【摘要】 证明了在均匀波导横截面S上有界变差并满足一定边值条件的横向矢量函数可以按横向未征矢量序列｛EeT，EμT｝或｛HeT，HμT）展开为级数，展开式按L2范数收敛于被展开的函数。同时还论证了在S上有界变去并在周界上为0或法向导数为0的纵向矢量函数可以分别按E模或H模的纵向本征关全展开。但如被展开的矢量函数在波导内并不满足齐次场方程，其纵向部分和横向部分只能分别展开。更多还原

【Abstract】 It is proved that in the transverse section S of the homogeneous waveguide the fornd-ed variational transverse vector functions satisfying certain conditions may be expanded as series of transverse vector eigen functions {EeT, EuT } or {HeT, HuT}, the expansion series converge to the ex-panded function according to the L2 normal. At same time, it is discussed that the fornded variation-al longitudinal vector function which itseIf or its normal derivative is equal to 0 at the circumforence of S may be expanded by the longitudina1 vector eigen functions of E mede or H mede. If the expanded vector function does not satisfy the homogeneous field equations, the longitudinal part and transverse part can only be expanded separately.更多还原