# Microparticle Manipulation and Imaging through a Self-Calibrated Liquid Crystal on Silicon Display
## 3 Results
### Microparticle Manipulation through the LCoS Display Generated Split-Lens Schemes  
In this subsection, we implement the method described in Section 2.2 to create a customized three dimensional light capsule to capture and spatially manipulate microparticles. The optical set-up implemented to such aim is given in Figure 10.  
The system is illuminated with a 532 nm wavelength laser (gem 532 Model, Laser Quantum) with the output power ranging from 50 mW to 2 W. Afterwards, one attenuator combined with a pinhole is inserted into the system to properly adjust the intensity. Then, light passing through an afocal system, formed by a divergent lens (L1,\(f_{1}\) as \(-\)100 mm) and a convergent lens (L2,\(f_{2}\) as 300 mm), is collimated and expanded. Next, the LCoS display is located perpendicular to the input beam. A linear polarizer (LP) placed before the LCoS is properly oriented to ensure a phase-only performance of the device. Under this scenario, we send two multiplexed phase distributions to the LCoS display: (i) the first one defines the continuous split-lens configuration (creates the light cone); and (ii) the second stands for a regular lens (configures the cone cork). See more details in explanation related to Figure 4. Specifically, the parameters set to implement the continuous split-lens are: the distance between sector centers to the origin of \(a\) = 1.07 mm, a focal length of \(f\) = 370 mm and an aperture of \(\phi\) = 2.07 mm (see Equations (4) and (5)). Conversely, the focal length for the regular lens is set 350 mm. Note that in this scheme, the focal length of the regular lens (i.e., 350 mm) is smaller than the continuous split-lens (i.e., 370 mm) which satisfies the structure described in Figure 4d. Finally, a convergent lens (L3) images the whole structure into a transparent container, in which a number of microparticles are stuck to the top face due to electrostatic forces. By taking into account all these experimental parameters, we have obtained an experimental optical bottle with an axial length of \(\sim\)6.5 mm. Now, this compacted optical  
Figure 10: LCoS display based microparticle manipulation system. Figure 9: Surface profiles of the measured LCoS display: (**a**) LCoS display surface profile before compensation; and (**b**) LCoS display surface profile after compensation. bottle is feasible to capture particles through photophoretic forces. The used transparent container is a square UV fused quartz cuvettes (Thorlab CV10Q3500) with its size of 45-10-10 mm and two sides polished. On the other hand, the used particles are carbon coated hollow glass microspheres (Cospheric HGMS-0.14 63-75 \(\upmu\)m) with their diameters ranging from 63-75 \(\upmu\)m. Moreover, the particle density is 0.14 g/cm\({}^{3}\) and the mass ranged from 18.3-30.9 ng. Here, we want to note that apart from the carbon coated microsphere, the pure carbon particles [36] or the absorbing silicon particles [37] are also feasible to be trapped. As told before, particles are preliminarily stuck to the container inner surface by electrostatic forces. At this moment, these particles are not able to enter into the optical bottle structure because light capsule is sealed. The central cross section figure corresponding to this light capsule structure is given in Figure 11a. However, optical bottle can be opened from the top by multiplying an azimuthal sector with a constant phase within the continuous lens phase distribution, as detailed in Section 2.2. As a consequence, the resulting central cross section is provided in Figure 11b, this scheme enabling particles to enter into the light structure. By softly tapping the above side of the container, we forced particles to land into the capsule and they can be trapped by photophoretic forces exerted by the light structure. Finally, we closed the upper section of the light structure once again, by removing the triangle gap, and the complete optical bottle was recovered (see Figure 11c). Once the optical bottle is sealed, the particle is stably contained into this light structure.