Anomalous quantum transport phenomena observed in fractal photonic lattices

Fractals are complex structures that usually exhibit self-similarity and have a non-integer dimension. The terminology “fractal” was first introduced by the famous mathematician Benoit B. Mandelbrot. He noticed that here and there, many natural objects were fractals, such as snowflakes, branching trees, coastline, etc. Outside of nature, fractal patterns or structures are also artificially created. One famous fractal type, Sierpinski gaskets, are widely used not only in the decoration of churches in ancient times, but also in modern artificial device engineering. So far, the feature of fractality has been reported in a wide range of fields including quantum mechanics, optics, finance, physiology, etc.