<sec> With the development of laser technology, the application scope of nondiffracting beams, such as Bessel beams, Mathieu beams, cosine beams, and parabolic beams, which remain invariant along their propagation, continues to expand. During its propagation, the main lobes of these beams tend to bend towards off-axis position, which is called self-accelerating (or self-bending) property. A Bessel-like beam with self-acceleration can realize the propagation of the main lobe along a curved trajectory while maintaining the non-diffraction. Because of the above property, Bessel-like beams have been utilized in various areas such as guiding particles along arbitrarily curved trajectories, self-accelerating beams in nonlinear medium, plasma guidance, and laser-assisted guiding of electric discharges around objects. </sec><sec> In this paper, we propose a method of bending the trajectory of Bessel-like beams by using a magnetic fluid deformable mirror (MFDM) instead of traditional spatial light modulator (SLM) and Pancharatnam-Berry (PB) phase manipulation. The MFDM provides a method without pixelation, where all parameters can be rapidly modified for fine-tuning. Furthermore, compared with the conventional deformable mirror, the MFDM has the advantages of a continuous and smooth mirror surface, large shape deformation, low manufacture cost, easy extension, and large inter-actuator stroke. Therefore, it is easy for the MFDM to generate the ideal shape of an axicon. Firstly, according to geometric analysis, the asymmetrical mirror profile to produce a self-accelerating Bessel-like optical beam is proposed. The proposed mirror profile can be used to compensate for the difference in optical path length for each annular slice of the axicon. If a collimated Gaussian beam is incident on the mirror combining the axicon and the asymmetrical mirror profiles, which can obtain Bessel-like beams with arbitrarily curved trajectories. Secondly, the resultant of the self-accelerating Bessel-like beams along parabolic trajectories is validated by the simulation in MATLAB. Finally, a prototype of MFDM consisting of the dual-layer arrays of miniature electromagnetic coils, a Maxwell coil and the magnetic fluid filled in a circular container is fabricated for the experiment. The experimental results show that the Bessel-like beams propagate along the parabolic trajectories, with the MFDM used, and the accuracy of the curved trajectories is verified. The proposed method in this paper opens a new experimental way to the study of Bessel-like beam; the theoretical approach can also be generalized mathematically for other non-paraxial beam propagation. </sec>

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Magnetic fluid is a stable colloidal suspension of nano-sized, single-domain ferri/ferromagnetic particles dispersed in a liquid carrier. The liquid can be magnetized by the ferromagnetic particles aligned with the external magnetic field, which can be used as a wavefront corrector to correct the large aberrations up to more than 100 µm in adaptive optics (AO) systems. Since the measuring range of the wavefront sensor is normally small, the application of the magnetic fluid deformable mirror (MFDM) is limited with the WFS based AO system. In this paper, based on the MFDM model and the relationship between the second moment (SM) of the aberration gradients and the far-field intensity distribution, a model-based wavefront sensorless (WFSless) control algorithm is proposed for the MFDM. The correction performance of MFDM using the model-based control algorithm is evaluated in a WFSless AO system setup with a prototype MFDM, where a laser beam with unknown aberrations is supposed to produce a focused spot on the CCD. Experimental results show that the MFDM can be used to effectively compensate for unknown aberrations in the imaging system with the proposed model-based control algorithm.