Alias Transformation of Structured Beam and Holography in Real and Fourier Space Based on Dielectric Metasurface

Structured beams are analytical solutions to wave equations that possess specific spatial profiles and rigorous transmission properties. Holography enables wavefront reconstruction by recording objective wavefront information. In this study, comprehensive wavefront control by transforming a structured beam in real space is proposed and experimentally verified, and optical holography is reconstructed in Fourier space. To obtain an arbitrary profile of the structured beam, alias transformation is performed to rebuild the coordinate system to form arbitrary user-defined shapes. Subsequently, the complex amplitude control of the metasurface to encode the alias-transformed structured beam accordingly is applied. This allows the conventional standard Hermite–Gaussian and Laguerre–Gaussian modes to be transformed into their corresponding shapes while maintaining their distinct features. Holography is realized based on pure phase modulation by interleaving the information with a structured beam, which fully utilizes the space-bandwidth product of the metasurface. These distinctive optical phenomena in both spaces expand the definition of conventional structured beams and enable further developments in laser fabrication, optical manipulation, and optical displays.