Research On The Work-Energy Principle Based Characteristic Mode Theory For Scattering Systems

Electromagnetic(EM)scattering systems widely exist in EM engineering domain.For a certain objective scattering system,all of its working modes constitute a linear space —— modal space.Characteristic mode theory(CMT)can effectively construct a basis of the space —— characteristic modes(CMs),and the CMs only depend on the inherent physical properties of the objective system,such as the topological structure and the material parameter of the objective system.Thus,CMT is very valuable for analyzing and designing the inherent EM scattering characters of the objective system.Since Prof.Harrington et al.transformed the framework for carrying CMT from Prof.Garbacz's scattering matrix(SM)framework to integral equation(IE)framework,the theoretical research and engineering application of CMT have achieved quick developments.But,IE-based CMT(IE-CMT)still has some important problems which have not been completely solved,for example:Old Problem 1(OP1).The IE-based CM formulations are usually derived from various EM field boundary conditions,and the boundary conditions are mathematical equations.What physical properties do the CMs constructed by the mathematical equations have? In other words,what physical picture does IE-CMT have? This is one of the important questions in IE-CMT researching domain in recent years,and it has not been completely answered,and then some phenomena which have not been fully explained have appeared.Unexplained Phenomenon A.The CMs derived from the electric field integral equation based CMT(EFIE-CMT)for metallic scattering systems can guarantee the orthogonality among modal far fields,but the CMs derived from the volume integral equation based CMT(VIE-CMT)for lossy material scattering systems cannot guarantee the orthogonality among modal far fields;Unexplained Phenomenon B.The physical meanings of the characteristic values calculated from VIE-CMT and EFIE-CMT are not the same;Unexplained Phenomenon C.For a certain objective metallic scattering system,the CMs derived from EFIE-CMT,magnetic field integral equation based CMT(MFIE-CMT),and combined field integral equation based CMT(CFIE-CMT)are not the same.Old Problem 2(OP2).For a metallic scattering system,non-radiative mode set(such as internal resonant mode set)is an important part of whole modal space.But,IE-CMT cannot construct non-radiative modes,so cannot provide a complete CM set to the objective metallic scattering system.Old Problem 3(OP3).Existing IE-CMT cannot provide effective CM formulations to some material scattering systems which have complicated topological structures(such as stacked dielectric resonator antennas)or complicated material parameters(such as Lüneburg lens antenna).Old Problem 4(OP4).Existing IE-CMT cannot provide effective CM formulations to some metal-material composite scattering systems which have complicated topological structures(such as printed microstrip antennas)or complicated material parameters.Old Problem 5(OP5).For some complicated scattering systems,it is not completely solved how to effectively suppress the spurious CMs derived from IE-CMT.This dissertation is committed to further sovling the above-mentioned old problems OP1~OP5.In the process of solving old problems OP1,OP3,and OP4,and after having solved old problems OP2 and OP5,this dissertation also raises a series of new questions as follows:New Problem 1(NP1).In the process of solving old problem OP1,this dissertation raises a new question on “Whether or not IE is the best framework for carrying CMT?”.New Problem 2(NP2).After having solved old problem OP2,this dissertation raises a new question on “the detailed classification for working modes and the orthogonal decomposition for modal space”.New Problem 3(NP3).In the process of solving old problem OP3,this dissertation raises a new question on “How to derive the mathematical expressions of the surface equivalence principle for complicated material scattering systems?”.New Problem 4(NP4).In the process of solving old problem OP4,this dissertation raises a new question on “How to establish the line-surface equivalence principle of complicated metal-material composite scattering systems,and how to derive the corresponding mathematical expressions?”.New Problem 5(NP5).After having solved old problem OP5,this dissertation raises a new question on “the physical meaning and numerical influence of the singular EM current term(SCT)contained in the CM formulations of complicated scattering systems”.Focusing on above {OP1,NP1},{OP2,NP2},…,and {OP5,NP5},this dissertation does some innovative works.The main contributions of this dissertation are as follows:Main Contribution 1.The contribution in the aspect of solving {OP1,NP1}After some studies,this dissertation finds out that IE is not the best framework for carrying CMT.This dissertation proposes a completely new framework for carrying CMT —— work-energy principle(WEP)framework,and at the same time proposes a completely new method for constructing CMs —— orthogonalizing driving power operator(DPO)method.In new WEP framework and based on new orthogonalizing DPO method,this dissertation draws a clear physical picture for the IE-CMT established by Prof.Harrington et al.—— constructing a series of steadily working modes which have not net energy exchange in any integral period.Employing the physical picture,this dissertation reveals the causes of the unexplained phenomena A,B,and C mentioned above.Main Contribution 2.The contribution in the aspect of solving {OP2,NP2}This dissertation derives the mathematical expression of the WEP corresponding to metallic scattering systems,and then obtains the operator expression of the driving power(DP)corresponding to metallic scattering systems.In new WEP framework and based on new orthogonalizing DPO method,this dissertation proves that the CM set constructed by the traditional IE-CMT for metallic scattering systems is not complete,and provides a practical method for completing the CM set.Based on the complete CM set,this dissertation orthogonally decomposes whole modal space and detailedly classifies all working modes,and then orthogonally decomposes various working modes in the simplest way.The obtained modal simplest orthogonal decomposition is very valuable for revealing the working mechanism of various modes.Main Contribution 3.The contribution in the aspect of solving {OP3,NP3}This dissertation generalizes the traditional surface equivalence principle(SEP)of material scattering systems to generalized surface equivalence principle(GSEP)from the aspects of external EM environment,system topological structure,and system material parameter,and derives the corresponding mathematical expressions.This dissertation derives the mathematical expression of the WEP corresponding to material scattering systems,and then obtains the operator expression of the DP corresponding to material scattering systems.In new WEP framework and based on new orthogonalizing DPO method and employing newly obtained GSEP,this dissertation generalizes the traditional IE-CMT for material scattering systems from the aspects of external environment,topological structure,and material parameter,and the CM formulations built in this dissertation are completely new.The new formulations have advantages over the traditional formulations in the aspects of applicable range,expression form,physical picture,and computational burden.In addition,the new formulations have not been able to be effectively established in traditional IE framework.Main Contribution 4.The contribution in the aspect of solving {OP4,NP4}This dissertation establishes the line-surface equivalence principle(LSEP)for complicated metal-material composite scattering systems,and derives the corresponding mathematical expressions.This dissertation derives the mathematical expression of the WEP corresponding to metal-material composite scattering systems,and then obtains the operator expression of the DP corresponding to metal-material composite scattering systems.In new WEP framework and based on new orthogonalizing DPO method and employing newly obtained LSEP,this dissertation derives the CM formulations for complicated metal-material composite scattering systems,and the obtained CM formulations have a very wide applicable range from the aspects of external environment,topological structure,and material parameter,and the CM formulations derived in this dissertation are completely new.The new CM formulations have advantages over the traditional formulations,and the new formulations have not been able to be effectively established in traditional IE framework.Main Contribution 5.The contribution in the aspect of solving {OP5,NP5}In new WEP framework and based on new orthogonalizing DPO method and employing newly obtained GSEP and LSEP,this dissertation deeply studies the forming reasons and the suppressing methods for spurious CMs,which widely exist in CMT,and systematically summarizes the operating process for suppressing the spurious CMs for arbitrary scattering systems.This dissertation reveals the physical meaning of the SCTs in the DPOs of material scattering systems and metal-material composite scattering systems,and also researches the influence of the SCTs on the numerical performance of CM formulations.To verify the correctness and validity of the above results and conclusions,this dissertation provides general mathematical proofs or special numerical evidence to the results and conclusions.