The Intrinsic Problems And Applications, Based On The Electromagnetic Field Of The Vector Theory Of Partial Differential Operators

The new method of the eigenvalue problem of electromagnetic field——Vector partial differential operator is researched in this dissertation. The waveguideand resonant cavity is researched as an application.Based on complete projection theorem, the series of the eigenfuntion of vectorLaplace operator are solved. The orthogonality and complement of the series of theeigenfunction are proved and the unitary coefficients of the series of theeigenfunction are obtained. The series of the eigenfunction of double rotationaoperator are obtained and the completment is proved. The general, simple form,accurat method for simulating the eigenvalue problem of electromagnetic field isdeveloped. The demonstration of the complement established the rigorous theoreticalfoundation for calculating electromagnetic field.The eigenfunction transformation in scalar field space is extended to theeigenvalue transformation in vector field space, and dyadic Delta function anddyadic Green's function in the popular form are defined. The form of dyadic Green'sfuntion is improved. The general expression of resolving inhomogeneous boundaryvalue problems by dyadic Green's function is obtained.Dyadic Green's function is used to resolve high order modes characteristics ofhyteromophic waveguide. By vector identity manipulation, the calculation of dyadicGreen's functions is simplified. The cutoff frequencies of the higher order modes aredetermined with the singular value decomposition technique. Because of its analyticform, the solution will be useful in the rigorous analysis of many practicalmicrowave components and circuits.Numerical method is used to simulating the resonant cavity in three dimensionalsthecture and two scalar wave fimctions are used to calcu1ating the field. Theresonant frequency spectrum, the distributing figures of electric and magnetic fieldare obtained. The spurious modes are eliminated in the resonant spectrum by thecalculation of pure rotational field. ms method may be used in the research ofincomPlereness in waveguide and resonat cavity with comPlicated structUre.