  We show that hyperbolic electromagnetic metamaterials implemented as
multilayers based on two material constituents arranged according to Thue-Morse
(ThM) aperiodic sequence may exhibit strong nonlocal effects, manifested as the
appearance of additional extraordinary waves which are not predicted by
standard effective-medium-theory (local) models. From the mathematical
viewpoint, these effects can be associated with stationary points of the
transfer-matrix trace, and can be effectively parameterized via the trace-map
formalism. We show that their onset is accompanied by a strong wavevector
dependence in the effective constitutive parameters. In spite of the inherent
periodicity enforced by the unavoidable (Bloch-type) supercell terminations, we
show that such strong nonlocality is retained at any arbitrarily high-order
iterations, i.e., approaching the actual aperiodic regime. Moreover, for
certain parameter configurations, at a given wavelength and for two given
material layers, these effects may be significantly less prominent when the
same layers are arranged in a standard periodic fashion. Our findings indicate
that the (aperiodic) positional order of the layers constitutes an effective
and technologically inexpensive additional degree of freedom in the engineering
of optical nonlocality.
