# Complex Wavefront Shaping through a Multi-Core Fiber
## 4 On-the-Fly Closed-Loop Control of Rotating Profile  
Complex wavefront shaping through an MCF can be a vital tool for MCF-based optical manipulation. We reported that the orientation of the cell can be controlled by a dynamically modulated asymmetric intensity profile. Due to the optical force depending on the intensity of the beam, precise intensity modulation of the asymmetric beam profile leads to optical force control. This provides higher degree of freedom for biological optical manipulation and can be implemented for cell mechanical measurements [36]. Since the Core-GS algorithm demonstrates powerful capability for manipulating the distal far-field intensity distribution, it is capable of manipulating the magnitude of the asymmetric intensity in the targeted light field. To demonstrate this, a dual-spot profile, for which the orientation and intensity can be characterized intuitively, is employed as the input intensity image. The intensity difference between both spots can be step modulated numerically. The experimental distal far-field through the MCF (Figure 5) characterized the robust intensity modulation employing the Core-GS algorithm. A similar double-lobe intensity profile is reported in [13], using wavefront shaping through a few-mode fiber. However, intensity unbalanced double-lobe beam profile could  
Figure 4: Principle of the Core-GS algorithm. Intensity distribution and a random phase constitute the light field at the target plane, which is numerically back propagated to the source plane for retrieving the approximated phase at the source plane. A core distribution map is applied on both amplitude and phase image at the source plane for better simulation of the light propagation through the MCF. The complex light field is then forward propagated to the target plane to get the approximated phase image, which is used to constitute the complex light field at the target plane for the next iteration. The iteration stops while the correlation between forward propagated and the targeted intensity distribution reaches the threshold. Figure 5: (**a**) Intensity modulated dual-spot light field through a multi-core fiber employing Core-GS algorithm. The scale bar shows a length of 5 \(\upmu\)m. (**b**) Normalized mean intensity of both spots and the corresponding modulated input target intensity. lead to unstable cell rotation around more than one axis and unwanted movements of the cell. Due to the precise intensity modulation capability of the Core-GS algorithm, MCF-based dual-beam traps can have an advantage in complex wavefront control and intensity modulation in the trapping region with resolution close to diffraction limit. Therefore, we implement Core-GS algorithm to retrieve the modulation hologram for a rotating double-spot light field at the distal field. However, the internal intensity differences between both spots during the rotation are still obvious (Figure 8d) due to the minor inter-core crosstalk [37] and discrepancies of the calibration quality between cores. Therefore, we demonstrate a closed-loop control of the rotating dual-spot profile with the Core-GS (Figure 6 IV-VII). The retrieved source phase in each iteration is combined with the distortion compensation hologram and displayed on the SLM immediately. The camera captured distal light field is on-the-fly evaluated with digital imaging processing. The internal intensity difference between both spots is employed as the feedback for closed-loop control; therefore, the target intensity for the next iteration is modulated accordingly. This method enables individual intensity control of both spots for a near-perfect rotation of a dual-spot with balanced intensity.