CN113076680A - Topological optimization-based super-surface retroreflector microstructure design method - Google Patents
Topological optimization-based super-surface retroreflector microstructure design method Download PDFInfo
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Abstract
The invention provides a topological optimization-based super-surface retroreflector microstructure design method, which comprises the following steps of: establishing a super-surface multi-channel reflector; dividing a design domain into regular rectangular sub-grid arrays by a two-dimensional periodic grid, and describing the configurations of different microstructures by the difference combination of metal layers in the two-dimensional sub-grid arrays; acquiring the length and the width of the supercell according to the incident angle and the specific frequency of the incident wave obliquely incident to the multichannel reflector; constructing a two-dimensional matrix, and enabling each array element in the two-dimensional matrix to represent the attachment or the loss of the metal layer in the corresponding design domain sub-grid; modeling the scattering characteristic of a two-dimensional periodic array consisting of the supercells, and carrying out configuration optimization on the super-surface microstructures in the supercells by using a design target that the ratio of the reflection power of the multichannel reflector to the reverse direction of the required specific frequency at the incident angle to the total reflection power in all directions is the maximum. The invention takes the supercell as a design domain, obtains reasonable metal patch distribution and realizes the super surface retro-reflector with the maximum retro-reflection power ratio.
Description
Technical Field
The invention relates to the field of retro-reflectors, in particular to a micro-structure optimization method for a retro-reflector based on a super surface.
Background
Retroreflection is a particular physical phenomenon in which an incident wave is reflected on a reflective surface in the direction of the wave's incidence. Since the discovery, the method attracts the attention of researchers related to the research field by virtue of unique response characteristics, and with the continuous development of an electromagnetic field theory and a preparation process, the retroreflection has great application potential in the fields of target identification, satellite communication, ship navigation and rescue, radar scattering cross section enhancement, remote sensing, traffic guidance and the like. For example, in the field of target identification, a retro-reflector is mounted on a target to be identified, when a detection wave scans the retro-reflector, the retro-reflector reflects the detection wave back to a detector with strong echo power, and therefore the target identification degree is improved. As another example, in a traffic guidance instruction, a retro-reflector is used on a guide to ensure visibility of a guide card at night. Currently, retro-reflective realization frequency bands already cover the light wave band, the millimeter wave band and the microwave band.
For the retro-reflection of obliquely incident waves, conventional methods such as metal corner reflectors, hollow echo reflectors, eaton lenses, metal gratings, etc. are designed based on a three-dimensional metal structure or three-dimensional distribution design of materials in reflector elements, and the applicability of these conventional methods is greatly limited. The planar retroreflection antenna, Atta antenna, is a two-dimensional planar reflector attached by a metal etched structure, and the occurrence of the planar retroreflection antenna changes the realization form of the retroreflection antenna from a three-dimensional structure to a two-dimensional structure. Each period of the antenna array comprises four one-dimensional arranged microstrip patch antennas with the same size, the two patches are connected through a microstrip type transmission line, and the length of the transmission line is used for adjusting the electrical length between the two antennas so as to adjust the phase. Through the transmission lines with different phase shifts, the phase gradient caused by the external oblique incident plane wave can be reversed, so that the antenna array reversely transmits the beam. The inverse gradient returns the wavefront radiation back to the direction of incidence. However, the complexity of transmission lines limits the extension of retro-reflective antennas to bands above millimeter-wave. In recent years, corresponding research has shown that a reasonable sub-wavelength super-surface array can control the propagation direction of electromagnetic wave reflection and refraction. Researchers in the relevant research field have given more applicability to two-dimensional periodic super-surfaces, including two-dimensional super-surface retro-reflectors. The retro-reflective properties are achievable by the superposition of the reflection phases of the elements of the array of non-periodic super-surfaces. However, larger scale super-surface arrays are required due to the large number of different phase discrete elements required in phase superposition. Another type of meta-surface based retroreflector is based on a two-dimensional periodic array of phase-gradient meta-surfaces, studies have shown that planar phase-gradient meta-surfaces can produce multi-channel reflections, including retro-reflective channels. The phase gradient metasurface consists of a two-dimensional periodic array of supercells, and the MS array will produce unidirectional retroreflection when each supercell comprises a set of one-dimensional copper grids with linear phase changes. However, if too many copper grid substructures exist in the supercell, the size of the substructures is required to be far smaller than the working wavelength, which has a high requirement on the preparation precision, if design and preparation errors exist, gradient phase discontinuity is generated, the retroreflection efficiency is reduced, and it is necessary to find a retroreflection implementation form with low number of substructures.
Disclosure of Invention
According to the technical problem that the conventional supercell is difficult to prepare, the design method of the super surface retro-reflector microstructure based on topological optimization is provided. The invention takes the supercell as a design domain, obtains reasonable metal patch distribution and realizes the super surface retro-reflector with the maximum retro-reflection power ratio.
The technical means adopted by the invention are as follows:
the invention discloses a topological optimization-based super-surface retroreflector microstructure design method, which is characterized by comprising the following steps of:
obtaining the conditions of material selection and size limitation of a dielectric substrate, and establishing a super-surface multichannel reflector with a periodic metal etching microstructure array according to the generalized Snell's law, wherein the super-surface multichannel reflector comprises the dielectric substrate, a metal grounding plate is arranged on the lower side of the dielectric substrate, and a metal microstructure is arranged on the surface of the upper side of the dielectric substrate;
dividing a composition cycle of the super-surface array into a super-cell, taking the attachment range of the metal microstructure on the upper side of the super-cell surface substrate as a design domain, dividing the design domain into a regular rectangular sub-grid array by using a two-dimensional periodic grid, controlling and adjusting the attachment and the loss of a rectangular metal layer in each sub-grid, and describing the configurations of different microstructures by using the difference combination of the metal layers in the two-dimensional sub-grid array;
acquiring the length and the width of the supercell according to the incident angle of incident waves obliquely incident to the multichannel reflector and the required specific frequency of the incident waves;
constructing a two-dimensional matrix, and enabling each array element in the two-dimensional matrix to represent the attachment or the loss of a metal layer in the corresponding design domain sub-grid, wherein each array element in the two-dimensional matrix is a binary number;
modeling a two-dimensional periodic array consisting of supercells, calculating scattering characteristics of the two-dimensional periodic array, carrying out configuration optimization on a supercell inner super surface microstructure based on a genetic algorithm by using a design target that the ratio of reflection power of an incident wave with a required specific frequency in the reverse direction of the incident angle to total reflection power in each direction is the maximum, and obtaining an optimal retro-reflector structure.
Further, the obtaining the length and the width of the supercell according to the incident angle of the incident wave obliquely incident to the multichannel reflector and the required specific frequency thereof comprises:
the supercell width was calculated according to the following manner:
wherein d is the supercell width, lambda0Is the incident wavelength, c is the speed of light in vacuum, f0To a desired specific frequency, thetainIs an angle of incidence, θin∈[19.5deg,90deg]；
And the length of the supercell is 2 d.
Further, modeling the scattering characteristics of the two-dimensional periodic array consisting of the supercells, designing the maximum ratio of the reverse reflected power of the required specific frequency at the incident angle to the total reflected power in each direction by using the multichannel reflector, and optimizing the configuration of the ultrasurface microstructure in the supercells on the basis of a genetic algorithm to obtain an optimal retroreflector structure, wherein the method comprises the following steps of:
find X＝[x11,x12,x13,x14…x1n；x21,x22,x23,x24…x2n；…；xm1,xm2,xm3,xm4…xmn]
wherein X represents a design variable two-dimensional matrix, m and n respectively represent the number of rows and columns of the two-dimensional matrix X, and each array element X in the matrixij(i∈[1,m]j∈[1,n]) Denotes attachment and deletion of a metal layer, xij1 denotes a metal layer attached in the subgrid, xij0 denotes the missing metal layer in the sub-grid, D (X) is the scattering cross section area of the far-field double-station radar in each direction normalized by the pitch plane, D (X; -theta)in) Normalizing the far field two station radar scattering cross-sectional area of retro-reflection direction for the pitch plane, and D (X) and D (X; -thetain) All are obtained by numerical calculation methods.
Further, the configuration optimization of the super-surface microstructure in the super cell based on the genetic algorithm to obtain the optimal retroreflector structure comprises the following steps:
defining population size, i.e. number of individuals in population is p, every individual is represented by gene sequence G, G is one-dimensional binary array, gene number is m x n bits, every gene is GkExpressed by 0 or 1, the relationship between each array element of the two-dimensional matrix design variable X and each individual gene is as follows:
xij＝gi×n+j(i∈[1,m],j∈[1,n])；
generating p random binary arrays as an initial population, wherein each random number is used as a gene sequence of each individual, establishing a super-surface super-cell array multi-channel reflector corresponding to each individual gene array in the generation, evaluating design target values of each reflector established in the generation by a numerical calculation method, and then entering an optimization process;
in the optimization process, the optimal variable X is selected from the previous generation populationoptGenerating a next generation population by cross variation as a male parent of the next generation population, establishing a corresponding super-surface super-cell array reflector by using a gene sequence of each individual in the population, evaluating a design target corresponding to each multi-channel reflector of the newly generated population, and finding out a multi-channel reflector with the optimal design target in the generation;
setting an iteration algebra preset value Z, when the comparison between the design target of the current generation and the design target of the previous Z generation is smaller than a threshold value Y, the ratio of the reflection power of the obtained super-surface microstructure at the reverse angle reaches the maximum value, stopping the optimization process, otherwise, executing the optimization process again, and entering the design target comparison and evaluation of the next generation of population;
in the evaluation of each individual design target of a generation population by a numerical calculation method, the numerical calculation based on finite element is carried out on the reflection characteristic of a super-surface array established by corresponding design variables of each individual, the reflection characteristic of the array is firstly calculated with lower finite element calculation grid precision, a judgment threshold value alpha is given, and when-theta is higher than theta, the judgment threshold value alpha is obtainedinIf the scattering cross section area of the direction normalization double-station radar is larger than a threshold value alpha, the reflection characteristic of the array reflector is calculated again with higher calculation grid precision, the reflection characteristic and the design target value of the individual are stored, the next individual reflection characteristic is calculated, and if the-theta is larger than the threshold value alpha, the reflection characteristic of the individual is calculatedinAnd if the scattering sectional area of the direction normalization double-station radar is not larger than the threshold value alpha, directly storing the reflection characteristic and the design target value of the individual at the moment, and calculating the reflection characteristic of the next individual.
Compared with the prior art, the invention has the following advantages:
the invention realizes the retroreflection of oblique incidence electromagnetic waves by taking the two-dimensional plane type superlattice array as a realization form, thereby avoiding the limitation of the application space of the three-dimensional retroreflector; the super-cell is used as a design domain, the super-surface retro-reflector is realized by obtaining reasonable metal patch distribution, and because the invention does not require the gradient continuity of the response phase corresponding to the multi-substructure in the super-cell, the problem that the gradient phase discontinuity caused by external errors damages a retro-reflection forming mechanism can be avoided, and the requirement on high preparation precision is reduced; the invention takes the ratio of the reflection power in the retro-reflection direction to the total reflection power in each direction as the maximum design target, does not adjust the response phase only by taking the size of each substructure in the multi-substructure supercell as a design variable, but designs the whole structure of the supercell, can obtain better impedance matching characteristic while meeting the retro-reflection characteristic, and has the advantages of high reflection power ratio in the retro-reflection direction and extremely low reflectivity in other directions. The invention is beneficial to accurately realizing a feasible, efficient and stable two-dimensional planar type retroreflector.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings needed to be used in the description of the embodiments or the prior art will be briefly introduced below, and it is obvious that the drawings in the following description are some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to these drawings without creative efforts.
FIG. 1 is a schematic diagram of an optimization process for obtaining an optimal two-dimensional super-surface retroreflector microstructure according to the present invention.
FIG. 2 is a schematic diagram of a multi-channel retro-reflector array, incident waves and retro-reflected waves according to the present invention.
FIG. 3a is a schematic diagram of the design domain and the supercell of the present invention.
FIG. 3b is a layout diagram of the design field and metal patch of the present invention.
FIG. 4a is a schematic diagram of a supercell for retroreflection of 10GHz incident waves at-30 deg.
FIG. 4b is a schematic diagram of the metal patch distribution of the embodiment for retroreflection of 10GHz incident waves at-30 deg.
Fig. 5 is a three-dimensional reflection pattern of a retroreflector designed under the condition that 10GHz incident waves are radiated at an oblique angle of 30 degrees.
Fig. 6 is a two-dimensional elevation reflection pattern of a retroreflector designed under the condition that 10GHz incident waves are radiated at an oblique angle of 30 degrees.
Detailed Description
In order to make the technical solutions of the present invention better understood, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
It should be noted that the terms "first," "second," and the like in the description and claims of the present invention and in the drawings described above are used for distinguishing between similar elements and not necessarily for describing a particular sequential or chronological order. It is to be understood that the data so used is interchangeable under appropriate circumstances such that the embodiments of the invention described herein are capable of operation in sequences other than those illustrated or described herein. Furthermore, the terms "comprises," "comprising," and "having," and any variations thereof, are intended to cover a non-exclusive inclusion, such that a process, method, system, article, or apparatus that comprises a list of steps or elements is not necessarily limited to those steps or elements expressly listed, but may include other steps or elements not expressly listed or inherent to such process, method, article, or apparatus.
At present, the supercell of the existing retro-reflector is realized by a plurality of unit cells or copper grids, and the error of the individual unit cells can cause the discontinuity of phase gradient and influence the retro-reflection efficiency. Reducing the number of superintracellular unit cells is beneficial to reducing the requirement on high preparation precision. If the number of the superintracellular unit cells is reduced to two, and the two unit cell microstructures are reasonably designed, better impedance matching can be obtained while retroreflection is realized, the retroreflection power ratio is improved, retroreflection is more stable, and the advantage of wide-angle range adaptability is favorably realized. The applicant takes the supercell as a design domain, and obtains reasonable metal patch distribution to realize the super surface retro-reflector with the maximum reflected power ratio.
Based on the research and development background, the invention provides a topological optimization-based method for designing a micro-structure of a super-surface retroreflector, which comprises the following steps:
s1, obtaining the material selection and size limiting conditions of the dielectric substrate, and establishing the super-surface multi-channel reflector with the periodic metal etching microstructure array according to the generalized Snell' S law, wherein the super-surface multi-channel reflector comprises the dielectric substrate, a grounding plate fully attached with metal on the lower side of the substrate, and a metal microstructure on the upper side of the substrate. Fig. 2 is a schematic diagram of a multi-channel retro-reflector array, incident waves and retro-reflected waves.
S2, dividing a composition cycle of the super-surface array into a super-cell, taking the attachment range of the metal microstructure on the upper side surface of the super-cell substrate as a design domain, dividing the design domain into regular rectangular sub-grid arrays by two-dimensional periodic grids, controlling and adjusting the attachment and the loss of rectangular metal layers in each sub-grid, and describing the configurations of different microstructures by the difference combination of the metal layers in the two-dimensional sub-grid arrays. FIG. 3a is a schematic diagram of the design domain and the super cell of the present invention, and FIG. 3b is a schematic diagram of the design domain and the metal patch distribution diagram of the present invention.
And S3, acquiring the length and the width of the supercell according to the incident angle of the incident wave obliquely incident to the multichannel reflector and the required specific frequency of the incident wave.
Specifically, the incident wave is at an incident angle θinObliquely directed multi-channel reflector with the specific frequency f of incident wave0. Wherein the oblique angle of incidence thetainI.e. the angle between the obliquely incident wave and the normal perpendicular to the reflecting surface, thetain∈[19.5deg,90deg]. The supercell width is
Wherein λ is0Is the incident wavelength and c is the speed of light in vacuum. The horizontal length of the supercell along the wave propagation is 2 d.
And S4, constructing a two-dimensional matrix, and enabling each array element in the two-dimensional matrix to represent the attachment or the loss of the metal layer in the corresponding design domain sub-grid, wherein each array element in the two-dimensional matrix is a binary number.
S5, modeling the scattering characteristic of a two-dimensional periodic array composed of the supercells, designing the maximum ratio of the reflection power of the multichannel reflector to the reverse direction of the required specific frequency at the incident angle to the total reflection power in each direction, optimizing the configuration of the ultrasurface microstructure in the supercells based on a genetic algorithm, and obtaining the optimal retroreflector structure.
Specifically, the multi-channel reflector is used for reversing-theta at the incidence angle for the required specific frequency in the supercell topology optimization processinThe maximum ratio of the direction reflected power to the total reflected power in each direction is a design target, and the adopted optimization formula is as follows:
find X＝[x11,x12,x13,x14…x1n；x21,x22,x23,x24…x2n；…；xm1,xm2,xm3,xm4…xmn]
wherein X represents a design variable, m and n respectively represent the row number and the column number of a two-dimensional matrix X of the design variable, and each array element X in the matrixij(i∈[1,m]j∈[1,n]) Denotes attachment and deletion of a metal layer, xij1 denotes a metal layer attached in the subgrid, xij0 indicates a missing metal layer within the subgrid. D (X) is the scattering cross section area of the far field double-station radar in each direction normalized by the pitch surface, D (X; -theta)in) And normalizing the scattering sectional area of the far-field double-station radar in the retro-reflection direction for the pitch surface, wherein the scattering sectional area of the normalized double-station radar is obtained by a numerical calculation method. Further, fig. 1 is a schematic diagram of an optimization process for obtaining an optimal two-dimensional super-surface retroreflector microstructure in an embodiment, where the optimal design variable is obtained by using a genetic algorithm, that is, the maximum reflection efficiency at a specific angle is obtained, and the method includes the following steps:
s501, defining the size of a population, namely the number of individuals in the population is p, and each individual is composed of genesSequence G, G is a one-dimensional binary array, the gene number is m × n, and each gene GkRepresented by 0 or 1. The relation between each array element of the two-dimensional matrix design variable X and each individual gene is as follows:
xij＝gi×n+j(i∈[1,m],j∈[1,n]) (3)
s502, generating p random binary arrays as an initial population, wherein each random number is used as a gene sequence of each individual, establishing a super-surface super-cell array multi-channel reflector corresponding to each individual gene array in the generation, evaluating design target values of each reflector established in the generation through a numerical calculation method, and then entering an optimization process.
S503, in the optimization process, selecting the optimal variable X from the previous generation populationoptGenerating a next generation population by cross variation as a male parent of the next generation population, establishing a corresponding super-surface super-cell array reflector by using a gene sequence of each individual in the population, evaluating a design target corresponding to each multi-channel reflector of the newly generated population, and finding out a multi-channel reflector with the optimal design target in the generation;
s504, an iteration algebra preset value Z is set, when the comparison between the design target of the current generation and the design target of the previous Z generation is smaller than a threshold value Y, the proportion of the reflection power of the obtained super-surface microstructure at the reverse angle reaches the maximum value, the optimization process is stopped, otherwise, the optimization process returns to S503, and the next generation of population design target comparison and evaluation are carried out.
S505, in the evaluation of each individual design target of a generation population by a numerical calculation method, the numerical calculation based on finite element is carried out on the reflection characteristic of the super-surface array established by each individual corresponding design variable, the reflection characteristic of the array is firstly calculated with lower finite element calculation grid precision, a judgment threshold value alpha is given, and when-theta is reachedinIf the scattering cross section area of the direction normalization double-station radar is larger than a threshold value alpha, the reflection characteristic of the array reflector is calculated again with higher calculation grid precision, the reflection characteristic and the design target value of the individual are stored, the next individual reflection characteristic is calculated, and if the-theta is larger than the threshold value alpha, the reflection characteristic of the individual is calculatedinDirection-normalized double station mineWhen the scattering sectional area is not larger than the threshold value alpha, the reflection characteristic and the design target value of the individual at the moment are directly stored, and the next body reflection characteristic is calculated.
The scheme and effect of the present invention will be further explained by specific application examples.
Fig. 4a is a schematic diagram of a supercell for retroreflection of 10GHz incident waves in the direction of-30 ° in the embodiment, fig. 4b is a metal patch distribution diagram for retroreflection of 10GHz incident waves in the direction of-30 ° in the embodiment, fig. 5 is a three-dimensional reflection pattern of a retroreflector designed under the condition that 10GHz incident waves are radiated at an oblique angle of 30 ° in the embodiment, and fig. 6 is a two-dimensional elevation reflection pattern of the retroreflector designed under the condition that 10GHz incident waves are radiated at an oblique angle of 30 ° in the embodiment. In this embodiment, the dielectric substrate of the reflector is FR4, the thickness of the dielectric board is 1.5mm, copper layers are attached to the upper and lower sides of the substrate, the copper layer on the lower side is filled with copper, the copper layer on the upper side is an etched microstructure array, and the thickness of the copper layer is 0.02 mm. Let the incident wave frequency in question be 10GHz, the incident wave be a TE wave with an incident angle of 30 degrees in the elevation direction, and the electric field direction be along the X direction in the figure.
The supercell width d is 15mm, the length 2d is 30mm, two square copper-clad areas with a x a being 14.4mm x 14.4mm are designed according to the formula (1), one square area is discretized into 12 x 12 grids, each grid size is designed into a sub-grid with a discretized area being 1.2mm x 1.2mm, and the copper-clad layer size in the sub-grid is set to be 1.21mm x 1.21mm in order to ensure the connection of the adjacent sub-grids.
The super-cell and the microstructure designed by topology optimization are shown in fig. 4a and 4 b. As can be seen from the three-dimensional reflection directional diagram of the retroreflector in fig. 5, after the 30 ° oblique incident wave passes through the designed super-surface retroreflector, the main lobe direction is concentrated and points to the original incident direction, i.e., the-30 ° direction, and no obvious side lobe exists in other directions. Whereas in conventional reflection the RCS will show a maximum in the 30 ° direction.
The above-mentioned serial numbers of the embodiments of the present invention are merely for description and do not represent the merits of the embodiments.
In the above embodiments of the present invention, the descriptions of the respective embodiments have respective emphasis, and for parts that are not described in detail in a certain embodiment, reference may be made to related descriptions of other embodiments.
In the embodiments provided in the present application, it should be understood that the disclosed technology can be implemented in other ways. The above-described embodiments of the apparatus are merely illustrative, and for example, the division of the units may be a logical division, and in actual implementation, there may be another division, for example, multiple units or components may be combined or integrated into another system, or some features may be omitted, or not executed. In addition, the shown or discussed mutual coupling or direct coupling or communication connection may be an indirect coupling or communication connection through some interfaces, units or modules, and may be in an electrical or other form.
The units described as separate parts may or may not be physically separate, and parts displayed as units may or may not be physical units, may be located in one place, or may be distributed on a plurality of units. Some or all of the units can be selected according to actual needs to achieve the purpose of the solution of the embodiment.
In addition, functional units in the embodiments of the present invention may be integrated into one processing unit, or each unit may exist alone physically, or two or more units are integrated into one unit. The integrated unit can be realized in a form of hardware, and can also be realized in a form of a software functional unit.
The integrated unit, if implemented in the form of a software functional unit and sold or used as a stand-alone product, may be stored in a computer readable storage medium. Based on such understanding, the technical solution of the present invention may be embodied in the form of a software product, which is stored in a storage medium and includes instructions for causing a computer device (which may be a personal computer, a server, or a network device) to execute all or part of the steps of the method according to the embodiments of the present invention. And the aforementioned storage medium includes: a U-disk, a Read-Only Memory (ROM), a Random Access Memory (RAM), a removable hard disk, a magnetic or optical disk, and other various media capable of storing program codes.
Finally, it should be noted that: the above embodiments are only used to illustrate the technical solution of the present invention, and not to limit the same; while the invention has been described in detail and with reference to the foregoing embodiments, it will be understood by those skilled in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some or all of the technical features may be equivalently replaced; and the modifications or the substitutions do not make the essence of the corresponding technical solutions depart from the scope of the technical solutions of the embodiments of the present invention.
Claims (4)
1. A method for designing a super-surface retroreflector microstructure based on topological optimization is characterized by comprising the following steps:
obtaining the conditions of material selection and size limitation of a dielectric substrate, and establishing a super-surface multichannel reflector with a periodic metal etching microstructure array according to the generalized Snell's law, wherein the super-surface multichannel reflector comprises the dielectric substrate, a metal grounding plate is arranged on the lower side of the dielectric substrate, and a metal microstructure is arranged on the surface of the upper side of the dielectric substrate;
dividing a composition cycle of the super-surface array into a super-cell, taking the attachment range of the metal microstructure on the upper side of the super-cell surface substrate as a design domain, dividing the design domain into a regular rectangular sub-grid array by using a two-dimensional periodic grid, controlling and adjusting the attachment and the loss of a rectangular metal layer in each sub-grid, and describing the configurations of different microstructures by using the difference combination of the metal layers in the two-dimensional sub-grid array;
acquiring the length and the width of the supercell according to the incident angle of incident waves obliquely incident to the multichannel reflector and the required specific frequency of the incident waves;
constructing a two-dimensional matrix, and enabling each array element in the two-dimensional matrix to represent the attachment or the loss of a metal layer in the corresponding design domain sub-grid, wherein each array element in the two-dimensional matrix is a binary number;
modeling a two-dimensional periodic array consisting of supercells, calculating scattering characteristics of the two-dimensional periodic array, carrying out configuration optimization on a supercell inner super surface microstructure based on a genetic algorithm by using a design target that the ratio of reflection power of an incident wave with a required specific frequency in the reverse direction of the incident angle to total reflection power in each direction is the maximum, and obtaining an optimal retro-reflector structure.
2. The method for designing the super-surface retro-reflector microstructure based on topology optimization according to claim 1, wherein the obtaining of the length and the width of the supercell according to the incident angle of the incident wave obliquely incident to the multi-channel reflector and the required specific frequency thereof comprises:
the supercell width was calculated according to the following manner:
wherein d is the supercell width, lambda0Is the incident wavelength, c is the speed of light in vacuum, f0To a desired specific frequency, thetainIs an angle of incidence, θin∈[19.5deg,90deg]；
And the length of the supercell is 2 d.
3. The method according to claim 1, wherein the modeling of the scattering properties of the two-dimensional periodic array of supercells is performed, the maximum ratio of the reverse reflected power of the multichannel reflector to the required specific frequency at the incident angle to the total reflected power in each direction is a design target, and the configuration optimization of the supercell internal super-surface microstructure is performed based on a genetic algorithm to obtain an optimal retroreflector structure, and the method comprises the following steps:
find X＝[x11,x12,x13,x14…x1n；x21,x22,x23,x24…x2n；…；xm1,xm2,xm3,xm4…xmn]
wherein X represents a design variable two-dimensional matrix, m and n respectively represent the number of rows and columns of the two-dimensional matrix X, and each array element X in the matrixij(i∈[1,m]j∈[1,n]) Denotes attachment and deletion of a metal layer, xij1 denotes a metal layer attached in the subgrid, xij0 denotes the missing metal layer in the sub-grid, D (X) is the scattering cross section area of the far-field double-station radar in each direction normalized by the pitch plane, D (X; -theta)in) Normalizing the far field two station radar scattering cross-sectional area of retro-reflection direction for the pitch plane, and D (X) and D (X; -thetain) All are obtained by numerical calculation methods.
4. The method for designing the super-surface retro-reflector microstructure based on the topological optimization according to claim 1, wherein the method for optimizing the configuration of the super-intracellular super-surface microstructure based on the genetic algorithm to obtain the optimal retro-reflector structure comprises the following steps:
defining population size, i.e. number of individuals in population is p, every individual is represented by gene sequence G, G is one-dimensional binary array, gene number is m x n bits, every gene is GkExpressed by 0 or 1, the relationship between each array element of the two-dimensional matrix design variable X and each individual gene is as follows:
xij＝gi×n+j(i∈[1,m],j∈[1,n])；
generating p random binary arrays as an initial population, wherein each random number is used as a gene sequence of each individual, establishing a super-surface super-cell array multi-channel reflector corresponding to each individual gene array in the generation, evaluating design target values of each reflector established in the generation by a numerical calculation method, and then entering an optimization process;
in the optimization process, the optimal variable X is selected from the previous generation populationoptAs a male parent of the next generation population, the next generation population is generated by cross mutation, from each of the populationsEstablishing a corresponding super-surface super-cell array reflector according to the gene sequence of the individual, evaluating a design target corresponding to each multi-channel reflector of the newly generated population, and finding out the multi-channel reflector with the optimal design target in the generation;
setting an iteration algebra preset value Z, when the comparison between the design target of the current generation and the design target of the previous Z generation is smaller than a threshold value Y, the ratio of the reflection power of the obtained super-surface microstructure at the reverse angle reaches the maximum value, stopping the optimization process, otherwise, executing the optimization process again, and entering the design target comparison and evaluation of the next generation of population;
in the evaluation of each individual design target of a generation population by a numerical calculation method, the numerical calculation based on finite element is carried out on the reflection characteristic of a super-surface array established by corresponding design variables of each individual, the reflection characteristic of the array is firstly calculated with lower finite element calculation grid precision, a judgment threshold value alpha is given, and when-theta is higher than theta, the judgment threshold value alpha is obtainedinIf the scattering cross section area of the direction normalization double-station radar is larger than a threshold value alpha, the reflection characteristic of the array reflector is calculated again with higher calculation grid precision, the reflection characteristic and the design target value of the individual are stored, the next individual reflection characteristic is calculated, and if the-theta is larger than the threshold value alpha, the reflection characteristic of the individual is calculatedinAnd if the scattering sectional area of the direction normalization double-station radar is not larger than the threshold value alpha, directly storing the reflection characteristic and the design target value of the individual at the moment, and calculating the reflection characteristic of the next individual.
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