  Recent studies on fully dielectric multilayered metamaterials have shown that
the negligibly small nonlocal effects (spatial dispersion) typically observed
in the limit of deeply subwavelength layers may be significantly enhanced by
peculiar boundary effects occurring in certain critical parameter regimes.
These phenomena, observed so far in periodic and randomly disordered
geometries, are manifested as strong differences between the exact optical
response of finite-size metamaterial samples and the prediction from
conventional effective-theory-medium models based on mixing formulae. Here,
with specific focus on the Thue-Morse geometry, we make a first step toward
extending the studies above to the middle-ground of aperiodically ordered
multilayers, lying in between perfect periodicity and disorder. We show that,
also for these geometries, there exist critical parameter ranges that favor the
buildup of boundary effects leading to strong enhancement of the (otherwise
negligibly weak) nonlocality. However, the underlying mechanisms are
fundamentally different from those observed in the periodic case, and exhibit
typical footprints (e.g., fractal gaps, quasi-localized states) that are
distinctive of aperiodic order. The outcomes of our study indicate that
aperiodic order plays a key role in the buildup of the aforementioned boundary
effects, and may also find potential applications to optical sensors, absorbers
and lasers.
