Fractal checkerboard zone plates

In this work, we introduce a novel diffractive optical element, the Fractal Checkerboard Zone Plate (FCZP). It is based on a two-dimensional binary matrix generated through iterative substitution rules that produce self-similar fractal geometries. Starting from a seed matrix, higher-order structures are constructed iteratively, defining the transmittance pattern of the lens with transparent and opaque rectangular regions. The axial irradiance distributions of FCZPs of various orders are analyzed and compared to those of equivalent periodic checkerboard zone plates (PCZPs). Although both exhibit a primary focal distance at the same position, FCZPs display intensity profiles with self-similar characteristics typical of diffractive fractal structures. Moreover, compared to other square fractal lenses, FCZPs offer higher relative diffraction efficiency. • A novel diffractive optical element, the Fractal Checkerboard Zone Plate (FCZP), is proposed. • FCZPs are constructed via iterative substitution rules, yielding self-similar fractal transmittance patterns. • Axial irradiance analysis reveals that FCZPs preserve the primary focus while exhibiting fractal intensity profiles. • Compared to other square fractal lenses, FCZPs demonstrate superior relative diffraction efficiency.