Linear light localization in two-dimensional fractional diffraction quasicrystals

We numerically investigate linear light localization in two-dimensional photonic quasicrystals incorporating fractional diffraction. Our findings reveal that localization arises when the potential depth exceeds a critical threshold, which diminishes rapidly with increasing order of discrete rotational symmetry. Notably, fractional diffraction modifies these thresholds, enabling localization in significantly shallower potentials compared to conventional systems-particularly under lower diffraction orders (where fractional effects are most pronounced). The resulting localized modes exhibit remarkable robustness, remaining insensitive to the initial position of the input beam. These results establish fractional-diffraction photonic quasicrystals as a versatile, tunable platform for precise manipulation of wave localization phenomena.