Analysis of polarization-dependent continuous 2π phase control mechanism for trapezoidal nano-antennas through multipole expansion method

In order to explore the polarization-dependent continuous 2π phase control mechanism of nano-antennas and to provide theoretical bases for the subsequent design of polarization beam splitters, unidirectional radiation antennas, and other devices, we design a trapezoidal nano-antenna structure with high transmission efficiency and polarization-dependent continuous 2π phase variation under the wavelengths of 600-1000 nm. Then we analyze the relationship between phase control and the excited electric/magnetic dipoles and quadrupoles under different linearly polarized incident light beams. The results show that, in the y -direction, the antenna mainly realizes polarization-dependent continuous 2π phase control at the wavelengths where the first Kerker's condition is satisfied. As the antenna's unidirectional angular radiation is mainly achieved by compensating the wavefront phase, based on the above analysis, the relationship between the maximum radiation angle of unidirectional angular radiation and the excited electric/magnetic dipoles and quadrupoles in the antenna is further analyzed. Finally, we also briefly consider the influence of the structural sizes of the designed antenna on the resonances and coupling of the excited electric/magnetic dipoles and quadrupoles under different linearly polarized incident light beams for future applications.