In the fields of light manipulation and localization, quasiperiodic photonic crystals, or photonic quasicrystals (PQs), are causing an upsurge in research because of their rotational symmetry and long-range orientation of transverse lattice arrays, as they lack translational symmetry. It allows for the optimization of well-established light propagation properties and has introduced new guiding features. Therefore, as a class, quasiperiodic photonic crystal fibers, or photonic quasicrystal fibers (PQFs), are considered to add flexibility and richness to the optical properties of fibers and are expected to offer significant potential applications to optical fiber fields. In this review, the fundamental concept, working mechanisms, and invention history of PQFs are explained. Recent progress in optical property improvement and its novel applications in fields such as dispersion control, polarization-maintenance, supercontinuum generation, orbital angular momentum transmission, plasmon-based sensors and filters, and high nonlinearity and topological mode transmission, are then reviewed in detail. Bandgap-type air-guiding PQFs supporting low attenuation propagation and regulation of photonic density states of quasiperiodic cladding and in which light guidance is achieved by coherent Bragg scattering are also summarized. Finally, current challenges encountered in the guiding mechanisms and practical preparation techniques, as well as the prospects and research trends of PQFs, are also presented.

A hollow-core fiber based on photonic quasicrystal arrays is theoretically proposed for high-quality light wave propagation with high polarization maintaining performance and low nonlinearity. This fiber, called hollow-core photonic quasicrystal fiber (HC-PQF), can simultaneously realize a high birefringence that reaches 1.345 × 10^?2 and a small nonlinear coefficient of 1.63 × 10^?3 W^?1·km^?1 at a communication wavelength of 1.55 μm due to the air-filled core and unique quasiperiodic fiber structure. To further demonstrate the controllability of the nonlinear coefficient and the application of sensor and polarization-maintaining fiber, the nonlinearity is investigated by filling different inert gases in the fiber core while the birefringence keeps a high order of 10^?2. In the wavelength range λ ∈ [1.53 μm, 1.57 μm], the dispersion is near zero and flattened. The HC-PQF is expected to be used for applications in optical communication, high power pulse transmission, polarization beam splitters, etc.