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The convergence of an approximate electric and an approximate magnetic potential function representing vector field in electromagnetic waveguides is discussed. The two potential functions are expresse...d in the form of integral of Green's functions and the boundary values of the vector field. Based on these expressions, it is proved that two approximate potential functions converge uniformly to their true potential functions, respectively, when the approximate field satisfies the boundary conditions in vector field in the sense of mean square. Then, the inequalities about convergence of the approximate potential functions on a boundary are deduced. Using the inequalities, it is also shown that the boundary conditions in vector field can be satisfied when the approximate potential functions are expressed by the finite series of modal functions.続きを見る
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