  There has been remarkable recent progress in the formation of nano-resonators
that support ultra-low-loss, compact dielectric photonic crystals with
exceptional high-Q modes that operate at visible or telecom wavelengths. New
insights into modal engineering have recently emerged from researchers
exploring exotic electronic phases in 2D materials. The phenomenon relates to a
twist in the angle between two layers of materials with high periodic spatial
ordering, such as graphene. A moire pattern forms, and at a particular magic
angle of twist, the electronic behavior significantly changes, enjoying a flat
energy-momentum dispersion relationship. There is an optical analog to the
electron twistronics: bilayer moire photonic crystal slabs can realize a
flat-band condition. Under these conditions, the propagating modes have zero
group velocity, thus giving rise to momentum-free trapping of Bloch waves in
both transverse and vertical directions, creating high quality-factors and
exceptionally small modal volumes that eventually lead to the enhancement of
the Purcell effect. The dramatically different means of light-localization
afforded by moire-structured cavities, very small mode volumes, and spatial
determination by the overall moire pattern can manipulate spontaneous emission.
This provides many opportunities for applications such as low-threshold lasing,
single-photon source, quantum electrodynamics, photonic circuit, and quantum
information processing.
