CN110705073A - High-frequency scattering method for coating complex target by anisotropic medium under point source excitation - Google Patents
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Abstract
The invention relates to a high-frequency scattering method for coating a complex target by an anisotropic medium under the excitation of a point source, which converts the spherical wave problem of an airspace into a familiar plane wave incident layered medium model in a spectral domain, and returns to the state of calculating an airspace scattering field through saddle point method approximate processing, so that the problem is simplified; in addition, the scattering process that point source excitation firstly penetrates into the anisotropic medium layer and then is reflected in the layer and finally transmitted is directly depicted and described, so that the transmission process of electromagnetic waves in each layer of the constructed PEC substrate anisotropic medium coating is clearly displayed, the PEC substrate anisotropic medium coating is more visualized, and the physical significance is more definite.
Description
Technical Field
The invention relates to a high-frequency modeling method for an anisotropic complex target, in particular to a high-frequency modeling method for the anisotropic complex target based on point source excitation, and belongs to the field of electromagnetic field calculation and application thereof.
Background
In modern military wars, the research on the scattering property of a complex coating target is of great importance, and the research on the radar property of an anisotropic medium coating target has wide requirements in the aspects of military stealth and penetration technologies and even terminal guidance radar working modes, which has great significance for national defense and aviation sea defense in China. With the development of modern sophisticated weapons, the poor detection of military targets is achieved by adjusting the anisotropic properties of the coating materials, including the direction of the optical axis of the medium, in terms of stealth design, which is significantly different from PEC targets and isotropic material coatings in terms of spatial and polarization properties of scattering and is more complex, thus placing higher demands on modeling of high frequency scattering of anisotropic medium coated complex targets.
In the past researches, the detection distance of a radar tends to be infinite far-field conditions, so that the obtained high-frequency solution of the scattering of the anisotropic material coated target is calculated under the condition of plane incident electromagnetic wave irradiation, but in actual measurement and application, particularly when a high-precision weapon such as an end-guided radar, a missile or an airplane approaches to the detection target, the incident electromagnetic wave generated under the limited source distance is generated, and the high-frequency algorithm research cannot be simply carried out under the plane wave incident condition. Based on that any excitation source can be composed of infinite point sources, the method lays a foundation for solving the problem of solving the high-frequency scattering of the anisotropic medium coated complex target under the condition of any source excitation in the follow-up further research, and firstly needs to solve the high-frequency solution of the point source excitation.
In the prior art, a target near-field RCS calculation model, a spherical wave incidence physical optical high-frequency algorithm and a time-domain near-field calculation complex target modeling algorithm are introduced in the prior art, but the problem of high-frequency scattering of an anisotropic medium coated complex target under the condition of point source excitation spherical wave incidence is not solved comprehensively from the anisotropic coating angle. In summary, the prior art does not disclose a high-frequency scattering modeling method based on anisotropic medium coating of a complex target under point source excitation.
Disclosure of Invention
Aiming at the technical problems in the prior art, the invention provides a high-frequency scattering modeling method for coating (uniaxial dielectric and biaxial dielectric) complex targets by anisotropic media based on point source excitation (including electric dipole and magnetic dipole excitation), which accords with theoretical derivation and engineering application, fills the technical gap of the existing high-frequency scattering algorithm meeting requirements of anisotropic coating and point source excitation simultaneously, has a result completely matched with commercial electromagnetic simulation software, provides estimated data for actual measurement, and has good effect.
In order to achieve the purpose, the invention adopts the following technical scheme:
a high-frequency scattering method for coating a complex target by an anisotropic medium under point source excitation is characterized by comprising the following steps:
step 1: in a homogeneous medium is oriented to
The electric field generated by the point source can be derived by a vector bit method or a dyadic Green function method, wherein the dyadic Green function method expresses the most direct relation between the source and the field, and then the magnetic field expression of the Hertz dipole is solved by a MAXWELL (Maxwellian equation system);
the dyadic green function method is implemented as follows:
in theory of high electromagnetic field, the electric field expression in the free space field-source relationship is:
are defined hereinAnd the free space electric dyadic Green function and the magnetic dyadic Green function are
The electromagnetic field expression can be written in a more compact form:
wherein the space electric dipole is
Magnetic dipole of
The integral calculation can obtain that when only an electric dipole exists in the space, the space domain electromagnetic field is as follows:
similarly, if only magnetic dipoles exist in the space, the spatial electromagnetic field is:
step 2: based on the step 1, the point source scalar wave equation in the air layer based on the spherical coordinate system is adopted:
assuming that its fourier transform exists, that is:
under electric dipole excitation:
under magnetic dipole excitation:
in the incident conditions of the two excitation sources, the generated field expressions can show the mutual dual relationship, so that the mutual dual relationship can be seen; the frequency domain scalar wave function is deduced, and the expression of the current element of the electric dipole in any direction in the free space in the spectral domain of the electric field and the magnetic field is as follows:
electric field in spectral domain:
magnetic field in spectral domain:
wherein,
the expression of the magnetic current element in any magnetic dipole moment direction in the free space in the spectral domain of the electric field and the magnetic field is as follows:
electric field in spectral domain:
magnetic field in spectral domain:
wherein,
as can be seen from this expression, the radiation field can be divided into two types, an upward traveling wave and a downward traveling wave;
and step 3: the downlink wave in the arbitrary point source incident field in the step 2 is incident to the anisotropic upper surface as incident wave, the primary reflection and interlayer transmission field are sequentially solved, and each secondary transmission field is transmitted to the air layer after being reflected for multiple times in the anisotropic medium layer, so that the corresponding physical transmission process in the invention can be visually shown;
the dielectric constant and the magnetic permeability of the anisotropic medium layer are set as follows:
the primary reflection field on the upper surface can degrade the original problem to a half-space problem, and under the condition of a half-space condition that the upper surface is an air layer and the lower surface is an anisotropic medium layer, the total scattering field on the upper surface only comprises an incident field, a direct field and a primary reflection field formed by point sources;
(1.1) solving the reflection field of the upper surface by adopting the point source field expression and the field expression in the anisotropic medium layer and the air layer and by using the boundary condition of the upper surface;
wherein,
(1.2) by utilizing the boundary condition of the boundary of the air layer and the anisotropic medium layer, a coefficient matrix of a wave field which is reflected by the upper surface of the anisotropic medium layer and moves downwards and a coefficient matrix of a field which is transmitted to the air layer can be obtained by a simultaneous equation system;
(1.3) obtaining the two groups of upward transmission coefficients of the top surface on the anisotropic medium layer
And the downstream reflection coefficient
Then, the field of the electromagnetic wave reflected and propagated in the anisotropic medium layer every time and the field transmitted to the air layer can be obtained by adopting a similar process; the method comprises the following steps that an expression mode of a transmission matrix is adopted, electromagnetic waves are reflected for n times in a layer and then transmitted to a field in an air layer, each secondary scattered field forms an geometric progression, and all the secondary scattered fields are superposed to obtain a total secondary scattered field;
namely:
wherein
and 4, step 4: through the above analysis, it is very clear which parts are contained in the total field in the air layer based on step 3, and the electric field expressions in the spectral domain are solved on the basis of the saddle point method, because the infinite complex integral approximate calculation can be solved by the saddle point method;
taking magnetic dipole excitation as an example, the spectral component expression of the point source direct field is as follows:
the spectral domain field satisfies the following integral form,
The following points of view are set,
wherein r isd，θd，
The method comprises the following steps of (1) knowing;
by the saddle point method, saddle points 1 and 2 are expressed as follows after eliminating the false saddle point:
the direct wavefield for the point source is as follows:
in the same way, the primary reflection field can be found as follows:
wherein
It can also be seen that the expressions saddle point 1 and saddle point 2, representing the distance of (x ', y ', -z ') to the field point, actually demonstrate a mirrored source point, i.e. the solution of the reflected field in the case of a point source half-space is the solution of its image source in unbounded space; the saddle point obtained by the total secondary scattering field can be obtained by the sum of the secondary scattering fields reflected and transmitted in the n layers in the dielectric layer:
the secondary scattered field expression is:
and 5, obtaining a space-domain physical optical scattering field solution of the single triangular plane sheet coated by the anisotropic medium based on the step 4, wherein according to an equivalent principle, the scattering field can be regarded as a radiation field of surface equivalent electromagnetic flow, a Stewarton-Zealand equation exists, and the radiation field of equivalent electromagnetic flow radiation can be expressed as
Finding the equivalent electromagnetic current on the surface of the coating layer with respect to the origin coordinates:
substituting a Sterlon-Cwland equation to obtain a P0 solution of a single patch;
and finally, obtaining a scattering field of the whole target by superposing N triangular surface elements illuminated by incident waves:
the invention brings the following beneficial effects:
the invention provides a far-field scattered field solving method based on an anisotropic coating target under the condition of point source excitation, which has the advantages that the spherical wave problem of an airspace is converted into a familiar plane wave incident layered medium model in a spectrum domain, and the method returns to the state of calculating the airspace scattered field through saddle point approximate processing, so that the problem is simplified; in addition, the scattering process that point source excitation firstly penetrates into the anisotropic medium layer and then is reflected in the layer and finally transmitted is directly depicted and described, so that the transmission process of electromagnetic waves in each layer of the constructed PEC substrate anisotropic medium coating is clearly displayed, the PEC substrate anisotropic medium coating is more visualized, and the physical significance is more definite.
Drawings
FIG. 1 is a flow chart of a high frequency modeling method based on anisotropic complex target under point source excitation in the present invention.
Figure 2 is a ray path schematic of the PEC substrate anisotropic media coating of the present invention (wherein,
(1) exciting a primary transmission field incident on the upper surface of the dielectric layer and downwards transmitting the primary transmission field into the anisotropic dielectric layer for power supply
(2) Is a reflection field reflected after the primary transmission field in the anisotropic medium layer is incident on the boundary of the bottom layer
(3) Is the reflection field of the medium reflection field as the incident field after being incident on the upper surface of the dielectric layer
(4) Is (3) the reflected field after the intermediate field is incident again on the bottom surface as the incident field
)。
Fig. 3 is a first setup interface in an embodiment.
FIG. 4 is a second setup interface in an example embodiment.
Figure 5 is a diagram showing the results of the electric field far field.
FIG. 6 is a schematic diagram of the calculated far field electric field.
FIG. 7 is a graph showing the results of the comparison.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is further described in detail with reference to examples. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
The invention adopts the following technical scheme:
starting from a wave equation, deducing a field equation of a point source in a Fourier transform mode, decomposing spherical waves into superposition of plane waves, giving the superposition in a spectral domain mode, and combining the previous research of incidence of the plane waves on the anisotropic coating target to form a high-frequency scattering result of the point source excitation anisotropic coating target under the condition of a space domain; comprises the following steps:
s1, starting from a wave equation, giving spectral domain expression of a point source (electric type and magnetic type hertzian dipole) radiation field in a free space, decomposing spherical waves into plane waves for superposition, and using the plane waves as an excitation source to enter;
s2, carrying out geometric modeling on the complex target, decomposing the complex target by adopting a traditional triangular patch subdivision modeling mode, and describing the shape of the target through the information of the surface element, the point and the edge.
S3, performing electromagnetic modeling on the complex target, and solving the physical optical solution of the single triangular plane sheet under the point source incidence anisotropic coating condition in S1, wherein the physical optical solution comprises the following components:
s31, subdividing the shape of the electrically large-size complex target by a triangular plane sheet to enable the subdivided anisotropic coating surface element electromagnetic scattering model to meet the far field condition under the point source irradiation condition;
s32, applying a high-frequency local field principle of tangent plane approximation, and solving equivalent surface electromagnetic flow of any electric type and magnetic type point source excitation anisotropic material coating plane element by adopting spectral domain full-wave solution;
s33, obtaining a dyadic Green function representing the electromagnetic problem according to the judgment of the number of the illuminated surfaces of the incident wave, and then deriving a physical optical solution of the illuminated surface patch scattered field by adopting a saddle point method to carry out asymptotic calculation;
s4, superposing scattering fields of a plurality of triangular plane sheets illuminated by incident waves by an S33 according to a Stratton-Chu (Sterlon-Verland) formula and a far-field approximate condition to finally obtain a whole complex anisotropic coated high-frequency physical optical scattering field solution;
according to the preferred embodiment, the invention mainly converts the point source (electric dipole and magnetic dipole) incidence problem in the airspace into the plane wave expansion problem of spherical waves in the spectral domain through the spectral domain method, then solves the scattering field based on the prior art that the plane waves are incident on the PEC substrate uniaxial electric anisotropic medium layer, and finally performs approximate calculation on infinite complex integral through the saddle point method, thereby obtaining the physical optical algorithm of the target electromagnetic scattering in the airspace.
In S31, when the electrically large and complex target surface is dispersed into a plurality of planar polygonal surface elements, the size of the subdivision of the triangular surface element needs to satisfy the requirement that the near-field scattering of the target under spherical wave incidence is approximated to the far-field scattering under local planar wave incidence, and generally, the requirement that the phase difference of the wave front is less than pi/8 is satisfied, so as to ensure that all surface elements are in the far field of the excitation source.
In S32, the geometric model of the point source excitation anisotropic layered medium in any direction is that the upper layer is an air layer, the point source is placed at r ═ x ', y ', z ' in the air layer, and the excitation direction is
The middle layer is an anisotropic medium layer with the thickness d, and the PEC substrate is arranged below the middle layer;
in said S32, the tangential plane surface field is solved for a surface field approximating a uniaxial electrically anisotropic medium coated infinite PEC plate, i.e. a surface area of finite point source incidence is equivalent to the calculation of an infinite coated plate model at the incidence of local plane waves. The method specifically comprises the following steps: dividing a radiation field in a point source spectral domain into an upgoing wave and a downgoing wave, wherein the upgoing wave is used as a part of a total field of a far zone and is a direct wave field of radiation; the down-going wave is used as an incident wave and is incident to the upper surface of the anisotropic layered medium model;
solving a primary reflection field of the downlink incident wave reaching a far field point through the reflection of the upper surface and a primary transmission field in the anisotropic medium layer formed through the downward transmission of the upper surface;
further solving each secondary scattered field formed by the field points of the primary transmission field, which are reflected in the layer and then transmitted to the air layer through multiple reflections;
in the S33, the saddle point method and the steepest descent method are common methods for the infinite negative integral approximate calculation, and the physical significance of the method is that the method describes the propagation direction of the ray electromagnetic field; the field in the spectral domain can be directly converted into a scattered field solution in the spatial domain by ray wave field approximation; the preferred embodiments of the present invention will be described below with reference to the accompanying drawings.
As shown in fig. 1, for the scattering problem characterization under any point source excitation, the hertzian dipole includes both an electric dipole and a magnetic dipole, and although the magnetic current or the magnetic current element does not actually exist, when the diameter of the current-carrying small coil is far smaller than the wavelength, the current-carrying small coil can be equivalent to the magnetic dipole;
solving the expression of the radiation field spectral domain of a point source in any direction in a free space, wherein the calculation comprises the following specific steps:
step 1: in a homogeneous medium is oriented toThe electric field generated by the point source can be derived by a vector bit method or a dyadic Green function method, wherein the dyadic Green function method expresses the most direct relation between the source and the field, and then the magnetic field expression of the Hertz dipole is solved by a MAXWELL (Maxwellian equation system);
the dyadic green function method is implemented as follows:
in theory of high electromagnetic field, the electric field expression in the free space field-source relationship is:
are defined herein
And the free space electric dyadic Green function and the magnetic dyadic Green function are
wherein the space electric dipole is
Magnetic dipole of
The integral calculation can obtain that when only an electric dipole exists in the space, the space domain electromagnetic field is as follows:
similarly, if only magnetic dipoles exist in the space, the spatial electromagnetic field is:
step 2: based on the step 1, the point source scalar wave equation in the air layer based on the spherical coordinate system is adopted:
assuming that its fourier transform exists, that is:
the expression of the scalar wave equation in the spectral domain can be found as follows:
under electric dipole excitation:
under magnetic dipole excitation:
in the incident conditions of the two excitation sources, the generated field expressions can show the mutual dual relationship, so that the mutual dual relationship can be seen; the frequency domain scalar wave function is deduced, and the expression of the current element of the electric dipole in any direction in the free space in the spectral domain of the electric field and the magnetic field is as follows:
electric field in spectral domain:
magnetic field in spectral domain:
wherein,
the expression of the magnetic current element in any magnetic dipole moment direction in the free space in the spectral domain of the electric field and the magnetic field is as follows: electric field in spectral domain:
magnetic field in spectral domain:
wherein,
as can be seen from this expression, the radiation field can be divided into two types, an upward traveling wave and a downward traveling wave;
and step 3: as shown in fig. 2, the downlink wave in the arbitrary point source incident field in step 2 is incident on the anisotropic upper surface as an incident wave, the primary reflection field and the interlayer transmission field are sequentially solved, and each secondary transmission field is transmitted to the air layer after being reflected for multiple times in the anisotropic medium layer, so that the corresponding physical propagation process in the invention can be visually shown;
the dielectric constant and the magnetic permeability of the anisotropic medium layer are set as follows:
the original problem can be degraded to a half-space problem by the primary reflection field of the upper surface, and in the case of the half-space problem that the upper surface is an air layer and the lower surface is an anisotropic medium layer, the total scattering field of the upper surface is only an incident field, a direct field and a primary reflection field formed by point sources.
(1.1) the reflection field of the upper surface can be solved by adopting the point source field expression and the field expression in the anisotropic medium layer and the air layer and further utilizing the boundary condition of the upper surface.
Wherein,
(1.2) by utilizing the boundary condition of the boundary of the air layer and the anisotropic medium layer, a coefficient matrix of a wave field which is reflected by the upper surface of the anisotropic medium layer and moves downwards and a coefficient matrix of a field which is transmitted to the air layer can be obtained by a simultaneous equation system;
(1.3) obtaining the two groups of upward transmission coefficients of the top surface on the anisotropic medium layer
And the downstream reflection coefficientThen, the field of the electromagnetic wave which is transmitted to the air layer and reflected in the anisotropic medium layer can be obtained by adopting a similar process. The electromagnetic wave is transmitted to the air after n times of reflection in the layer by adopting the expression mode of a transmission matrixAnd (3) forming an geometric series by the fields in the layer and all the secondary scattered fields, and superposing all the secondary scattered fields to obtain a total secondary scattered field.
Namely:
wherein
And 4, step 4: through the above analysis, it is very clear which parts are contained in the total field in the air layer based on step 3, and the electric field expressions in the spectral domain are solved on the basis of the saddle point method, because the infinite complex integral approximate calculation can be solved by the saddle point method;
taking magnetic dipole excitation as an example, the spectral component expression of the point source direct field is as follows:
the spectral domain field satisfies the following integral form,
The following points of view are set,
wherein r isd，θd，
The method comprises the following steps of (1) knowing;
by the saddle point method, saddle points 1 and 2 are expressed as follows after eliminating the false saddle point:
the direct wavefield for the point source is as follows:
in the same way, the primary reflection field can be found as follows:
wherein
It can also be seen that the expressions saddle point 1 and saddle point 2, representing the distance of (x ', y ', -z ') to the field point, actually demonstrate a mirrored source point, i.e. the solution of the reflected field in the case of a point source half-space is the solution of its image source in unbounded space; the saddle point obtained by the total secondary scattering field can be obtained by the sum of the secondary scattering fields reflected and transmitted in the n layers in the dielectric layer:
the secondary scattered field expression is:
and 5, obtaining a space-domain physical optical scattering field solution of the single triangular plane sheet coated by the anisotropic medium based on the step 4, wherein according to an equivalent principle, the scattering field can be regarded as a radiation field of surface equivalent electromagnetic flow, a Stewarton-Zealand equation exists, and the radiation field of equivalent electromagnetic flow radiation can be expressed as
Through the above steps, the possible writing of the equivalent electromagnetic flow on the coating layer surface with respect to the origin coordinates can be found as:
substituting a Sterlon-Verland equation to obtain a PO solution of a single patch;
and finally, obtaining a scattering field of the whole target by superposing N triangular surface elements illuminated by incident waves:
in conclusion, the method has the advantages of high calculation speed, high calculation precision, capability of well showing the physical propagation process and the like, can completely correspond to the calculation result of the commercial simulation software FEKO through modeling simulation, provides specific estimated data for the actual radar design, and saves the cost.
The MATLAB programming was performed according to the inventive steps above, calculating the final total scatter field, as opposed to FEKO calculations, here demonstrating the reasonable credibility of the described invention for the supplementary examples.
For the isotropic coating infinite plane model, 1) setting the medium in Feko to be a lossless isotropic medium
As shown in fig. 3.
2) The orientation of the magnetic dipole in Feko is set toThe source point is located at r' ═ 0, 0, 1, where the magnetic dipole moment Iml is 2; as shown in fig. 4.
In the far field calculation, in order to eliminate the influence of the distance, the amplitude of the far field electric field is multiplied by the radar distance set in the calculation program in the calculation example.
In FEKO, the results of the far field of the electric field are shown in FIG. 5.
The parameter setting of the algorithm is the same as FEKO, and respectively comprises the following parameters of the magnetic dipole direction and the source point position, and the lossless isotropy:
sox＝-2^0.5/2；soy＝0；soz＝2^0.5/2；
svx＝0：svy＝0；svz＝1；
epspp＝3；epsvv＝3；
the calculated far field electric field is shown in fig. 6. The comparative results are shown in FIG. 7.
Although the present invention has been described in detail with reference to preferred embodiments, the foregoing description should not be construed as limiting the present invention, and any modifications, equivalents, improvements and the like, which are within the spirit and principle of the present invention, will occur to those skilled in the art upon reading the foregoing description.
Claims (1)
1. A high-frequency scattering method for coating a complex target by an anisotropic medium under point source excitation is characterized by comprising the following steps:
step 1: in a homogeneous medium is oriented to
The electric field generated by the point source can be derived by a vector bit method or a dyadic Green function method, wherein the dyadic Green function method expresses the most direct relation between the source and the field, and then the magnetic field expression of the Hertz dipole is solved by a MAXWELL (Maxwellian equation system);
the dyadic green function method is implemented as follows:
in theory of high electromagnetic field, the electric field expression in the free space field-source relationship is:
are defined herein
And the free space electric dyadic Green function and the magnetic dyadic Green function are
The electromagnetic field expression can be written more compactForm (a):
wherein the space electric dipole is
Magnetic dipole of
The integral calculation can obtain that when only an electric dipole exists in the space, the space domain electromagnetic field is as follows:
similarly, if only magnetic dipoles exist in the space, the spatial electromagnetic field is:
step 2: based on the step 1, the point source scalar wave equation in the air layer based on the spherical coordinate system is adopted:
assuming that its fourier transform exists, that is:
the expression of the scalar wave equation in the spectral domain can be found as follows:
under electric dipole excitation:
under magnetic dipole excitation:
in the incident conditions of the two excitation sources, the generated field expressions can show the mutual dual relationship, so that the mutual dual relationship can be seen; the frequency domain scalar wave function is deduced, and the expression of the current element of the electric dipole in any direction in the free space in the spectral domain of the electric field and the magnetic field is as follows:
electric field in spectral domain:
magnetic field in spectral domain:
wherein,
the expression of the magnetic current element in any magnetic dipole moment direction in the free space in the spectral domain of the electric field and the magnetic field is as follows:
electric field in spectral domain:
magnetic field in spectral domain:
wherein,
as can be seen from this expression, the radiation field can be divided into two types, an upward traveling wave and a downward traveling wave;
and step 3: the downlink wave in the arbitrary point source incident field in the step 2 is incident to the anisotropic upper surface as incident wave, the primary reflection and interlayer transmission field are sequentially solved, and each secondary transmission field is transmitted to the air layer after being reflected for multiple times in the anisotropic medium layer, so that the corresponding physical transmission process in the invention can be visually shown;
the dielectric constant and the magnetic permeability of the anisotropic medium layer are set as follows:
the primary reflection field on the upper surface can degrade the original problem to a half-space problem, and under the condition of a half-space condition that the upper surface is an air layer and the lower surface is an anisotropic medium layer, the total scattering field on the upper surface only comprises an incident field, a direct field and a primary reflection field formed by point sources;
(1.1) solving the reflection field of the upper surface by adopting the point source field expression and the field expression in the anisotropic medium layer and the air layer and by using the boundary condition of the upper surface;
wherein,
(1.2) by utilizing the boundary condition of the boundary of the air layer and the anisotropic medium layer, a coefficient matrix of a wave field which is reflected by the upper surface of the anisotropic medium layer and moves downwards and a coefficient matrix of a field which is transmitted to the air layer can be obtained by a simultaneous equation system;
(1.3) obtaining the two groups of upward transmission coefficients of the top surface on the anisotropic medium layer
And the downstream reflection coefficient
Then, the field of the electromagnetic wave reflected and propagated in the anisotropic medium layer every time and the field transmitted to the air layer can be obtained by adopting a similar process; the electromagnetic wave is reflected for n times in the layer and transmitted to the field in the air layer, each secondary scattered field forms an geometric progression, and the electromagnetic wave is transmitted to the air layerAll the secondary scattered fields are superposed to obtain a total secondary scattered field;
namely:
wherein
and 4, step 4: through the above analysis, it is very clear which parts are contained in the total field in the air layer based on step 3, and the electric field expressions in the spectral domain are solved on the basis of the saddle point method, because the infinite complex integral approximate calculation can be solved by the saddle point method;
taking magnetic dipole excitation as an example, the spectral component expression of the point source direct field is as follows:
the spectral domain field satisfies the following integral form,
The following points of view are set,
wherein r isd，θd，
The method comprises the following steps of (1) knowing;
by the saddle point method, saddle points 1 and 2 are expressed as follows after eliminating the false saddle point:
θs＝θd，
the direct wavefield for the point source is as follows:
saddle points 1 and 2 represent the propagation direction of the direct wave field;
in the same way, the primary reflection field can be found as follows:
wherein
It can also be seen that the expressions saddle point 1 and saddle point 2, representing the distance of (x ', y ', -z ') to the field point, actually demonstrate a mirrored source point, i.e. the solution of the reflected field in the case of a point source half-space is the solution of its image source in unbounded space; the saddle point obtained by the total secondary scattering field can be obtained by the sum of the secondary scattering fields reflected and transmitted in the n layers in the dielectric layer:
θs＝θb，
the secondary scattered field expression is:
and 5, obtaining a space-domain physical optical scattering field solution of the single triangular plane sheet coated by the anisotropic medium based on the step 4, wherein according to an equivalent principle, the scattering field can be regarded as a radiation field of surface equivalent electromagnetic flow, a Stewarton-Zealand equation exists, and the radiation field of equivalent electromagnetic flow radiation can be expressed as
Finding the equivalent electromagnetic current on the surface of the coating layer with respect to the origin coordinates:
substituting a Sterlon-Verland equation to obtain a PO solution of a single patch;
and finally, obtaining a scattering field of the whole target by superposing N triangular surface elements illuminated by incident waves:
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