Theoretical limits and design method for levitation of a slit based metalens
N.S.T. Simon (TU Delft - Applied Sciences)
R.A. Norte – Mentor (TU Delft - Dynamics of Micro and Nano Systems)
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Abstract
Optical manipulation has recently become indispensable in various disciplines and optical levitation specif- ically offers many possibilities in highly sensitive motion detection. The counterintuitive "tractor beams" have therefore captivated research due to their possible new approach to levitation. The key principle in de- signing an optical pulling force is the enhancement of the forward momentum by the pulled object. The idea of using the light modulating capacities of a metalens to increase the forward momentum has been proposed in literature. Here, a simple theoretical analysis is done to give a simple formula for the optical pulling force (OPF) generated by a one-dimensional metalens. From there two parameters are determined to be limiting for the OPF generated by a metalens: the transmissivity and the numerical aperture of the lens. A large nu- merical aperture and a large transmissivity of the lens appear to be critical in obtaining an apparent optical pulling force. Unlike in traditional optical trapping, where the object must be confined at the focal spot and is therefore limited in size by diffraction and high local intensities, the metalens considered here is not placed at the focus itself. This configuration relaxes the geometric and diffraction-related constraints of conventional trapping and shifts the difficulty from maintaining a tightly confined focus to engineering a lens that can efficiently redirect momentum over a large angular range. A workflow to design one-dimensional slit-based metalenses is proposed taking into consideration the results from the theoretical analysis. The optimized metalens design achieves an accurate focal point, exhibiting a deviation of only 2.88% from the targeted focal length. Which is a competitive error compared to literature. The analytical formula predicts that optimized lenses can generate a linear force on the order of 10−12 N m/W, in good agreement with values reported in literature, thereby supporting the validity of the analytical model.