  We theoretically study the propagation of large-wavevector waves (volume
plasmon polaritons) in multilayer hyperbolic metamaterials with two levels of
structuring. We show that when the parameters of a subwavelength
metal-dielectric multilayer ("substructure") are modulated ("superstructured")
on a larger, wavelength scale, the propagation of volume plasmon polaritons in
the resulting multiscale hyperbolic metamaterials is subject to photonic band
gap phenomena. A great degree of control over such plasmons can be exerted by
varying the superstructure geometry. When this geometry is periodic, stop bands
due to Bragg reflection form within the volume plasmonic band. When a cavity
layer is introduced in an otherwise periodic superstructure, resonance peaks of
the Fabry-Perot nature are present within the stop bands. More complicated
superstructure geometries are also considered. For example, fractal Cantor-like
multiscale metamaterials are found to exhibit characteristic self-similar
spectral signatures in the volume plasmonic band. Multiscale hyperbolic
metamaterials are shown to be a promising platform for large-wavevector bulk
plasmonic waves, whether they are considered for use as a new kind of
information carrier or for far-field subwavelength imaging.
