Abstract
In photonic crystals the propagation of light is governed by their photonic
band structure, an ensemble of propagating states grouped into bands, separated
by photonic band gaps. Due to discrete symmetries in spatially strictly
periodic dielectric structures their photonic band structure is intrinsically
anisotropic. However, for many applications, such as manufacturing artificial
structural color materials or developing photonic computing devices, but also
for the fundamental understanding of light-matter interactions, it is of major
interest to seek materials with long range non-periodic dielectric structures
which allow the formation of {\it isotropic} photonic band gaps. Here, we
report the first ever 3D isotropic photonic band gap for an optimized
disordered stealthy hyperuniform structure for microwaves. The transmission
spectra are directly compared to a diamond pattern and an amorphous structure
with similar node density. The band structure is measured experimentally for
all three microwave structures, manufactured by 3D-Laser-printing for
meta-materials with refractive index up to $n=2.1$. Results agree well with
finite-difference-time-domain numerical investigations and a priori
calculations of the band-gap for the hyperuniform structure: the diamond
structure shows gaps but being anisotropic as expected, the stealthy
hyperuniform pattern shows an isotropic gap of very similar magnitude, while
the amorphous structure does not show a gap at all. The centimeter scaled
microwave structures may serve as prototypes for micrometer scaled structures
with bandgaps in the technologically very interesting region of infrared (IR).