Directional roof cutting(DRC)is one of the key techniques in non-pillar coal mining with self-formed entries(NCMSE)mining method.Due to the inability to accurately measure the expansion coefficient of the goaf rock ma...Directional roof cutting(DRC)is one of the key techniques in non-pillar coal mining with self-formed entries(NCMSE)mining method.Due to the inability to accurately measure the expansion coefficient of the goaf rock mass,the implementation of this technology often encounters design challenges,leading to suboptimal results and increased costs.This paper establishes a structural analysis model of the goaf working face roof,revealing the failure mechanism of DRC,and clarifies the positive role of DRC in improving the stress of the roadway surrounding rock and reducing the subsidence of the roof through numerical simulation experiments.On this basis,the paper further analyses the roadway pressure and roof settlement under different DRC design heights,and ultimately proposes an optimized design method for the DRC height.The results indicate that the implementation of DRC can significantly optimize the stress environment of the working face roadway surrounding rock.At the same time,during the application of DRC,three scenarios may arise:insufficient,reasonable,and excessive DRC height.Insufficient height will significantly reduce the effectiveness of the technology,while excessive height has little impact on the implementation effect but will greatly increase construction costs and difficulty.Engineering verification shows that the optimized DRC design method proposed in this paper reduces the peak stress of the protective coal pillar in the roadway by 27.2%and the central subsidence of the roof by 41.8%,demonstrating excellent application results.This method provides technical support for the further promotion of NCMSE mining method.展开更多
With the continuous development of social economy, in the process of building structure design, the design unit should not only consider the practicability and safety of the building, but also improve the aesthetics a...With the continuous development of social economy, in the process of building structure design, the design unit should not only consider the practicability and safety of the building, but also improve the aesthetics and economy of the building. This is why designers must ensure the safety, functionality, aesthetics and cost-effectiveness of the building when designing the building, and also consider the convenience of the building. Therefore, architectural design units must optimize the design. Only in this way can the various functions of architecture be unified and promote the stable development of China's construction industry. On this basis, the application of design optimization method in architectural structure design is analyzed and discussed. The rapid development of social economy has also improved people's quality of life. In this context, there are more stringent requirements for life and environment. In the process of architectural design, designers must actively use the construction method of architectural optimization, so that the comfort of the house can not only be improved, but also fully meet people's living needs. In addition, using the construction method to optimize the building can also significantly reduce the construction cost without affecting the house performance and quality, which can also greatly improve the economic benefits of engineering companies and promote the better development of China's construction industry.展开更多
The optimization of metamorphic mechanisms is different from that of the conventional mechanisms for its characteristics of multi-configuration. There exist complex coupled design variables and constraints in its mult...The optimization of metamorphic mechanisms is different from that of the conventional mechanisms for its characteristics of multi-configuration. There exist complex coupled design variables and constraints in its multiple different configuration optimization models. To achieve the compatible optimized results of these coupled design variables, an optimization method for metamorphic mechanisms is developed in the paper based on the principle of multidisciplinary design optimization（MDO）. Firstly, the optimization characteristics of the metamorphic mechanism are summarized distinctly by proposing the classification of design variables and constraints as well as coupling interactions among its different configuration optimization models. Further, collaborative optimization technique which is used in MDO is adopted for achieving the overall optimization performance. The whole optimization process is then proposed by constructing a two-level hierarchical scheme with global optimizer and configuration optimizer loops. The method is demonstrated by optimizing a planar five-bar metamorphic mechanism which has two configurations,and results show that it can achieve coordinated optimization results for the same parameters in different configuration optimization models.展开更多
The Distributed Propulsion Wing(DPW)presents prominent advantages in terms of energy conservation during flight,but the intense integration of propulsive internal flow with aerodynamic external flow brings significant...The Distributed Propulsion Wing(DPW)presents prominent advantages in terms of energy conservation during flight,but the intense integration of propulsive internal flow with aerodynamic external flow brings significant design challenges.To tackle this issue,this paper undertakes a comprehensive investigation of the aero-propulsive coupling performance of the DPW under both hovering and cruising conditions,and subsequently proposes a multi-level collaboration optimization design method based on the decomposition principle.Specifically,the complex 3D surfaces of DPW are systematically dissociated into simple 2D curves with inherent relationships for design.The decomposition is achieved based on the analysis results of the aero-propulsive coupling characteristics.And a DPW design case is conducted and subsequently analyzed in order to further validate the effectiveness and feasibility of the proposed design method.It is shown that a 115.75%drag reduction of DPW can be achieved at cruise under a specified thrust level.Furthermore,the DPW exhibits inherent characteristics of consistent lift-to-drag ratio with the thrust-drag balance constraint,regardless of variations in incoming flow velocity or total thrust.展开更多
A new multi-level analysis method of introducing the super-element modeling method, derived from the multi-level analysis method first proposed by O. F. Hughes, has been proposed in this paper to solve the problem of ...A new multi-level analysis method of introducing the super-element modeling method, derived from the multi-level analysis method first proposed by O. F. Hughes, has been proposed in this paper to solve the problem of high time cost in adopting a rational-based optimal design method for ship structural design. Furthermore,the method was verified by its effective application in optimization of the mid-ship section of a container ship. A full 3-D FEM model of a ship,suffering static and quasi-static loads, was used as the analyzing object for evaluating the structural performance of the mid-ship module, including static strength and buckling performance. Research results reveal that this new method could substantially reduce the computational cost of the rational-based optimization problem without decreasing its accuracy, which increases the feasibility and economic efficiency of using a rational-based optimal design method in ship structural design.展开更多
A fully automated optimization process is provided for the design of ducted propellers under open water conditions, including 3D geometry modeling, meshing, optimization algorithm and CFD analysis techniques. The deve...A fully automated optimization process is provided for the design of ducted propellers under open water conditions, including 3D geometry modeling, meshing, optimization algorithm and CFD analysis techniques. The developed process allows the direct integration of a RANSE solver in the design stage. A practical ducted propeller design case study is carried out for validation. Numerical simulations and open water tests are fulfilled and proved that the optimum ducted propeller improves hydrodynamic performance as predicted.展开更多
Few study gives guidance to design weighting filters according to the frequency weighting factors,and the additional evaluation method of automotive ride comfort is not made good use of in some countries.Based on the ...Few study gives guidance to design weighting filters according to the frequency weighting factors,and the additional evaluation method of automotive ride comfort is not made good use of in some countries.Based on the regularities of the weighting factors,a method is proposed and the vertical and horizontal weighting filters are developed.The whole frequency range is divided several times into two parts with respective regularity.For each division,a parallel filter constituted by a low-and a high-pass filter with the same cutoff frequency and the quality factor is utilized to achieve section factors.The cascading of these parallel filters obtains entire factors.These filters own a high order.But,low order filters are preferred in some applications.The bilinear transformation method and the least P-norm optimal infinite impulse response（IIR） filter design method are employed to develop low order filters to approximate the weightings in the standard.In addition,with the window method,the linear phase finite impulse response（FIR） filter is designed to keep the signal from distorting and to obtain the staircase weighting.For the same case,the traditional method produces 0.330 7 m · s^–2 weighted root mean square（r.m.s.） acceleration and the filtering method gives 0.311 9 m · s^–2 r.m.s.The fourth order filter for approximation of vertical weighting obtains 0.313 9 m · s^–2 r.m.s.Crest factors of the acceleration signal weighted by the weighting filter and the fourth order filter are 3.002 7 and 3.011 1,respectively.This paper proposes several methods to design frequency weighting filters for automotive ride comfort evaluation,and these developed weighting filters are effective.展开更多
Through a great deal calculation, the design and simulation analysis of stator parametric and rotor electromagnetic system of 1000MW turbo-generator are performed by using Ansoft Maxwell Rmxprt12.1 software. Besides. ...Through a great deal calculation, the design and simulation analysis of stator parametric and rotor electromagnetic system of 1000MW turbo-generator are performed by using Ansoft Maxwell Rmxprt12.1 software. Besides. the basic parameters of the generator, the geometry dimensions of the stator and rotor, type and sizes of the slots, coils and windings parameters and the way of windings connection are determined. The finite element model of electromagnetic systems of generator stator and rotor was constructed by Ansoft Maxwe112D3D 12.1, and the transient electromagnetic characteristics of generator was analyzed and simulated. The 3D geometric models of turbo-generator were established respectively by using PROE software, and the dynamic finite element model of generator structure was built by ANSYS workbench 11.0. In addition, the dynamic characteristics of stator iron core, stator frame were calculated respectively. The simulation calculation has shown that the structural parameters, material parameters, and the electromagnetic characteristics parameters for large turbogenerator that are put forward by this paper should be optimal. and the design plan and method suggested by this paper should be feasible. The paper provides an effective solution for the development of larger turbo-generator than 1000 MW.展开更多
In this paper,size and shape optimization problem of a machine gun system is addressed with an efficient hybrid method,in which a novel and flexible mesh morphing technique is employed to achieve fast parameterization...In this paper,size and shape optimization problem of a machine gun system is addressed with an efficient hybrid method,in which a novel and flexible mesh morphing technique is employed to achieve fast parameterization and modification of complexity structure without going back to CAD for reconstruction of geometric models or to finite element analysis（ FEA） for remodeling. Design of experiments（ DOE） and response surface method（ RSM） are applied to approximate the constitutive parameters of a machine gun system based on experimental tests. Further FEA,secondary development technique and genetic algorithm（ GA） are introduced to find all the optimal solutions in one go and the optimal design of the demonstrated machine gun system is obtained. Results of the rigid-flexible coupling dynamic analysis and exterior ballistics calculation validate the proposed methodology,which is relatively time-saving,reliable and has the potential to solve similar problems.展开更多
A grating is an important element of a phase-shifting point diffraction interferometer, and the grating constant and duty cycle have a great impact on the interferometer, so the design of a grating becomes significant...A grating is an important element of a phase-shifting point diffraction interferometer, and the grating constant and duty cycle have a great impact on the interferometer, so the design of a grating becomes significant. In order to measure the projection objective with a numerical aperture of 0.2, we present a joint optimization method of a pinhole and grating based on scalar diffraction and the finite difference time domain method. The grating constant and the film thickness are selected, and the duty cycle of the grating is optimized. The results show that in the grating processing the material chromium is adopted, the thickness is 200 nm, and the grating constant is 15 μm. When the duty cycle is 55%, the interference fringe contrast is the greatest. The feasibility of the design result is further verified by experiment.展开更多
To avoid the numerical complexities of the battery discharge law of electric-powered rotorcrafts,this study uses the Kriging method to model the discharge characteristics of Li-Po batteries under standard conditions.A...To avoid the numerical complexities of the battery discharge law of electric-powered rotorcrafts,this study uses the Kriging method to model the discharge characteristics of Li-Po batteries under standard conditions.A linear current compensation term and an ambient temperature compensation term based on radial basis functions are then applied to the trained Kriging model,leading to the complete discharged capacity-terminal voltage model.Using an orthogonal experimental design and a sequential method,the coefficients of the current and ambient temperature compensation terms are determined through robust optimization.An endurance calculation model for electric-powered rotorcrafts is then established,based on the battery discharge model,through numerical integration.Laboratory tests show that the maximum relative error of the proposed discharged capacity-terminal voltage model at detection points is 0.0086,and that of the rotorcraft endurance calculation model is 0.0195,thus verifying their accuracy.A flight test further demonstrates the applicability of the proposed endurance model to general electric-powered rotorcrafts.展开更多
The flexible and precise control of wavefronts of electromagnetic waves has always been a hot issue,and the emergence of metasurfaces has provided a platform to solve this problem,but their design and optimization rem...The flexible and precise control of wavefronts of electromagnetic waves has always been a hot issue,and the emergence of metasurfaces has provided a platform to solve this problem,but their design and optimization remain challenging.Here,we demonstrate two design and optimization methods for metagrating-based metalenses based on the highest manipulation efficiency and highest diffraction efficiency.The metalens operating at0.14 THz with numerical apertures of 0.434 is designed by these two methods for comparison.Then,the metalens is fabricated with photocuring 3D printing technology and an imaging system is built to characterize the distribution of focal spots.With the highest manipulation efficiency,the metalens shows a focal spot with the diameter of 0.93λand depth of focus(DOF)of 22.7λ,and the manipulation and diffraction efficiencies reach 98.1%and 58.3%.With the highest diffraction efficiency,the metalens shows a focal spot with the diameter of 0.91λand DOF of 24.6λ,and the manipulation and diffraction efficiencies reach 94.6%and 62.5%.The results show that the metalenses designed by both methods can perform a filamentous focal spot in the sub-wavelength scale with a long DOF;simultaneous high manipulation and diffraction efficiencies are obtained.A transmission imaging manner is used to verify the imaging capability of the metalenses,and the measurements are satisfactorily congruous with the anticipated results.The proposed methods can stably generate focal spots beyond the physical diffraction limit,which has a broad application in terahertz imaging,communications,etc.展开更多
基金funded by the National Natural Science Foundation of China(52074298)Beijing Municipal Natural Science Foundation(8232056)+1 种基金Guizhou Province science and technology plan project([2020]3008)Liulin Energy and Environment Academician Workstation(2022XDHZ12).
文摘Directional roof cutting(DRC)is one of the key techniques in non-pillar coal mining with self-formed entries(NCMSE)mining method.Due to the inability to accurately measure the expansion coefficient of the goaf rock mass,the implementation of this technology often encounters design challenges,leading to suboptimal results and increased costs.This paper establishes a structural analysis model of the goaf working face roof,revealing the failure mechanism of DRC,and clarifies the positive role of DRC in improving the stress of the roadway surrounding rock and reducing the subsidence of the roof through numerical simulation experiments.On this basis,the paper further analyses the roadway pressure and roof settlement under different DRC design heights,and ultimately proposes an optimized design method for the DRC height.The results indicate that the implementation of DRC can significantly optimize the stress environment of the working face roadway surrounding rock.At the same time,during the application of DRC,three scenarios may arise:insufficient,reasonable,and excessive DRC height.Insufficient height will significantly reduce the effectiveness of the technology,while excessive height has little impact on the implementation effect but will greatly increase construction costs and difficulty.Engineering verification shows that the optimized DRC design method proposed in this paper reduces the peak stress of the protective coal pillar in the roadway by 27.2%and the central subsidence of the roof by 41.8%,demonstrating excellent application results.This method provides technical support for the further promotion of NCMSE mining method.
文摘With the continuous development of social economy, in the process of building structure design, the design unit should not only consider the practicability and safety of the building, but also improve the aesthetics and economy of the building. This is why designers must ensure the safety, functionality, aesthetics and cost-effectiveness of the building when designing the building, and also consider the convenience of the building. Therefore, architectural design units must optimize the design. Only in this way can the various functions of architecture be unified and promote the stable development of China's construction industry. On this basis, the application of design optimization method in architectural structure design is analyzed and discussed. The rapid development of social economy has also improved people's quality of life. In this context, there are more stringent requirements for life and environment. In the process of architectural design, designers must actively use the construction method of architectural optimization, so that the comfort of the house can not only be improved, but also fully meet people's living needs. In addition, using the construction method to optimize the building can also significantly reduce the construction cost without affecting the house performance and quality, which can also greatly improve the economic benefits of engineering companies and promote the better development of China's construction industry.
基金the fundamental support of the National Natural Science Foundation of China (Nos. 51105013, 51125020)the Beijing Natural Science Foundation of China (No. 3133042)the fundamental support provided by the China Scholarship Council and the State Key Laboratory of Robotics and System (HIT)
文摘The optimization of metamorphic mechanisms is different from that of the conventional mechanisms for its characteristics of multi-configuration. There exist complex coupled design variables and constraints in its multiple different configuration optimization models. To achieve the compatible optimized results of these coupled design variables, an optimization method for metamorphic mechanisms is developed in the paper based on the principle of multidisciplinary design optimization（MDO）. Firstly, the optimization characteristics of the metamorphic mechanism are summarized distinctly by proposing the classification of design variables and constraints as well as coupling interactions among its different configuration optimization models. Further, collaborative optimization technique which is used in MDO is adopted for achieving the overall optimization performance. The whole optimization process is then proposed by constructing a two-level hierarchical scheme with global optimizer and configuration optimizer loops. The method is demonstrated by optimizing a planar five-bar metamorphic mechanism which has two configurations,and results show that it can achieve coordinated optimization results for the same parameters in different configuration optimization models.
基金co-supported by the Equipment Advance Research Project of China(No.50911040803)the National Defense Pre-research Foundation of China(No.2021-JCJQJJ-0805)the Aeronautical Science Foundation of China(No.2024Z006053001)。
文摘The Distributed Propulsion Wing(DPW)presents prominent advantages in terms of energy conservation during flight,but the intense integration of propulsive internal flow with aerodynamic external flow brings significant design challenges.To tackle this issue,this paper undertakes a comprehensive investigation of the aero-propulsive coupling performance of the DPW under both hovering and cruising conditions,and subsequently proposes a multi-level collaboration optimization design method based on the decomposition principle.Specifically,the complex 3D surfaces of DPW are systematically dissociated into simple 2D curves with inherent relationships for design.The decomposition is achieved based on the analysis results of the aero-propulsive coupling characteristics.And a DPW design case is conducted and subsequently analyzed in order to further validate the effectiveness and feasibility of the proposed design method.It is shown that a 115.75%drag reduction of DPW can be achieved at cruise under a specified thrust level.Furthermore,the DPW exhibits inherent characteristics of consistent lift-to-drag ratio with the thrust-drag balance constraint,regardless of variations in incoming flow velocity or total thrust.
基金Supported by the Project of Ministry of Education and Finance(No.200512)the Project of the State Key Laboratory of ocean engineering(GKZD010053-10)
文摘A new multi-level analysis method of introducing the super-element modeling method, derived from the multi-level analysis method first proposed by O. F. Hughes, has been proposed in this paper to solve the problem of high time cost in adopting a rational-based optimal design method for ship structural design. Furthermore,the method was verified by its effective application in optimization of the mid-ship section of a container ship. A full 3-D FEM model of a ship,suffering static and quasi-static loads, was used as the analyzing object for evaluating the structural performance of the mid-ship module, including static strength and buckling performance. Research results reveal that this new method could substantially reduce the computational cost of the rational-based optimization problem without decreasing its accuracy, which increases the feasibility and economic efficiency of using a rational-based optimal design method in ship structural design.
基金financially supported by the National Natural Science Foundation of China(Grant No.51009090)the State Key Laboratory of Ocean Engineering(Grant No.GKZD010063)
文摘A fully automated optimization process is provided for the design of ducted propellers under open water conditions, including 3D geometry modeling, meshing, optimization algorithm and CFD analysis techniques. The developed process allows the direct integration of a RANSE solver in the design stage. A practical ducted propeller design case study is carried out for validation. Numerical simulations and open water tests are fulfilled and proved that the optimum ducted propeller improves hydrodynamic performance as predicted.
文摘Few study gives guidance to design weighting filters according to the frequency weighting factors,and the additional evaluation method of automotive ride comfort is not made good use of in some countries.Based on the regularities of the weighting factors,a method is proposed and the vertical and horizontal weighting filters are developed.The whole frequency range is divided several times into two parts with respective regularity.For each division,a parallel filter constituted by a low-and a high-pass filter with the same cutoff frequency and the quality factor is utilized to achieve section factors.The cascading of these parallel filters obtains entire factors.These filters own a high order.But,low order filters are preferred in some applications.The bilinear transformation method and the least P-norm optimal infinite impulse response（IIR） filter design method are employed to develop low order filters to approximate the weightings in the standard.In addition,with the window method,the linear phase finite impulse response（FIR） filter is designed to keep the signal from distorting and to obtain the staircase weighting.For the same case,the traditional method produces 0.330 7 m · s^–2 weighted root mean square（r.m.s.） acceleration and the filtering method gives 0.311 9 m · s^–2 r.m.s.The fourth order filter for approximation of vertical weighting obtains 0.313 9 m · s^–2 r.m.s.Crest factors of the acceleration signal weighted by the weighting filter and the fourth order filter are 3.002 7 and 3.011 1,respectively.This paper proposes several methods to design frequency weighting filters for automotive ride comfort evaluation,and these developed weighting filters are effective.
文摘Through a great deal calculation, the design and simulation analysis of stator parametric and rotor electromagnetic system of 1000MW turbo-generator are performed by using Ansoft Maxwell Rmxprt12.1 software. Besides. the basic parameters of the generator, the geometry dimensions of the stator and rotor, type and sizes of the slots, coils and windings parameters and the way of windings connection are determined. The finite element model of electromagnetic systems of generator stator and rotor was constructed by Ansoft Maxwe112D3D 12.1, and the transient electromagnetic characteristics of generator was analyzed and simulated. The 3D geometric models of turbo-generator were established respectively by using PROE software, and the dynamic finite element model of generator structure was built by ANSYS workbench 11.0. In addition, the dynamic characteristics of stator iron core, stator frame were calculated respectively. The simulation calculation has shown that the structural parameters, material parameters, and the electromagnetic characteristics parameters for large turbogenerator that are put forward by this paper should be optimal. and the design plan and method suggested by this paper should be feasible. The paper provides an effective solution for the development of larger turbo-generator than 1000 MW.
基金Supported by the National Natural Science Foundation of China(51376090,51676099)
文摘In this paper,size and shape optimization problem of a machine gun system is addressed with an efficient hybrid method,in which a novel and flexible mesh morphing technique is employed to achieve fast parameterization and modification of complexity structure without going back to CAD for reconstruction of geometric models or to finite element analysis（ FEA） for remodeling. Design of experiments（ DOE） and response surface method（ RSM） are applied to approximate the constitutive parameters of a machine gun system based on experimental tests. Further FEA,secondary development technique and genetic algorithm（ GA） are introduced to find all the optimal solutions in one go and the optimal design of the demonstrated machine gun system is obtained. Results of the rigid-flexible coupling dynamic analysis and exterior ballistics calculation validate the proposed methodology,which is relatively time-saving,reliable and has the potential to solve similar problems.
基金supported by the Major Scientific Instrument Development Project of the National Natural Science Foundation of China(No.11627808)the National Natural Science Foundation of China(No.61675026)the National Science and Technology
文摘A grating is an important element of a phase-shifting point diffraction interferometer, and the grating constant and duty cycle have a great impact on the interferometer, so the design of a grating becomes significant. In order to measure the projection objective with a numerical aperture of 0.2, we present a joint optimization method of a pinhole and grating based on scalar diffraction and the finite difference time domain method. The grating constant and the film thickness are selected, and the duty cycle of the grating is optimized. The results show that in the grating processing the material chromium is adopted, the thickness is 200 nm, and the grating constant is 15 μm. When the duty cycle is 55%, the interference fringe contrast is the greatest. The feasibility of the design result is further verified by experiment.
文摘To avoid the numerical complexities of the battery discharge law of electric-powered rotorcrafts,this study uses the Kriging method to model the discharge characteristics of Li-Po batteries under standard conditions.A linear current compensation term and an ambient temperature compensation term based on radial basis functions are then applied to the trained Kriging model,leading to the complete discharged capacity-terminal voltage model.Using an orthogonal experimental design and a sequential method,the coefficients of the current and ambient temperature compensation terms are determined through robust optimization.An endurance calculation model for electric-powered rotorcrafts is then established,based on the battery discharge model,through numerical integration.Laboratory tests show that the maximum relative error of the proposed discharged capacity-terminal voltage model at detection points is 0.0086,and that of the rotorcraft endurance calculation model is 0.0195,thus verifying their accuracy.A flight test further demonstrates the applicability of the proposed endurance model to general electric-powered rotorcrafts.
基金Key Research and Development Program of Tianjin(23YFZCSN00090)Natural Science Foundation of Tianjin Municipality(23JCYBJC00300)+1 种基金Foundation of National Key Laboratory of Shock Wave and Detonation Physics(JCKYS2022212001)National Natural Science Foundation of China(62101518,61905177)。
文摘The flexible and precise control of wavefronts of electromagnetic waves has always been a hot issue,and the emergence of metasurfaces has provided a platform to solve this problem,but their design and optimization remain challenging.Here,we demonstrate two design and optimization methods for metagrating-based metalenses based on the highest manipulation efficiency and highest diffraction efficiency.The metalens operating at0.14 THz with numerical apertures of 0.434 is designed by these two methods for comparison.Then,the metalens is fabricated with photocuring 3D printing technology and an imaging system is built to characterize the distribution of focal spots.With the highest manipulation efficiency,the metalens shows a focal spot with the diameter of 0.93λand depth of focus(DOF)of 22.7λ,and the manipulation and diffraction efficiencies reach 98.1%and 58.3%.With the highest diffraction efficiency,the metalens shows a focal spot with the diameter of 0.91λand DOF of 24.6λ,and the manipulation and diffraction efficiencies reach 94.6%and 62.5%.The results show that the metalenses designed by both methods can perform a filamentous focal spot in the sub-wavelength scale with a long DOF;simultaneous high manipulation and diffraction efficiencies are obtained.A transmission imaging manner is used to verify the imaging capability of the metalenses,and the measurements are satisfactorily congruous with the anticipated results.The proposed methods can stably generate focal spots beyond the physical diffraction limit,which has a broad application in terahertz imaging,communications,etc.
