An exact formulation of the boundary value problem for an infinite lossless iris-loaded periodic wave guide with glide reflection symmetry has been obtained for TM wave propagation. The characteristic equation for the fundamental propagation constant β0 is solved for real as well as complex roots. The solutions are plotted in the form of k–β diagrams. The effect of variation of certain parameters is studied. On the basis of the periodicity of the solutions for β0 it is demonstrated that the effective period of this structure is half its translation period. A discussion of the k–β plots is presented and some comments on the properties of the complex waves in lossless periodic wave guides are included.

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