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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 nonperiodic dielectric structures which allow the formation of 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
metamaterials 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. Since they are more easily manufactured, prototyping centimeter scaled microwave structures may help
optimizing structures in the technologically very interesting region of infrared.