Dispersion and radiation properties for bound and leaky modes supported by 1-D printed periodic structures are investigated. A new type of Brillouin diagram is presented that accounts for different types of physical leakage, namely, leakage into one or more surface waves or also simultaneously into space. This new Brillouin diagram not only provides a physical insight into the dispersive behavior of such periodic structures, but it also provides a simple and convenient way to correctly choose the integration paths that arise from a spectral-domain moment-method analysis. Numerical results illustrate the usefulness of this new Brillouin diagram in explaining the leakage and stopband behavior for these types of periodic structures.
Baccarelli, P., Paulotto, S., Jackson, D.R., Oliner, A.A. (2007). A new Brillouin dispersion diagram for 1-D periodic printed structures. IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, 55(7), 1484-1495 [10.1109/tmtt.2007.900304].