Generation of ultra-long pure longitudinal magnetization fields using complex phase filters

Based on vector diffraction theory and the inverse Faraday effect (IFE), this study employs complex phase filters (CPFs) to modulate azimuthally polarized hyperbolic-sine-Gaussian vortex beams, achieving simultaneous optimization of the depth of focus and aspect ratio of magnetic needles, and generating magnetization chains with remarkable length and uniform magnetic spots. Specific results include the following: in a single lens system, a single-channel magnetization needle with a longitudinal full width at half-maximum (FWHM) of 87λ (aspect ratio of 249), and a dual-channel magnetization needle with a longitudinal FWHM of 87λ (aspect ratio of 322) were obtained; in a 4π system, single- and dual-channel magnetization chains with lengths exceeding 85λ were realized, with both transverse and longitudinal dimensions of the magnetic spots in the dual-channel chain measuring 0.27λ. Furthermore, by adjusting the parameter m (m is the order of the sine-hyperbolic-Gaussian beam), the axial intensity distribution of the structures can be effectively modulated. This work provides a new, to our knowledge, approach for applications such as multiple atoms trapping and transport, as well as ultrahigh-density magnetic storage.