anisotropic waveguide further comprises the steps of:
determining an effective refractive index n of a dual-anisotropic waveguide based on a propagation constant of the dual-anisotropic waveguide eff The method specifically comprises the following steps:
in a second aspect, the present invention provides a simulation system of a dual anisotropic waveguide, comprising:
an eigen equation determining unit for determining eigen equations of the dual anisotropic waveguide based on parameters of the dual anisotropic waveguide; the parameters include: electromagnetic coupling coefficient, magneto-electric coupling coefficient, relative permeability tensor, relative dielectric tensor;
the interpolation test unit is used for carrying out interpolation test on the eigenvalue to obtain a weak form partial differential equation of the eigenvalue;
a matrix conversion unit for converting the weak form partial differential equation into a matrix equation;
and the matrix solving unit is used for solving and obtaining the propagation constant of the double anisotropic waveguide and the electric field distribution of the eigenmodes based on the matrix equation.
In an alternative embodiment, the eigen equation is:
wherein χ is eh Is the electromagnetic coupling coefficient of the double anisotropic waveguide, χ he Is the magneto-electric coupling coefficient of the dual anisotropic waveguide,is the relative permeability tensor of the dual anisotropic waveguide, < >>Is the relative dielectric tensor, k of the dual anisotropic waveguide 0 As propagation constant in vacuum, e= [ E t E z ] T e -γz Electric field distribution for intrinsic mode of dual anisotropic waveguideGamma is the propagation constant of the light wave in the dual anisotropic waveguide, E t For the cross-section field, E z For the longitudinal field, z is the propagation direction.
In an alternative embodiment, the weak form partial differential equation of the eigenequation is:
wherein,hamiltonian for section field, +.>Is a unit vector in the x direction, +.>Is a unit vector in the y direction; />For the test function of the ith cross-sectional field, < >>For the j-th cross-sectional field interpolation function, +.>For the mth longitudinal field test function, +.>Interpolation function for the nth longitudinal field; a, a j ，a n The coefficients before the interpolation function to be solved are respectively.
In an alternative embodiment, the weak form partial differential equation is converted into a matrix equation, specifically:
wherein:
where dS represents the small triangle after the discretization, Δe represents the e-th small triangle,the third column term, χ, is the third row of the dielectric tensor eh,zz Is the third row and the third column of the electromagnetic coupling item, χ he,zz For a third row and a third column of magneto-electric coupling items, alpha represents a test function and an interpolation function of a section field, subscript i, j represents an ith, j, alpha represents a test function of a longitudinal field, and subscript m, n represents an mth, n;
wherein χ is eh,tt Columns 1, 2, χ representing rows 1, 2 of the electromagnetic coupling term he,tt Columns 1 and 2 of rows 1 and 2 of magneto-electric coupling items,column 1, 2 of row 3 representing the dielectric tensor>A third column representing rows 1, 2 of the dielectric tensor;
and +.>Are coefficients of the matrix equation.
In an alternative embodiment, the dual anisotropic waveguide emulation system further comprises:
a refractive index determination unit for determining an effective refractive index n of the double anisotropic waveguide based on a propagation constant of the double anisotropic waveguide eff The method specifically comprises the following steps:
in general, the above technical solutions conceived by the present invention have the following beneficial effects compared with the prior art:
the invention provides a simulation method and a simulation system of a double-anisotropic waveguide, and a method for solving the intrinsic problem of the double-anisotropic waveguide numerically based on a finite element algorithm. In this method, the user does not need to design a specific double anisotropic material, such as a split resonant ring, etc. The propagation constant and the eigenmode distribution of the dual-anisotropic waveguide can be solved by only defining the equivalent dual-anisotropic parameters of the material. The invention greatly saves the time for simulating the double anisotropic structure, and a user can arbitrarily define the double anisotropic item of the material and simulate the double anisotropic waveguide structure with arbitrary complexity.
Drawings
FIG. 1 is a flow chart of a simulation method of a dual anisotropic waveguide provided by an embodiment of the present invention;
FIG. 2 is a schematic diagram of a structure of a dual anisotropic elliptical waveguide according to an embodiment of the present invention;
FIG. 3 is a flow chart of a finite element algorithm provided by an embodiment of the present invention;
FIG. 4 is a graph showing the effective refractive index results of a double anisotropic elliptical waveguide calculated according to an embodiment of the present invention;
FIG. 5 is a pattern field distribution diagram of a dual anisotropic elliptical waveguide calculated in accordance with an embodiment of the present invention;
FIG. 6 is a graph showing the effective refractive index of a double anisotropic rectangular waveguide calculated in accordance with an embodiment of the present invention versus an analytical solution;
FIG. 7 is a schematic diagram of a simulation system for a dual anisotropic waveguide according to an embodiment of the present invention.
Detailed Description
The present invention will be described in further detail with reference to the drawings and examples, in order to make the objects, technical solutions and advantages of the present invention more apparent. It should be understood that the specific embodiments described herein are for purposes of illustration only and are not intended to limit the scope of the invention.
Fig. 1 is a flow chart of a simulation method of a dual anisotropic waveguide provided by an embodiment of the present invention, as shown in fig. 1, including the following steps:
step S110, determining an eigenvalue of the dual-anisotropic waveguide based on parameters of the dual-anisotropic waveguide; the parameters include: electromagnetic coupling coefficient, magneto-electric coupling coefficient, relative permeability tensor, relative dielectric tensor;
step S120, carrying out interpolation test on the eigenvalue to obtain a weak form partial differential equation of the eigenvalue;
step S130, converting the weak form partial differential equation into a matrix equation;
and step S140, solving and obtaining the propagation constant of the double anisotropic waveguide and the electric field distribution of the eigenmodes based on the matrix equation.
Fig. 2 is a schematic structural diagram of a dual anisotropic elliptical waveguide according to an embodiment of the present invention, as shown in fig. 2. The core is an elliptical core with a major axis of 0.25λ 0 Short axis of 0.2λ 0 ，λ 0 For the wavelength of light transmitted in the dual anisotropic waveguide, the refractive index of the core is 2, the outside is covered with the cladding, and the refractive index of the cladding is set to 1 (which can be regarded as an air layer).
The invention aims to solve the problem of designing an algorithm for calculating the intrinsic problem of the dual-anisotropic waveguide. The scheme of the invention is to calculate the effective refractive index of the double anisotropic waveguide and the field distribution of modes based on a finite element algorithm. The specific flow of the invention is shown in figure 3, the invention firstly obtains the intrinsic equation of the double anisotropic waveguide through theoretical derivation, and then the solving area is discretized into a plurality of small triangles. The weak form of the small triangle unit is obtained by testing the eigenvalue, and then the weak form is converted into a matrix form which is more convenient for computer calculation. After the triangular weak form matrix is obtained, the integral in each matrix element is calculated analytically through Jacobian transformation, and then the weak form matrix of the whole area is assembled through the relation between the local code and the global code. Finally, solving the quadratic eigenvalue problem through MATLAB code PALM.
In addition, in order for the user to conveniently use the program of the present invention, the present invention also designs a graphical user interface in which the user can customize the dielectric tensor, electromagnetic (magneto-electric) coupling coefficient, wavelength, and number of modes to be solved of the material.
Because no effective means for simulating the double-anisotropic waveguide exists in the market at present, the algorithm fills the gap and makes a certain contribution to the development of metamaterials and topology photonics.
First the eigenvalue of the double anisotropy is as follows:
wherein the method comprises the steps ofIs the electromagnetic (magnetoelectric) coupling coefficient, +.>Is the relative permeability tensor->K is the relative dielectric tensor 0 As propagation constant in vacuum, e= [ E t E z ] T e -γz The electric field distribution is to be calculated. Taking the magnetic permeability into consideration, which is always a constant, and testing the magnetic permeability through an interpolation function, the weak form is obtained as follows:
where gamma is the propagation constant to be solved for,the cross-sectional field and the longitudinal field are test functions, respectively. In the simulation method provided by the invention, the invention has no limitation on dielectric tensors, namely:
however, there are certain limitations to the double anisotropy term as follows:
by passing throughThe conversion of the weak form into a matrix form is as follows:
wherein:
matrix arrayThe complete matrix needed to solve the dual anisotropic waveguide is obtained. By solving the quadratic eigenvalue equation, the invention can obtain the propagation constant:
field distribution of eigenmodes:
E M ＝[E t E z ]
fig. 4 shows the change of the effective refractive index of the elliptical waveguide model shown in fig. 2 calculated by the algorithm with the magneto-electric coupling coefficient. The invention makes the magneto-electric coupling coefficient only be χ 12 The term is the imaginary number χ 12 =iΔχ, and the other terms are all 0. The plus sign '+' in fig. 4 represents the first mode of the dual-anisotropy elliptical waveguide, the propagation constant of which is not substantially dependent on the dual-anisotropyThe term changes and varies. Asterisks indicate the second mode of the double anisotropic elliptical waveguide, the propagation constant of which decreases with increasing Δχ.
In addition, when using the software of the present invention, first the user needs to design a structure and discretize in the COMSOL or other finite element based simulation software. The fabricated structure and Mesh are then imported through a Mesh module. After the structure is introduced, parameters of materials, such as dielectric tensor, magneto-electric coupling coefficient and the like, are set through a Material module. Finally, a user can set solving wavelength and solving mode number in the solution module, and can Solve the eigenvalue and the eigenvector of the obtained structure by clicking the computer button. The time required to solve 2000 cells is approximately 20s, and after the solution is completed, the effective refractive index and the field distribution of the mode can be checked in the Post module.
Fig. 5 shows the calculated field distribution of the first mode of the dual anisotropic elliptical waveguide of fig. 4 for Δχ=0.3. Fig. 5 (a) shows the Ex component of mode 1, fig. 5 (b) shows the Ey component of mode 1, and fig. 5 (c) shows the Ez component of mode 1. As shown in FIG. 5, the dual anisotropic waveguide simulation method provided by the invention can effectively simulate the field distribution of the waveguide.
In order to verify the correctness of the calculation method of the invention, the invention applies the same weak form to the double anisotropic rectangular waveguide structure. Since the contributions of the boundaries (the field values at the boundaries are very small and negligible) are not considered in the weak form of the invention, the invention should choose perfect magnetic conductor boundary conditions instead of perfect electrical conductor boundary conditions, corresponding to rectangular waveguides. The method compares the TM01 mode with the TM10 mode respectively, and the result shows that the effective refractive index of the mode calculated by the method is completely consistent with the analysis solution, so that the correctness of the method is verified.
When compared with the analysis result, the invention derives the mode effective refractive index of the rectangular waveguide with perfect magnetic conductor boundary conditions. The double anisotropic parameters set in the invention in rectangular waveguide are as follows:
for the TM0n mode, the expression of its effective refractive index is as follows:
for TMn0 mode, the expression of its effective refractive index is as follows:
wherein k is c In order to truncate the propagation constant,d is the waveguide width. The dielectric tensor and the magnetic permeability set by the invention are respectively as follows:
it can be seen that the algorithm has a high degree of accuracy.
Fig. 6 is a graph comparing the effective refractive index calculated by the simulation method provided by the present invention with the analytical solution. The comparative structure is a rectangular waveguide wrapped by a perfect magnetic conductor boundary condition, and the refractive index of the waveguide is 2. By changing Deltaχ, it is easy to see that the effective refractive index of the double-anisotropy rectangular waveguide calculated by the simulation method provided by the invention is almost completely matched with the analytical solution, and the reliability of the simulation method provided by the invention is proved.
FIG. 7 is a schematic diagram of a simulation system of a dual anisotropic waveguide according to an embodiment of the present invention, as shown in FIG. 7, including:
an eigen equation determination unit 710 for determining eigen equations of the dual anisotropic waveguide based on parameters of the dual anisotropic waveguide; the parameters include: electromagnetic coupling coefficient, magneto-electric coupling coefficient, relative permeability tensor, relative dielectric tensor;
the interpolation test unit 720 is configured to perform an interpolation test on the eigen equation to obtain a weak form partial differential equation of the eigen equation;
a matrix conversion unit 730 for converting the weak form partial differential equation into a matrix equation;
and a matrix solving unit 740, configured to solve to obtain the propagation constant and the electric field distribution of the eigenmodes of the dual anisotropic waveguide based on the matrix equation.
It should be understood that the detailed functions of the respective units in fig. 7 may be referred to the description of the foregoing method embodiment, and are not described herein.
It will be readily appreciated by those skilled in the art that the foregoing description is merely a preferred embodiment of the invention and is not intended to limit the invention, but any modifications, equivalents, improvements or alternatives falling within the spirit and principles of the invention are intended to be included within the scope of the invention.
Claims (6)
1. The simulation method of the double anisotropic waveguide is characterized by comprising the following steps of:
determining an eigen equation of the dual anisotropic waveguide based on parameters of the dual anisotropic waveguide; the parameters include: electromagnetic coupling coefficient, magneto-electric coupling coefficient, relative permeability tensor, relative dielectric tensor; the eigen equation is:
wherein,is the electromagnetic coupling coefficient of the dual anisotropic waveguide, +.>Is the magneto-electric coupling coefficient of the dual anisotropic waveguide,is double in numberThe relative permeability tensor of the anisotropic waveguide, +.>Is the relative dielectric tensor of the dual anisotropic waveguide, < >>Is a propagation constant in vacuum, +.>Electric field distribution for intrinsic mode of dual anisotropic waveguide, +.>For the propagation constant of light waves in a dual anisotropic waveguide, < >>For the cross-section field +.>For longitudinal field, z is propagation direction;
performing interpolation test on the eigenvalue to obtain a weak form partial differential equation of the eigenvalue; the weak form partial differential equation of the eigen equation is:
wherein,hamiltonian for section field, +.>Is a unit vector in the x direction, +.>Is a unit vector in the y direction; />For the test function of the ith cross-sectional field, < >>For the j-th cross-sectional field interpolation function, +.>For the mth longitudinal field test function, +.>Interpolation function for the nth longitudinal field; />，/>Respectively the coefficients before interpolation functions to be solved;
converting the weak form partial differential equation into a matrix equation;
and solving to obtain the propagation constant and the electric field distribution of the eigenmodes of the dual-anisotropic waveguide based on the matrix equation.
2. A method of simulation of a dual anisotropic waveguide according to claim 1, wherein the weak form partial differential equation is converted into a matrix equation, in particular:
wherein:；/>；
，/>；；
where dS represents a small triangle after discretization,represents the e-th triangle,/->Third column term of third row for dielectric tensor,>a third row and a third column of the electromagnetic coupling item,>third row and third column of magneto-electric coupling item, ">Test function and interpolation function representing section field, subscript i, j represents ith, j,/-th>A test function representing a longitudinal field, and subscript m, n representing the mth, n;
；
；
；
；/>；
wherein,columns 1, 2 of rows 1, 2 representing electromagnetic coupling items, +.>Columns 1, 2 of row 1, 2 representing magneto-electric coupling items, +.>Column 1, 2 of row 3 representing the dielectric tensor>A third column representing rows 1, 2 of the dielectric tensor;
；/>；/>；
、/>and +.>Are coefficients of the matrix equation.
3. The method of simulating a dual anisotropic waveguide of claim 1, further comprising the steps of:
determination of effective refractive index of a dual-anisotropic waveguide based on propagation constant of the dual-anisotropic waveguideThe method specifically comprises the following steps:。
4. a simulation system for a dual anisotropic waveguide, comprising:
an eigen equation determining unit for determining eigen equations of the dual anisotropic waveguide based on parameters of the dual anisotropic waveguide; the parameters include: electromagnetic coupling coefficient, magneto-electric coupling coefficient, relative permeability tensor, relative dielectric tensor; the eigen equation is:
wherein,is the electromagnetic coupling coefficient of the dual anisotropic waveguide, +.>Is the magneto-electric coupling coefficient of the dual anisotropic waveguide,is the relative permeability tensor of the dual anisotropic waveguide, < >>Is the relative dielectric tensor of the dual anisotropic waveguide, < >>Is a propagation constant in vacuum, +.>Electric field distribution for intrinsic mode of dual anisotropic waveguide, +.>For the propagation constant of light waves in a dual anisotropic waveguide, < >>For the cross-section field +.>For longitudinal field, z is propagation direction;
the interpolation test unit is used for carrying out interpolation test on the eigenvalue to obtain a weak form partial differential equation of the eigenvalue; the weak form partial differential equation of the eigen equation is:
wherein,hamiltonian for section field, +.>Is a unit vector in the x direction, +.>Is a unit vector in the y direction; />For the test function of the ith cross-sectional field, < >>For the j-th cross-sectional field interpolation function, +.>For the mth longitudinal field test function, +.>Interpolation function for the nth longitudinal field; />，/>Respectively the coefficients before interpolation functions to be solved;
a matrix conversion unit for converting the weak form partial differential equation into a matrix equation;
and the matrix solving unit is used for solving and obtaining the propagation constant of the double anisotropic waveguide and the electric field distribution of the eigenmodes based on the matrix equation.
5. The simulation system of a dual anisotropic waveguide according to claim 4, wherein the weak form partial differential equation is converted into a matrix equation, in particular:
wherein:；/>；
，/>；；
where dS represents a small triangle after discretization,represents the e-th triangle,/->Third column term of third row for dielectric tensor,>a third row and a third column of the electromagnetic coupling item,>third row and third column of magneto-electric coupling item, ">Test function and interpolation function representing section field, subscript i, j represents ith, j,/-th>A test function representing a longitudinal field, and subscript m, n representing the mth, n;
；
；
；
；/>；
wherein,columns 1, 2 of rows 1, 2 representing electromagnetic coupling items, +.>Columns 1, 2 of row 1, 2 representing magneto-electric coupling items, +.>Column 1, 2 of row 3 representing the dielectric tensor>A third column representing rows 1, 2 of the dielectric tensor;
；/>；；
、/>and +.>Are coefficients of the matrix equation.
6. The dual anisotropic waveguide simulation system of claim 4, further comprising:
a refractive index determination unit for determining an effective refractive index of the double anisotropic waveguide based on a propagation constant of the double anisotropic waveguideThe method specifically comprises the following steps: />。
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202010975266.3A CN112231947B (en) | 2020-09-16 | 2020-09-16 | Simulation method and system for double anisotropic waveguides |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202010975266.3A CN112231947B (en) | 2020-09-16 | 2020-09-16 | Simulation method and system for double anisotropic waveguides |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN112231947A CN112231947A (en) | 2021-01-15 |
| CN112231947B true CN112231947B (en) | 2024-02-23 |
Family
ID=74108267
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN202010975266.3A Active CN112231947B (en) | 2020-09-16 | 2020-09-16 | Simulation method and system for double anisotropic waveguides |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN112231947B (en) |
Families Citing this family (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN113065251B (en) * | 2021-03-31 | 2023-04-25 | 北京环境特性研究所 | Method and device for obtaining propagation amplitude of strong coupling waveguide |
| CN113849880B (en) * | 2021-08-16 | 2024-06-25 | 长沙理工大学 | Roadbed non-uniform humidity field determination method considering wet-force coupling effect |
| CN116842601B (en) * | 2023-09-04 | 2023-11-10 | 东莘电磁科技(成都)有限公司 | Method for determining field distribution on arbitrary three-dimensional curved section in circular waveguide |
Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN103235888A (en) * | 2013-04-27 | 2013-08-07 | 杭州电子科技大学 | Method for accurately calculating electromagnetic scattering of bianisotropic medium ball |
| CN106980736A (en) * | 2017-04-11 | 2017-07-25 | 吉林大学 | A kind of ocean controllable source electromagnetic method finite element forward modeling method of anisotropic medium |
Family Cites Families (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US20150268128A1 (en) * | 2014-03-21 | 2015-09-24 | Canon Kabushiki Kaisha | Calculating Nonlinear Kerr Coefficient for a Waveguide |
-
2020
- 2020-09-16 CN CN202010975266.3A patent/CN112231947B/en active Active
Patent Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN103235888A (en) * | 2013-04-27 | 2013-08-07 | 杭州电子科技大学 | Method for accurately calculating electromagnetic scattering of bianisotropic medium ball |
| CN106980736A (en) * | 2017-04-11 | 2017-07-25 | 吉林大学 | A kind of ocean controllable source electromagnetic method finite element forward modeling method of anisotropic medium |
Non-Patent Citations (1)
| Title |
|---|
| 精细积分法在含各向异性介质波导不连续性问题中的应用;杨红卫;慕振峰;王震;;物理学报;20130708(13);全文 * |
Also Published As
| Publication number | Publication date |
|---|---|
| CN112231947A (en) | 2021-01-15 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN112231947B (en) | Simulation method and system for double anisotropic waveguides | |
| Li et al. | Multidisciplinary robust design optimization considering parameter and metamodeling uncertainties | |
| Çekinmez et al. | Integral-equation formulations of plasmonic problems in the visible spectrum and beyond | |
| CN110673337B (en) | Rapid vector analysis method for multi-core waveguide transmission characteristics | |
| Crawford et al. | Unconditionally stable time stepping method for mixed finite element Maxwell solvers | |
| Gorgizadeh et al. | Eigenmode computation of cavities with perturbed geometry using matrix perturbation methods applied on generalized eigenvalue problems | |
| Lai et al. | Second kind integral equation formulation for the mode calculation of optical waveguides | |
| Tian et al. | Modeling of metasurfaces using discontinuous Galerkin time-domain method based on generalized sheet transition conditions | |
| Lee et al. | Parallel iterative FEM solver with initial guess for frequency domain electromagnetic analysis | |
| Wang et al. | Unconditionally stable FDTD method based on LOD scheme for analysis of 2-D periodic structures | |
| Capilla et al. | Validation of the SHNC time-dependent transport code based on the spherical harmonics method for complex nuclear fuel assemblies | |
| Wang et al. | A Multilevel Method With Novel Correction Strategy for Parallel Finite-Element Analysis of Electromagnetic Problems | |
| Koning et al. | Vector finite-element modeling of the full-wave Maxwell equations to evaluate power loss in bent optical fibers | |
| Wiltshaw et al. | Analytical solutions for Bloch waves in resonant phononic crystals: deep-subwavelength energy splitting and mode steering between topologically protected interfacial and edge states | |
| El-Henawy et al. | Photonic device sensitivity analysis methods: towards process variation-aware silicon photonics design | |
| Wang et al. | A spurious-free domain decomposition method for 3-D Maxwell’s eigenvalue problems | |
| Modak et al. | New applications of Orthomin (1) algorithm for K-eigenvalue problem in Reactor Physics | |
| Pissoort et al. | Comparative study of three methods for the simulation of two-dimensional photonic crystals | |
| Yan et al. | Cutoff wavenumber analysis of arbitrarily shaped waveguides using regularized method of fundamental solutions with excitation sources | |
| Pissoort et al. | Termination of periodic waveguides by PMLs in time-harmonic integral equation-like techniques | |
| Kuang et al. | A Novel High-Order Symplectic Compact FDTD Schemes for Optical Waveguide Simulation | |
| Zhu et al. | Analysis of photonic crystals using the hybrid finite‐element/finite‐difference time domain technique based on the discontinuous Galerkin method | |
| Wu et al. | A finite element model order reduction technique for multiscale electromagnetic problems | |
| Ouchetto et al. | Handling periodic boundary conditions on arbitrary mesh | |
| Huang et al. | Research on the Integrated Method for Power Equipment State Simulation and Reconstruction |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |