m-bonacci metamaterial multilayers: location of the zero-average index bandgap edges.

We examine quasiperiodic multilayers arranged in m-bonacci sequences, which combine ordinary positive-index materials and dispersive metamaterials with negative index in a certain frequency range. When the volume-averaged refractive index of the nonperiodic multilayer equals zero, the structure does not propagate light radiation and exhibits a forbidden band. We identify some analytical expressions to determine the upper and lower limits of the above zero-average refractive-index bandgap. We recognize that these limits are not explicitly dependent on the geometrical parameters of the stack of layers.