Fig. 1. (a) Five-fold Penrose lattice tiling pattern^[5]. (b) Diffraction pattern of the five-fold Penrose-type PQ structure^[5]. (c) 1D Fibonacci sequence generated by the 2D PQ lattice using the cut-and-project method^[5]. (d) Fabricated silica-based twelve-fold symmetric quasicrystals^[23]. (e) Multiple diffracted beams from the entrance face of the twelve-fold symmetric quasicrystals^[23]. (f) and (g) Fabricated Si-based twelve-fold PQ and Sunflower-type PQ structures by E-beam lithography system^[64].

Fig. 2. Upper circular diagram showing the potential technological applications with the optical properties optimized using the structure and material manipulation based on a PQF. The bottom arrow indicates the PQF evolution from the first fabricated PCF^[67] to the first reported PQ structure^[16], to the first proposed PQF^[68], to the hollow-core PQF^[72], to the Ge-doped PQF^[99], to the OAM-supported PQF^[95], and to the PQF-based sensor^[96].

Fig. 3. The upper row shows the Stampfli-type PQF. (a) The first-order PQF, (b) the second-order PQF, and (c) the second-order PQF with a π/6 rotation of the near-core ring of the air holes. The middle row shows the Penrose-type PQF. (d) The eight-fold PQF, (e) the ten-fold PQF, and (f) the twelve-fold PQF. The bottom row shows the Sunflower-type PQF. (g) The six-fold PQF, (h) the seven-fold PQF, and (i) the eight-fold PQF.

Fig. 4. (a) Index-guiding solid-core PQF. (b) The air-guiding hollow-core PQF.

Fig. 5. (a) Phase diagram of the second-order mode for the eight-air-hole-ring square and the triangular PCFs^[100]. (b) The normalized V parameter for the Stampfli-type PQF^[68]. (c) The normalized V parameter for the Sunflower-type PQF^[85].

Fig. 6. Negative dispersion for the different PQF designs: (a) the small outer core^[69], (b) the large outer core^[110], and (c) the doped inner core^[111]. (d) The normal dispersion for the Ge-doped PQF design^[73]: the electric field distribution in the inner core and outer core at 1.06 µm and the obtained normal dispersion.

Fig. 7. High birefringence silica-based PQF at 1.55 µm obtained by breaking the structure symmetry. (a) The Penrose-type PQF with a birefringence of 1.4207 × 10^-2[114]. (b) The Stampfli-type PQF with a birefringence of 3.86 × 10^-2[71].

Fig. 8. (a)–(d) Large mode area PQF and (e)–(f) highly nonlinear PQF. (a) The large-core PQF^[116]. (b) The Yb-doped large pitch PQF^[75]. (c) The gradient-diameter Sunflower-type PQF [with a large effective mode area and a low bending loss shown in (d)]^[91]. (e) The twin bow-tie silica-based PQF^[76]. (f) The annular core Stampfli-type PQF^[109]. (g) The tellurite elliptical core PQF [with high nonlinearity shown in (h)]^[117].

Fig. 9. OAM-supported PQF. (a) The dual-cladding Stampfli-type PQF, and the electric field distribution and the helix phase^[95]. (b) The dual-core dispersion compensation of the Sunflower-type PQF, and the electric field distribution^[122]. (c) The GeO₂-doped Sunflower-type PQF, and the electric field distribution^[123]. (d) The GeO₂-doped Sunflower-type PQF, and the electric field distribution and the helix phase^[124].

Fig. 10. (a) The SEM image of the fabricated ring-core PQF^[88]. (b) The measured CCD images of the OAM with l = 1 (top) and l = 2 (bottom) output signals and with (left) intensities and (right) phases.

Fig. 11. PQF-based sensor. (a) The dual-core PQF (left), and the interference spectrum used for sensing the external temperature (right)^[126].(b) The mechanism of the surface plasmon resonance PQF sensor. When the sensor is put in the target analyte, the coupling loss peak shifts. (c) The Stampfli-type PQF with a surface-coated ITO layer^[128]. (d) The Penrose-type PQF with a D-shaped analyte channel^[89]. (e) The U-shaped Stampfli-type PQF^[90]. (f) The hybrid-size air hole PQF with a micro D-shaped analyte channel^[129].

Fig. 12. (a) Profile of the OAM-SPR photonic quasi-crystal fiber sensor^[131]. The figure outlined with the red rectangular dotted line shows the coupling field distribution. (b) Basic setup of the proposed fiber sensor for refractive index sensing.

Fig. 13. Supercontinuum generation based on the highly nonlinear PQF. (a) The silica-based Sunflower-type PQFs with a defect-core^[132]. (b) The As₂Se₃-based Stampfli-type PQF^[83]. (c) The Ge₁₅Sb₁₅Se₇₀-based Sunflower-type PQF^[135]. (d) The Ge_11.5As₂₄Se_64.5-based Stampfli-type PQF^[82].

Fig. 14. (a)–(d) Cross-sectional images of the sol–gel-derived microstructure fibers^[139] and the 3D printing of PCF^[141]. (a) The endlessly single-mode design. (b) The high delta, highly nonlinear fiber. (c) The dual-core structure. (d) The circular-core PCF. (e) The PCF polarization beam splitter enabled by the 3D printing of the PCF designs. A beam with an arbitrary polarization (yellow beam) is split into its horizontal (red beam) and vertical (green beam) polarization components. (f) The helically twisted coreless PCF. (g) The PBG hollow-core PCF. (h) The anti-resonant hollow-core PCF. (i) The fractal ring-core PCF.

Fig. 15. Description of a potential preparation process of a PQF using the sol–gel method.

Table 1. Flattened and Near-Zero Dispersion Based on the PQF Structure

Table 2. Performance Parameters of the PQF-Based Sensors