Researchers have developed multifocal diffractive lenses that utilize aperiodically structured Lucas sequences. These lenses enable focusing light at multiple distinct focal points along the optical axis, a capability not possessed by conventional lenses. This advancement represents a significant step in the design of compact and efficient optics for applications requiring precise light control at different depths, such as in microscopy or 3D imaging systems.

The design is based on manipulating light diffraction using micro- and nanoscale structures, organized according to patterns derived from Lucas sequences. Unlike periodic sequences, the aperiodicity of these structures allows for greater flexibility in light energy distribution, enabling the creation of multiple foci with specific intensity and position characteristics. This approach contrasts with previous bifocal or trifocal diffractive lenses, which often sacrificed efficiency or image quality to achieve multiple focal points.

The main innovation lies in the application of algorithms based on the mathematical properties of Lucas sequences to optimize the lens geometry. This allows for precise control over the phase of incident light, directing it towards the desired focal points. The results demonstrate the ability to generate four distinct focal points with high efficiency and low aberration, overcoming the limitations of previous multifocal designs. The fabrication of these lenses is carried out using standard microfabrication techniques, facilitating their future implementation in optical devices.

This development opens new avenues for creating compact and multifunctional optical systems in fields such as bioimaging, where the ability to focus at different depths without moving the lens is crucial. It also has potential implications in virtual/augmented reality and remote sensing systems. Next steps include exploring the integration of these lenses into commercial devices and investigating designs with a greater number of focal points or dynamic focusing capabilities.