A number of relationships are given in this paper which allow to connect the values of S-matrices elements of open nodes with a discrete spatial spectrum (waveguides and gratings) on various sheets of analytic continuation of a frequency parameter, to find zeroes of these elements, etc. According to it, a scheme of reconstructing frequency dependences of S-matrices by the known sets of complex eigen frequencies has been constructed. A number of simple expressions are presented due to which one can carry out an effective analysis of the resonance properties of diffraction characteristics of various modes.