Structured light scattering by a complex conjugate medium: the role of orbital angular momentum

Structured light beams carrying orbital angular momentum (OAM) offer unique opportunities for optical manipulation, sensing, and communications due to their tunable topological properties. Understanding how these beams interact with advanced optical materials is essential for developing next-generation photonic devices. Here we present a theoretical investigation of Gaussian vortex beam (GVB) scattering by a complex conjugate medium (CCM) sphere, a lossless metamaterial characterized by conjugate permittivity and permeability that supports non-attenuated wave propagation. Using generalized Lorenz–Mie theory combined with vector angular spectrum decomposition, we derive analytical expressions for beam shape coefficients and compute far-field scattering intensity and efficiency across four polarization states. The obtained results reveal that increasing the OAM mode number amplifies both scattering intensity and efficiency through excitation of additional internal field modes, while larger beam waist radii expand the interaction cross-section with the scatterer. The scattering response exhibits pronounced sensitivity to GVB configuration parameters, with the helical phase profile enabling selective coupling to specific multipolar resonances of the CCM sphere. These findings demonstrate that structured vortex beams provide additional degrees of freedom for controlling light-metamaterial interactions beyond conventional Gaussian illumination, with potential implications for OAM-based filtering, optical trapping in engineered media, and the design of phase-sensitive metamaterial devices.