Application of the aperiodic Mephisto Waltz sequence in the design of diffractive lenses

In this work, we present the design of a new quadrifocal diffractive lens based on the aperiodic Mephisto Waltz sequence. The proposed diffractive optical element (DOE), coined as the Mephisto Waltz Zone Plate (MWZP), allows the formation of four focal planes along the direction of propagation. The optical characteristics of this lens are directly correlated with the properties of the aperiodic sequence used in its design. The focusing properties of the MWZP have been analytically and experimentally studied, demonstrating that they preserve the inherent self-similarity characteristics of the aperiodic sequence. This self-similarity, along with the quadrifocal properties, highlights the potential of the MWZP in advanced optical applications, offering new capabilities in controlling light propagation and focusing.