Propagation dynamics and optical manipulation of perfect self-similar Bessel beams in linear and nonlinear regimes

Non-diffracting beams are a special type of optical field that can resist diffraction and maintain a constant transverse profile during propagation. Self-similar beams, on the other hand, are a special type of optical field that maintains the shape of the transverse intensity profile but scales in size during propagation. Although they are not the same, perfect self-similar Bessel beams (PSBBs) as an intermediate mode between non-diffracting beams and self-similar beams, maintain a strictly self-similar transverse profile and constant intensity during propagation. Here, we start from the linear propagation dynamics of PSBBs, and the nonlinear self-focusing in a biased photorefractive strontium-barium niobate (SBN) crystal, and demonstrate the optical manipulation of Rayleigh particles with PSBBs. The power flow, trapping force, and torque of PSBBs all decrease with the propagation distance, while the orbital angular momentum (OAM) and corresponding angular momentum density (AMD) remain constant during propagation. In a nonlinear medium, the intensity of the beam shows an alternating multi-foci along the propagation direction, characterized by periodic local enhancement and broadening. The attenuation rate of the trapping force is fast and the propagation stability is much lower than that in the linear case. Our work not only reveals the unique properties of PSBBs but also has significant implications for in-depth understanding of the optical field control in nonlinear media and the construction of advanced photonic devices.