CN110247194A - The upper transmittance prediction technique and system of the double-deck bandpass-type frequency selecting structures - Google Patents
The upper transmittance prediction technique and system of the double-deck bandpass-type frequency selecting structures Download PDFInfo
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Abstract
The invention discloses the upper transmittance prediction techniques and system of a kind of double-deck bandpass-type frequency selecting structures.This method comprises: obtaining electromagnetism wave parameter and medium parameter；Electromagnetism wave parameter includes wave vector in the frequency and vacuum of plane of incidence electromagnetic wave, and medium parameter includes the dielectric constant of each layer overwrite media and the dielectric constant and magnetic conductivity of magnetic conductivity, the dielectric constant of each layer intermediate medium and magnetic conductivity and each layer substrate dielectric；Wave vector normal component and mould admittance are determined according to electromagnetism wave parameter and medium parameter；Objective function is generated according to wave vector normal component and mould admittance；The minimum of calculating target function；The upper transmittance of the double-deck bandpass-type frequency selecting structures is determined according to the minimum of objective function.Using method and system of the invention, having can be in such a way that the upper transmittance of the double-deck bandpass-type frequency selecting structures quickly selects coated by dielectric, so that it is determined that being easiest to the advantages of realizing the medium arrangement form that design performance requires.
Description
Technical field
The present invention relates to communication and em filtering technical fields, more particularly to a kind of double-deck bandpass-type frequency selecting structures
Upper transmittance prediction technique and system.
Background technique
Frequency-selective surfaces (Frequency Selective Surface, FSS) are widely used in the electromagnetism of various frequency ranges
Filter.It is that an important design refers to internal transmission factor in the design process of the bandpass-type FSS element such as radome
Mark.Usually require that the higher the better for band internal transmission factor when design, and it is then more lower better with outer transmissivity, and deviate saturating when center frequency-band
The rate of penetrating can reduce rapidly.
The transmission characteristic of the double-deck FSS causes people due to the requirement close to people to ideal frequency selection characteristic
Extensive interest, although the frequency of bilayer FSS selects characteristic close to the ideal case of people, difficult point is that band internal transmission factor is difficult to mention
It is high.Currently, predicted transmittance mostly is laid particular emphasis on for the research of the transmissivity of the double-deck bandpass-type frequency selecting structures, and still, transmission
The prediction of rate can not provide the optimization direction of the double-deck bandpass-type frequency selecting structures design.The medium for how designing high-quality adds
Load mode meets design performance requirement, improves band internal transmission factor, is research worker's urgent problem to be solved.
Summary of the invention
The object of the present invention is to provide a kind of upper transmittance prediction technique of double-deck bandpass-type frequency selecting structures and it is
System, having can be in such a way that the upper transmittance of the double-deck bandpass-type frequency selecting structures quickly selects coated by dielectric, thus really
Surely it is easiest to the advantages of realizing the medium arrangement form that design performance requires.
To achieve the above object, the present invention provides following schemes:
A kind of upper transmittance prediction technique of bilayer bandpass-type frequency selecting structures, comprising:
The double-deck bandpass-type frequency selecting structures are located in vacuum environment；Since electromagnetic wave irradiation side, the bilayer band logical
Type frequency selecting structures successively include M layers of overwrite media, first frequency selection surface, N layers of intermediate medium, second frequency selection table
Face and L layers of substrate dielectric；
Obtain electromagnetism wave parameter and medium parameter；The electromagnetism wave parameter includes the frequency and vacuum of plane of incidence electromagnetic wave
Middle wave vector, the medium parameter include each layer overwrite media dielectric constant and magnetic conductivity, each layer intermediate medium dielectric it is normal
The dielectric constant and magnetic conductivity of several and magnetic conductivity and each layer substrate dielectric；
Wave vector normal component and mould admittance are determined according to the electromagnetism wave parameter and the medium parameter；
Objective function is generated according to the wave vector normal component and the mould admittance；
Calculate the minimum of the objective function；
The upper transmittance of the double-deck bandpass-type frequency selecting structures is determined according to the minimum of the objective function.
Optionally, wave vector normal component and mould admittance are determined according to the electromagnetism wave parameter and the medium parameter, specifically
Include:
According to the frequency f of the plane of incidence electromagnetic wave, incident electromagnetic wave angular frequency is determined using the π of formula ω=2 f；
According to the incident frequencies f, using formulaDetermine the Electromagnetic Wave Propagation in i-th layer of medium
Constant k(i)；Wherein ε(i)For the dielectric constant of i-th layer of medium；μ(i)For the magnetic conductivity of i-th layer of medium；
According to wave vector in the vacuumUsing formulaDetermine wave vector tangential component in vacuumIts
Coordinate z-axis is established in the middle dielectric thickness direction along the double-deck bandpass-type frequency selecting structures,For z coordinate direction vector；
According to the Electromagnetic Wave Propagation constant k in i-th layer of medium(i)And wave vector tangential component in the vacuumUsing formulaDetermine the wave vector normal component γ in i-th layer of medium(i)；Wherein ktIt is described true
Aerial wave vector tangential componentMould；Im () indicates to take the imaginary part of plural number；
According to the wave vector normal component γ in i-th layer of medium(i), using formula
Determine the mould admittance in i-th layer of mediumWherein r indicates polarized state；TE polarization indicates the polarization of transverse electric field；TM polarization indicates
Transverse magnetic polarization.
Optionally, objective function is generated according to the wave vector normal component and the mould admittance, specifically included:
According to the wave vector normal component γ in n-th layer medium(n)With the mould admittance in n-th layer mediumDetermine transmission square
Battle array；The transmission matrix includes the first transmission matrix, the second transmission matrix and third transmission matrix；
The coefficient of the objective function is determined according to the transmission matrix；
Objective function is generated according to the coefficient of the objective function.
Optionally, according to the wave vector normal component γ in n-th layer medium(n)With the mould admittance in n-th layer mediumIt determines
Transmission matrix specifically includes:
The first transmission matrix is calculated according to the following formula
The second transmission matrix is calculated according to the following formula
Third transmission matrix Γ is calculated according to the following formula(m,n):
In formula, znThe z coordinate of n-th of dielectric interface, γ when to be started counting from plane electromagnetic wave incident side(n+1)It is
Wave vector normal component in n+1 layers of medium, ξ(n+1)For the mould admittance in (n+1)th layer of medium, I is unit matrix, and m, n are nature
Number；
The coefficient that the objective function is determined according to the transmission matrix, specifically includes:
According to b1=-juMBΩC12/ a calculates the coefficient b of the objective function F (x, y)1；
According to b2=-juBΩCM12/ a calculates the coefficient b of the objective function F (x, y)2；
According to c=Γ11/ a calculates the coefficient c of the objective function F (x, y)；
Wherein,
Γ=Γ(0,M+N+L+1),
ΓMB=Γ(M+1,M+N+L+1),
ΓB=Γ(M+N+1,M+N+L+1),
In formula, M indicates the total number of plies of blanket dielectric layer, and N indicates the total number of plies of middle dielectric layer, and L indicates the total layer of substrate dielectric layer
Number, ΩC12Representing matrix ΩCThe element of 1st row, the 2nd column, ΩCM12Representing matrix ΩCMThe element of 1st row, the 2nd column, Γ11Table
Show the element of the 1st row of matrix Γ, the 1st column, ΩM12Representing matrix ΩMThe element of 1st row, the 2nd column, ΩM22Representing matrix ΩM2nd
The element of row, the 2nd column, zMThe z coordinate of m-th dielectric interface, γ when to be started counting from plane electromagnetic wave incident side(M+1)For
Wave vector normal component in M+1 layers of medium, ΓMB,11Representing matrix ΓMBThe element of 1st row, the 1st column, ΓMB,21Representing matrix
ΓMBThe element of 2nd row, the 1st column, ΓB,11Representing matrix ΓBThe element of 1st row, the 1st column, ΓB,21Representing matrix ΓB2nd row,
The element of 1st column, γ(M+N+1)For the wave vector normal component in M+N+1 layers of medium, zM+NTo be opened from plane electromagnetic wave incident side
The z coordinate of the M+N dielectric interface when beginning to count；
Objective function is generated according to the coefficient of the objective function, is specifically included:
According to coefficient b1、b2Objective function F (x, y)=xy+b is generated with c1x+b2y+c。
The present invention also provides a kind of upper transmittance forecasting systems of double-deck bandpass-type frequency selecting structures, comprising:
Parameter acquisition module, for obtaining electromagnetism wave parameter and medium parameter；The electromagnetism wave parameter includes plane of incidence
Wave vector in the frequency and vacuum of electromagnetic wave, the medium parameter include the dielectric constant of each layer overwrite media and magnetic conductivity, each
The layer dielectric constant of intermediate medium and the dielectric constant and magnetic conductivity of magnetic conductivity and each layer substrate dielectric；
Wave vector normal component and mould admittance computation module, for being determined according to the electromagnetism wave parameter and the medium parameter
Wave vector normal component and mould admittance；
Objective function generation module, for generating objective function according to the wave vector normal component and the mould admittance；
Objective function minimum computing module, for calculating the minimum of the objective function；
Upper transmittance determining module, for determining the double-deck bandpass-type frequency selection according to the minimum of the objective function
The upper transmittance of structure.
Optionally, the wave vector normal component and mould admittance computation module, specifically include:
Incoming electromagnetic angular frequency computing unit, for the frequency f according to the plane of incidence electromagnetic wave, using formula ω
=2 π f determine incident electromagnetic wave angular frequency；
Electromagnetic Wave Propagation constant calculations module is used for according to the incident frequencies f, using formula
Determine the Electromagnetic Wave Propagation constant k in i-th layer of medium(i)；Wherein ε(i)For the dielectric constant of i-th layer of medium；μ(i)It is situated between for i-th layer
The magnetic conductivity of matter；
Wave vector tangential component computing module in vacuum, for according to wave vector in the vacuumUsing formulaDetermine wave vector tangential component in vacuumMedium wherein along the double-deck bandpass-type frequency selecting structures is thick
Coordinate z-axis is established in degree direction,For z coordinate direction vector；
Wave vector normal component computing module, for according to the Electromagnetic Wave Propagation constant k in i-th layer of medium(i)And the vacuum
Middle wave vector tangential componentUsing formulaDetermine the wave vector method in i-th layer of medium
To component γ(i)；Wherein ktIt is wave vector tangential component in the vacuumMould；Im () indicates to take the imaginary part of plural number；
Mould admittance computing unit, for according to the wave vector normal component γ in i-th layer of medium(i), using formulaDetermine the mould admittance in i-th layer of mediumWherein r indicates polarized state；
TE polarization indicates the polarization of transverse electric field；TM polarization indicates transverse magnetic polarization.
Optionally, objective function generation module specifically includes:
Transmission matrix generation unit, for according to the wave vector normal component γ in n-th layer medium(n)In n-th layer medium
Mould admittanceDetermine transmission matrix；The transmission matrix includes that the first transmission matrix, the second transmission matrix and third transmit square
Battle array；
Objective function coefhcient computing unit, for determining the coefficient of the objective function according to the transmission matrix；
Objective function generation unit, for generating objective function according to the coefficient of the objective function.
Optionally, the transmission matrix generation unit, specifically includes:
First transmission matrix generates subelement, for calculating the first transmission matrix according to the following formula
Second transmission matrix generates subelement, for calculating the second transmission matrix according to the following formula
Third transmission matrix generates subelement, for calculating third transmission matrix Γ according to the following formula(m,n):
In formula, znThe z coordinate of n-th of dielectric interface, γ when to be started counting from plane electromagnetic wave incident side(n+1)It is
Wave vector normal component in n+1 layers of medium, ξ(n+1)For the mould admittance in (n+1)th layer of medium, I is unit matrix, and m, n are nature
Number；
Objective function coefhcient computing unit, specifically includes:
Coefficient b1Computation subunit, for according to b1=-juMBΩC12/ a calculates the coefficient b of the objective function F (x, y)1；
Coefficient b2Computation subunit, for according to b2=-juBΩCM12/ a calculates the coefficient b of the objective function F (x, y)2；
Coefficient c computation subunit, for according to c=Γ11/ a calculates the coefficient c of the objective function F (x, y)；
Wherein,
Γ=Γ(0,M+N+L+1),
ΓMB=Γ(M+1,M+N+L+1),
ΓB=Γ(M+N+1,M+N+L+1),
In formula, M indicates the total number of plies of blanket dielectric layer, and N indicates the total number of plies of middle dielectric layer, and L indicates the total layer of substrate dielectric layer
Number, ΩC12Representing matrix ΩCThe element of 1st row, the 2nd column, ΩCM12Representing matrix ΩCMThe element of 1st row, the 2nd column, Γ11Table
Show the element of the 1st row of matrix Γ, the 1st column, ΩM12Representing matrix ΩMThe element of 1st row, the 2nd column, ΩM22Representing matrix ΩM2nd
The element of row, the 2nd column, zMThe z coordinate of m-th dielectric interface, γ when to be started counting from plane electromagnetic wave incident side(M+1)For
Wave vector normal component in M+1 layers of medium, ΓMB,11Representing matrix ΓMBThe element of 1st row, the 1st column, ΓMB,21Representing matrix
ΓMBThe element of 2nd row, the 1st column, ΓB,11Representing matrix ΓBThe element of 1st row, the 1st column, ΓB,21Representing matrix ΓB2nd row,
The element of 1st column, γ(M+N+1)For the wave vector normal component in M+N+1 layers of medium, zM+NTo be opened from plane electromagnetic wave incident side
The z coordinate of the M+N dielectric interface when beginning to count；
Objective function generation unit, specifically includes:
Objective function generates subelement, for according to coefficient b1、b2Objective function F (x, y)=xy+b is generated with c1x+b2y
+c。
Optionally, the upper transmittance determining module, specifically includes:
Upper transmittance computing unit, for according to objective function F (x, the y)=xy+b1x+b2The minimum min of y+c
(| F |), using formulaCalculate the upper transmittance T of the double-deck bandpass-type frequency selecting structurestop, wherein | F |
For the mould of objective function F (x, y), | a | it is the mould of a.
Compared with prior art, the beneficial effects of the present invention are:
The invention proposes the upper transmittance prediction techniques and system of a kind of double-deck bandpass-type frequency selecting structures, pass through
Obtain the frequency of plane of incidence electromagnetic wave, in vacuum wave vector, the dielectric constant of overwrite media and magnetic conductivity, intermediate medium Jie
The dielectric constant and magnetic conductivity of electric constant and magnetic conductivity and substrate dielectric can determine bilayer zone flow-through frequency selecting structures
Upper transmittance, illustrating the double-deck bandpass-type frequency selecting structures, there are one and frequency-selective surfaces FSS and unit a period of time shape
Unrelated upper transmittance, the upper transmittance that can use the double-deck bandpass-type frequency selecting structures quickly select coated by dielectric side
Formula and given electromagnetic wave irradiation mode design attainable transmission maxima by array and unit a period of time, can determine most
The medium arrangement form that design performance easy to accomplish requires is avoided proposing blindness, unpractical performance requirement, be solved existing
The problem of double-deck bandpass-type frequency selecting structures design optimization direction cannot be provided by only passing through the calculating of transmissivity in technology.
Detailed description of the invention
It in order to more clearly explain the embodiment of the invention or the technical proposal in the existing technology, below will be to institute in embodiment
Attached drawing to be used is needed to be briefly described, it should be apparent that, the accompanying drawings in the following description is only some implementations of the invention
Example, for those of ordinary skill in the art, without any creative labor, can also be according to these attached drawings
Obtain other attached drawings.
Fig. 1 is the upper transmittance prediction technique flow chart of the double-deck bandpass-type frequency selecting structures in the embodiment of the present invention；
Fig. 2 is the upper transmittance forecasting system structure chart of the double-deck bandpass-type frequency selecting structures in the embodiment of the present invention；
Fig. 3 is double-decker array frequency selecting structures diagrammatic cross-section in the embodiment of the present invention；
Fig. 4 is the effective transmission line model of double-decker array frequency selecting structures in the embodiment of the present invention；
Fig. 5 is another double-decker array frequency selecting structures diagrammatic cross-section in the embodiment of the present invention；
Fig. 6 is FSS array structure schematic diagram in the embodiment of the present invention；
Fig. 7 is transmissivity comparison diagram under 0 degree of incidence angle in the embodiment of the present invention；
Fig. 8 is 60 degree of incidence angles in the embodiment of the present invention, the lower transmissivity comparison diagram of TE polarized electromagnetic wave irradiation；
Fig. 9 is 60 degree of incidence angles in the embodiment of the present invention, the lower transmissivity comparison diagram of TM polarized electromagnetic wave irradiation；
Figure 10 is 15 degree of incidence angles in the embodiment of the present invention, the lower transmissivity comparison diagram of TE polarized electromagnetic wave irradiation；
Figure 11 is another kind FSS array structure schematic diagram in the embodiment of the present invention.
Specific embodiment
Following will be combined with the drawings in the embodiments of the present invention, and technical solution in the embodiment of the present invention carries out clear, complete
Site preparation description, it is clear that described embodiments are only a part of the embodiments of the present invention, instead of all the embodiments.It is based on
Embodiment in the present invention, it is obtained by those of ordinary skill in the art without making creative efforts every other
Embodiment shall fall within the protection scope of the present invention.
The object of the present invention is to provide a kind of upper transmittance prediction technique of double-deck bandpass-type frequency selecting structures and it is
System, having can be in such a way that the upper transmittance of the double-deck bandpass-type frequency selecting structures quickly selects coated by dielectric, thus really
Surely it is easiest to the advantages of realizing the medium arrangement form that design performance requires.
In order to make the foregoing objectives, features and advantages of the present invention clearer and more comprehensible, with reference to the accompanying drawing and specific real
Applying mode, the present invention is described in further detail.
Embodiment
Fig. 1 is a kind of upper transmittance prediction technique of double-deck bandpass-type frequency selecting structures provided in an embodiment of the present invention
Flow chart, as shown in Figure 1, a kind of upper transmittance prediction technique of bilayer bandpass-type frequency selecting structures, the double-deck bandpass-type frequency
Rate selection structure is located in vacuum environment；The double-deck bandpass-type frequency selecting structures from bottom to top successively include M layers of overwrite media, the
One frequency-selective surfaces, N layer middle dielectric layer, second frequency selection surface and L layers of substrate dielectric layer；Plane electromagnetic wave is by covering
Medium lower surface is incident to the double-deck bandpass-type frequency selecting structures.
Coordinate system is established according to the double-deck bandpass-type frequency selecting structures and plane electromagnetic wave direction of illumination；Coordinate system z-axis
Frequency selecting structures thickness direction is taken, transmissive side is directed toward by electromagnetic wave incident side；Coordinate system x-axis and y-axis and frequency selecting structures
Dielectric interface it is parallel, origin takes on the first layer overwrite media lower surface of incident side.
A kind of upper transmittance prediction technique of bilayer bandpass-type frequency selecting structures, specific steps include:
Step 101: obtaining electromagnetism wave parameter and medium parameter；Electromagnetism wave parameter include plane of incidence electromagnetic wave frequency and
Wave vector in vacuum, medium parameter include each layer overwrite media dielectric constant and magnetic conductivity, each layer intermediate medium dielectric it is normal
The dielectric constant and magnetic conductivity of several and magnetic conductivity and each layer substrate dielectric.
Step 102: wave vector normal component and mould admittance are determined according to electromagnetism wave parameter and medium parameter.The step is specifically wrapped
It includes:
According to the frequency f of plane of incidence electromagnetic wave, incident electromagnetic wave angular frequency is determined using the π of formula ω=2 f；
According to incident frequencies f, using formulaDetermine the Electromagnetic Wave Propagation constant k in i-th layer of medium(i)；Wherein ε(i)For the dielectric constant of i-th layer of medium；μ(i)For the magnetic conductivity of i-th layer of medium；Wherein, 1≤i≤M+N+L.
According to wave vector in vacuumUsing formulaDetermine wave vector tangential component in vacuumWherein edge
Coordinate z-axis is established in the dielectric thickness direction of the double-deck bandpass-type frequency selecting structures,For z coordinate direction vector.
According to the Electromagnetic Wave Propagation constant k in i-th layer of medium(i)And wave vector tangential component in vacuumUsing formulaDetermine the wave vector normal component γ in i-th layer of medium(i)；Wherein ktIt is in vacuum
Wave vector tangential componentMould；Im () indicates to take the imaginary part of plural number.
According to the wave vector normal component γ in i-th layer of medium(i), using formula
Determine the mould admittance in i-th layer of mediumWherein r indicates polarized state；TE polarization indicates the polarization of transverse electric field；TM polarization indicates
Transverse magnetic polarization.
Step 103: objective function is generated according to wave vector normal component and mould admittance.The step specifically includes:
The first transmission matrix is calculated according to the following formula
The second transmission matrix is calculated according to the following formula
Third transmission matrix Γ is calculated according to the following formula(m,n):
In formula, znThe z coordinate of n-th of dielectric interface, γ when to be started counting from plane electromagnetic wave incident side(n+1)It is
Wave vector normal component in n+1 layers of medium, ξ(n+1)For the mould admittance in (n+1)th layer of medium, I is unit matrix, and m, n are nature
Number, wherein 1≤m≤M+N+L, 1≤n≤M+N+L.
According to b1=-juMBΩC12The coefficient b of/a calculating target function F (x, y)1；
According to b2=-juBΩCM12The coefficient b of/a calculating target function F (x, y)2；
According to c=Γ11The coefficient c of/a calculating target function F (x, y)；
Wherein,
Γ=Γ(0,M+N+L+1),
ΓMB=Γ(M+1,M+N+L+1),
ΓB=Γ(M+N+1,M+N+L+1),
In formula, in formula, M indicates the total number of plies of blanket dielectric layer, and N indicates the total number of plies of middle dielectric layer, and L indicates substrate dielectric layer
Total number of plies, ΩC12Representing matrix ΩCThe element of 1st row, the 2nd column, ΩCM12Representing matrix ΩCMThe element of 1st row, the 2nd column, Γ11
The element of the 1st row of representing matrix Γ, the 1st column, ΩM12Representing matrix ΩMThe element of 1st row, the 2nd column, ΩM22Representing matrix ΩMThe
The element of 2 rows, the 2nd column, zMThe z coordinate of m-th dielectric interface, γ when to be started counting from plane electromagnetic wave incident side(M+1)
For the wave vector normal component in M+1 layers of medium, ΓMB,11Representing matrix ΓMBThe element of 1st row, the 1st column, ΓMB,21Indicate square
Battle array ΓMBThe element of 2nd row, the 1st column, ΓB,11Representing matrix ΓBThe element of 1st row, the 1st column, ΓB,21Representing matrix ΓB2nd
The element of row, the 1st column, γ(M+N+1)For the wave vector normal component in M+N+1 layers of medium, zM+NFor from plane electromagnetic wave incident side
The z coordinate of the M+N dielectric interface when starting counting.
According to coefficient b1、b2Objective function F (x, y)=xy+b is generated with c1x+b2y+c。
Step 104: the minimum min of calculating target function (| F |).
Step 105: the upper transmittance of the double-deck bandpass-type frequency selecting structures is determined according to the minimum of objective function.
According to objective function F (x, y)=xy+b1x+b2The minimum min (| F |) of y+c uses formula
Calculate the upper transmittance T of the double-deck bandpass-type frequency selecting structurestop, wherein | F | it is the mould of objective function F (x, y), | a | it is a
Mould.
Fig. 2 is a kind of upper transmittance forecasting system of double-deck bandpass-type frequency selecting structures provided in an embodiment of the present invention
Structure chart, as shown in Fig. 2, a kind of upper transmittance forecasting system of bilayer bandpass-type frequency selecting structures includes:
Parameter acquisition module 201, for obtaining electromagnetism wave parameter and medium parameter；Electromagnetism wave parameter includes plane of incidence electricity
Wave vector in the frequency and vacuum of magnetic wave, medium parameter include among the dielectric constant and magnetic conductivity, each layer of each layer overwrite media
The dielectric constant and magnetic conductivity of the dielectric constant and magnetic conductivity of medium and each layer substrate dielectric.
Wave vector normal component and mould admittance computation module 202, for determining wave vector according to electromagnetism wave parameter and medium parameter
Normal component and mould admittance.
Wave vector normal component and mould admittance computation module 202, specifically include:
Incoming electromagnetic angular frequency computing unit, for the frequency f according to plane of incidence electromagnetic wave, using the π of formula ω=2
F determines incident electromagnetic wave angular frequency；
Electromagnetic Wave Propagation constant calculations module is used for according to incident frequencies f, using formulaIt determines
Electromagnetic Wave Propagation constant k in i-th layer of medium(i)；Wherein ε(i)For the dielectric constant of i-th layer of medium；μ(i)For i-th layer of medium
Magnetic conductivity；
Wave vector tangential component computing module in vacuum, for according to wave vector in vacuumUsing formulaDetermine wave vector tangential component in vacuumWherein along the dielectric thickness side of the double-deck bandpass-type frequency selecting structures
To establishing coordinate z-axis,For z coordinate direction vector；
Wave vector normal component computing module, for according to the Electromagnetic Wave Propagation constant k in i-th layer of medium(i)And vacuum medium wave
Swear tangential componentUsing formulaDetermine the wave vector normal direction point in i-th layer of medium
Measure γ(i)；Wherein ktIt is wave vector tangential component in vacuumMould；Im () indicates to take the imaginary part of plural number；
Mould admittance computing unit, for according to the wave vector normal component γ in i-th layer of medium(i), using formulaDetermine the mould admittance in i-th layer of mediumWherein r indicates polarized state；TE
Polarization indicates the polarization of transverse electric field；TM polarization indicates transverse magnetic polarization.
Objective function generation module 203, for generating objective function according to wave vector normal component and mould admittance.
Objective function generation module 203, specifically includes:
Transmission matrix generation unit, for according to the wave vector normal component γ in n-th layer medium(n)In n-th layer medium
Mould admittanceDetermine transmission matrix；Transmission matrix includes the first transmission matrix, the second transmission matrix and third transmission matrix.
Transmission matrix generation unit, specifically includes:
First transmission matrix generates subelement, for calculating the first transmission matrix according to the following formula
Second transmission matrix generates subelement, for calculating the second transmission matrix according to the following formula
Third transmission matrix generates subelement, for calculating third transmission matrix Γ according to the following formula(m,n):
In formula, znThe z coordinate of n-th of dielectric interface, γ when to be started counting from plane electromagnetic wave incident side(n+1)It is
Wave vector normal component in n+1 layers of medium, ξ(n+1)For the mould admittance in (n+1)th layer of medium, I is unit matrix, and m, n are nature
Number.
Objective function coefhcient computing unit, for determining the coefficient of objective function according to transmission matrix.
Objective function coefhcient computing unit, specifically includes:
Coefficient b1Computation subunit, for according to b1=-juMBΩC12The coefficient b of/a calculating target function F (x, y)1。
Coefficient b2Computation subunit, for according to b2=-juBΩCM12The coefficient b of/a calculating target function F (x, y)2。
Coefficient c computation subunit, for according to c=Γ11The coefficient c of/a calculating target function F (x, y).
Wherein,
Γ=Γ(0,M+N+L+1),
ΓMB=Γ(M+1,M+N+L+1),
ΓB=Γ(M+N+1,M+N+L+1),
In formula, M indicates the total number of plies of blanket dielectric layer, and N indicates the total number of plies of middle dielectric layer, and L indicates the total layer of substrate dielectric layer
Number, ΩC12Representing matrix ΩCThe element of 1st row, the 2nd column, ΩCM12Representing matrix ΩCMThe element of 1st row, the 2nd column, Γ11Table
Show the element of the 1st row of matrix Γ, the 1st column, ΩM12Representing matrix ΩMThe element of 1st row, the 2nd column, ΩM22Representing matrix ΩM2nd
The element of row, the 2nd column, zMThe z coordinate of m-th dielectric interface, γ when to be started counting from plane electromagnetic wave incident side(M+1)For
Wave vector normal component in M+1 layers of medium, ΓMB,11Representing matrix ΓMBThe element of 1st row, the 1st column, ΓMB,21Representing matrix
ΓMBThe element of 2nd row, the 1st column, ΓB,11Representing matrix ΓBThe element of 1st row, the 1st column, ΓB,21Representing matrix ΓB2nd row,
The element of 1st column, γ(M+N+1)For the wave vector normal component in M+N+1 layers of medium, zM+NTo be opened from plane electromagnetic wave incident side
The z coordinate of the M+N dielectric interface when beginning to count.
Objective function generation unit, for generating objective function according to the coefficient of objective function.
Objective function generation unit, specifically includes:
Objective function generates subelement, for according to coefficient b1、b2Objective function F (x, y)=xy+b is generated with c1x+b2y
+c。
Objective function minimum computing module 204, the minimum min (| F |) for calculating target function.
Upper transmittance determining module 205, for determining the double-deck bandpass-type frequency selection according to the minimum of objective function
The upper transmittance of structure.
Upper transmittance determining module 205, specifically includes:
Upper transmittance computing unit, for according to objective function F (x, y)=xy+b1x+b2The minimum min (| F |) of y+c, is adopted
Use formulaCalculate the upper transmittance T of the double-deck bandpass-type frequency selecting structurestop, wherein | F | it is target letter
The mould of number F (x, y), | a | it is the mould of a.
Fig. 3 is double-decker array frequency selecting structures diagrammatic cross-section, as shown in figure 3, double-decker array frequency selecting structures have
There are M layers of overwrite media, N layers of intermediate medium and L layers of substrate dielectric, first frequency selects FSS array in surface to be arranged in overwrite media
Between intermediate medium, second frequency selects FSS array in surface to be arranged between intermediate medium and substrate dielectric.It is most lower in Fig. 3
Side and top side are vacuum, and the z axis of reference axis is along dielectric thickness direction, and interface z coordinate is respectively z from top to bottom0~
zM+N+LIf the dielectric constant and magnetic conductivity of i-th layer of medium are ε(i)And μ(i)；If plane of incidence wave frequency is f, incident direction
Vector is
Fig. 4 is the effective transmission line model of double-decker array frequency selecting structures, the equivalent inductance of the first FSS array, capacitor
Parameter is (L1,C1), the equivalent inductance of the 2nd FSS array, capacitance parameter are (L2,C2), the equivalent impedance of i-th layer of medium is Zi。
Fig. 5 is another double-decker array frequency selecting structures diagrammatic cross-section, and the structure is for examining proposition method of the present invention
Accuracy, the double-decker array frequency selecting structures, it include 1 layer of overwrite media, 3 layers of intermediate medium and 1 layer of substrate dielectric；Figure
6 be frequency-selective surfaces FSS array structure schematic diagram corresponding with double-decker array frequency selecting structures in Fig. 5, two layers of frequency choosing
It is identical to select surface FSS array, is all that etching inside radius 3.6mm, slit width 0.5mm circular ring shape obtain on copper foil, circular ring shape unit
Square arrangement, spacing 10mm；ε in figurerThe relative dielectric constant and tangent loss of medium are respectively indicated with tan δ.
As shown in fig. 7, Fig. 7 is under 0 degree of incidence angle of double-decker array frequency selecting structures shown in fig. 5, mutual conductance nanofarad is calculated
The comparison for the upper transmittance that the transmissivity and the present invention tested with exemplar provide, it can be seen that the calculating of transmissivity
As a result the upper transmittance provided without departing from the present invention with test result.
As shown in figure 8, Fig. 8 is 60 degree of incidence angles of double-decker array frequency selecting structures shown in fig. 5, TE polarized electromagnetic wave
Under irradiation, the comparison for the upper transmittance that the transmissivity and the present invention that mutual conductance nanofarad calculates and exemplar is tested provide, therefrom
It can be seen that the upper transmittance that the calculated result and test result of transmissivity are provided without departing from the present invention.
As shown in figure 9, Fig. 9 is 60 degree of incidence angles of double-decker array frequency selecting structures shown in fig. 5, TM polarized electromagnetic wave
Under irradiation, the comparison for the upper transmittance that the transmissivity and the present invention that mutual conductance nanofarad calculates and exemplar is tested provide, therefrom
It can be seen that the upper transmittance that the calculated result and test result of transmissivity are provided without departing from the present invention.
As shown in Figure 10, Figure 10 is to use and identical coated by dielectric mode shown in Fig. 5 and Fig. 6, as shown in figure 11, frequency
When rate selection surface FSS array changes compact arranged side's annular element into, under 15 degree of incidence angles, the irradiation of TE polarized electromagnetic wave,
Mutual conductance nanofarad calculate and FInite Element (finite element method, FEM) transmissivity for being calculated and the present invention to
The comparison of upper transmittance out, it can be seen that the upper transmittance that the present invention provides is can be by the conjunction of array element
Reason designs to approach.
The invention discloses a kind of method for quick predicting of double-deck bandpass-type frequency selecting structures upper transmittance, based on essence
The theoretical method for really solving plan periodic structure electromagnetic scattering problems, has derived in the double-deck bandpass-type frequency selecting structures transmissivity
Limit calculation method；According to the design feature of limited big frequency selecting structures it is found that the electrical property of limited big frequency selecting structures is logical
Often from the big frequency selecting structures succession of plane limitless, therefore the upper transmittance can be used for quickly estimating bilayer zone in engineering
The transmissivity that flow-through frequency selecting structures are likely to be breached, for instructing the design optimization direction of the double-deck bandpass-type frequency selecting structures
Or the coated by dielectric mode of difference is avoided to design.
Using the double-deck bandpass-type frequency selecting structures upper transmittance calculation method of the invention, upper transmittance and array
Equivalent capacity, inductance parameters (L1, C1) and (L2, C2) it is unrelated, therefore no matter incident array of designs, as long as each layer medium is constant
And incoming electromagnetic waveshape is constant, the field transmissivity (the ratio between transmitted field amplitude and in-field amplitude) of the bilayer frequency selecting structures
Upper transmittance can not be higher than.
The field upper transmittance for the double-deck bandpass-type frequency selecting structures that the present invention provides, can extend to limited thickness battle array
The situation of column, and it is unrelated with the internal structure feature of array, internal structure feature has included: whether perfact conductor and limited thickness
Inside array whether embedding medium.
Used herein a specific example illustrates the principle and implementation of the invention, and above embodiments are said
It is bright to be merely used to help understand method and its core concept of the invention；At the same time, for those skilled in the art, foundation
Thought of the invention, there will be changes in the specific implementation manner and application range.To sum up, the content of the present specification should not manage
Solution is limitation of the present invention.
Claims (10)
1. a kind of upper transmittance prediction technique of bilayer bandpass-type frequency selecting structures characterized by comprising
The double-deck bandpass-type frequency selecting structures are located in vacuum environment；Since electromagnetic wave irradiation side, the bilayer bandpass-type frequency
Rate selection structure successively include M layer overwrite media, first frequency selection surface, N layers of intermediate medium, second frequency select surface and
L layers of substrate dielectric；
Obtain electromagnetism wave parameter and medium parameter；The electromagnetism wave parameter includes the frequency and vacuum medium wave of plane of incidence electromagnetic wave
Vector, the medium parameter include each layer overwrite media dielectric constant and magnetic conductivity, each layer intermediate medium dielectric constant and
The dielectric constant and magnetic conductivity of magnetic conductivity and each layer substrate dielectric；
Wave vector normal component and mould admittance are determined according to the electromagnetism wave parameter and the medium parameter；
Objective function is generated according to the wave vector normal component and the mould admittance；
Calculate the minimum of the objective function；
The upper transmittance of the double-deck bandpass-type frequency selecting structures is determined according to the minimum of the objective function.
2. the upper transmittance prediction technique of bilayer bandpass-type frequency selecting structures according to claim 1, feature exist
In determining wave vector normal component and mould admittance according to the electromagnetism wave parameter and the medium parameter, specifically include:
According to the frequency f of the plane of incidence electromagnetic wave, incident electromagnetic wave angular frequency is determined using the π of formula ω=2 f；
According to the incident frequencies f, using formulaDetermine the Electromagnetic Wave Propagation constant k in i-th layer of medium(i)；Wherein ε(i)For the dielectric constant of i-th layer of medium；μ(i)For the magnetic conductivity of i-th layer of medium；
According to wave vector in the vacuumUsing formulaDetermine wave vector tangential component in vacuumWherein
Coordinate z-axis is established in dielectric thickness direction along the double-deck bandpass-type frequency selecting structures,For z coordinate direction vector；
According to the Electromagnetic Wave Propagation constant k in i-th layer of medium(i)And wave vector tangential component in the vacuumUsing formulaAnd Im (γ(i))≤0 determines the wave vector normal component γ in i-th layer of medium(i)；Wherein ktIt is described true
Aerial wave vector tangential componentMould；Im () indicates to take the imaginary part of plural number；
According to the wave vector normal component γ in i-th layer of medium(i), using formula
Determine the mould admittance in i-th layer of mediumWherein r indicates polarized state；TE polarization indicates the polarization of transverse electric field；TM polarization indicates
Transverse magnetic polarization.
3. the upper transmittance prediction technique of bilayer bandpass-type frequency selecting structures according to claim 2, feature exist
In generating objective function according to the wave vector normal component and the mould admittance, specifically include:
According to the wave vector normal component γ in n-th layer medium(n)With the mould admittance in n-th layer mediumDetermine transmission matrix；Institute
Stating transmission matrix includes the first transmission matrix, the second transmission matrix and third transmission matrix；
The coefficient of the objective function is determined according to the transmission matrix；
Objective function is generated according to the coefficient of the objective function.
4. the upper transmittance prediction technique of bilayer bandpass-type frequency selecting structures according to claim 3, feature exist
In,
According to the wave vector normal component γ in n-th layer medium(n)With the mould admittance in n-th layer mediumIt determines transmission matrix, has
Body includes:
The first transmission matrix is calculated according to the following formula
The second transmission matrix is calculated according to the following formula
Third transmission matrix Γ is calculated according to the following formula(m,n):
In formula, znThe z coordinate of n-th of dielectric interface, γ when to be started counting from plane electromagnetic wave incident side(n+1)It is (n+1)th
Wave vector normal component in layer medium, ξ(n+1)For the mould admittance in (n+1)th layer of medium, I is unit matrix, and m, n are natural number；
The coefficient that the objective function is determined according to the transmission matrix, specifically includes:
According to b1=-juMBΩC12/ a calculates the coefficient b of the objective function F (x, y)1；
According to b2=-juBΩCM12/ a calculates the coefficient b of the objective function F (x, y)2；
According to c=Γ11/ a calculates the coefficient c of the objective function F (x, y)；
Wherein,
Γ=Γ(0,M+N+L+1),
ΓMB=Γ(M+1,M+N+L+1),
ΓB=Γ(M+N+1,M+N+L+1),
In formula, M indicates the total number of plies of blanket dielectric layer, and N indicates the total number of plies of middle dielectric layer, and L indicates the total number of plies of substrate dielectric layer,
ΩC12Representing matrix ΩCThe element of 1st row, the 2nd column, ΩCM12Representing matrix ΩCMThe element of 1st row, the 2nd column, Γ11Indicate square
The element of the 1st row of battle array Γ, the 1st column, ΩM12Representing matrix ΩMThe element of 1st row, the 2nd column, ΩM22Representing matrix ΩM2nd row,
The element of 2 column, zMThe z coordinate of m-th dielectric interface, γ when to be started counting from plane electromagnetic wave incident side(M+1)For M+1
Wave vector normal component in layer medium, ΓMB,11Representing matrix ΓMBThe element of 1st row, the 1st column, ΓMB,21Representing matrix ΓMB2nd
The element of row, the 1st column, ΓB,11Representing matrix ΓBThe element of 1st row, the 1st column, ΓB,21Representing matrix ΓBWhat the 2nd row, the 1st arranged
Element, γ(M+N+1)For the wave vector normal component in M+N+1 layers of medium, zM+NWhen to be started counting from plane electromagnetic wave incident side
The z coordinate of the M+N dielectric interface；
Objective function is generated according to the coefficient of the objective function, is specifically included:
According to coefficient b1、b2Objective function F (x, y)=xy+b is generated with c1x+b2y+c。
5. the upper transmittance prediction technique of bilayer bandpass-type frequency selecting structures according to claim 4, feature exist
In determining the upper transmittance of the double-deck bandpass-type frequency selecting structures according to the minimum of the objective function, specifically include:
According to objective function F (x, the y)=xy+b1x+b2The minimum min (| F |) of y+c, using formula
Calculate the upper transmittance T of the double-deck bandpass-type frequency selecting structurestop, wherein | F | it is the mould of objective function F (x, y), | a | it is a
Mould.
6. a kind of upper transmittance forecasting system of bilayer bandpass-type frequency selecting structures characterized by comprising
Parameter acquisition module, for obtaining electromagnetism wave parameter and medium parameter；The electromagnetism wave parameter includes plane of incidence electromagnetism
Wave vector in the frequency and vacuum of wave, the medium parameter include in the dielectric constant and magnetic conductivity, each layer of each layer overwrite media
Between the dielectric constant of medium and the dielectric constant and magnetic conductivity of magnetic conductivity and each layer substrate dielectric；
Wave vector normal component and mould admittance computation module, for determining wave vector according to the electromagnetism wave parameter and the medium parameter
Normal component and mould admittance；
Objective function generation module, for generating objective function according to the wave vector normal component and the mould admittance；
Objective function minimum computing module, for calculating the minimum of the objective function；
Upper transmittance determining module, for determining the double-deck bandpass-type frequency selecting structures according to the minimum of the objective function
Upper transmittance.
7. the upper transmittance forecasting system of bilayer bandpass-type frequency selecting structures according to claim 6, feature exist
In the wave vector normal component and mould admittance computation module specifically include:
Incoming electromagnetic angular frequency computing unit, for the frequency f according to the plane of incidence electromagnetic wave, using the π of formula ω=2
F determines incident electromagnetic wave angular frequency；
Electromagnetic Wave Propagation constant calculations module is used for according to the incident frequencies f, using formulaIt determines
Electromagnetic Wave Propagation constant k in i-th layer of medium(i)；Wherein ε(i)For the dielectric constant of i-th layer of medium；μ(i)For i-th layer of medium
Magnetic conductivity；
Wave vector tangential component computing module in vacuum, for according to wave vector in the vacuumUsing formulaDetermine wave vector tangential component in vacuumWherein along the medium of the double-deck bandpass-type frequency selecting structures
Thickness direction establishes coordinate z-axis,For z coordinate direction vector；
Wave vector normal component computing module, for according to the Electromagnetic Wave Propagation constant k in i-th layer of medium(i)And the vacuum medium wave
Swear tangential componentUsing formulaAnd Im (γ(i))≤0 determines the wave vector normal direction point in i-th layer of medium
Measure γ(i)；Wherein ktIt is wave vector tangential component in the vacuumMould；Im () indicates to take the imaginary part of plural number；
Mould admittance computing unit, for according to the wave vector normal component γ in i-th layer of medium(i), using formulaDetermine the mould admittance in i-th layer of mediumWherein r indicates polarized state；TE
Polarization indicates the polarization of transverse electric field；TM polarization indicates transverse magnetic polarization.
8. the upper transmittance forecasting system of bilayer bandpass-type frequency selecting structures according to claim 7, feature exist
In objective function generation module specifically includes:
Transmission matrix generation unit, for according to the wave vector normal component γ in n-th layer medium(n)It is led with the mould in n-th layer medium
It receivesDetermine transmission matrix；The transmission matrix includes the first transmission matrix, the second transmission matrix and third transmission matrix；
Objective function coefhcient computing unit, for determining the coefficient of the objective function according to the transmission matrix；
Objective function generation unit, for generating objective function according to the coefficient of the objective function.
9. the upper transmittance forecasting system of bilayer bandpass-type frequency selecting structures according to claim 8, feature exist
In,
The transmission matrix generation unit, specifically includes:
First transmission matrix generates subelement, for calculating the first transmission matrix according to the following formula
Second transmission matrix generates subelement, for calculating the second transmission matrix according to the following formula
Third transmission matrix generates subelement, for calculating third transmission matrix Γ according to the following formula(m,n):
In formula, znThe z coordinate of n-th of dielectric interface, γ when to be started counting from plane electromagnetic wave incident side(n+1)It is (n+1)th
Wave vector normal component in layer medium, ξ(n+1)For the mould admittance in (n+1)th layer of medium, I is unit matrix, and m, n are natural number；
Objective function coefhcient computing unit, specifically includes:
Coefficient b1Computation subunit, for according to b1=-juMBΩC12/ a calculates the coefficient b of the objective function F (x, y)1；
Coefficient b2Computation subunit, for according to b2=-juBΩCM12/ a calculates the coefficient b of the objective function F (x, y)2；
Coefficient c computation subunit, for according to c=Γ11/ a calculates the coefficient c of the objective function F (x, y)；
Wherein,
Γ=Γ(0,M+N+L+1),
ΓMB=Γ(M+1,M+N+L+1),
ΓB=Γ(M+N+1,M+N+L+1),
In formula, M indicates the total number of plies of blanket dielectric layer, and N indicates the total number of plies of middle dielectric layer, and L indicates the total number of plies of substrate dielectric layer,
ΩC12Representing matrix ΩCThe element of 1st row, the 2nd column, ΩCM12Representing matrix ΩCMThe element of 1st row, the 2nd column, Γ11Indicate square
The element of the 1st row of battle array Γ, the 1st column, ΩM12Representing matrix ΩMThe element of 1st row, the 2nd column, ΩM22Representing matrix ΩM2nd row,
The element of 2 column, zMThe z coordinate of m-th dielectric interface, γ when to be started counting from plane electromagnetic wave incident side(M+1)For M+1
Wave vector normal component in layer medium, ΓMB,11Representing matrix ΓMBThe element of 1st row, the 1st column, ΓMB,21Representing matrix ΓMB2nd
The element of row, the 1st column, ΓB,11Representing matrix ΓBThe element of 1st row, the 1st column, ΓB,21Representing matrix ΓBWhat the 2nd row, the 1st arranged
Element, γ(M+N+1)For the wave vector normal component in M+N+1 layers of medium, zM+NWhen to be started counting from plane electromagnetic wave incident side
The z coordinate of the M+N dielectric interface；
Objective function generation unit, specifically includes:
Objective function generates subelement, for according to coefficient b1、b2Objective function F (x, y)=xy+b is generated with c1x+b2y+c。
10. the upper transmittance forecasting system of bilayer bandpass-type frequency selecting structures according to claim 9, feature exist
In the upper transmittance determining module specifically includes:
Upper transmittance computing unit, for according to objective function F (x, the y)=xy+b1x+b2Y+c minimum min (| F
|), using formulaCalculate the upper transmittance T of the double-deck bandpass-type frequency selecting structurestop, wherein | F | be
The mould of objective function F (x, y), | a | it is the mould of a.
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