__m-bonacci metamaterial multilayers: location of the zero-average index bandgap edges__

We examine quasiperiodic multilayers arranged in m-bonacci sequences, which combine ordinary positiveindex
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.